| ID | Decision | Category | Original | Edited | Reasoning |
|---|---|---|---|---|---|
01JW5RGMJ5Q6PWBY4RTDQDA8G9 |
Localize | Units (simple) | Question
A kite has an area of $1.2$ m$^2$. One of its diagonals measures $150$ cm.
What is the length of the other diagonal in centimetres?
Answer:
|
Question
A kite has an area of $1.2$ ft$^2$. One of its diagonals measures $150$ in.
What is the length of the other diagonal in inches?
Answer:
|
Classifier: The question contains multiple metric units (m^2, cm) and the AU spelling "centimetres". Per the decision rules, any metric unit requires classification into a units category. Verifier: The text contains metric units (m^2, cm) and the AU spelling "centimetres", requiring localization. |
01JW5RGMGP8GBFQVQYX3Q2VX3M |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
An experiment that involves spinning a $5$-section spinner, drawing a coloured card, then flipping a coin based on the card's colour is a multi-step experiment.
Options:
|
Multiple Choice
True or false:
An experiment that involves spinning a $5$-section spinner, drawing a colored card, then flipping a coin based on the card's color is a multi-step experiment.
Options:
|
Classifier: Contains the AU spelling "coloured" and "colour", which require conversion to US spelling "colored" and "color". Verifier: The text contains "coloured" and "colour's", which are AU/British spellings of "colored" and "color's". |
01JW5RGMH6NRAEWQ3APH030RHD |
Localize | Terminology | Multiple Choice
Which type of graph contains gaps between the bars?
Options:
|
Multiple Choice
Which type of graph contains gaps between the bars?
Options:
|
Classifier: The term "Column graph" is the standard AU term for what is almost exclusively called a "Bar graph" in US K-12 education. While "column graph" is understood, "bar graph" is the required terminology for US localization. Verifier: The term "Column graph" is a specific Australian curriculum term for what is called a "Bar graph" in the US. This requires localization for the US school context. |
01JW5RGMH9DJ7H12G0P8H1PV53 |
Localize | Terminology | Multiple Choice
True or false:
A graph of the number of books read in a month can be represented using a column graph, because the data is discrete and counts are distinct.
Options:
|
Multiple Choice
True or false:
A graph of the number of books read in a month can be represented using a bar graph, because the data is discrete and counts are distinct.
Options:
|
Classifier: Uses the AU term "column graph" which maps to "bar graph" in US English. Verifier: The text uses the term "column graph", which is the standard Australian term for what is called a "bar graph" in the US. |
01JW5RGMJC3A3CYXZP0H9K7C9Y |
Localize | Units (simple) | Multiple Choice
True or false:
The cubic metre (m$^3$), is a base SI unit.
Options:
|
Multiple Choice
True or false:
The cubic meter (m$^3$), is a base SI unit.
Options:
|
Classifier: Contains the metric unit "cubic metre" and the AU spelling "metre". Verifier: The text contains the metric unit "cubic metre" with AU spelling ("metre"). |
01JW5RGMFT61JZN8E91EH9E1WG |
Localize | Units (simple) | Multiple Choice
A store sets product prices based on a pricing system.
Which pricing system would result in the fewest distinct price values, making the price data most clearly discrete?
Options:
|
Multiple Choice
A store sets product prices based on a pricing system.
Which pricing system would result in the fewest distinct price values, making the price data most clearly discrete?
Options:
|
Classifier: The presence of the metric unit "gram" triggers the units conversion category. Verifier: The presence of the metric unit "gram" requires RED classification per rule 3. |
01JW5RGMM312SC7TRESYV9A1FS |
Localize | Terminology | Multiple Choice
True or false:
The turning point of $y = 3x^2 - 12x + 1$ is $(2, -11)$
Options:
|
Multiple Choice
True or false:
The vertex of $y = 3x^2 - 12x + 1$ is $(2, -11)$
Options:
|
Classifier: The term "turning point" is the standard AU/UK term for what is referred to as the "vertex" in US mathematics curricula. Verifier: The term "turning point" is the standard AU/UK term for what is referred to as the "vertex" in US mathematics curricula. This requires localization for the US market. |
01JW5RGMG3B6DW8W7GP02TQ9S6 |
Localize | Spelling (AU-US) | Multiple Choice
A dataset is summarised by a box plot.
The interquartile range is $20$ units and the third quartile is $70$ units.
If the dataset contains $300$ data points, which of the following statements is correct?
Options:
|
Multiple Choice
A dataset is summarized by a box plot.
The interquartile range is $20$ units and the third quartile is $70$ units.
If the dataset contains $300$ data points, which of the following statements is correct?
Options:
|
Classifier: The word "summarised" uses the AU/UK 's' spelling instead of the US 'z' spelling ("summarized"). Verifier: The word "summarised" is the AU/UK spelling. US spelling is "summarized". Per rule 1, AU spelling requires RED classification. |
01JW5RGMK637EEJJ980X4SMB2S |
Localize | Spelling (AU-US) | Multiple Choice
A spinner has four unequal sectors with probabilities: $R = 0.3$, $B = 0.25$, $G = 0.2$, $Y = 0.25$.
After $200$ spins, the results are: $R = 55$, $B = 50$, $G = 45$, $Y = 50$.
Which colour shows the largest positive difference between experimental and theoretical probability?
Options:
|
Multiple Choice
A spinner has four unequal sectors with probabilities: $R = 0.3$, $B = 0.25$, $G = 0.2$, $Y = 0.25$.
After $200$ spins, the results are: $R = 55$, $B = 50$, $G = 45$, $Y = 50$.
Which color shows the largest positive difference between experimental and theoretical probability?
Options:
|
Classifier: The text contains the AU spelling "colour", which needs to be localized to the US spelling "color". Verifier: The text contains the AU spelling "colour", which needs to be localized to the US spelling "color". |
01JW5RGMMEP5V1FR6TN161T9Q3 |
Localize | Terminology | Multiple Choice
True or false:
If a parabola has its turning point at $(p,q)$ and passes through $(r,s)$, then $s = a(r-p)^2+q$ must be satisfied for some non-zero constant $a$.
Options:
|
Multiple Choice
True or false:
If a parabola has its vertex at $(p,q)$ and passes through $(r,s)$, then $s = a(r-p)^2+q$ must be satisfied for some non-zero constant $a$.
Options:
|
Classifier: Contains the AU-specific term "turning point", which in a US context is typically referred to as the "vertex". Verifier: The term "turning point" is standard in AU/UK pedagogy for the vertex of a parabola, whereas "vertex" is the standard term in US pedagogy. |
01JW5RGMG0P6R63XGRY7GDJ75Y |
Localize | Terminology | Multiple Choice
True or false:
Postal codes are nominal data, so higher postal codes represent higher geographic areas.
Options:
|
Multiple Choice
True or false:
Zip codes are nominal data, so higher zip codes represent higher geographic areas.
Options:
|
Classifier: The term "Postal codes" is used in Australia (and Canada/UK), whereas the US uses "ZIP codes". This is a terminology mapping required for localization. Verifier: The term "Postal codes" is the standard term in Australia, whereas the US uses "ZIP codes". This requires terminology localization. |
01JVJ2GWQVR72VHR8S5N5S96GH |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following equations represents a non-linear function whose graph is a circle with its centre not at the origin?
Options:
|
Multiple Choice
Which of the following equations represents a non-linear function whose graph is a circle with its center not at the origin?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to "center" for US localization. Verifier: Contains the AU spelling "centre", which requires localization to "center". |
01JVJ2RBFAYTYA6TDNRC13MRS2 |
Localize | Units (simple) | Multiple Choice
Convert $4.5$ tonnes : $750$ kg : $300000$ g into a simplified ratio.
Options:
|
Multiple Choice
Convert $4.5$ tons : $750$ lbs : $300000$ oz into a simplified ratio.
Options:
|
Classifier: Contains metric units (tonnes, kg, g). Note: "tonnes" is the metric spelling, further confirming the need for localization. Verifier: Contains metric units (tonnes, kg, g). "Tonnes" is also the metric/AU spelling. |
01JVJ2RBF6QTKZPYNPTDGVGKF8 |
Localize | Units (simple) | Multiple Choice
Convert the ratio $2.5$ km : $750$ m : $120000$ cm to a simplified ratio.
Options:
|
Multiple Choice
Convert the ratio $2.5$ mi : $750$ ft : $120000$ in to a simplified ratio.
Options:
|
Classifier: Contains multiple metric units (km, m, cm) which require conversion to US customary units for a US audience. Verifier: Contains multiple metric units (km, m, cm) which require conversion to US customary units. |
01JW5RGMJ7C6BRR63EKJXY3E4S |
Localize | Answer set | Multiple Choice
The area of a trapezium is $108$ m$^2$.
Its height is $9$ m.
If one parallel side is $4$ m longer than the other, find the lengths of the two parallel sides.
Options:
|
Multiple Choice
The area of a trapezoid is $108$ ft$^2$.
Its height is $9$ ft.
If one parallel side is $4$ ft longer than the other, find the lengths of the two parallel sides.
Options:
|
Classifier: The term "trapezium" is used, which must be localized to "trapezoid" in a US context. Additionally, metric units (m, m^2) are present. Terminology/Answer set consistency is prioritized here as the shape name is a fundamental classification difference. Verifier: The term "trapezium" is a regional term that must be localized to "trapezoid" for US contexts. It also contains metric units (m, m^2). Terminology change is the primary driver. |
01JW5RGMHDH29PYKN1MQBE2DMW |
Localize | Terminology | Multiple Choice
Fill in the blank:
Two lines have the same gradient but different $y$-intercepts. These lines are $[?]$
Options:
|
Multiple Choice
Fill in the blank:
Two lines have the same slope but different $y$-intercepts. These lines are $[?]$
Options:
|
Classifier: The term "gradient" is the standard AU term for what is called "slope" in US school mathematics. Verifier: The text uses the term "gradient", which is the standard AU term for "slope" in US school mathematics. |
01JW5RGMJC3A3CYXZP0FTF77T9 |
Localize | Units (simple) | Multiple Choice
The SI base unit for length is the metre (m).
Which of these is a derived SI unit for area?
Options:
|
Multiple Choice
The SI base unit for length is the meter (m).
Which of these is a derived SI unit for area?
Options:
|
Classifier: The text contains multiple metric units ("metre", "Litre", "Hectare") and AU-specific spellings ("metre", "Litre"). Per rule 6, units conversion/presence takes precedence over spelling. Verifier: The text contains AU spellings of metric units ("metre", "Litre") and refers to metric units ("Hectare"). Per rule 1 and 3, this requires RED classification. |
01JW5RGMKR1GS0E7NSXRWGCJ5F |
Localize | Units (simple) | Multiple Choice
A rectangle has a length that is $3$ metres more than its width.
If the area of the rectangle is equal to its perimeter, which equation represents this situation?
Options:
|
Multiple Choice
A rectangle has a length that is $3$ feet more than its width.
If the area of the rectangle is equal to its perimeter, which equation represents this situation?
Options:
|
Classifier: Contains the metric unit "metres" which also uses AU/UK spelling. Per rule 6, units conversion is the most impactful change. Verifier: Contains the metric unit "metres" which also uses AU/UK spelling. Per rule 5, units conversion is the most impactful change. |
01JW5RGMH73S1A99NZGDXVD9S1 |
Localize | Terminology | Multiple Choice
Two data sets are collected:
Data set A: Time students spend reading in hours
Data set B: Favourite book genres in a class.
Which graphs best suit the data?
A) Column graph for both
B) Histogram for A, column graph for B
C) Histogram for both
D) Column graph for A, histogram for B
Options:
|
Multiple Choice
Two data sets are collected:
Data set A: Time students spend reading in hours
Data set B: Favorite book genres in a class.
Which graphs best suit the data?
A) Bar graph for both
B) Histogram for A, bar graph for B
C) Histogram for both
D) Bar graph for A, histogram for B
Options:
|
Classifier: The term "Column graph" is standard in Australia, whereas the US equivalent is typically "Bar graph". Additionally, "Favourite" uses AU spelling. Verifier: The text contains the AU spelling "Favourite" (US: "Favorite") and the AU specific term "Column graph" (US: "Bar graph"). Per rule 5, terminology is the more impactful change. |
01JW5RGMMHYDVV0347WH3EDVA6 |
Localize | Terminology | Multiple Choice
True or false:
If a parabola has equation $y=k(x-m)(x-n)$, its turning point always occurs at $x = \dfrac{m+n}{2}$.
Options:
|
Multiple Choice
True or false:
If a parabola has equation $y=k(x-m)(x-n)$, its vertex always occurs at $x = \dfrac{m+n}{2}$.
Options:
|
Classifier: Contains the AU-specific term "turning point", which in a US context is typically referred to as the "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for a US audience. |
01JW5RGMMGXYVTX8HY3NJFTZF7 |
Localize | Terminology | Multiple Choice
If a parabola in the form $y = a(x-p)(x-q)$ has its turning point at $(2, -18)$ and one $x$-intercept at $x=5$, what is the other $x$-intercept?
Options:
|
Multiple Choice
If a parabola in the form $y = a(x-p)(x-q)$ has its vertex at $(2, -18)$ and one $x$-intercept at $x=5$, what is the other $x$-intercept?
Options:
|
Classifier: Contains the AU-specific term "turning point", which in a US context is typically referred to as the "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for a US audience. |
01JW5RGMMGXYVTX8HY3JPN8WR9 |
Localize | Terminology | Multiple Choice
A parabola $y = a(x-p)(x-q)$ has x-intercepts at $x=-5$ and $x=3$.
It passes through the point $(0, -15)$.
Find its turning point.
Options:
|
Multiple Choice
A parabola $y = a(x-p)(x-q)$ has x-intercepts at $x=-5$ and $x=3$.
It passes through the point $(0, -15)$.
Find its vertex.
Options:
|
Classifier: Contains the AU-specific term "turning point", which in a US context is typically referred to as the "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for a US audience. |
01JW5RGMQPJRPKG8KMH5NXK6SM |
Localize | Units (simple) | Multiple Choice
The sample variance ($s^2$) for a set of measurements is calculated to be $2.25$ m$^2$.
What is the sample standard deviation ($s$) in metres?
Options:
|
Multiple Choice
The sample variance ($s^2$) for a set of measurements is calculated to be $2.25$ ft$^2$.
What is the sample standard deviation ($s$) in feet?
Options:
|
Classifier: The text contains the metric unit "metres" (AU spelling) and "m", which requires conversion to US customary units or at least spelling localization to "meters" per the hierarchy rules where any metric unit triggers a RED category. Verifier: The text contains the metric unit "metres" (AU spelling) and "m", which requires conversion to US customary units or at least spelling localization to "meters". Per rule 3, any metric unit triggers RED. |
01JW5RGMQXVG6RPJMQEMME5SXF |
Localize | Spelling (AU-US) | Multiple Choice
A researcher is analysing factors that influence student performance on standardised mathematics tests.
Which of the following cannot be used as an explanatory variable in this study?
Options:
|
Multiple Choice
A researcher is analyzing factors that influence student performance on standardized math tests.
Which of the following cannot be used as an explanatory variable in this study?
Options:
|
Classifier: Contains AU/UK spellings "analysing" and "standardised" which require conversion to US "analyzing" and "standardized". Verifier: The text contains AU/UK spellings "analysing" and "standardised" (used multiple times), which require localization to US English ("analyzing", "standardized"). |
01JW5RGMQ260X6ZWFBNYPBNZB2 |
Localize | Units (simple) | Multiple Choice
A chord of length $8\sqrt{3}$ cm is in a circle of radius $8$ cm.
Find the area of the minor segment formed by this chord.
Hint: The minor segment is the smaller segment made by the chord.
Options:
|
Multiple Choice
A chord of length $8\sqrt{3}$ in is in a circle of radius $8$ in.
Find the area of the minor segment formed by this chord.
Hint: The minor segment is the smaller segment made by the chord.
Options:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion for US localization. Verifier: The question and answers contain metric units (cm and cm^2) which require conversion for US localization. The conversion is straightforward (simple). |
01JW7X7JXV48396RQTNTKNXA27 |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ represent a location on the Cartesian plane.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ represent a location on the Cartesian plane.
Options:
|
Classifier: The answer choice "Co-ordinates" uses a hyphen which is common in AU/UK English but typically omitted in US English ("Coordinates"). While often a stylistic choice, in the context of localization, the hyphenated version is a signal for non-US spelling. Verifier: The answer choice "Co-ordinates" uses a hyphen, which is the standard AU/UK spelling, whereas US English uses "Coordinates". This requires localization to the US spelling. |
01JW7X7JWPCQFR56NAQB56H6S7 |
Localize | Spelling (AU-US) | Multiple Choice
Scaling involves changing the $\fbox{\phantom{4000000000}}$ of a shape.
Options:
|
Multiple Choice
Scaling involves changing the $\fbox{\phantom{4000000000}}$ of a shape.
Options:
|
Classifier: The answer set contains the AU spelling "colour", which requires conversion to the US spelling "color". Verifier: The answer set contains the AU spelling "colour", which requires localization to the US spelling "color". |
01JW5RGMR0JS4ZCQ655G1M3E7H |
Localize | Units (simple) | Multiple Choice
Which of the following datasets contains both categorical and numerical variables?
Options:
|
Multiple Choice
Which of the following datasets contains both categorical and numerical variables?
Options:
|
Classifier: Contains the metric unit "litres" with AU spelling. This requires both spelling correction and potentially unit conversion/localization. Verifier: Contains the metric unit "litres" with AU spelling. This requires both spelling correction to "liters" and unit conversion/localization as per the decision rules (ANY metric unit = at least RED.units_simple_conversion). |
01JW7X7JX3Y69JQDZ39G17T6BD |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a three-dimensional solid with all points on its surface equidistant from its centre.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a three-dimensional solid with all points on its surface equidistant from its center.
Options:
|
Classifier: Contains the AU spelling "centre", which must be localized to "center" for US English. Verifier: The text contains the AU/British spelling "centre", which requires localization to "center" for US English. |
01JW7X7JXDPPH38DFGQKXYKTEY |
Localize | Terminology | Multiple Choice
$\fbox{\phantom{4000000000}}$ equations are a set of two or more equations with multiple variables.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ of equations is a set of two or more equations with multiple variables.
Options:
|
Classifier: The term "Simultaneous equations" is the standard term in AU/UK curricula, whereas the US curriculum almost exclusively uses "Systems of equations". This is a terminology mapping issue. Verifier: The term "Simultaneous equations" is the standard terminology in the Australian curriculum, whereas the US curriculum uses "Systems of equations". This requires localization for the US market. |
01JW7X7JX6E6B88K2SPD1YPKB8 |
Localize | Spelling (AU-US) | Multiple Choice
The $\fbox{\phantom{4000000000}}$ of rotation refers to how many degrees an object is turned.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ of rotation refers to how many degrees an object is turned.
Options:
|
Classifier: The answer set contains the AU spelling "centre", which requires localization to the US spelling "center". Verifier: The answer choice "centre" is the AU/British spelling and requires localization to the US spelling "center". |
01JW7X7JXXHGXYVYM3QCSH3TV6 |
Localize | Spelling (AU-US) | Multiple Choice
Powers do not $\fbox{\phantom{4000000000}}$ over addition or subtraction, meaning $(a + b)^n$ is not equal to $a^n + b^n$.
Options:
|
Multiple Choice
Exponents do not $\fbox{\phantom{4000000000}}$ over addition or subtraction, meaning $(a + b)^n$ is not equal to $a^n + b^n$.
Options:
|
Classifier: The answer choice "factorise" uses the AU/UK "-ise" suffix, which must be localized to the US "-ize" suffix ("factorize"). Verifier: The answer choice "factorise" uses the AU/UK "-ise" suffix, which must be localized to the US "-ize" suffix ("factorize"). |
01JW7X7JXZGD25TM7V8NM0PN66 |
Localize | Spelling (AU-US) | Multiple Choice
Tree diagrams can be used to visualise and solve problems involving $\fbox{\phantom{4000000000}}$ events.
Options:
|
Multiple Choice
Tree diagrams can be used to visualize and solve problems involving $\fbox{\phantom{4000000000}}$ events.
Options:
|
Classifier: The word "visualise" uses the AU/UK "-ise" spelling, which requires conversion to the US "visualize". Verifier: The word "visualise" in the question content uses the AU/UK "-ise" spelling, which requires conversion to the US "visualize". |
01JW7X7JY1FVNJEHQNM6FN79SF |
Localize | Spelling (AU-US) | Multiple Choice
Factorising by grouping is a $\fbox{\phantom{4000000000}}$ used to factorise expressions with four or more terms.
Options:
|
Multiple Choice
Factoring by grouping is a $\fbox{\phantom{4000000000}}$ used to factor expressions with four or more terms.
Options:
|
Classifier: Contains the AU spelling "Factorising" and "factorise", which require conversion to US spelling "Factorizing" and "factorize". Verifier: The text contains "Factorising" and "factorise", which are AU/British spellings. The US equivalent is "Factorizing" and "factorize". |
01JW7X7JY3VK0HPMSH2HANQQYA |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ a denominator means rewriting a fraction so that the denominator no longer contains a radical.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ a denominator means rewriting a fraction so that the denominator no longer contains a radical.
Options:
|
Classifier: Contains the AU spelling "Rationalising" in the answer set, which requires conversion to US spelling "Rationalizing". Verifier: The answer set contains "Rationalising", which is the AU/British spelling. The US spelling is "Rationalizing". |
01JW7X7JY51DBG4AS3ZCDRY4DJ |
Localize | Spelling (AU-US) | Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the distance from the centre of a circle to any point on its circumference.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the distance from the center of a circle to any point on its circumference.
Options:
|
Classifier: Contains the AU spelling "centre", which requires conversion to US spelling "center". Verifier: The text contains the AU/British spelling "centre", which requires localization to the US spelling "center". |
01JW7X7JYX0CNBRQ3VSQNW75KV |
Localize | Answer set | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a quadrilateral with four right angles and opposite sides equal.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a quadrilateral with four right angles and opposite sides equal.
Options:
|
Classifier: The answer set contains the term "trapezium", which in the US refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to a quadrilateral with one pair of parallel sides (which the US calls a "trapezoid"). Even though the correct answer here is "rectangle", the presence of "trapezium" in the distractor set requires localization to "trapezoid" for US consistency. Verifier: The presence of "trapezium" in the answer set requires localization to "trapezoid" for US audiences, as the two terms have different definitions in US vs AU/UK geometry. |
01JW7X7JZDD9Y77VG3QPTZ88K8 |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ is the study of collecting, analysing, interpreting, presenting and organising data.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ is the study of collecting, analyzing, interpreting, presenting and organizing data.
Options:
|
Classifier: The text contains two instances of AU-specific spelling: "analysing" (US: analyzing) and "organising" (US: organizing). Verifier: The text contains "analysing" and "organising", which are AU/British spellings (US: analyzing, organizing). This requires RED classification per rule 1. |
01JW7X7JZFEE9F01MQH9884S3N |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ is the process of rewriting an expression as a product of its factors.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ is the process of rewriting an expression as a product of its factors.
Options:
|
Classifier: The answer choice "Factorising" uses the AU 's' spelling, which requires conversion to the US 'z' spelling ("Factorizing"). Verifier: The answer choice "Factorising" uses the AU/UK spelling with an 's'. US English requires "Factorizing" with a 'z'. |
01JW7X7JZKM0WX5C9CWY86EW2Q |
Localize | Answer set | Multiple Choice
A rhombus is a $\fbox{\phantom{4000000000}}$ with all sides equal in length.
Options:
|
Multiple Choice
A rhombus is a $\fbox{\phantom{4000000000}}$ with all sides equal in length.
Options:
|
Classifier: The answer set contains the term "trapezium", which is the standard AU/UK term for a quadrilateral with one pair of parallel sides. In the US, this is called a "trapezoid". This requires localization for answer set consistency. Verifier: The term "trapezium" is used in the answer set. In Australia/UK, a trapezium is a quadrilateral with one pair of parallel sides, whereas in the US, this is called a "trapezoid". This requires localization for terminology consistency. |
01JW7X7JZXAPGHM98QYZNDCJTF |
Localize | Terminology | Multiple Choice
$\fbox{\phantom{4000000000}}$ is an acronym that represents the order of operations in mathematics.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ is an acronym that represents the order of operations in math.
Options:
|
Classifier: The text refers to "BODMAS" as the acronym for order of operations. In the US, "PEMDAS" is the standard school terminology. This requires localization of the acronym and potentially the distractors. Verifier: The text uses "BODMAS", which is the standard acronym for order of operations in Australia/UK, whereas "PEMDAS" is the standard in the US. This is a school-context terminology difference. |
01JW7X7JZQG135AV20PV4G3CKB |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ organises data by showing the number of times each value occurs.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ organizes data by showing the number of times each value occurs.
Options:
|
Classifier: The text contains the AU spelling "organises", which needs to be converted to the US spelling "organizes". Verifier: The source text contains the word "organises", which is the AU/UK spelling. The US spelling is "organizes". |
01JW7X7K0AXANF34QAV3A12E7M |
Localize | Units (simple) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a unit of weight equal to $1000$ grams.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a unit of weight equal to $2000$ pounds.
Options:
|
Classifier: The text contains multiple metric units ("grams", "kilogram", "milligram", "gram") and the AU/UK spelling of "tonne". Any metric unit requires RED classification per decision rules. Verifier: The text contains multiple metric units ("grams", "kilogram", "milligram", "gram") and the AU/UK spelling of "tonne". Per rule 3, any metric unit requires RED classification. |
01JW5RGMJDT4PGJC3ZMMW14WPR |
Localize | Units (simple) | Multiple Choice
If a length is $5$ millimetres (mm), how many metres is this?
Options:
|
Multiple Choice
If a length is $5$ inches (in), how many feet is this?
Options:
|
Classifier: Contains metric units "millimetres" and "metres" with AU spelling. Requires conversion or localization of the unit system/spelling. Verifier: The text contains metric units ("millimetres", "metres") with AU spelling. |
KxWduPEl38xEoFKhCXPC |
Localize | Units (simple) | Question
Convert $15$ L to m$^3$.
Answer:
|
Question
Convert $15$ gal to ft$^3$.
Answer:
|
Classifier: The question explicitly uses metric units ("L" for litres and "m^3" for cubic metres) and asks for a conversion between them. This requires localization to US customary units or a decision on metric pedagogy. Verifier: The question explicitly uses metric units ("L" for litres and "m^3" for cubic metres) and asks for a conversion. Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
LPuRMFMXDuPmjbYfRDuZ |
Localize | Spelling (AU-US) | Question
Write $x^2+2x+3x+6$ in factorised form.
Options:
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Question
Write $x^2+2x+3x+6$ in factored form.
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling. In US English, this must be "factorized". Verifier: The word "factorised" is the AU/UK spelling. US English requires "factorized". Per rule 1, AU spelling always requires RED classification. |
M9bv9Su5Yj4g2hSzw2dm |
Localize | Spelling (AU-US) | Question
In a group of travel enthusiasts, $11\%$ have travelled to neither France nor the USA, while $40\%$ have only travelled to the USA and $25\%$ have only travelled to France.
What percentage of them have travelled to both countries?
Answer:
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Question
In a group of travel enthusiasts, $11\%$ have traveled to neither France nor Canada, while $40\%$ have only traveled to Canada and $25\%$ have only traveled to France.
What percentage of them have traveled to both countries?
Answer:
|
Classifier: Contains the AU/UK spelling "travelled" (double 'l'), which requires conversion to the US spelling "traveled". Verifier: The word "travelled" is used multiple times, which is the AU/UK spelling. US spelling is "traveled". |
MfPY2agKZAl8cJ6hTB4C |
Localize | Terminology | Question
Which number greater than $55$ completes the Pythagorean triple?
$\{48, 55, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Answer:
|
Question
Which number greater than $55$ completes the Pythagorean triple?
$\{48, 55, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Answer:
|
Classifier: Contains the AU school term "right-angled triangle", which should be localized to "right triangle" in a US context. Verifier: The hint contains "right-angled triangle", which is the standard AU term for what is called a "right triangle" in the US. |
LtapqSkcY9T5EYMgygQl |
Localize | Units (simple) | Question
A sector has a radius of $2$ cm and an area of $4$ cm$^2$.
What is the central angle of the sector in degrees?
Answer:
|
Question
A sector has a radius of $2$ in and an area of $4$ in$^2$.
What is the central angle of the sector in degrees?
Answer:
|
Classifier: The question contains metric units ("cm" and "cm$^2$") which require conversion to US customary units (e.g., inches). Verifier: The question contains metric units ("cm" and "cm^2") which require conversion to US customary units. |
01JW7X7K0DKXXN0ABZGZEJXKT5 |
Localize | Terminology | Multiple Choice
The $\fbox{\phantom{4000000000}}$ of a line is a measure of its steepness.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ of a line is a measure of its steepness.
Options:
|
Classifier: The term "gradient" is the standard AU/UK term for the steepness of a line, whereas "slope" is the standard US term. While both appear in the answer set, the primary term being tested/defined in this context is "gradient". Verifier: The term "gradient" is the standard AU/UK term for the steepness of a line, whereas "slope" is the standard US term. This is a school-context terminology difference. |
MewhS6WEJeXsR6pRvdaI |
Localize | Spelling (AU-US) | Multiple Choice
Which of these is true for the curve of a normal distribution?
Options:
|
Multiple Choice
Which of these is true for the curve of a normal distribution?
Options:
|
Classifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre" in one of the answer choices, which requires localization to "center". |
Ln1XJa9cIcs0ZyKUu8L5 |
Localize | Units (simple) | Question
What is the average velocity?
Velocity $v(t)=t^2+t+2t^3$ m/s
$t_{initial}=3$ seconds
$t_{final}=6$ seconds
Answer:
|
Question
What is the average velocity?
Velocity $v(t)=t^2+t+2t^3$ ft/s
$t_{initial}=3$ seconds
$t_{final}=6$ seconds
Answer:
|
Classifier: The text contains metric units ("m/s") which require localization to US customary units or a decision on metric usage in US physics contexts. Per rules, any metric unit triggers a RED category. Verifier: The question contains the metric unit "m/s" (metres per second). Per the decision rules, any metric unit requires at least a RED classification. Since it is a simple calculation of average velocity from a polynomial without complex interlinked unit conversions, simple_conversion is appropriate. |
MF1kP1olIoyvwDhKcBCr |
Localize | Terminology | Multiple Choice
What is the derivative of $\ln{(\sin{(x)})}$?
Options:
|
Multiple Choice
What is the derivative of $\ln{(\sin{(x)})}$?
Options:
|
Classifier: The answer set contains the notation "\cosec", which is the standard AU/UK abbreviation for cosecant. In the US, "\csc" is the standard notation. Verifier: The answer set contains the notation "\cosec", which is the standard AU/UK abbreviation for cosecant. In the US, "\csc" is the standard notation. |
MCIizIDI85pY5hH99K5h |
Localize | Spelling (AU-US) | Multiple Choice
How is $281$ written in words?
Options:
|
Multiple Choice
How is $281$ written in words?
Options:
|
Classifier: The correct answer "Two hundred and eighty-one" uses the conjunction "and" between the hundreds and tens place. While common in AU/UK English, US English pedagogy typically omits the "and" (e.g., "Two hundred eighty-one") as "and" is reserved for the decimal point. This is a stylistic/spelling convention difference in number naming. Verifier: The inclusion of "and" in "Two hundred and eighty-one" is a hallmark of AU/UK number naming pedagogy, whereas US pedagogy explicitly teaches to omit "and" unless representing a decimal point. |
LXbU1A1avYx61GfynEPq |
Localize | Terminology | Question
The equation $-3x+5y=-15$ can be written as $y=mx+c$, where $m$ is the gradient of the line.
What is the value of $m$ ?
Answer:
|
Question
The equation $-3x+5y=-15$ can be written as $y=mx+b$, where $m$ is the slope of the line.
What is the value of $m$ ?
Answer:
|
Classifier: The term "gradient" is used to describe the slope of a line, and the form "y=mx+c" is used. In US curriculum, "slope" is the standard term, and "y=mx+b" is the standard form. Verifier: The text uses "gradient" (AU/UK) instead of "slope" (US) and the form "y=mx+c" (AU/UK) instead of "y=mx+b" (US). This requires localization for the US market. |
M34RKSwgfBf4fwjSQ8zR |
Localize | Units (simple) | Question
The distance between the park and the supermarket is $4860$ m.
Shane travelled $1020$ m by bus, $750$ m by rented bicycle, and $372$ m on foot.
How much distance does he still need to cover?
Answer:
|
Question
The distance between the park and the supermarket is $4860$ ft.
Shane traveled $1020$ ft by bus, $750$ ft by rented bicycle, and $372$ ft on foot.
How much distance does he still need to cover?
Answer:
|
Classifier: The text contains the metric unit 'm' (metres) multiple times, which requires conversion to US customary units (e.g., feet or yards) for US localization. Verifier: The question uses the metric unit "m" (metres) multiple times, which requires conversion to US customary units. The calculation is a simple subtraction of values, fitting the simple conversion category. |
LdWlXJ4ihplVd7Ig0KNi |
Localize | Units (simple) | Question
A student wants to find the mass of a block of wood that has a volume of $1000$ cm$^3$ and a density of $0.6$ g/cm$^3$.
What is the mass of the block of wood in grams?
Answer:
|
Question
A student wants to find the mass of a block of wood that has a volume of $1000$ in$^3$ and a density of $0.6$ oz/in$^3$.
What is the mass of the block of wood in ounces?
Answer:
|
Classifier: The question contains multiple metric units (cm^3, g/cm^3, grams) which require localization to US customary units or a policy-based decision on metric usage in science contexts. Per rules, any metric unit triggers a RED classification. Verifier: The question contains metric units (cm^3, g/cm^3, grams) which require localization. Simple conversion is appropriate as it is a straightforward density calculation. |
LNLAPstXLR56Ok9G88mt |
Localize | Terminology | Multiple Choice
In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$, $AB \cong DE$, and $AC \cong DF$.
Which congruency test proves $\triangle ABC \cong \triangle DEF$?
Options:
|
Multiple Choice
In $\triangle ABC$ and $\triangle DEF$, $\angle A \cong \angle D$, $AB \cong DE$, and $AC \cong DF$.
Which congruence theorem proves $\triangle ABC \cong \triangle DEF$?
Options:
|
Classifier: The answer choice "RHS" (Right-angle, Hypotenuse, Side) is a standard AU/UK term for triangle congruence that is typically referred to as "HL" (Hypotenuse-Leg) in the US. Additionally, "congruency test" is more commonly "congruence theorem/postulate" in the US. Verifier: The term "RHS" (Right-angle, Hypotenuse, Side) is the AU/UK equivalent of the US "HL" (Hypotenuse-Leg) theorem. "Congruency test" is also more common in AU than US "congruence theorem". |
Mmyze4gEJjrAGS7masE6 |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
The mass of the garbage collected in a day from a city is best measured in $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The weight of the trash collected in a day from a city is best measured in $[?]$.
Options:
|
Classifier: The question and answer set are entirely based on metric units (Grams, Kilograms, Tonnes, Milligrams). Per decision rules, any metric unit requires classification into a units category. Additionally, "Tonnes" is the AU spelling (US is "tons" or "metric tons"). Verifier: The question is based on metric units (Grams, Kilograms, Tonnes, Milligrams). "Tonnes" is also the AU spelling. Per rule 3, any metric unit requires RED classification. |
Mj5XX3NdOdFq1QjoIRRQ |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
The prime factorisation of $140$ is $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The prime factorization of $140$ is $[?]$.
Options:
|
Classifier: Contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: The text contains "factorisation", which is the AU/UK spelling. US spelling is "factorization". |
01JW7X7K0KK1V98MPJGPZ1WRTB |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a diagram used to visualise the possible outcomes of a multi-stage experiment.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a diagram used to visualize the possible outcomes of a multi-stage experiment.
Options:
|
Classifier: The word "visualise" uses the AU/UK 's' spelling and requires conversion to the US 'z' spelling ("visualize"). Verifier: The word "visualise" uses the AU/UK 's' spelling and requires conversion to the US 'z' spelling ("visualize"). |
LI6pycPRLnQ5cty2R0TR |
Localize | Terminology | Multiple Choice
Which of the following is not a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Options:
|
Multiple Choice
Which of the following is not a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Options:
|
Classifier: The hint contains the term "right-angled triangle", which is the standard AU/UK term. In the US, this is localized to "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas the US uses "right triangle". This requires localization for terminology. |
LByjMBe1bGBJYFAOha64 |
Localize | Units (simple) | Multiple Choice
A particle moves in a straight line with velocity $v(t)=t^3-6t^2+25$ m/s for time $t\geq0$ (seconds).
Find the direction in which the particle is moving at $t=5$ s.
Options:
|
Multiple Choice
A particle moves in a straight line with velocity $v(t)=t^3-6t^2+25$ ft/s for time $t\geq0$ (seconds).
Find the direction in which the particle is moving at $t=5$ s.
Options:
|
Classifier: The text contains the metric unit "m/s" (metres per second). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains metric units "m/s" and "s" (seconds). Per rule 3, any metric unit requires RED classification. Since the conversion is a straightforward unit change and doesn't involve complex re-derivation of coefficients in the provided function, simple_conversion is appropriate. |
LzeAl1DNb6FEgza923j2 |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $24x^{2}y^{2}-6xy^2$
Options:
|
Multiple Choice
Factor $24x^{2}y^{2}-6xy^2$
Options:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Factorize"). Verifier: The word "Factorise" is the AU/UK spelling and requires localization to "Factorize" for the US locale. |
NIoNLZrSqw5bRDTaoNgB |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
To rationalise the denominator of ${\Large\frac{c}{a+\sqrt{b}}}$, multiply and divide it with the radical conjugate of the denominator.
Options:
|
Multiple Choice
True or false:
To rationalize the denominator of ${\Large\frac{c}{a+\sqrt{b}}}$, multiply and divide it by the radical conjugate of the denominator.
Options:
|
Classifier: Contains the AU spelling "rationalise", which needs to be converted to the US spelling "rationalize". Verifier: The text contains the AU/British spelling "rationalise", which must be changed to the US spelling "rationalize". |
NSfjOzHB17CtNFZt1BKb |
Localize | Terminology | Question
A random survey of $650$ people was conducted, and their responses recorded, with $164$ people agreeing that maths was their favourite subject at school.
Find the margin of error of a $98\%$ confidence interval constructed from this data.
Answer:
|
Question
A random survey of $650$ people was conducted, and their responses recorded, with $164$ people agreeing that math was their favorite subject at school.
Find the margin of error of a $98\%$ confidence interval constructed from this data.
Answer:
|
Classifier: Contains the AU-specific term "maths", which should be localized to "math" for a US audience. Also uses "favourite" (AU spelling), but terminology is the higher priority flag. Verifier: Contains "maths" (terminology) and "favourite" (spelling). Terminology is the higher priority flag. |
NaK44FbzmzEvVHSxma9K |
Localize | Units (simple) | Question
Find the area of a sector of radius $10$ cm with a central angle of $\frac{\pi}{6}$ radians.
Answer:
|
Question
Find the area of a sector of radius $10$ in with a central angle of $\frac{\pi}{6}$ radians.
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) and "cm^2", which requires conversion to US customary units or a different unit strategy for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. It is a simple conversion as it involves a single numeric radius and a standard area formula. |
NIhAzbNNMtABpW0QOG9b |
Localize | Units (simple) | Question
The displacement function of a car is $s(t)=4t^2+5t+15$ km for $0\leq t\leq 7$ h.
Find the car's average velocity from $t=1$ to $t=4$ hours.
Answer:
|
Question
The displacement function of a car is $s(t)=4t^2+5t+15$ mi for $0\leq t\leq 7$ h.
Find the car's average velocity from $t=1$ to $t=4$ hours.
Answer:
|
Classifier: Contains metric units "km" and "km/h" which require conversion to US customary units (miles and mph). Verifier: The question contains metric units "km" and "km/h" which require conversion to US customary units. Since the conversion is a straightforward numeric change to the result of the calculation, simple_conversion is appropriate. |
N7CFTViC8OLAZfUlGLvn |
Localize | Terminology | Multiple Choice
Fill in the blank:
The gradient-intercept form of the linear equation $5x+3y=11$ is $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The slope-intercept form of the linear equation $5x+3y=11$ is $[?]$.
Options:
|
Classifier: The term "gradient-intercept form" is the standard AU term for what is called "slope-intercept form" in the US. Verifier: "Gradient-intercept form" is the specific Australian curriculum term for what is known as "slope-intercept form" in the US. |
NubDdlOB2XtIkcSvNLuV |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
It is mandatory for every organisation to pay dividends to its stakeholders.
Options:
|
Multiple Choice
True or false:
It is mandatory for every organization to pay dividends to its stakeholders.
Options:
|
Classifier: The word "organisation" uses the AU/UK 's' spelling; the US standard is "organization". Verifier: The word "organisation" uses the AU/UK 's' spelling; the US standard is "organization". Per rule 1, AU spelling always requires RED classification. |
NifZRu6ZkjU9GwosBvOl |
Localize | Terminology | Question
Which number less than $85$ completes the Pythagorean triple?
$\{13,[?],85\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Answer:
|
Question
Which number less than $85$ completes the Pythagorean triple?
$\{13,[?],85\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Answer:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" in a US context. Verifier: The hint contains the term "right-angled triangle", which is the standard AU/UK term. In the US, "right triangle" is used. This requires localization. |
Nr3Ye62lTYrG3alF5F5d |
Localize | Units (simple) | Multiple Choice
An object has an initial velocity of $38$ m/s and moves with a constant acceleration $a(t)=-5t$ m/s$^2$ for all $t\geq0$.
State whether the speed of the object is increasing or decreasing at $t=4$ s.
Options:
|
Multiple Choice
An object has an initial velocity of $38$ ft/s and moves with a constant acceleration $a(t)=-5t$ ft/s$^2$ for all $t\geq0$.
State whether the speed of the object is increasing or decreasing at $t=4$ s.
Options:
|
Classifier: Contains metric units (m/s and m/s^2) which require conversion for US localization. Verifier: The question contains metric units (m/s and m/s^2) which require conversion for US localization. Since it's a simple physics problem with a few values and no complex formula re-derivation needed for the conversion, simple_conversion is appropriate. |
Nw9ztwo7Lm2W3RNlbJVj |
Localize | Units (simple) | Question
An object moves with a displacement given by the function $s(t)=2t^2+5t-2$ m for $t\geq 0$ s.
Find the speed at $t=0$ s.
Hint: First, find the velocity function.
Answer:
|
Question
An object moves with a displacement given by the function $s(t)=2t^2+5t-2$ ft for $t\geq 0$ s.
Find the speed at $t=0$ s.
Hint: First, find the velocity function.
Answer:
|
Classifier: The text contains metric units ("m", "s", "m/s") which require localization to US customary units. Verifier: The text contains metric units "m" (metres) and "s" (seconds) in a physics context. While there is a function $s(t)$, the units are explicitly stated as "m" and "s", requiring conversion. It is simple because it's a single value calculation. |
NZ96RvfOXVcWwhPUHLfm |
Localize | Terminology | Multiple Choice
A vehicle crossing a bridge can be represented by the parabolic function $y = -3(x - 4)^2 + 7$.
What is its turning point?
Options:
|
Multiple Choice
A vehicle crossing a bridge can be represented by the parabolic function $y = -3(x - 4)^2 + 7$.
What is its vertex?
Options:
|
Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In a US context, "vertex" is the required term. Verifier: The term "turning point" is the standard AU school term for what is called the "vertex" of a parabola in the US. |
NVOheqYpjmc8y9FdfJeJ |
Localize | Spelling (AU-US) | Multiple Choice
How can seasonality be adjusted for the given data?
The deseasonalised value is $0.714 \ \times$ the actual value.
Options:
|
Multiple Choice
How can seasonality be adjusted for the given data?
The deseasonalized value is $0.714 \ \times$ the actual value.
Options:
|
Classifier: Contains the AU spelling "deseasonalised", which requires conversion to the US spelling "deseasonalized". Verifier: The text contains "deseasonalised", which is the AU spelling of the US "deseasonalized". |
NtprxR8ozAe2GKWCAxHC |
Localize | Terminology | Multiple Choice
Convert the equation $y = -4x^2 + 8x -7$ to turning point form.
Options:
|
Multiple Choice
Convert the equation $y = -4x^2 + 8x -7$ to vertex form.
Options:
|
Classifier: The term "turning point form" is the AU equivalent of the US "vertex form" for quadratic equations. Verifier: The term "turning point form" is the AU equivalent of the US "vertex form" for quadratic equations. |
O4tJqa6xZNVGucsDzJfY |
Localize | Units (simple) | Question
Location coordinates are given as:
Point $X$ $=0^\circ,145^\circ{W}$
Point $Y$ $=0^\circ,90^\circ{W}$
What is the shortest distance between the two points (to the nearest kilometre), where the radius of the Earth is $6400$ km?
Answer:
|
Question
Location coordinates are given as:
Point $X$ $=0^\circ,145^\circ{W}$
Point $Y$ $=0^\circ,90^\circ{W}$
What is the shortest distance between the two points (to the nearest mile), where the radius of the Earth is $6400$ mi?
Answer:
|
Classifier: The text contains metric units ("kilometre", "km") which require localization to US customary units or at least classification as a unit conversion task. It also contains the AU spelling "kilometre". Verifier: The text contains the metric unit "kilometre" (AU spelling) and "km". This requires conversion to US customary units (miles) or at least classification as a unit conversion. |
NzgHdEqROtr9gcjyavY0 |
Localize | Units (simple) | Multiple Choice
The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$.
If the container initially has $10$ litres of water, what is the volume after $t$ hours?
Options:
|
Multiple Choice
The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$.
If the container initially has $10$ gallons of water, what is the volume after $t$ hours?
Options:
|
Classifier: The text contains the metric unit "litres", which requires both a spelling change (to "liters") and a unit conversion to US customary units (e.g., gallons) per the localization rules. Verifier: Contains the metric unit "litres", which requires spelling change and unit conversion. |
NxWQ66JtQd5TdKz882rz |
Localize | Units (simple) | Question
Maria runs a bakery and sells freshly baked strawberry cake at a profit of $\$10$ and Belgian cakes at a gain of $\$14$ each.
She uses $1$ kg refined flour for a strawberry cake and $1.5$ kg for the Belgian cake.
A strawberry cake needs $1.5$ hours to prepare, while a Belgian cake gets ready in $1$ hour.
Maria can work only for $8$ hours in a day and buys not more than $10$ kg of refined flour for cakes daily.
How much time does she need to prepare Belgian cakes in the day for maximum profit?
Hint: Do you know the number of Belgian cakes does she bake in a day?
Answer:
|
Question
Maria runs a bakery and sells freshly baked strawberry cake at a profit of $\$10$ and Belgian cakes at a gain of $\$14$ each.
She uses $1$ lb refined flour for a strawberry cake and $1.5$ lb for the Belgian cake.
A strawberry cake needs $1.5$ hours to prepare, while a Belgian cake gets ready in $1$ hour.
Maria can work only for $8$ hours in a day and buys not more than $10$ lb of refined flour for cakes daily.
How much time does she need to prepare Belgian cakes in the day for maximum profit?
Hint: Do you know the number of Belgian cakes she bakes in a day?
Answer:
|
Classifier: The problem uses metric units ("kg") which must be converted for a US audience. Verifier: The problem uses metric units "kg" (kilograms) which require conversion to US customary units (pounds). |
OD1jvJjy6chQeIvjjEP1 |
Localize | Units (simple) | Multiple Choice
An object has the velocity function $v(t)=2t+3$ m s$^{-1}$.
Find the displacement function $s(t)$ if $s(0)=-1$ m.
Options:
|
Multiple Choice
An object has the velocity function $v(t)=2t+3$ ft/s.
Find the displacement function $s(t)$ if $s(0)=-1$ ft.
Options:
|
Classifier: The text contains metric units "m s^-1" (metres per second) and "m" (metres) used in a physics/calculus context. These require conversion to US customary units or a check against US physics curriculum standards. Verifier: The text contains metric units "m s^-1" and "m" which require localization. |
OAE8jY1PW2nwmrSfZXLU |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Hannah took a $\$12000$ loan at $15\%$ annual interest, compounded monthly, with monthly payments of $\$3094.30$ over $4$ months.
This loan is modelled by the given recurrence relation :
$V_0=12000$ ; $V_{n+1}=1.0125V_n-3094.30$
where $V_n$ represents the balance of the loan after $n$ payments.
The loan can be fully repaid in $4$ months with this payment.
Options:
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Multiple Choice
True or false:
Hannah took a $\$12000$ loan at $15\%$ annual interest, compounded monthly, with monthly payments of $\$3094.30$ over $4$ months.
This loan is modeled by the given recurrence relation :
$V_0=12000$ ; $V_{n+1}=1.0125V_n-3094.30$
where $V_n$ represents the balance of the loan after $n$ payments.
The loan can be fully repaid in $4$ months with this payment.
Options:
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Classifier: Contains the AU/UK spelling "modelled" (double 'l'), which should be "modeled" in US English. Verifier: The text contains "modelled", which is the AU/UK spelling. The US spelling is "modeled". |
O2VTR93elgl87xZaDu1F |
Localize | Units (complex) | Multiple Choice
A body starts from rest and moves in a straight line. Its velocity function is given by $v(t)=3t^2-4t$ m/s.
What will be the position of the body at time $t$ ?
Hint: $s(t)=\int v(t)$ and the constant will be the initial position of the object
Options:
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Multiple Choice
A body starts from rest and moves in a straight line. Its velocity function is given by $v(t)=3t^2-4t$ ft/s.
What will be the position of the body at time $t$ ?
Hint: $s(t)=\int v(t)$ and the constant will be the initial position of the object
Options:
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Classifier: The question and answers contain metric units ("m/s" and "m"). According to the decision rules, any metric unit found anywhere in the text triggers a RED classification for conversion. Verifier: The question contains a velocity function v(t) defined in metric units (m/s). Per rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients (integration in this case) should be classified as RED.units_complex_converted. |
OohT77JzB1liXABcVhM7 |
Localize | Terminology | Question
A product originally costs $\$800$.
It is marked up by $\$80$.
Then it is increased by another $10\%$ before a $10\%$ GST is added.
How much GST is included in the total price?
Answer:
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Question
A product originally costs $\$800$.
It is marked up by $\$80$.
Then it is increased by another $10\%$ before a $10\%$ sales tax is added.
How much sales tax is included in the total price?
Answer:
|
Classifier: The text refers to "GST" (Goods and Services Tax), which is the specific consumption tax system in Australia. In a US context, this would typically be localized to "sales tax" or a similar concept, as the US does not have a GST. Verifier: The text uses "GST" (Goods and Services Tax), which is a specific tax terminology used in Australia (and other Commonwealth countries) but not in the US, where "sales tax" is used. This falls under terminology_school_context. |
OMWOwx0GTM97mfbBrKD9 |
Localize | Terminology | Multiple Choice
What is the principal axis of $\cos{x}$ ?
Options:
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Multiple Choice
What is the midline of $\cos{x}$ ?
Options:
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Classifier: The term "principal axis" in the context of trigonometric functions (the horizontal line halfway between the maximum and minimum values) is commonly referred to as the "midline" or "midline equation" in US curriculum. Verifier: The term "principal axis" is used in AU/UK curricula to describe the horizontal center line of a trigonometric function; in the US, this is standardly called the "midline". |
OMCfxIF006giY1H5wm7L |
Localize | Terminology | Multiple Choice
What is the turning point of the parabola $y=x^{2}+4x+3$ ?
Options:
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Multiple Choice
What is the vertex of the parabola $y=x^{2}+4x+3$ ?
Options:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian/British term for what is almost exclusively called the "vertex" in US mathematics curricula. |
Oo9h76RDa3P91s07WPEu |
Localize | Units (simple) | Multiple Choice
A zookeeper needs $4$ hectares per elephant.
If the zoo is $20$ hectares, and $x$ is the number of elephants he can buy, which inequality represents this?
Options:
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Multiple Choice
A zookeeper needs $4$ acres per elephant.
If the zoo is $20$ acres, and $x$ is the number of elephants he can buy, which inequality represents this?
Options:
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Classifier: The text contains the metric unit "hectares". According to the decision rules, any metric unit requires classification into a RED.units category. Verifier: The text contains the metric unit "hectares". According to rule 3, any metric unit requires at least RED.units_simple_conversion. Since the math is a simple inequality based on a single conversion/comparison, simple_conversion is appropriate. |
OFnfQr9mNsVlT6LUm6nS |
Localize | Units (simple) | Question
A garment factory plans to produce jeans and trousers from 30 meters of fabric, aiming for minimum profit with low input.
Each pair of jeans requires 2.5 m of fabric and 30 minutes to make, while each trouser requires 2.8 m of fabric and 45 minutes.
They expect a profit of $\$2$ on jeans and $\$3$ on trousers, with a maximum of 420 minutes available for production. Let:
$x = $ number of jeans
$y = $ number of trousers
Write an expression for the objective function for the garment factory's profit.
Options:
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Question
A garment factory plans to produce jeans and pants from 30 feet of fabric, aiming for minimum profit with low input.
Each pair of jeans requires 2.5 ft of fabric and 30 minutes to make, while each pair of pants requires 2.8 ft of fabric and 45 minutes.
They expect a profit of $\$2$ on jeans and $\$3$ on pants, with a maximum of 420 minutes available for production. Let:
$x = $ number of jeans
$y = $ number of pants
Write an expression for the objective function for the garment factory's profit.
Options:
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Classifier: The text contains metric units "meters" and "m". Note: although "meters" is spelled in the US way in the first instance, "m" is a metric unit, and the context of fabric measurement in meters is a metric-system problem. Additionally, "trousers" is more common in AU/UK, whereas "pants" is preferred in US, but the presence of metric units is the primary driver for RED. Verifier: The text contains metric units ("meters", "m") and the term "trousers", both of which trigger RED classification. Metric units are the primary driver. |
PhdV7hVGXDbY53KbwOiO |
Localize | Spelling (AU-US) | Question
Write 'one hundred and eighty-two thousand and six hundred' as a number.
Answer:
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Question
Write 'one hundred eighty-two thousand six hundred' as a number.
Answer:
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Classifier: The text uses the word "and" in the middle of a whole number ("one hundred and eighty-two thousand..."). While not strictly a spelling error, US English pedagogy typically omits "and" when writing whole numbers (reserving "and" for the decimal point), making this an AU-specific convention. However, looking at the specific category definitions, if this is considered a stylistic/convention difference, it is closest to spelling/terminology. More importantly, the prompt rules for GREEN are very strict; this is not bi-dialect neutral. Verifier: The text uses "and" within a whole number ("one hundred and eighty-two thousand..."). In US pedagogy, "and" is strictly reserved for the decimal point in number names. This is an AU-specific convention that requires localization. |
OvNjz2VQXQPwO8zMhMY7 |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
A scatterplot can be used to visualise the relationship between two numerical variables.
Options:
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Multiple Choice
True or false:
A scatterplot can be used to visualize the relationship between two numerical variables.
Options:
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Classifier: The word "visualise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("visualize"). Verifier: The word "visualise" is AU/UK spelling and requires localization to "visualize" for US English. |
PWVLdtVteCTHjbsltxed |
Localize | Units (simple) | Question
What is $10$ m$^2$ in cm$^2$ ?
Answer:
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Question
What is $10$ ft$^2$ in in$^2$ ?
Answer:
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Classifier: The question explicitly asks for a conversion between metric units (m^2 to cm^2). Any presence of metric units requires localization to US customary units or a different pedagogical approach per the decision rules. Verifier: The question involves converting between metric units (m^2 and cm^2), which requires localization to US customary units or a different pedagogical approach. |
PKQGClyXhtpLKL6TVZqR |
Localize | Units (simple) | Question
A farmer is measuring a piece of land shaped like a kite. The diagonals of the land are $12$ m and $8$ m.
What is the area of the land?
Answer:
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Question
A farmer is measuring a piece of land shaped like a kite. The diagonals of the land are $12$ ft and $8$ ft.
What is the area of the land?
Answer:
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Classifier: The text contains metric units ("m" for metres and "m$^2$" for square metres) which require conversion to US customary units. Verifier: The question contains metric units ("m" and "m$^2$") which require conversion to US customary units. |
PIfK34nrL63FrZQ6LXDk |
Localize | Units (simple) | Question
The perimeter of an equilateral triangle is $123$ cm.
What is the length of one side?
Answer:
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Question
The perimeter of an equilateral triangle is $123$ in.
What is the length of one side?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) in both the question and the suffix field. This requires localization to US customary units (e.g., inches). Verifier: The text contains the metric unit "cm" in the question and the suffix. This requires localization to US customary units. |
PGEOKKcLCNmJmuiJm3Hd |
Localize | Units (simple) | Question
How many litres are there in $6$ m$^3$ ?
Answer:
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Question
How many gallons are there in $6$ ft$^3$ ?
Answer:
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Classifier: The text contains the AU spelling "litres" and the metric units "litres", "m^3", and "L". This requires both spelling and unit localization. Units conversion is the higher priority classification. |
OrFZ9pT1SMhAIX6IHTMl |
Localize | Units (complex) | Question
The displacement function of a particle is given by $s(t)=19t^2+14t-8$ m for $0\leq t\leq50$ s.
Find the speed at $t=15$ s.
Answer:
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Question
The displacement function of a particle is given by $s(t)=19t^2+14t-8$ ft for $0\leq t\leq50$ s.
Find the speed at $t=15$ s.
Answer:
|
Classifier: The text contains metric units "m" (metres) and "m/s" (metres per second). Per the decision rules, any metric unit requires localization. Verifier: While the classifier correctly identified metric units ("m", "m/s"), it chose simple_conversion. Rule 4 states that if equations define quantities in metric (e.g., s(t) = 19t^2 + 14t - 8 m), it should be classified as RED.units_complex_converted. |
P1dIOseDhevDzuA601jj |
Localize | Units (simple) | Question
A boy went out to buy snacks from a store that was $500$ m away from his home, and he returned after some time.
What was his displacement?
Answer:
|
Question
A boy went out to buy snacks from a store that was $500$ ft away from his home, and he returned after some time.
What was his displacement?
Answer:
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Classifier: The text contains the metric unit 'm' (metres) in both the content and the suffix, which requires conversion to US customary units (e.g., feet or yards). Verifier: The text contains the metric unit 'm' (metres) which requires conversion to US customary units. |
PmPwMFfb2uz7WbVV7BLs |
Localize | Units (complex) | Question
A particle's displacement is given by $s(t)=2t^2+t-5$ m for $0\leq t\leq 4$ s.
Find the particle's average velocity over the first $3$ seconds.
Answer:
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Question
A particle's displacement is given by $s(t)=2t^2+t-5$ ft for $0\leq t\leq 4$ s.
Find the particle's average velocity over the first $3$ seconds.
Answer:
|
Classifier: The question contains metric units ("m" for metres and "s" for seconds) and uses the AU/UK notation for units (m s^-1). These require localization to US customary units or at least review for unit standards. Verifier: The question contains metric units ("m" for metres and "s" for seconds) and uses the AU/UK notation for units (m s^-1). Per rule 4, because the metric units are embedded within a function/equation defining displacement (s(t)=2t^2+t-5 m), it should be classified as RED.units_complex_converted rather than simple. |
P8jo0n6QWoVNYY08PTFt |
Localize | Units (complex) | Question
The displacement function of a particle is $s(t)=4t^2-3$ mm for $0\leq t\leq5$ s.
Find the displacement of the particle at $t=2.5$ s.
Answer:
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Question
The displacement function of a particle is $s(t)=4t^2-3$ in for $0\leq t\leq5$ s.
Find the displacement of the particle at $t=2.5$ s.
Answer:
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Classifier: The question contains the metric unit "mm" (millimetres), which requires localization/classification as a unit conversion task. Verifier: The question contains the metric unit "mm" (millimetres). Per rule 4, because the metric unit is part of a defined function/equation (s(t)=4t^2-3 mm), it should be classified as RED.units_complex_converted rather than simple conversion. |
PgmrbNfm62R12P06ssDu |
Localize | Units (simple) | Question
Find the density of an ice cube of mass $2$ g and volume $0.27$ cm$^3$.
Answer:
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Question
Find the density of an ice cube of mass $2$ oz and volume $0.27$ in$^3$.
Answer:
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Classifier: The question contains metric units ("g" and "cm^3") which require localization for a US audience. Verifier: The question contains metric units ("g" and "cm^3") which require localization for a US audience. It is a simple conversion as it involves a single calculation for density. |
P5gqeH5Drpa9wZdeSfWT |
Review | Review | Multiple Choice
Write $ 529630$ in words.
Options:
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Multiple Choice
Write $ 529630$ in words.
Options:
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Classifier: The answer choices reflect different conventions for writing numbers in words. Specifically, the use of 'and' (e.g., 'six hundred and thirty') is standard in AU/UK but often omitted in US math pedagogy ('six hundred thirty'). Because this involves a specific pedagogical style choice for US localization, it is marked as uncertain/policy-dependent. Verifier: The answer choices contain the AU/UK convention of using "and" in whole numbers (e.g., "six hundred and thirty"), which is a specific pedagogical difference from the US standard ("six hundred thirty"). Per rule 1, AU-specific linguistic conventions require RED classification. Since it is a spelling/style convention for writing numbers, RED.spelling_only is the most appropriate leaf. |
P4pEpnDtFJlUG5D5OYb2 |
Localize | Spelling (AU-US) | Multiple Choice
What is $x^4-16$ in fully factorised form?
Options:
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Multiple Choice
What is $x^4-16$ in fully factored form?
Options:
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Classifier: Contains the AU spelling 'factorised', which needs to be converted to the US spelling 'factorized'. Verifier: Contains the AU spelling 'factorised', which must be localized to 'factorized' for US audiences. |
P6ZiLAIEUpI4sO6VEtyQ |
Localize | Units (simple) | Question
A particle has the displacement function $s(t)=2t^3+2t^2-12t$ cm for $t\geq 0$ s.
Find the initial speed of the particle.
Answer:
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Question
A particle has the displacement function $s(t)=2t^3+2t^2-12t$ in for $t\geq 0$ s.
Find the initial speed of the particle.
Answer:
|
Classifier: Contains metric units 'cm' and 'cm s$^{-1}$' which require localization to US customary units. Verifier: Contains metric units 'cm' and 'cm s^-1' which require conversion. Although it contains a function, the conversion is a simple scalar change to the coefficients/result, fitting simple conversion. |
PhUmoiBDtYtV7GS230xg |
Review | Review | Multiple Choice
Which of the following is not true with respect to the interest rate of a fixed interest rate personal loan?
Options:
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Multiple Choice
Which of the following is not true with respect to the interest rate of a fixed interest rate personal loan?
Options:
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Classifier: The text contains the word "term" in the context of a loan duration ("full term of the loan"). While common in both dialects, "term" is listed in the decision rules as a potential policy-dependent word (GRAY.term_semester_quarter_policy). Additionally, financial contexts sometimes vary in terminology, though "fixed interest rate personal loan" is generally neutral. Verifier: The word "term" in the context of "term of the loan" refers to duration and is standard financial terminology in both AU and US English. It does not refer to school semesters or quarters, which is the intent of the GRAY.term_semester_quarter_policy category. The content is bi-dialect neutral. |
PEZfSIH6uGZeHZjmfnTz |
Localize | Units (simple) | Question
Fill in the blank.
Location coordinates are given as:
Point $X$ $=54^\circ{N},85^\circ{W}$
Point $Y$ $=[?]^\circ{S},85^\circ{W}$
The shortest distance between the two points is approximately $11170$ km, where the radius of the Earth is $6400$ km.
Answer:
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Question
Fill in the blank.
Location coordinates are given as:
Point $X$ $=54^\circ{N},85^\circ{W}$
Point $Y$ $=[?]^\circ{S},85^\circ{W}$
The shortest distance between the two points is approximately $11170$ miles, where the radius of the Earth is $6400$ miles.
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers) multiple times, which requires localization to US customary units (miles) or a decision on whether to retain metric for geographic contexts. Per the decision rules, any metric unit found anywhere results in a RED classification. Verifier: The text contains the metric unit "km" (kilometers) multiple times. According to the decision rules, any metric unit requires RED classification. This is a simple conversion of distance values. |
PLBnKukwppMgJEkcHjH1 |
Localize | Terminology | Multiple Choice
Which of the following equations has a turning point $(h,k)$?
Options:
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Multiple Choice
Which of the following equations has a vertex $(h,k)$?
Options:
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Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola/curve. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU term for what is typically called the "vertex" in US mathematics. |
Pg1hY03MBYzqR3mfMUe6 |
Localize | Terminology | Multiple Choice
Which number less than $24$ completes the Pythagorean triple?
$\{[?],24,30\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Options:
|
Multiple Choice
Which number less than $24$ completes the Pythagorean triple?
$\{[?],24,30\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Options:
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Classifier: The hint contains the term "right-angled triangle", which is the standard AU/UK term. In the US, this is localized to "right triangle". Verifier: The hint contains "right-angled triangle", which is the standard AU/UK term. In the US, this is localized to "right triangle". |
PRTGvPs0zpQLVP1bDGFr |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following equations represents a circle centred at $(-5,4)$ with a radius of $625$ units?
Options:
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Multiple Choice
Which of the following equations represents a circle centered at $(-5,4)$ with a radius of $625$ units?
Options:
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Classifier: The text contains the AU spelling "centred", which needs to be converted to the US spelling "centered". Verifier: The text contains "centred", which is the AU spelling. Per rule 1, any AU spelling requires RED classification. |
PZzjlb5cTvK52wjqVMdl |
Localize | Units (simple) | Multiple Choice
The volume of a cube is $729$ cm$^3$.
What is the length of each side?
Hint: Side of a cube =$\sqrt[3] {Volume}$
Options:
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Multiple Choice
The volume of a cube is $729$ in$^3$.
What is the length of each side?
Hint: Side of a cube =$\sqrt[3] {Volume}$
Options:
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Classifier: The question and the answer choices use metric units (cm and cm^3), which requires localization for a US audience. Verifier: The question and answers use metric units (cm and cm^3), which requires localization. |
PoooSxHg3H5VGdVwFC5g |
Localize | Terminology | Question
$5$ friends share $20$ lollies equally between them.
How many do they each get?
Answer:
|
Question
$5$ friends share $20$ pieces of candy equally between them.
How many do they each get?
Answer:
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Classifier: The term "lollies" is a specific Australian/British term for candy or sweets. In a US educational context, this would typically be localized to "candies" or "pieces of candy". Verifier: The term "lollies" is a specific Australian/British term for candy or sweets, which requires localization for a US context. |
Pt4O2kefhxZNrESdTir3 |
Localize | Terminology | Question
$18$ lollies are shared among a group of students.
If every student gets $2$ lollies, how many students are there?
Answer:
|
Question
$18$ pieces of candy are shared among a group of students.
If every student gets $2$ pieces of candy, how many students are there?
Answer:
|
Classifier: The term "lollies" is an AU-specific term for candy and requires localization for a US audience. Verifier: The term "lollies" is an AU-specific term for candy and requires localization. |
PmfCRg5qZ8y2fFAYriSL |
Localize | Spelling (AU-US) | Question
Simone has four types of pants: jeans, capri, linen, and formal. She also has six different coloured tops: red, blue, pink, white, beige, and black.
If each outfit is equally likely, what is the probability she chooses the beige top and linen pants?
Answer:
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Question
Simone has four types of pants: jeans, capri, linen, and formal. She also has six different colored tops: red, blue, pink, white, beige, and black.
If each outfit is equally likely, what is the probability she chooses the beige top and linen pants?
Answer:
|
Classifier: Contains the AU spelling "coloured", which needs to be converted to the US spelling "colored". Verifier: Contains the AU spelling "coloured", which needs to be converted to the US spelling "colored". |
QC7Z0x9YDIkKcjOUyNYZ |
Localize | Units (simple) | Question
The minute hand of a watch is $15$ cm long.
How far does its tip move in $40$ minutes?
Answer:
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Question
The minute hand of a watch is $15$ in long.
How far does its tip move in $40$ minutes?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units (e.g., inches) for a US audience. |
QMTxpQH6VEe4ekgYamoS |
Localize | Units (simple) | Question
Find the circumference of a circle with a radius of $4.5$ cm.
Answer:
|
Question
Find the circumference of a circle with a radius of $4.5$ in.
Answer:
|
Classifier: The text contains the metric unit "cm" (centimeters) in both the question content and the suffix field, which requires conversion to US customary units (e.g., inches) for US localization. Verifier: The question contains the metric unit "cm" (centimeters) in the content and suffix, which requires simple conversion to US customary units (inches). |
QHE7EXGLGU1YZifbk6zF |
Localize | Terminology | Multiple Choice
Which of the following is the highest common factor of $4mn$ and $2m^4$ ?
Options:
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Multiple Choice
Which of the following is the greatest common factor of $4mn$ and $2m^4$ ?
Options:
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Classifier: Contains "highest common factor" (HCF), which is the standard AU/UK term. The US equivalent is "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US uses "greatest common factor" (GCF). This requires localization for the US market. |
QKQtQjC2HaUY23fLW3PW |
Localize | Units (simple) | Question
Calculate the surface area of a half-cylinder with a height of $12$ m and a radius of $9$ m.
Answer:
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Question
Calculate the surface area of a half-cylinder with a height of $12$ ft and a radius of $9$ ft.
Answer:
|
Classifier: The text uses "m" (metres) and "m$^2$" (square metres) as units of measurement. Any metric unit triggers a RED classification. Verifier: The question uses metric units "m" and "m$^2$". Per rule 3, this must be RED. Since it is a straightforward surface area calculation with few values, simple_conversion is appropriate. |
Q4fbyp7yiX6MwHVKHFJk |
Localize | Answer set | Multiple Choice
Which season comes just before winter?
Options:
|
Multiple Choice
Which season comes just before winter?
Options:
|
Classifier: The answer set contains "Autumn", which is the standard term in AU, whereas "Fall" is more common in the US. Additionally, the seasons in the Southern Hemisphere (AU) occur at different times than in the Northern Hemisphere (US), and the distractor "May" implies an AU seasonal context (where May is late Autumn). This requires localization for terminology and potentially conceptual consistency. Verifier: The use of "Autumn" (vs "Fall") and the inclusion of "May" as a distractor for a season preceding winter indicates a specific hemispheric/locale context that requires localization for US/other markets. |
QJeOnosaMAY1J7eHN4u8 |
Localize | Spelling (AU-US) | Question
The cost price of a hand watch is $\$370$. Daniel bought it through a hire-purchase agreement by paying a deposit of $\$70$ and nine monthly instalments of $\$40$.
Find the total cost of buying this watch by hire-purchase.
Answer:
|
Question
The cost price of a watch is $\$370$. Daniel bought it through an installment loan by paying a deposit of $\$70$ and nine monthly installments of $\$40$.
Find the total cost of buying this watch by installment loan.
Answer:
|
Classifier: The term "instalments" is the AU/UK spelling; the US spelling is "installments". While "hire-purchase" is also more common in AU/UK (US often uses "installment plan" or "rent-to-own"), the spelling difference is a clear RED signal. Verifier: The text contains "instalments", which is the AU/UK spelling (US: installments). It also uses "hire-purchase", a term more common in AU/UK contexts, but the spelling difference alone confirms the RED classification. |
QHzShPJ0uufnd0LodoJg |
Localize | Terminology | Multiple Choice
Classify the solution(s) to the following simultaneous equations.
$y=x+2$
$2y=2x+4$
Options:
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Multiple Choice
Classify the solution(s) to the following system of equations.
$y=x+2$
$2y=2x+4$
Options:
|
Classifier: "Simultaneous equations" is common in AU/UK, but also widely understood and used in US high school algebra alongside "systems of equations". It does not strictly require localization as it is not an AU-only term, though "systems" is more common in the US. Given the strict rules for RED, this remains GREEN as it is bi-dialect neutral. Verifier: "Simultaneous equations" is the standard AU/UK term for what is almost exclusively called a "system of equations" in US pedagogy. While understandable, it is a distinct school-context terminology difference that triggers RED under the localization policy. |
QLJF1TUtwGWtxlgRZph1 |
Localize | Units (simple) | Question
How many kilolitres are there in $5 \ 000 \ 000$ millilitres?
Answer:
|
Question
How many gallons are there in $5 \ 000 \ 000$ fluid ounces?
Answer:
|
Classifier: The question explicitly asks for conversion between metric units (kilolitres and millilitres). Additionally, "kilolitres" and "millilitres" use the AU/UK spelling (US uses "kiloliters" and "milliliters"). Units conversion takes precedence over spelling. Verifier: The question involves metric unit conversion and uses AU/UK spellings ("kilolitres", "millilitres"). Per rule 5, units conversion takes precedence. |
QjHdAoeu3yYXiTD0YkMm |
Localize | Units (simple) | Question
The perimeter of a square is twice the perimeter of a rectangle with dimensions $12$ cm by $8$ cm.
Find the length of each side of the square.
Answer:
|
Question
The perimeter of a square is twice the perimeter of a rectangle with dimensions $12$ in by $8$ in.
Find the length of each side of the square.
Answer:
|
Classifier: Contains the metric unit "cm", which requires localization for US audiences. Verifier: The text contains the metric unit "cm", which requires conversion to US customary units. This is a simple conversion as it involves basic geometric perimeters. |
Qt95rl1mpPz4C9OYh8g7 |
Localize | Units (simple) | Question
Find the perimeter of a rectangle whose length is $4$ m and width is $3$ m.
Answer:
|
Question
Find the perimeter of a rectangle whose length is $4$ ft and width is $3$ ft.
Answer:
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Classifier: The text contains the metric unit "m" (metres), which requires conversion to US customary units (e.g., feet or inches) for US localization. Verifier: The question uses metric units ("m" for metres), which requires conversion to US customary units. |
QqBkuuSBQQ2JJzvhVj26 |
Localize | Terminology | Multiple Choice
True or false:
The parabola with turning point $(-3,\ -4)$ that passes through $(-5,\ -8)$ has the equation $y = -2(x + 3)^2 - 4$.
Options:
|
Multiple Choice
True or false:
The parabola with vertex $(-3,\ -4)$ that passes through $(-5,\ -8)$ has the equation $y = -2(x + 3)^2 - 4$.
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US curriculum. This requires localization for terminology. |
PvKNuGM1eOWm7hiIxDZD |
Localize | Units (simple) | Multiple Choice
$3$ kg of oranges and $4$ kg of apples cost $\$24$.
$4$ kg of oranges and $3$ kg of apples cost $\$22$.
Which statement is correct?
Options:
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Multiple Choice
$3$ lbs of oranges and $4$ lbs of apples cost $\$24$.
$4$ lbs of oranges and $3$ lbs of apples cost $\$22$.
Which statement is correct?
Options:
|
Classifier: The text contains the metric unit "kg" (kilograms) multiple times, which requires localization to US customary units (e.g., pounds) for a US audience. Verifier: The text contains the metric unit "kg" (kilograms) multiple times. This is a simple unit conversion scenario as it involves a system of linear equations with a few discrete values. |
QKPPCG8dByUAT846WA27 |
Localize | Units (simple) | Question
Find the distance of point $A$ from the equator if the coordinate of point $A$ is $(56^\circ N,120^\circ E)$.
Hint: Take Earth's radius to be $6371$ km
Answer:
|
Question
Find the distance of point $A$ from the equator if the coordinate of point $A$ is $(56^\circ N,120^\circ E)$.
Hint: Take Earth's radius to be $6371$ miles
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers) in the hint and the suffix. According to the decision rules, any metric unit requires classification into a RED.units category. Verifier: The question contains the metric unit "km" in the hint and suffix. Per rule 3, any metric unit requires a RED classification. |
QZbJPTcHQHt4z2X74pYm |
Localize | Spelling (AU-US) | Question
Factorise $125x^3-y^3$.
Express your answer in the form $(ax+by)(cx^2+dxy+ey^2)$.
Options:
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Question
Factor $125x^3-y^3$.
Express your answer in the form $(ax+by)(cx^2+dxy+ey^2)$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which requires conversion to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires conversion to the US spelling "Factorize". |
QhAZkpmp2ctNc75UkDVo |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank.
Displacement ${s}$ of an object is defined as the $[?]$.
Options:
|
Multiple Choice
Fill in the blank.
Displacement ${s}$ of an object is defined as the $[?]$.
Options:
|
Classifier: Contains the AU/UK spelling "travelled", which requires conversion to the US spelling "traveled". Verifier: The word "travelled" in the answer choices is the AU/UK spelling; the US spelling is "traveled". Per rule 1, any AU spelling requires RED classification. |
QeqI5vkFK3jbj3r59kwC |
Localize | Terminology | Multiple Choice
What is the $x$-intercept of the truncus $y = \frac{3}{x^2}$?
Options:
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Multiple Choice
What is the $x$-intercept of the graph of $y = \frac{3}{x^2}$?
Options:
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Classifier: The term "truncus" is a specific Australian/Victorian curriculum term for a function of the form y = a/(x-h)^2 + k. In the US, this is typically referred to as a rational function or specifically a "reciprocal squared function", but "truncus" is not used in US pedagogy. Verifier: The term "truncus" is a specific term used in the Australian (specifically Victorian VCE) curriculum to describe a reciprocal squared function. It is not used in US mathematics pedagogy and requires localization. |
QtQ0GkMPAh5vzKF0qAR5 |
Localize | Units (simple) | Question
A garment factory is planning to produce some jeans and trousers out of $30$ meters of fabric available for social causes keeping in mind that they make a minimum profit at low input.
They need $2.5$ m fabric and $30$ minutes to make one pair of jeans and $2.8$ m fabric, and $45$ minutes to manufacture a trouser.
They plan to gain just $\$2$ on jeans and $\$3$ on trousers.
The time spent on the process is not more than $420$ minutes.
What is the maximum gain from the factory?
Answer:
|
Question
A garment factory is planning to produce some jeans and pants out of $30$ yards of fabric available for social causes keeping in mind that they make a minimum profit at low input.
They need $2.5$ yd fabric and $30$ minutes to make one pair of jeans and $2.8$ yd fabric, and $45$ minutes to manufacture a pair of pants.
They plan to gain just $\$2$ on jeans and $\$3$ on pants.
The time spent on the process is not more than $420$ minutes.
What is the maximum gain from the factory?
Answer:
|
Classifier: The text contains metric units "meters" and "m". Although "meters" uses US spelling, the use of the metric system itself in a word problem context requires localization to US customary units. Verifier: The question uses metric units ("meters", "m"), which requires conversion to US customary units. Although the spelling "meters" is US-style, the system of measurement itself must be localized. |
QztklYGXzYNDKsyustIG |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $axy^{2}-2ax^{2}y$
Options:
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Multiple Choice
Factor $axy^{2}-2ax^{2}y$
Options:
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Classifier: The text uses the AU/UK spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text uses "Factorise", which is AU/UK spelling. Rule 1 states AU spelling always requires RED classification. |
QyCoOTH7nxsoZQaGJoNL |
Localize | Spelling (AU-US) | Multiple Choice
What is $x^6-y^{14}$ in factorised form?
Options:
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Multiple Choice
What is $x^6-y^{14}$ in factored form?
Options:
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Classifier: The text uses the AU spelling "factorised" (with an 's'), which requires conversion to the US spelling "factorized" (with a 'z'). Verifier: The text uses the AU spelling "factorised" (with an 's') in both the question and the first answer choice, which requires conversion to the US spelling "factorized" (with a 'z'). |
R3qaslcZ11F6Qq5qBEwo |
Localize | Units (simple) | Question
A one year old weighs $10$ kilograms and $540$ grams.
What is this weight in grams?
Answer:
|
Question
A one-year-old weighs $10$ pounds and $540$ ounces.
What is this weight in ounces?
Answer:
|
Classifier: The question is specifically about converting between metric units (kilograms and grams). This is a metric-pedagogy question that requires localization to US customary units or a decision on whether to keep metric for science/math standards. Per rules, any metric unit = RED.units_simple_conversion. Verifier: The question explicitly uses and asks for conversion between metric units (kilograms, grams). |
R2pO6oNoMyHBoDyCXpjr |
Localize | Units (simple) | Question
Delhi, India and Xinjiang, China have coordinates $(29^\circ N,77^\circ E)$ and $(41^\circ N,77^\circ E)$.
Calculate the shortest distance between Delhi and Xinjiang, given that the Earth's radius is $6400$ km.
Answer:
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Question
New York City, NY and Montreal, Canada have coordinates $(29^\circ N,77^\circ E)$ and $(41^\circ N,77^\circ E)$.
Calculate the shortest distance between New York City and Montreal, given that the Earth's radius is $6400$ mi.
Answer:
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Classifier: The question contains the metric unit "km" (kilometers) and provides the Earth's radius in km, which requires localization to miles for a US context. Verifier: Contains metric unit "km" which requires conversion for US localization. |
RB8LBi7O2qqGcHpEOw9E |
Localize | Units (simple) | Question
Express $200$ cm as a percentage of $400$ cm.
Answer:
|
Question
Express $200$ in as a percentage of $400$ in.
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units or a different context per the decision rules. Verifier: The text contains the metric unit "cm", which requires conversion to US customary units. |
RDQJfeaZObZ22qpeVNgL |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
$10$ nanometres $=[?]$ metres
Options:
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Multiple Choice
Fill in the blank:
$10$ nanometers $=[?]$ meters
Options:
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Classifier: The text contains metric units ('nanometres' and 'metres') and uses the AU/UK spelling ('metres' vs US 'meters'). Per rule 6, units conversion/presence is the most impactful change. Verifier: The text contains metric units ('nanometres' and 'metres') and uses the AU/UK spelling ('metres' vs US 'meters'). This is a simple unit conversion question. |
R42thXBGKvsccRhrfW8s |
Localize | Units (simple) | Multiple Choice
A study finds that exercising for $30$–$90$ minutes per day improves fitness levels. The weight loss is related to exercise duration by the equation:
$\text{weight loss} = 2 + 0.1 \times \text{exercise minutes}$
Which of the following exercise times represents an interpolation?
Options:
|
Multiple Choice
A study finds that exercising for $30$–$90$ minutes per day improves fitness levels. The weight loss is related to exercise duration by the equation:
$\text{weight loss} = 2 + 0.1 \times \text{exercise minutes}$
Which of the following exercise times represents an interpolation?
Options:
|
Classifier: The answer choices contain the metric unit "kg" (kilograms), which requires localization to US customary units (e.g., pounds). Verifier: The answer choices contain the metric unit "kg" (kilograms), which requires conversion to US customary units (pounds) for a US audience. |
RFHnZP7uRDO3OeE4suYN |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank.
Deseasonalised figure of a time series $=[?]$
Options:
|
Multiple Choice
Fill in the blank.
Deseasonalized figure of a time series $[?]$
Options:
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Classifier: Contains the AU/UK spelling 'Deseasonalised' which requires conversion to the US spelling 'Deseasonalized'. Verifier: Contains the AU/UK spelling 'Deseasonalised' which requires conversion to the US spelling 'Deseasonalized'. |
STTuhSTa5HBoGuyPlszt |
Localize | Units (simple) | Question
How many grams are in $2$ kg and $45$ g of peanuts?
Answer:
|
Question
How many ounces are in $2$ lb and $45$ oz of peanuts?
Answer:
|
Classifier: The question explicitly uses and asks for conversions between metric units (grams, kg, g). According to the decision rules, any metric unit found anywhere requires classification into a RED.units category. Verifier: The question contains metric units (grams, kg, g), which requires a RED classification according to the decision rules. It is a simple conversion. |
RSxbTvlIilTMbxdNjxiU |
Localize | Units (simple) | Question
Convert $2$ kg and $50$ g into grams.
Answer:
|
Question
Convert $2$ lb and $50$ oz into ounces.
Answer:
|
Classifier: Contains metric units "kg" (kilograms) and "g" (grams). Any metric unit requires localization. Verifier: Contains metric units "kg" and "g" which require conversion for US localization. |
RyC5O2tA50i2tZr6RcZg |
Localize | Units (simple) | Question
Two observers are standing on opposite sides of a $25$ m tall tower.
The angles of elevation to the top of the tower from their positions are $30°$ and $60°$, respectively.
Calculate the distance between the two observers.
Answer:
|
Question
Two observers are standing on opposite sides of a $25$ ft tall tower.
The angles of elevation to the top of the tower from their positions are $30°$ and $60°$, respectively.
Calculate the distance between the two observers.
Answer:
|
Classifier: The text contains the metric unit "m" (metres) in both the question body and the suffix field, which requires conversion to US customary units. Verifier: The text contains the metric unit "m" (metres) in the content and suffix, which requires conversion to US customary units. |
SRYt76K5mY3bgDIogvaG |
Localize | Units (simple) | Question
Fill in the blank:
$\frac{3}{4}$ kg $=[?]$ g
Answer:
|
Question
Fill in the blank:
$\frac{3}{4}$ lb $=[?]$ oz
Answer:
|
Classifier: The question explicitly asks for a conversion between metric units (kg to g). Per decision rules, any metric unit requires RED classification. Verifier: The question involves metric units (kg and g). Per decision rule 3, any metric unit requires at least RED.units_simple_conversion. |
SydtmtzSwO3hI21I9L7Z |
Localize | Spelling (AU-US) | Question
Find the number of distinct prime factors that $90$ has using prime factorisation.
Answer:
|
Question
Find the number of distinct prime factors that $90$ has using prime factorization.
Answer:
|
Classifier: Contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: Contains "factorisation", which is the AU/UK spelling. US spelling is "factorization". |
RqMkIHTnYMEWDv3WTK1f |
Localize | Units (simple) | Question
Convert $1$ m$^2$ to mm$^2$.
Answer:
|
Question
Convert $1$ ft$^2$ to in$^2$.
Answer:
|
Classifier: The question explicitly uses metric units ("m^2" and "mm^2"), which requires localization to US customary units or a decision on metric pedagogy per the decision rules. Verifier: The question involves converting between metric units (m^2 to mm^2), which requires localization or a pedagogy-based decision. It is a simple conversion. |
RNYfHnDBwoKiRmUki1o8 |
Localize | Spelling (AU-US) | Question
Rob is buying a laptop and can choose from $12$-inch, $14$-inch, or $16$-inch models in black, white, silver, grey, or gold.
How many total options does he have?
Answer:
|
Question
Rob is buying a laptop and can choose from $12$-inch, $14$-inch, or $16$-inch models in black, white, silver, gray, or gold.
How many total options does he have?
Answer:
|
Classifier: The text uses "inch" which is a US customary unit (and also used globally for screen/laptop sizes). The spelling "grey" is common in AU/UK, but "gray" is US; however, "grey" is often accepted in US English and the context of laptop colors makes this a weak signal for RED compared to the explicit use of inches. No other AU-specific terminology or metric units are present. Verifier: The text contains the word "grey". While "grey" is used in the US, it is the standard AU spelling, and per the strict instructions (Rule 1), AU spelling requires RED classification. Since there are no metric units or terminology changes, RED.spelling_only is the correct leaf. |
SLRP5g0xMVQj2MlJQWOn |
Localize | Terminology | Multiple Choice
True or false:
If a factorised cubic function has a repeated factor and a linear factor, then the repeated factor corresponds to one of the turning points.
Options:
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Multiple Choice
True or false:
If a factored cubic function has a repeated factor and a linear factor, then the repeated factor corresponds to one of the turning points.
Options:
|
Classifier: Contains "factorised" (AU spelling) and "turning points" (AU terminology for US "vertex" or "extrema"). "Factorised" requires spelling conversion and "turning points" requires terminology conversion. Verifier: Contains "factorised" (AU spelling) and "turning points" (AU terminology for US "vertex" or "extrema"). Per rule 5, terminology is the more impactful change. |
SYjh9iKOKBthS8Yr6jvx |
Localize | Units (simple) | Question
A plane flies $100$ km on a bearing of $025^\circ \text{T}$.
How far east does the plane fly?
Hint: Use trigonometry to determine the distance travelled.
Answer:
|
Question
A plane flies $100$ mi on a bearing of $025^\circ \text{T}$.
How far east does the plane fly?
Hint: Use trigonometry to determine the distance traveled.
Answer:
|
Classifier: The question contains the metric unit "km" (kilometers), which requires conversion or review for US localization. It also uses "bearing of 025^\circ \text{T}" which is common in AU/UK navigation contexts but less common in US K-12 math compared to standard position angles, though the metric unit is the primary trigger. Verifier: The question uses the metric unit "km" (kilometers) and the AU/UK navigation convention "bearing of 025° T". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
RnaJIS4qsLfIp97ckgEf |
Localize | Terminology | Question
An item costs $\$720$ excluding GST.
What is the amount paid including GST?
Answer:
|
Question
An item costs $\$720$ excluding sales tax.
What is the amount paid including sales tax?
Answer:
|
Classifier: The term "GST" (Goods and Services Tax) is specific to the Australian (and other Commonwealth) tax systems. In a US context, this would typically be "sales tax". Verifier: The term "GST" (Goods and Services Tax) is a specific tax terminology used in Australia, New Zealand, and Canada. In the US, "Sales Tax" is the equivalent term. This requires localization. |
RNWcFDZ78vmqkyca36R7 |
Localize | Units (simple) | Multiple Choice
What is the volume, in litres, of a cube with a side length of $10$ cm?
Options:
|
Multiple Choice
What is the volume, in gallons, of a cube with a side length of $10$ in?
Options:
|
Classifier: The text contains metric units ("cm", "litres", "L") and the AU spelling "litres". Per rule 6, units conversion is the most impactful change. Verifier: The text contains metric units ("cm", "litres", "L") and the AU spelling "litres". Per rule 5, units conversion is the most impactful change. |
SkPw5ggrbDnDjPUFWl2Q |
Localize | Terminology | Question
Tom buys a refrigerator whose cost price is $\$3,000$. He pays a deposit of $\$500$. He must pay the remaining amount by making ten monthly payments of $\$295$.
Calculate the flat rate of interest for this hire-purchase agreement.
Answer:
|
Question
Tom buys a refrigerator whose cost price is $\$3,000$. He pays a deposit of $\$500$. He must pay the remaining amount by making ten monthly payments of $\$295$.
Calculate the flat rate of interest for this installment loan.
Answer:
|
Classifier: Contains "hire-purchase agreement", which is a common Commonwealth term for what is typically called an "installment plan" or "rent-to-own" in the US. Also uses "p.a." (per annum), which while understood, is more frequent in AU/UK contexts than US K-12. Verifier: The term "hire-purchase agreement" is a specific Commonwealth/AU term for installment buying, and "p.a." (per annum) is the standard AU notation for interest rates, whereas US contexts typically use "APR" or "per year". |
SWG36e9AnYKmZYyRqOeH |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following correctly splits the middle term in $x^2 +6x + 8$ so it can be factorised by grouping?
Options:
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Multiple Choice
Which of the following correctly splits the middle term in $x^2 +6x + 8$ so it can be factored by grouping?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling instead of the US 'z' spelling. Verifier: The word "factorised" is used in the source text, which is the AU/UK spelling. Per rule 1, AU spelling always requires RED classification. |
SHSntJAIEUH13pQ5NyWG |
Localize | Terminology | Multiple Choice
Which graph would best display the number of students who received different test scores?
Options:
|
Multiple Choice
Which graph would best display the number of students who received different test scores?
Options:
|
Classifier: The term "Column graph" is standard AU terminology for what is almost exclusively called a "Bar graph" in US K-12 education. "Picture graph" is also more commonly "Pictograph" in the US, though "Picture graph" is sometimes used. Verifier: The term "Column graph" is the standard Australian curriculum term for what is called a "Bar graph" in the US. "Picture graph" is also more commonly "Pictograph" in US K-12. |
SXn25tElDcxi8L3FazJ4 |
Localize | Terminology | Multiple Choice
What is the turning point of the parabola $y=6x^{2}-36x+6$ ?
Options:
|
Multiple Choice
What is the vertex of the parabola $y=6x^{2}-36x+6$ ?
Options:
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Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU school term for what is typically called the "vertex" in US K-12 mathematics. |
S9DhqVhWsdbko7BgKEQj |
Localize | Units (simple) | Question
The longitudes of point $A$ and point $B$ are $10^\circ E$ and $30^\circ W$ respectively.
Find the distance between them if they both lie on the equator, given that the Earth's radius is 6400 km.
Answer:
|
Question
The longitudes of point $A$ and point $B$ are $10^\circ E$ and $30^\circ W$ respectively.
Find the distance between them if they both lie on the equator, given that the Earth's radius is 6400 miles.
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers) multiple times, which requires localization to US customary units (miles) or a decision on maintaining metric for scientific context, but per rules, any metric unit triggers this category. Verifier: The question contains the metric unit "km" (kilometers) in both the content and the suffix. Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
S6j2jMW3lRTbWKYna9Mw |
Localize | Units (simple) | Multiple Choice
True or false:
In triangle $\text{ABC}$, $\angle B=35^\circ,AB=6$ cm and $AC=3.5$ cm. It is possible to find a unique value for $\angle C$.
Options:
|
Multiple Choice
True or false:
In triangle $\text{ABC}$, $\angle B=35^\circ,AB=6$ in and $AC=3.5$ in. It is possible to find a unique value for $\angle C$.
Options:
|
Classifier: The text contains the metric unit "cm", which requires localization to US customary units or a unitless context per US localization standards. Verifier: The text contains the metric unit "cm", which requires localization. It is a simple conversion as it involves static side lengths in a geometry problem. |
RYX0LPqfIgiNMA6Hpf5y |
Localize | Terminology | Multiple Choice
Which of the following is a hybrid function?
Options:
|
Multiple Choice
Which of the following is a piecewise function?
Options:
|
Classifier: The term "hybrid function" is the standard Australian term for what is called a "piecewise function" in the United States. Verifier: The term "hybrid function" is the specific Australian curriculum term for what is known as a "piecewise function" in the US. This requires localization of terminology. |
Se6EDuleXdhv4B1K7jXD |
Localize | Units (simple) | Multiple Choice
An object moves in a straight line and its displacement function is given by $s(t)=t^2-2t-5$ metres where time $t$ is in seconds.
Find the acceleration function for the object.
Options:
|
Multiple Choice
An object moves in a straight line and its displacement function is given by $s(t)=t^2-2t-5$ feet where time $t$ is in seconds.
Find the acceleration function for the object.
Options:
|
Classifier: Contains metric units ("metres", "m/s^2") and AU spelling ("metres"). Per rule 6, units conversion is the most impactful change. Verifier: The text contains the metric unit "metres" (AU spelling) and "m/s^2". Per Rule 1 and Rule 3, any metric unit or AU spelling requires RED classification. The conversion is simple as it involves identifying the derivative/units rather than complex formula re-derivation. |
SxTsh39VGUviFYBE4wi0 |
Localize | Terminology | Multiple Choice
Determine whether $\triangle ABC$ is scalene, isosceles, or equilateral given that $A=(0,0,-5)$, $B=(5,0,0)$ and $C=(0,-5,0)$.
Options:
|
Multiple Choice
Determine whether $\triangle ABC$ is scalene, isosceles, or equilateral given that $A=(0,0,-5)$, $B=(5,0,0)$ and $C=(0,-5,0)$.
Options:
|
Classifier: The answer set contains the term "Right angled triangle", which is the standard AU/UK term. The US equivalent is "Right triangle". Per rule 6, terminology takes precedence over GREEN. Verifier: The answer choice "Right angled triangle" is the standard AU/UK term, whereas the US uses "Right triangle". This requires localization. |
SzCFVwQoFtAqdbuB9OCf |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
The point at which both axes intersect is called the $[?]$ on the Cartesian plane.
Options:
|
Multiple Choice
Fill in the blank:
The point at which both axes intersect is called the $[?]$ on the Cartesian plane.
Options:
|
Classifier: The answer choice "Centre" uses the AU/UK spelling, which requires localization to the US spelling "Center". Verifier: The answer choice "Centre" uses AU/UK spelling, which requires localization to US "Center". |
USs2lA74TYf55gA3u2lq |
Localize | Units (simple) | Question
How many grams are in $2.5$ kg of potatoes?
Answer:
|
Question
How many ounces are in $2.5$ lb of potatoes?
Answer:
|
Classifier: The question explicitly uses metric units (grams, kg) and asks for a conversion between them. Per the decision rules, any metric unit requires classification into a RED.units category. Verifier: The question uses metric units (grams, kg) and requires a simple conversion. |
TPKnl3DbcRugMGljaY3k |
Localize | Units (simple) | Question
A cone of height $h=18$ cm is inscribed in a sphere of radius $r=10$ cm.
Find the radius of the cone.
Answer:
|
Question
A cone of height $h=18$ in is inscribed in a sphere of radius $r=10$ in.
Find the radius of the cone.
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires localization to US customary units per the decision rules. Verifier: The text contains the metric unit "cm". Since it involves a simple geometric relationship (cone inscribed in a sphere) with a few numeric values and no complex physics equations, simple conversion is appropriate. |
UML4l9F2Ogys1wS1QD1G |
Localize | Units (simple) | Question
A sector has a radius of $3.16$ cm and an area of $24.964$ cm$^2$.
Find its arc length.
Answer:
|
Question
A sector has a radius of $3.16$ in and an area of $24.964$ in$^2$.
Find its arc length.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^2$" which require conversion to US customary units. The calculation is a simple geometric relationship (Area = 0.5 * r * arc length), making it a simple conversion. |
TSXw0teZUNypRn9KeWxs |
Localize | Units (simple) | Multiple Choice
True or false:
If the velocity of a particle is $-5$ m/s, then the object is moving to the right.
Options:
|
Multiple Choice
True or false:
If the velocity of a particle is $-5$ ft/s, then the object is moving to the right.
Options:
|
Classifier: The text contains the metric unit "m/s" (metres per second), which triggers a mandatory RED classification for units. Verifier: The text contains the metric unit "m/s" (metres per second), which requires localization. |
UuHbGBRRPtbEw5Wfqb0v |
Localize | Terminology | Multiple Choice
True or false:
The gradient-intercept form of a linear equation is $y=mx+c$, where $m$ is the gradient and $c$ is the y-intercept.
Options:
|
Multiple Choice
True or false:
The slope-intercept form of a linear equation is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.
Options:
|
Classifier: The text uses "gradient-intercept form" and the term "gradient", which are standard in AU/UK. In the US, this is almost exclusively referred to as "slope-intercept form" and "slope". Additionally, it uses the formula "y=mx+c", whereas the US standard is "y=mx+b". Verifier: The use of "gradient" instead of "slope" and the formula "y=mx+c" instead of "y=mx+b" are distinct markers of AU/UK school context terminology compared to the US. |
Uz6uZYTurfu64vLEqmUw |
Localize | Units (simple) | Question
The velocity function of an object moving in a straight line is $v(t)=2t-1$ m/s.
Find its change in displacement from $t=1$ to $t=3$ seconds.
Answer:
|
Question
The velocity function of an object moving in a straight line is $v(t)=2t-1$ ft/s.
Find its change in displacement from $t=1$ to $t=3$ seconds.
Answer:
|
Classifier: The text contains metric units ("m/s" and "m" as a suffix for displacement), which requires localization to US customary units (e.g., ft/s and ft) per the decision rules. Verifier: The question contains metric units "m/s" and "m" (metres), which requires RED classification for conversion to US customary units. |
VgpAaIbrcNCh4oKsOxaB |
Localize | Terminology | Question
A student has mastered $50.2\%$ of $500$ maths skills.
How many skills remain to be mastered?
Answer:
|
Question
A student has mastered $50.2\%$ of $500$ math skills.
How many skills remain to be mastered?
Answer:
|
Classifier: Contains the term "maths", which is the standard AU/UK term and needs to be localized to "math" for US audiences. Verifier: Contains the term "maths", which is the standard AU/UK term and requires localization to "math" for US audiences. |
UTZS4pmnd9E0HX5ErNpy |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
$750$ cm$^3=[?]$ L
Options:
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Multiple Choice
Fill in the blank:
$750$ in$^3=[?]$ gal
Options:
|
Classifier: The question involves converting between metric units (cm^3 and L). Verifier: The question involves converting between metric units (cm^3 and L). |
W1qjF4QJQTwGBkZFGYAB |
Localize | Terminology | Question
In a pair of vertically opposite angles, one angle measures $50^\circ$.
What is the measure of the other angle in the pair?
Answer:
|
Question
In a pair of vertical angles, one angle measures $50^\circ$.
What is the measure of the other angle in the pair?
Answer:
|
Classifier: The term "vertically opposite angles" is the standard AU/UK term for what is called "vertical angles" in the US. Verifier: The term "vertically opposite angles" is the standard AU/UK term for what is called "vertical angles" in the US. This is a terminology difference in a school context. |
Vf6GoHUGaWsCZhNT5eUM |
Localize | Units (simple) | Question
Calculate the volume (in litres) of a cylindrical tank with a height of $5$ m and a base area of $4$ m$^2$.
Hint: 1 m$^3$= 1000 litres
Answer:
|
Question
Calculate the volume (in gallons) of a cylindrical tank with a height of $5$ ft and a base area of $4$ ft$^2$.
Hint: 1 ft$^3$= 1000 gallons
Answer:
|
Classifier: Contains metric units (m, m^2, m^3) and AU-specific spelling of "litres". Per rule 6, units conversion is the most impactful change. Verifier: Contains metric units (m, m^2, m^3) and the AU spelling "litres". Simple conversion is appropriate as it is a basic volume calculation. |
Tg6nJJtjm1ETbaN0x5A7 |
Localize | Units (simple) | Multiple Choice
The perimeter of an isosceles triangle is $30$ cm.
The base is $2$ cm less than the sum of the equal sides.
What are the measures of the sides?
Options:
|
Multiple Choice
The perimeter of an isosceles triangle is $30$ in.
The base is $2$ in less than the sum of the equal sides.
What are the measures of the sides?
Options:
|
Classifier: The text contains the metric unit "cm" (centimetres) multiple times in both the question and the answer set, which requires conversion to US customary units (e.g., inches). Verifier: The question and answers contain the metric unit "cm" (centimetres), which requires conversion to US customary units. The conversion is simple as it involves linear measurements in a geometric context. |
Vh3Q6z2cxfNUDxtqpCAm |
Localize | Units (simple) | Question
Find the area of a sector with arc length $24$ cm and radius $12$ cm.
Hint: Use $l=r\theta$ and $A=\frac{1}{2}\theta{r}^{2}$
Answer:
|
Question
Find the area of a sector with arc length $24$ in and radius $12$ in.
Hint: Use $l=r\theta$ and $A=\frac{1}{2}\theta{r}^{2}$
Answer:
|
Classifier: Contains metric units (cm, cm^2) which require conversion for US localization. Verifier: Contains metric units (cm, cm^2) which require conversion. |
VrvLjS5LTpH4clqqZ04l |
Localize | Units (simple) | Question
An object moving in a straight line has velocity function $v(t)=t^2-5$ m/s for $t\geq0$ s.
Find the speed of the object at $t=1$ s.
Answer:
|
Question
An object moving in a straight line has velocity function $v(t)=t^2-5$ ft/s for $t\geq0$ s.
Find the speed of the object at $t=1$ s.
Answer:
|
Classifier: The text contains metric units ("m/s" and "s") which require localization/conversion according to the decision rules. Verifier: The text contains metric units "m/s" and "s", which require RED classification per rule 3. |
VyxWztBvdqRK0BqCnPPm |
Localize | Units (simple) | Question
A particle is moving with a velocity of $3t^2-4$ m/s for time $0\leq t\leq 10$ seconds.
What is the average speed for the first two seconds?
Write your answer to the nearest whole number.
Answer:
|
Question
A particle is moving with a velocity of $3t^2-4$ ft/s for time $0\leq t\leq 10$ seconds.
What is the average speed for the first two seconds?
Write your answer to the nearest whole number.
Answer:
|
Classifier: The question contains metric units ("m/s") which require conversion or localization for a US audience. Verifier: The question contains the metric unit "m/s" (metres per second), which requires conversion for a US audience. It is a simple conversion as it involves a single unit-bearing value in the expression and a straightforward calculation. |
VaScgqzXGLxPQHbCXJ8u |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following equations represents a circle centred at $(3,5)$ with a radius of $16$ units?
Options:
|
Multiple Choice
Which of the following equations represents a circle centered at $(3,5)$ with a radius of $16$ units?
Options:
|
Classifier: The word "centred" is the AU/UK spelling. The US spelling is "centered". While "units" is mentioned, it is used generically (coordinate geometry) rather than as a metric unit. Verifier: The text contains "centred", which is the AU/UK spelling. The US spelling is "centered". As per rule 1, AU spelling always requires RED classification. |
WC4ngeSjb0SvRdBxTWGK |
Localize | Terminology | Multiple Choice
Out of $1500$ school students, $250$ were surveyed on whether they like maths.
What is the sample size?
Options:
|
Multiple Choice
Out of $1500$ school students, $250$ were surveyed on whether they like math.
What is the sample size?
Options:
|
Classifier: The text uses the term "maths", which is the standard AU/UK term. In the US, the term is "math". Verifier: The text uses "maths", which is the standard AU/UK term for the US "math". This is a terminology difference. |
WSjjWrw5bVLRfWniOtbu |
Localize | Spelling (AU-US) | Question
$\text{Pr}(A)=0.3$, $\text{Pr}(B)=0.5$ and $\text{Pr}(A \cap B)= 0.2$.
Given this information, find $\text{Pr}( A \cup B)$.
Hint: It may be helpful to use a Venn diagram to visualise this situation.
Answer:
|
Question
$\text{Pr}(A)=0.3$, $\text{Pr}(B)=0.5$ and $\text{Pr}(A \cap B)= 0.2$.
Given this information, find $\text{Pr}( A \cup B)$.
Hint: It may be helpful to use a Venn diagram to visualize this situation.
Answer:
|
Classifier: The word "visualise" uses the AU/UK 's' spelling instead of the US 'z' spelling. Verifier: The word "visualise" in the hint field is the AU/UK spelling. Per rule 1, any AU spelling requires RED classification. |
WX7LPUzYl6AumZWR8DV1 |
Localize | Units (complex) | Multiple Choice
A boy was playing with his toy car, and the car was moving with the velocity $v(t)=-9t^2+7t+22$ cm/s.
Find the direction in which the toy car was moving at $t=3$ s.
Options:
|
Multiple Choice
A boy was playing with his toy car, and the car was moving with the velocity $v(t)=-9t^2+7t+22$ in/s.
Find the direction in which the toy car was moving at $t=3$ s.
Options:
|
Classifier: The text contains the metric unit "cm/s" which requires localization to US customary units (e.g., in/s). Verifier: The question contains a metric unit "cm/s" within a velocity function v(t). Per rule 4, equations defining quantities in metric (e.g., v(t) = -9t^2 + 7t + 22 cm/s) should be classified as RED.units_complex_converted rather than simple conversion, as they may require formula review. |
W4MoaeU9p1TTsvLzUKg1 |
Localize | Terminology | Multiple Choice
Find the equation of the parabola whose turning point is at $(-1,-5)$ and passes through $(-2,-13)$.
Options:
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Multiple Choice
Find the equation of the parabola whose vertex is at $(-1,-5)$ and passes through $(-2,-13)$.
Options:
|
Classifier: The text uses the term "turning point" to refer to the vertex of a parabola. In a US school context, "vertex" is the standard term used for this concept. Verifier: The term "turning point" is the standard AU term for what is called the "vertex" of a parabola in the US school context. |
WfmDWMffkjqDFPbDhwwo |
Localize | Terminology | Question
Fill in the blank:
Ellen took an interest-only loan of $\$30000$ at $8.5\%$ annual interest, compounded fortnightly. To find her quarterly payment using a finance solver, the value of $Pp/Y$ or $P/Y = [?]$.
Answer:
|
Question
Fill in the blank:
Ellen took an interest-only loan of $\$30000$ at $8.5\%$ annual interest, compounded every two weeks. To find her quarterly payment using a finance solver, the value of $Pp/Y$ or $P/Y = [?]$.
Answer:
|
Classifier: The term "fortnightly" is common in AU but rare/unused in US educational contexts (usually "every two weeks"). Additionally, "finance solver" often refers to specific calculator functions (like TI-84 TVM Solver) used in the AU curriculum. Verifier: The term "fortnightly" is a distinct AU/UK term (US uses "every two weeks" or "bi-weekly"). Additionally, the reference to "finance solver" and specific variables like "Pp/Y" or "P/Y" refers to the TVM solver on calculators (like the TI-84 or Casio) which is a specific pedagogical focus in the Australian General Mathematics/Further Mathematics curriculum. |
WhAlMWRIJQx1eUo5CPAK |
Localize | Units (simple) | Question
The taxi fare is $\$15$ for the first kilometre and $\$10$ for each additional kilometre.
What is the total fare for a $6$-kilometre journey?
Answer:
|
Question
The taxi fare is $\$15$ for the first mile and $\$10$ for each additional mile.
What is the total fare for a $6$-mile journey?
Answer:
|
Classifier: The text contains the metric unit "kilometre" (AU spelling) multiple times. This requires conversion to US customary units (miles) or at least a spelling change to "kilometer", but per rule 6, units conversion takes precedence. Verifier: The text contains "kilometre", which is both a metric unit and an AU spelling. Per rule 5, units conversion takes precedence over spelling. |
WoBKlUj87l13iwqoPzsK |
Localize | Units (simple) | Question
Fill in the blank:
$62.460$ kL $=[?]$ L
Answer:
|
Question
Fill in the blank:
$62.460$ gal $=[?]$ fl oz
Answer:
|
Classifier: Contains metric units "kL" (kiloliters) and "L" (liters). Any metric unit requires classification as RED.units_simple_conversion. Verifier: The question contains metric units "kL" (kiloliters) and "L" (liters). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
WbQnQdqgOjmxkyfZl5G0 |
Localize | Terminology | Multiple Choice
Which of the following is a solution to the given simultaneous equations below?
$2y+7x=-5$
$5y-7x=12$
Options:
|
Multiple Choice
Which of the following is a solution to the given system of equations below?
$2y+7x=-5$
$5y-7x=12$
Options:
|
Classifier: The term "simultaneous equations" is the standard AU/UK term for what is almost exclusively called a "system of equations" in US mathematics. Verifier: The term "simultaneous equations" is the standard AU/UK term, whereas US curriculum almost exclusively uses "system of equations". |
WsuFUBiWtUcZBfAAsAMb |
Localize | Units (simple) | Question
One day in winter, it snowed $\frac{50}{8}$ cm.
The following day, $\frac{45}{8}$ cm of snow fell.
How much less snow fell on the second day?
Answer:
|
Question
One day in winter, it snowed $\frac{50}{8}$ in.
The following day, $\frac{45}{8}$ in of snow fell.
How much less snow fell on the second day?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units (e.g., inches) for US localization. Verifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units. |
Wp4KMMSGzkGl5VRBCqEF |
Localize | Units (simple) | Question
By the SAS congruency rule, $\Delta ABC \cong \Delta PQR$.
For $\angle A=30^\circ$, $\overline{AB}=15$ cm and $\overline{AC}=12$ cm, what is the measure of $\overline{PQ}$?
Answer:
|
Question
By the SAS congruence rule, $\Delta ABC \cong \Delta PQR$.
For $\angle A=30^\circ$, $\overline{AB}=15$ in and $\overline{AC}=12$ in, what is the measure of $\overline{PQ}$?
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires conversion to US customary units (inches) for US localization. It also uses "congruency", though units are the higher priority flag. Verifier: The question contains the metric unit "cm" in the content and suffix, which requires conversion for US localization. The conversion is simple as it involves a single value and no complex equations. |
WhuGGUpaUNbGMCjREFqh |
Localize | Terminology | Multiple Choice
What is the formula for the principal, $P$, of a loan, if the following are given: time, $t$ years, amount invested, $A$, and interest rate, $r\%$ per annum.
Options:
|
Multiple Choice
What is the formula for the principal, $P$, of a loan, if the following are given: time, $t$ years, amount invested, $A$, and interest rate, $r\%$ per year.
Options:
|
Classifier: The term "per annum" is standard in AU/UK financial contexts but is typically replaced by "per year" or "annually" in US K-12 math contexts. More importantly, "interest rate, r% per annum" is a specific phrasing style. However, the most distinct AU signal is the use of "per annum" in a school context. Verifier: The term "per annum" is characteristic of AU/UK financial math pedagogy; US K-12 contexts typically use "per year" or "annually". |
XN0h6lU4HZFdSYuPVzxx |
Localize | Spelling (AU-US) | Question
Factorise $x^2+x$
Answer:
|
Question
Factor $x^2+x$
Answer:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Factorize"). Verifier: The word "Factorise" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("Factorize"). |
XGO148Za0UWNs0GX1KwK |
Localize | Spelling (AU-US) | Question
Factorising $x^2-5x-14$ gives an expression of the form $(x+a)(x+b)$
Find the value of $a+b$.
Answer:
|
Question
Factoring $x^2-5x-14$ gives an expression of the form $(x+a)(x+b)$
Find the value of $a+b$.
Answer:
|
Classifier: Contains the AU spelling "Factorising", which needs to be converted to the US spelling "Factorizing". Verifier: The text contains "Factorising", which is AU/British spelling. Per rule 1, AU spelling always requires RED classification. |
Wv1ZpZXv03uQDuas38Mo |
Localize | Terminology | Multiple Choice
True or false:
$f(x)=|x-2|$ can be represented as a hybrid function.
Options:
|
Multiple Choice
True or false:
$f(x)=|x-2|$ can be represented as a piecewise function.
Options:
|
Classifier: The term "hybrid function" is the standard AU term for what is known as a "piecewise function" in the US. This requires terminology localization. Verifier: "Hybrid function" is a specific Australian curriculum term for what is called a "piecewise function" in the US. |
Wzl011z6zWPffVH86O3Y |
Localize | Terminology | Question
Find the highest common factor of $54,288$ and $360$.
Answer:
|
Question
Find the greatest common factor of $54,288$ and $360$.
Answer:
|
Classifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US equivalent is typically "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US equivalent is "greatest common factor" (GCF). This requires RED classification per rule 1. |
Xjye5Tl63l38VEpXISca |
Localize | Terminology | Question
A washing machine costs $\$1200$, including GST.
What is the price excluding GST?
Answer:
|
Question
A washing machine costs $\$1200$, including sales tax.
What is the price excluding sales tax?
Answer:
|
Classifier: Contains "GST" (Goods and Services Tax), which is the specific consumption tax used in Australia. In a US context, this would typically be localized to "sales tax" or removed, as the US does not have a GST. Verifier: The term "GST" (Goods and Services Tax) is specific to the Australian tax system and requires localization to "sales tax" or similar for a US context. |
YLurE5G8YqeHs2lKU6Kn |
Localize | Units (simple) | Question
Fill in the blank:
$8254$ cm$^{3}=[?]$ L
Answer:
|
Question
Fill in the blank:
$8254$ in$^{3}=[?]$ gal
Answer:
|
Classifier: Contains metric units (cm^3 and L) which require conversion or localization per the decision rules. Verifier: The question explicitly uses metric units (cm^3 and L), which requires RED classification per rule 3. |
Y7jXsuOg5bhW7Pdw0BjU |
Localize | Terminology | Question
Find the highest common factor of $65$, $156$ and $262$.
Answer:
|
Question
Find the greatest common factor of $65$, $156$ and $262$.
Answer:
|
Classifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US equivalent is "greatest common factor" (GCF). Verifier: "Highest common factor" (HCF) is the standard AU/UK term, whereas the US equivalent is "greatest common factor" (GCF). |
XM2PPwGqVzEfyLSIbPP3 |
Localize | Units (simple) | Question
I take two and a half hours to run $1.5$ km.
What is my average speed in km per hour?
Answer:
|
Question
I take two and a half hours to run $1.5$ mi.
What is my average speed in miles per hour?
Answer:
|
Classifier: The question explicitly uses metric units ("km", "km per hour", "km/h") which require localization to US customary units (miles). Verifier: The question uses metric units ("km", "km per hour", "km/h") which require conversion to US customary units (miles). It is a simple conversion as it involves a single rate calculation. |
YQmLi5yndl7J19TjQXK7 |
Localize | Units (textual) | Multiple Choice
Which of the following is the imperial unit of mass?
Options:
|
Multiple Choice
Which of the following is the US customary unit of mass?
Options:
|
Classifier: The question and answers refer to units of mass conceptually ("Kilograms", "Grams", "Miligrams") rather than as specific measurements. Note: "Miligrams" is also a misspelling of "Milligrams". Verifier: The question explicitly discusses units of mass ("Kilograms", "Grams", "Miligrams") in a conceptual/textual way. |
Xw9qquvghPpS904rtmFX |
Localize | Units (simple) | Question
The radii of circles $A$ and $B$ are $20$ cm and $10$ cm, respectively.
The circumference of circle $C$ is equal to the sum of the circumferences of $A$ and $B$.
Find the radius of circle $C$.
Answer:
|
Question
The radii of circles $A$ and $B$ are $20$ in and $10$ in, respectively.
The circumference of circle $C$ is equal to the sum of the circumferences of $A$ and $B$.
Find the radius of circle $C$.
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires localization to US customary units or a decision on metric usage in US curriculum. Verifier: The text contains the metric unit "cm" in the content and suffix, requiring conversion for US localization. |
YETljIGuFg49NQC7URB3 |
Localize | Units (simple) | Question
Find the area of a quadrant of a circle if the circumference of the circle is $12$ m.
Hint: A quadrant is a quarter of a circle.
Answer:
|
Question
Find the area of a quadrant of a circle if the circumference of the circle is $12$ ft.
Hint: A quadrant is a quarter of a circle.
Answer:
|
Classifier: Contains the metric unit "m" (metres) and "m^2", which requires conversion to US customary units (e.g., feet/inches). Verifier: Contains metric units "m" (metres) and "m^2" which require conversion to US customary units. |
XGwlupoasbU4DBfH2ZM4 |
Localize | Units (simple) | Question
In triangle $ABC$, $\overline{BC} = 11$ cm, $\overline{AB} = 15$ cm, and $\angle{ABC} = 25.5^\circ$.
Find $\overline{AC}$.
Answer:
|
Question
In triangle $ABC$, $\overline{BC} = 11$ in, $\overline{AB} = 15$ in, and $\angle{ABC} = 25.5^\circ$.
Find $\overline{AC}$.
Answer:
|
Classifier: Contains the metric unit "cm" multiple times, which requires localization to US customary units. Verifier: The question contains the metric unit "cm" in both the content and the suffix, requiring conversion to US customary units. |
YYwzwwyvARp5SRqmrJn6 |
Localize | Spelling (AU-US) | Question
Bill makes a purchase of $\$2000$ and pays a deposit of $\$500$ and agrees to pay the rest in $7$ instalments, each worth $\$250$ in a year.
Calculate the flat rate of interest.
Answer:
|
Question
Bill makes a purchase of $\$2000$ and pays a deposit of $\$500$ and agrees to pay the rest in $7$ installments, each worth $\$250$ in a year.
Calculate the flat rate of interest.
Answer:
|
Classifier: The problem uses standard financial terminology ("purchase", "deposit", "instalments", "flat rate of interest"). While "instalments" is the preferred AU/UK spelling, it is also an accepted (though less common) variant in the US; however, the prompt rules for GREEN focus on the absence of metric units and specific AU school terms. "Flat rate of interest" is a universal mathematical concept. No metric units or AU-specific school levels are present. Verifier: The text contains the word "instalments", which is the AU/UK spelling. The US spelling is "installments". Per rule 1, any AU spelling disqualifies GREEN. |
YBRJQietR8EWif7ULLfY |
Localize | Units (simple) | Question
A factory has $30$ metres of fabric and $420$ minutes to make pairs of jeans and trousers.
Each pair of jeans requires $2.5$ metres of fabric, $30$ minutes of labour, and brings a profit of $\$2$.
Each pair of trousers requires $2.8$ metres of fabric, $45$ minutes of labour, and brings a profit of $\$3$.
How many pairs of jeans should the factory produce to maximise the total profit?
Answer:
|
Question
A factory has $30$ feet of fabric and $420$ minutes to make pairs of jeans and pants.
Each pair of jeans requires $2.5$ feet of fabric, $30$ minutes of labor, and brings a profit of $\$2$.
Each pair of pants requires $2.8$ feet of fabric, $45$ minutes of labor, and brings a profit of $\$3$.
How many pairs of jeans should the factory produce to maximize the total profit?
Answer:
|
Classifier: Contains metric units ("metres") which require conversion to US customary units. Also contains AU spellings ("metres", "labour", "maximise"). Per rule 6, units conversion takes precedence over spelling. Verifier: Contains metric units ("metres") and AU spellings ("metres", "labour", "maximise"). Per rule 5, units conversion takes precedence. |
YIdwWGugF8psKni8EqEr |
Localize | Units (simple) | Multiple Choice
To boil between $10$ and $60$ litres of water, the time required is given by the equation:
$\text{time} = 2 + 2.5 \times \text{volume of water}$
Which of the following data represents an extrapolation?
Options:
|
Multiple Choice
To boil between $10$ and $60$ gallons of water, the time required is given by the equation:
$\text{time} = 2 + 2.5 \times \text{volume of water}$
Which of the following data represents an extrapolation?
Options:
|
Classifier: Contains the metric unit "litres", which also uses AU-specific spelling. Per rule 1, any metric unit requires classification outside of GREEN. Verifier: The text contains the metric unit "litres", which uses AU/British spelling and requires conversion to US customary units (gallons) for a US audience. |
X88xhw8DIx9Per7kblnE |
Localize | Terminology | Multiple Choice
Fill in the blank:
GST is applied to goods and services sold $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
Sales tax is applied to goods and services sold $[?]$.
Options:
|
Classifier: The term "GST" (Goods and Services Tax) is specific to the Australian (and other Commonwealth) tax systems. In a US context, this would typically refer to "Sales Tax" or would not be applicable in this format. This is a locale-specific economic/school context term. Verifier: The term "GST" (Goods and Services Tax) is a specific tax system used in Australia and other Commonwealth countries. In the US, "Sales Tax" is the equivalent term. This requires localization of the economic context. |
XOzVfbXXNEP8JtYPdetM |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following correctly splits the middle term in $x^2 + 5x -6$ so it can be factorised by grouping?
Options:
|
Multiple Choice
Which of the following correctly splits the middle term in $x^2 + 5x -6$ so it can be factored by grouping?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The word "factorised" is the AU/British spelling; the US spelling is "factorized". This requires a spelling-only change. |
XqclHP1ceC6Ip39mgqie |
Localize | Terminology | Multiple Choice
Which of the following represents the correct gradient-intercept form for the linear equation $2x+3y-6=0$?
Options:
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Multiple Choice
Which of the following represents the correct slope-intercept form for the linear equation $2x+3y-6=0$?
Options:
|
Classifier: The term "gradient-intercept form" is the standard AU/UK term for what is almost exclusively called "slope-intercept form" in US curriculum. Verifier: The term "gradient-intercept form" is the standard AU/UK term, whereas "slope-intercept form" is used in the US. This requires localization for school context. |
YIk0u73J5aF0kY4gMaWM |
Localize | Units (complex) | Multiple Choice
A car starts from rest and has a velocity of $v(t)=24t^2-4$ km/h for time $t\geq0$.
Find the displacement function $s(t)$ for the car at any time $t$.
Options:
|
Multiple Choice
A car starts from rest and has a velocity of $v(t)=24t^2-4$ mi/h for time $t\geq0$.
Find the displacement function $s(t)$ for the car at any time $t$.
Options:
|
Classifier: Contains metric units "km/h" and "m" (metres) in the answer choices. Per rule 1, any metric unit requires localization. Verifier: While the classifier correctly identified the presence of metric units ("km/h" and "m"), this should be classified as RED.units_complex_converted because the metric units are embedded within a functional equation (v(t)=24t^2-4 km/h). Converting this to US customary units (mph and feet/miles) would require re-deriving or scaling the coefficients of the function, which fits the definition of complex conversion. |
YOM7wqPzF1vpFk7AiiNY |
Localize | Units (simple) | Multiple Choice
In a right-angled triangle, the hypotenuse is $20$ cm, and one side is $x$ cm.
Express the length of the other side in terms of $x$ cm.
Options:
|
Multiple Choice
In a right triangle, the hypotenuse is $20$ in, and one side is $x$ in.
Express the length of the other side in terms of $x$ in.
Options:
|
Classifier: The text contains metric units ("cm") and the AU-specific term "right-angled triangle" (US: "right triangle"). Per rule 6, units conversion is the most impactful change. Verifier: The text contains the metric unit "cm" and the AU-specific term "right-angled triangle" (US: "right triangle"). Per rule 5, units conversion is the most impactful change. |
YZSoTHse6JTynxxlsbNk |
Localize | Units (simple) | Question
Find the area of a circle whose circumference is $22$ cm.
Answer:
|
Question
Find the area of a circle whose circumference is $22$ in.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. |
YjzUoBHZnUm9av5Ou4SC |
Localize | Spelling (AU-US) | Question
What is $x(x+3)+7(x+3)$ in factorised form?
Answer:
|
Question
What is $x(x+3)+7(x+3)$ in factored form?
Answer:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/British spelling. US spelling is "factorized". |
ZBAXxz4aSmmvkQTdHbtI |
Localize | Units (simple) | Question
A triangle has sides of $13$ cm and $14$ cm, and a semiperimeter of $21$ cm.
What is its area?
Answer:
|
Question
A triangle has sides of $13$ in and $14$ in, and a semiperimeter of $21$ in.
What is its area?
Answer:
|
Classifier: The question contains metric units ("cm" and "cm$^2$") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm$^2$") which require conversion to US customary units. It is a simple conversion as it involves a basic geometric area calculation with few values. |
ZmC0sEhWGdeQHTd5gtlq |
Localize | Units (simple) | Question
Fill in the blank:
$4.5$ mm$^2=[?]$ cm$^2$
Answer:
|
Question
Fill in the blank:
$4.5$ in$^2=[?]$ ft$^2$
Answer:
|
Classifier: The question explicitly requires conversion between metric units (mm^2 to cm^2). Any metric unit presence triggers this category. Verifier: The question involves converting between metric units (mm^2 to cm^2), which requires RED classification. |
YbUQIgPI1Z9RWN68TXWv |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is an example of numerical data?
Options:
|
Multiple Choice
Which of the following is an example of numerical data?
Options:
|
Classifier: Contains the AU spelling "colour" which needs to be converted to "color". Verifier: Contains the AU spelling "colour" in the answer choices, which requires localization to "color". |
ZuEfSYxiBcTcznoZUoXe |
Localize | Spelling (AU-US) | Question
What is the $y$-coordinate of the centre of the circle $(x-7)^2+(y-4)^2=25$?
Answer:
|
Question
What is the $y$-coordinate of the center of the circle $(x-7)^2+(y-4)^2=25$?
Answer:
|
Classifier: The text contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The text contains "centre", which is the AU spelling of "center". |
ZJRWkAFJN7VabqZ0hjpD |
Localize | Units (simple) | Question
An amusement park is located $3$ km east and $2$ km north of a museum.
What is the true bearing of the amusement park from the museum?
Answer:
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Question
An amusement park is located $3$ mi east and $2$ mi north of a museum.
What is the bearing of the amusement park from the museum?
Answer:
|
Classifier: The text contains metric units ("km") which require conversion to US customary units (miles). It also uses "true bearing" and the notation "$^\circ \text{T}$", which is common in AU/UK navigation contexts but less common in US K-12 math, though the metric unit is the primary trigger. Verifier: The text contains metric units ("km") which require conversion to US customary units. The use of "true bearing" and "$^\circ \text{T}$" notation is also a strong indicator of AU/UK curriculum context, but the metric unit is the primary trigger for RED. |
ZoqfXECqvL8NRSwuDNil |
Localize | Units (simple) | Question
Find the distance around the edge of a circular swimming pool whose radius is $5.4$m.
Answer:
|
Question
Find the distance around the edge of a circular swimming pool whose radius is $5.4$ft.
Answer:
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Classifier: The question uses the metric unit 'm' (metres) for the radius and the answer suffix. Verifier: The question uses the metric unit "m" (metres), which necessitates a RED classification. |
ZSlQpYOwj7hEihpPAOYd |
Localize | Terminology | Multiple Choice
Which of the following is true?
A hire purchase payment $[?]$ the cost of the item purchased.
Options:
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Multiple Choice
Which of the following is true?
An installment loan payment $[?]$ the cost of the item purchased.
Options:
|
Classifier: "Hire purchase" is a common term in AU/UK/Commonwealth countries for what is typically called "installment plan" or "rent-to-own" in the US. It is a specific financial/educational term that requires localization. Verifier: "Hire purchase" is a specific financial term used in AU/UK/Commonwealth curricula that corresponds to "installment plan" or "rent-to-own" in the US. |
ZMHl4D7bbsIN5ZFIyfx8 |
Localize | Units (simple) | Multiple Choice
True or false:
A runner was running in a marathon with a velocity of $12$ m/s and an acceleration of $3$ m/s$^2$.
The speed of the runner was increasing with time.
Options:
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Multiple Choice
True or false:
A runner was running in a marathon with a velocity of $12$ ft/s and an acceleration of $3$ ft/s$^2$.
The speed of the runner was increasing with time.
Options:
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Classifier: The text contains metric units for velocity ("m/s") and acceleration ("m/s$^2$"), which require localization to US customary units (e.g., ft/s). Verifier: The text contains metric units for velocity ("m/s") and acceleration ("m/s$^2$"), which require conversion to US customary units. |
a20bb594-7fe1-4322-9e11-607fbdf9d0df |
Localize | Answer set | Question
Why do the parallel sides matter when defining a trapezium?
Answer:
|
Question
Why do the parallel sides matter when defining a trapezoid?
Answer:
|
Classifier: The term "trapezium" is used. In the US, this shape (a quadrilateral with at least one pair of parallel sides) is called a "trapezoid". This requires a terminology change in both the question and the answer. Verifier: The term "trapezium" is the standard AU/UK term for what is called a "trapezoid" in the US. This requires terminology localization. |
ZBhoNXqLOnvoOy6gFRKg |
Localize | Terminology | Multiple Choice
The equation $5x-2y=3$ can be written as $y=mx+c$, where $m$ is the gradient of the line.
What is the value of $c$ ?
Options:
|
Multiple Choice
The equation $5x-2y=3$ can be written as $y=mx+b$, where $m$ is the slope of the line.
What is the value of $b$ ?
Options:
|
Classifier: The term "gradient" is used to describe the slope of a line. In US school contexts, "slope" is the standard term. Additionally, the equation form $y=mx+c$ is used, whereas the US standard is typically $y=mx+b$. Verifier: The term "gradient" is used instead of the US standard "slope", and the formula $y=mx+c$ is used instead of $y=mx+b$. |
Zut7xVSiBS42OOkAgCUJ |
Localize | Spelling (AU-US) | Multiple Choice
Which type of graph is most suitable for representing car sales for different coloured cars ?
Options:
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Multiple Choice
Which type of graph is most suitable for representing car sales for different colored cars?
Options:
|
Classifier: The text contains the AU spelling "coloured", which needs to be localized to the US spelling "colored". Verifier: The text contains "coloured", which is the AU spelling of "colored". |
a3b4cbac-cf20-4204-89e1-51310788b55e |
Localize | Spelling (AU-US) | Question
How can converting ratios to percentages simplify understanding data in surveys?
Hint: Visualise how percentages quantify survey results.
Answer:
|
Question
How can converting ratios to percentages simplify understanding data in surveys?
Hint: Visualize how percentages quantify survey results.
Answer:
|
Classifier: The word "Visualise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Visualize"). Verifier: The word "Visualise" in the hint field is AU/UK spelling and requires conversion to "Visualize" for US localization. |
a4sXXmmnSuKm6JShFYR0 |
Localize | Units (simple) | Multiple Choice
Which of the following examples of data is not discrete?
Options:
|
Multiple Choice
Which of the following examples of data is not discrete?
Options:
|
Classifier: The text contains the metric unit "m" (metres) in the context of a physical measurement (running 100 m), which requires localization to US customary units or acknowledgment of metric usage. Verifier: The text contains the metric unit "m" (metres) in the context of a physical measurement (100 m), which requires localization. |
a9i5sHyk5ZeSZ1FVRz6K |
Localize | Spelling (AU-US) | Question
Rationalise the denominator and simplify ${\Large\frac{1}{1+\sqrt{2}}}$ .
Options:
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Question
Rationalize the denominator and simplify ${\Large\frac{1}{1+\sqrt{2}}}$ .
Options:
|
Classifier: Contains the AU/UK spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: Contains "Rationalise", which is the AU/UK spelling. US spelling is "Rationalize". |
a56c45cf-036b-49b8-807e-d64d95a9eff2 |
Localize | Spelling (AU-US) | Question
How does factorising a quadratic equation help in solving it?
Hint: Find factors that add to $b$ and multiply to $ac$ in $ax^2 + bx + c$.
Answer:
|
Question
How does factoring a quadratic equation help in solving it?
Hint: Find factors that add to $b$ and multiply to $ac$ in $ax^2 + bx + c$.
Answer:
|
Classifier: The text uses the AU spelling "factorising" (multiple instances), which needs to be converted to the US spelling "factorizing". Verifier: The text uses the AU spelling "factorising", which requires localization to the US spelling "factorizing". |
aFmddY5hqIauElIvAq2r |
Localize | Units (simple) | Question
Cal lives $\frac{1}{5}$ km from the museum.
Sophia lives $\frac{3}{5}$ km from the museum.
How much closer is Cal to the museum than Sophia?
Answer:
|
Question
Cal lives $\frac{1}{5}$ mi from the museum.
Sophia lives $\frac{3}{5}$ mi from the museum.
How much closer is Cal to the museum than Sophia?
Answer:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles) for US localization. Verifier: The question uses "km" (kilometres), which is a metric unit requiring conversion to US customary units (miles). |
ZuSBm2920s6lT4G4x2fL |
Localize | Units (simple) | Multiple Choice
Sarah's rectangular cake tin has a base area of $180$ cm$^2$. The length is $3$ cm longer than the width.
What are the dimensions of the cake tin?
Options:
|
Multiple Choice
Sarah's rectangular cake pan has a base area of $180$ in$^2$. The length is $3$ in longer than the width.
What are the dimensions of the cake pan?
Options:
|
Classifier: The question and answers contain metric units ("cm" and "cm^2") which require conversion to US customary units for localization. Verifier: The question uses metric units (cm and cm^2) which require conversion to US customary units. The math is a simple quadratic/area problem, fitting simple conversion. |
aKjlsIm51sM9Kuc87bQL |
Localize | Spelling (AU-US) | Question
What are the coordinates of the centre of the circle $(x+11)^2+(y+7)^2=r^2$?
Answer:
|
Question
What are the coordinates of the center of the circle $(x+11)^2+(y+7)^2=r^2$?
Answer:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: Contains the AU spelling "centre", which needs to be localized to the US spelling "center". |
aM7hPr9KvEesZAn4kbDP |
Review | Review | Question
A student picked up $12$ pieces of rubbish on Monday and $25$ pieces on Tuesday.
How many pieces of rubbish did they pick up in total?
Answer:
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Question
A student picked up $12$ pieces of trash on Monday and $25$ pieces on Tuesday.
How many pieces of trash did they pick up in total?
Answer:
|
Classifier: The term "rubbish" is highly characteristic of AU/UK English, whereas "trash" or "litter" is more common in US English. While understandable, it often triggers localization in educational contexts. However, it is not a technical math term or a spelling difference, so I am marking as uncertain to defer to specific style guide policy on general vocabulary. Verifier: The term "rubbish" is a distinct AU/UK term for "trash" or "garbage". While the classifier was uncertain, this is a clear terminology difference that requires localization in an educational context. |
ab998875-19eb-48cc-ac1d-5c31875be8e6 |
Localize | Spelling (AU-US) | Question
How does understanding powers relate to recognising exponential growth in real-world situations?
Answer:
|
Question
How does understanding powers relate to recognizing exponential growth in real-world situations?
Answer:
|
Classifier: The word "recognising" uses the AU/UK 's' spelling; the US equivalent is "recognizing". Verifier: The word "recognising" is used in the source text, which is the AU/UK spelling. The US spelling is "recognizing". Per rule 1, any AU spelling requires RED classification. |
aZHDzoz31MwMlxsfF5Xb |
Localize | Terminology | Multiple Choice
Fill in the blank:
The full form of GST is $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
GST stands for $[?]$.
Options:
|
Classifier: The question asks for the full form of "GST" (Goods and Services Tax). While GST exists in some other countries, it is the standard consumption tax in Australia, whereas the US uses "Sales Tax". This is a locale-specific financial/mathematical term. Verifier: The question specifically asks for the definition of "GST" (Goods and Services Tax), which is the specific consumption tax system used in Australia (and New Zealand/Canada/India), whereas the US uses "Sales Tax". This is a locale-specific terminology requirement. |
akzLZ6gJUKNvEtKkO9t9 |
Localize | Units (simple) | Question
What is $2000$ litres in m$^3$ ?
Options:
|
Question
What is $2000$ gallons in ft$^3$ ?
Options:
|
Classifier: The text contains the metric unit "litres" (AU spelling) and "m^3". This requires both spelling correction (liters) and, per policy, any metric unit triggers a RED classification for US localization planning. Verifier: The text contains the metric unit "litres" (AU spelling) and requires conversion to "m^3". Per rule 1 and 3, metric units and AU spelling require RED classification. Simple conversion is appropriate as it is a direct unit change. |
bAIkUX5nmROgG6QoGPKv |
Localize | Terminology | Multiple Choice
What does the M stand for in BODMAS?
Options:
|
Multiple Choice
What does the M stand for in PEMDAS?
Options:
|
Classifier: The question refers to "BODMAS", which is the AU/UK acronym for order of operations (US uses PEMDAS). Additionally, the answer choice "Maths" is a specific AU term for "Math". Verifier: The text uses "BODMAS" (AU/UK acronym for order of operations) and the term "Maths", both of which require localization for a US audience. |
b03d1a0c-3991-4278-aa40-48606f46a834 |
Localize | Spelling (AU-US) | Question
Why do points further from the centre of rotation travel further than points closer to centre?
Answer:
|
Question
Why do points farther from the center of rotation travel farther than points closer to the center?
Answer:
|
Classifier: Contains the AU spelling "centre" multiple times, which needs to be converted to the US spelling "center". Verifier: Contains "centre" multiple times, which is the AU spelling (US: center). |
aef25bb2-8b2f-4942-9b2a-689b9eb94fce |
Localize | Spelling (AU-US) | Question
Why is understanding shading important for identifying solution regions in inequality graphs?
Hint: Visualise how shading helps interpret graph solutions.
Answer:
|
Question
Why is understanding shading important for identifying solution regions in inequality graphs?
Hint: Visualize how shading helps interpret graph solutions.
Answer:
|
Classifier: The word "visualise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("visualize"). Verifier: The word "Visualise" in the hint field uses the AU/UK spelling and requires localization to "Visualize" for the US. |
b422a62e-75ae-4576-9578-191e2457d2a1 |
Localize | Spelling (AU-US) | Question
Why does a circle stay the same shape all the way around?
Answer:
|
Question
Why does a circle stay the same shape all the way around?
Answer:
|
Classifier: The answer content contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The answer text contains "centre", which is the AU spelling. This requires localization to "center". |
b9840725-4bf7-45d8-9cb7-1d548e531d63 |
Localize | Units (simple) | Question
How can choosing the right unit of volume make calculations easier?
Answer:
|
Question
How can choosing the right unit of volume make calculations easier?
Answer:
|
Classifier: The text contains metric units ("litres", "mL") and AU-specific spelling ("litres"). Per the decision rules, any metric unit requires at least simple conversion classification. Verifier: The text contains metric units ("litres", "mL") and the AU spelling "litres". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
b2b00a57-f89f-43d1-af01-1ffe6909942d |
Localize | Terminology | Question
Why do we complete the square to convert a quadratic to turning point form?
Hint: Add and subtract the square term to balance the equation.
Answer:
|
Question
Why do we complete the square to convert a quadratic to vertex form?
Hint: Add and subtract the square term to balance the equation.
Answer:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is known as "vertex form" in the US. This requires terminology localization. Verifier: The term "turning point form" is the standard Australian/British term for what is called "vertex form" in the US. This is a terminology difference. |
b44928a9-927e-4d18-a8f6-868156760104 |
Localize | Spelling (AU-US) | Question
What makes the origin special in a unit circle?
Answer:
|
Question
What makes the origin special in a unit circle?
Answer:
|
Classifier: The answer content contains the AU spelling "centre", which requires conversion to "center". Verifier: The answer text contains "centre", which is the AU spelling. This requires localization to "center". |
b40464e6-c6f4-4958-8e61-46465b5c39e2 |
Localize | Terminology | Question
Why does $x = \frac{-b}{2a}$ give the $x$-coordinate of the turning point of a parabola?
Answer:
|
Question
Why does $x = \frac{-b}{2a}$ give the $x$-coordinate of the vertex of a parabola?
Answer:
|
Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard AU curriculum term for what is typically called the "vertex" in the US. |
b53a324b-17af-45d4-a9b2-49022800f6f7 |
Localize | Spelling (AU-US) | Question
Why is the general form of a quadratic equation useful for modelling certain real-world problems?
Answer:
|
Question
Why is the general form of a quadratic equation useful for modeling certain real-world problems?
Answer:
|
Classifier: Contains the AU spelling "modelling", which requires conversion to the US spelling "modeling". Verifier: Contains "modelling", which is the AU/UK spelling. US spelling is "modeling". |
b77a0dd9-e3ef-49c1-a3e8-da292de1fee2 |
Localize | Spelling (AU-US) | Question
Why does the 'split method' for factorising $ax^2+bx+c$ rely on finding two numbers that multiply to $a \times c$ and sum to $b$?
Hint: Focus on how factors reveal patterns in quadratics.
Answer:
|
Question
Why does the 'split method' for factoring $ax^2+bx+c$ rely on finding two numbers that multiply to $a \times c$ and sum to $b$?
Hint: Focus on how factors reveal patterns in quadratics.
Answer:
|
Classifier: The text contains the AU spelling "factorising", which requires conversion to the US spelling "factorizing". Verifier: The text contains the AU spelling "factorising", which requires localization to the US spelling "factorizing". |
b3c6d01a-7aae-4b29-9eed-539b9c4abf7a |
Localize | Spelling (AU-US) | Question
How does understanding sets relate to organising information?
Answer:
|
Question
How does understanding sets relate to organizing information?
Answer:
|
Classifier: The text uses "organising" and "organise", which are AU spellings. The US equivalent is "organizing" and "organize". Verifier: The text uses "organising" and "organise", which are AU spellings (US: organizing/organize). |
b4931c8f-1d36-4551-89aa-56fb30660d7b |
Localize | Spelling (AU-US) | Question
Why do some quadratic expressions require factorising by grouping?
Hint: Group terms into smaller factorable expressions.
Answer:
|
Question
Why do some quadratic expressions require factoring by grouping?
Hint: Group terms into smaller factorable expressions.
Answer:
|
Classifier: The question content contains the AU spelling "factorising", which needs to be localized to the US spelling "factorizing". Verifier: The question content contains "factorising", which is the AU spelling. This requires localization to "factorizing". |
b576fc56-a82d-4439-8ff3-f3b26b5e809e |
Localize | Terminology | Question
Why does $a^{r-n}$ mean $\frac{a^r}{a^n}$?
Hint: Use the index law for division: $a^m / a^n = a^{m-n}$.
Answer:
|
Question
Why does $a^{r-n}$ mean $\frac{a^r}{a^n}$?
Hint: Use the exponent law for division: $a^m / a^n = a^{m-n}$.
Answer:
|
Classifier: Uses the term "index law", which is standard AU/UK terminology for what is typically called "exponent rules" or "laws of exponents" in the US. Verifier: Uses "index law", which is specific AU/UK terminology for "exponent rules" or "laws of exponents". |
b8LBXvY1zJ9xRLeIXT2J |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is considered categorical data?
Options:
|
Multiple Choice
Which of the following is considered categorical data?
Options:
|
Classifier: Contains the AU spelling "Favourite", which needs to be converted to the US spelling "Favorite". Verifier: Contains the AU spelling "Favourite" in the answer choices, which requires localization to "Favorite". |
b930ad21-a4e1-4339-9320-da439975f196 |
Localize | Spelling (AU-US) | Question
What makes solving quadratic equations of the form $x^2 = a$, given $a>0$, give two answers?
Hint: Visualise how symmetry creates two roots.
Answer:
|
Question
What makes solving quadratic equations of the form $x^2 = a$, given $a>0$, give two answers?
Hint: Visualize how symmetry creates two roots.
Answer:
|
Classifier: The text contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint field contains the word "Visualise", which is the AU/UK spelling. US spelling is "Visualize". |
ay6c4sigYwx3LDehOO0K |
Localize | Terminology | Multiple Choice
Which of the following is the equation of a quartic with turning point $(5,-2)$?
Options:
|
Multiple Choice
Which of the following is the equation of a quartic with vertex $(5,-2)$?
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for what is referred to as the "vertex" in US curriculum for parabolas and higher-order polynomials. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US mathematics curriculum for parabolas and higher-order polynomials. |
b9f5cfda-8ce2-4ead-8737-7ef15029d78b |
Localize | Spelling (AU-US) | Question
In real-world modelling with quadratic equations, why might finding scenarios with exactly one solution be important?
Hint: Think about how verifying each step prevents errors in the final result.
Answer:
|
Question
In real-world modeling with quadratic equations, why might finding scenarios with exactly one solution be important?
Hint: Think about how verifying each step prevents errors in the final result.
Answer:
|
Classifier: The text contains AU-specific spellings "modelling" and "maximise" which require conversion to US English "modeling" and "maximize". Verifier: The text contains AU spellings "modelling" and "maximise" which require localization to US English "modeling" and "maximize". |
bEnVt73581IRBy5e56pN |
Localize | Units (complex) | Multiple Choice
An object starts from $2$ m to the right of the fixed point and moves in a straight line with velocity $v(t)=12t+2$ m/s for time $t\geq0$.
Find the object's displacement function.
Options:
|
Multiple Choice
An object starts from $2$ ft to the right of the fixed point and moves in a straight line with velocity $v(t)=12t+2$ ft/s for time $t\geq0$.
Find the object's displacement function.
Options:
|
Classifier: The text contains multiple metric units ("m" for metres and "m/s" for metres per second) which require conversion to US customary units. Verifier: The question involves metric units ("m", "m/s") embedded within kinematic equations (velocity and displacement functions). Per rule 4, equations defining quantities in metric or requiring re-deriving coefficients should be classified as units_complex_converted. |
b8eae23e-0f56-445f-bc94-61d85b94ef9f |
Localize | Spelling (AU-US) | Question
What makes finding your journey's start time easy on a timetable?
Answer:
|
Question
What makes finding your trip's start time easy on a schedule?
Answer:
|
Classifier: Contains the AU spelling "organised", which needs to be converted to the US spelling "organized". Verifier: Contains the AU spelling "organised" in the answer content, which requires localization to "organized". |
bccd0e87-7bd7-45da-84fc-c110b09eb90e |
Localize | Terminology | Question
Why is understanding factors important in maths?
Answer:
|
Question
Why is understanding factors important in math?
Answer:
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Classifier: The text uses the term "maths", which is the standard AU/UK term and needs to be localized to "math" for a US audience. Verifier: The text uses "maths", which is the standard AU/UK term and requires localization to "math" for US audiences. |
bfvJVwxEMHbX1jaXIGpX |
Localize | Units (simple) | Question
A bike tyre has a diameter of $70$ cm.
How far will it travel after $4$ revolutions?
Answer:
|
Question
A bike tire has a diameter of $70$ in.
How far will it travel after $4$ revolutions?
Answer:
|
Classifier: The question contains the metric unit 'cm' (centimetres) and 'tyre' (AU spelling). According to the decision rules, any metric unit requires classification into a units category. Verifier: The question contains the metric unit 'cm' and the AU spelling 'tyre'. Per rule 5, units conversion is the most impactful change. It is a simple conversion as it involves a single geometric calculation (circumference). |
ba1433c5-d7a4-44c8-8619-c700fae03b6d |
Localize | Spelling (AU-US) | Question
Why does a linear growth rule involve adding or subtracting the same value repeatedly?
Hint: Visualise how each step adds an equal amount.
Answer:
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Question
Why does a linear growth rule involve adding or subtracting the same value repeatedly?
Hint: Visualize how each step adds an equal amount.
Answer:
|
Classifier: The hint contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint field contains "Visualise", which is the AU/UK spelling. This requires localization to the US spelling "Visualize". |
babe3619-6127-4dfd-8b83-0df93231b8a3 |
Localize | Spelling (AU-US) | Question
Why does the wave repeat in the graph of $\sin(x)$?
Hint: Visualise how angles on the unit circle repeat every $360$ degrees or $2\pi$ radians.
Answer:
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Question
Why does the wave repeat in the graph of $\sin(x)$?
Hint: Visualize how angles on the unit circle repeat every $360$ degrees or $2\pi$ radians.
Answer:
|
Classifier: The hint contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint field contains "Visualise", which is the AU/UK spelling. This requires localization to the US spelling "Visualize". |
bi73P6iR8DFb0qoIBXg6 |
Localize | Answer set | Multiple Choice
Which season comes just after spring?
Options:
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Multiple Choice
Which season comes just after spring?
Options:
|
Classifier: The answer set contains the term "Autumn", which is the standard AU/UK term for the season. In a US localization context, this must be changed to "Fall" to ensure the answer set is consistent with US dialect. Verifier: The term "Autumn" is used in the answer set. In US English, "Fall" is the standard term for this season. This requires localization for dialect consistency. |
btpwNli3JjDpR9Y3aUi2 |
Localize | Spelling (AU-US) | Question
Rationalise the denominator and simplify ${\Large\frac{44}{\sqrt{11}}}$ .
Options:
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Question
Rationalize the denominator and simplify ${\Large\frac{44}{\sqrt{11}}}$ .
Options:
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Classifier: Contains the AU/UK spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: The word "Rationalise" uses the AU/UK 's' spelling and must be changed to the US 'z' spelling "Rationalize". |
boTsRtgjU5Ofi6JQymgB |
Localize | Terminology | Question
Ellen took an interest-only loan of $\$30000$ at $8.5\%$ annual interest, compounded fortnightly.
Find her quarterly payment using a finance solver.
Answer:
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Question
Ellen took an interest-only loan of $\$30000$ at $8.5\%$ annual interest, compounded every two weeks.
Find her quarterly payment using a finance solver.
Answer:
|
Classifier: The term "fortnightly" is a distinct AU/UK term that is not used in US English (where "every two weeks" or "bi-weekly" is used). Verifier: The term "fortnightly" is a distinct AU/UK term that requires localization for a US audience (e.g., to "every two weeks"). |
c4hFgSfnDu1clmiRpdkm |
Localize | Units (simple) | Question
Find the volume of a rectangular prism that has a height of $12$ cm and a base with an area of $6$ cm$^2$.
Answer:
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Question
Find the volume of a rectangular prism that has a height of $12$ in and a base with an area of $6$ in$^2$.
Answer:
|
Classifier: The text contains metric units (cm, cm^2, cm^3) which require conversion for US localization. Verifier: The question contains metric units (cm, cm^2, cm^3) which require conversion for US localization. It is a simple conversion as it involves a single calculation (12 * 6). |
bmzjazXJWdWjgIA7IHD8 |
Localize | Terminology | Question
At what annual interest rate will $\$4500$ grow to $\$6390$ in $3\frac{1}{2}$ years?
Answer:
|
Question
At what annual interest rate will $\$4500$ grow to $\$6390$ in $3\frac{1}{2}$ years?
Answer:
|
Classifier: The suffix uses "p.a." (per annum), which is common in AU/UK contexts but typically replaced with "per year" or omitted in favor of "annual interest rate" in US K-12 math. More importantly, "p.a." is a specific abbreviation that often triggers localization to "per year". Verifier: The use of "p.a." (per annum) is a specific financial abbreviation common in AU/UK but typically localized to "per year" or "annual" in US K-12 contexts. |
blUhU4LtIHe0wo4xQYsP |
Localize | Units (simple) | Question
Find the distance of Lebanon$(34^\circ{N},36^\circ{E})$ from the North Pole.
Give your answer to the nearest whole number.
Hint: Take Earth's radius to be $6371$ km
Answer:
|
Question
Find the distance of Lebanon$(34^\circ{N},36^\circ{E})$ from the North Pole.
Give your answer to the nearest whole number.
Hint: Take Earth's radius to be $6371$ miles
Answer:
|
Classifier: The text contains metric units ("km") in the hint, suffix, and answer value. Per decision rules, any metric unit requires classification into a units category. Verifier: The question uses metric units ("km") in the hint and suffix. Per rule 3, any metric unit requires RED classification. Since it involves a single radius value and a distance calculation, it is a simple conversion. |
c2523527-cb6f-4d69-ad32-d8d9048231a0 |
Localize | Terminology | Question
How does understanding angles help you classify triangles?
Answer:
|
Question
How does understanding angles help you classify triangles?
Answer:
|
Classifier: The text uses the AU-specific term "right-angled" to describe a triangle, which should be localized to "right" in a US context. Verifier: The answer text contains the term "right-angled", which is the standard AU/UK term for what is called a "right" triangle in the US. This requires terminology localization. |
c9e93957-5864-477a-962e-2b74c189cffa |
Localize | Terminology | Question
How does the $9$ times tables relate to counting by $9$s?
Answer:
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Question
How do the $9$ times tables relate to counting by $9$s?
Answer:
|
Classifier: The term "times tables" is the standard AU/UK plural form; the US equivalent is typically singular "times table" or "multiplication tables". Verifier: The term "times tables" (plural) is the standard Australian/British usage, whereas US English typically uses "times table" (singular) or "multiplication tables". This is a valid terminology distinction for school context. |
cY36O97DEXf7GMhkPVcZ |
Localize | Terminology | Question
The cost of a service is $\$90$ excluding GST.
How much GST will be paid for this service?
Answer:
|
Question
The cost of a service is $\100$ excluding sales tax.
How much sales tax will be paid for this service?
Answer:
|
Classifier: The term "GST" (Goods and Services Tax) is specific to the Australian (and other Commonwealth) tax systems. In a US context, this would typically be "sales tax". Verifier: The term "GST" (Goods and Services Tax) is specific to Australian and Commonwealth tax systems; the US equivalent is "sales tax". |
ca4XHVle6xF4EQKgzY8q |
Localize | Units (simple) | Question
The area of a parallelogram is $45$ cm$^2$ and its base has length $9$ cm.
Find the height of the parallelogram.
Answer:
|
Question
The area of a parallelogram is $45$ in$^2$ and its base has length $9$ in.
Find the height of the parallelogram.
Answer:
|
Classifier: The question contains metric units ("cm" and "cm^2") which require localization to US customary units or a decision on metric usage per US standards. Verifier: The question uses metric units ("cm" and "cm^2"), which requires localization for a US context. It is a simple conversion as it involves a basic geometric formula with few values. |
c5e1f2f8-fb3e-4320-b560-4ac8fe62eee9 |
Localize | Spelling (AU-US) | Question
How can recognising the natural exponential function simplify solving problems in finance and biology?
Hint: Focus on how $e^x$ applies to diverse contexts.
Answer:
|
Question
How can recognizing the natural exponential function simplify solving problems in finance and biology?
Hint: Focus on how $e^x$ applies to diverse contexts.
Answer:
|
Classifier: Contains the AU/UK spelling "recognising", which requires conversion to the US spelling "recognizing". Verifier: The text contains "recognising" (used in both the question and answer), which is the AU/UK spelling and requires localization to "recognizing" for the US. |
cab76b31-510a-46ce-a754-738deb67bafb |
Localize | Terminology | Question
Why is the null factor law useful?
Answer:
|
Question
Why is the zero product property useful?
Answer:
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Classifier: The term "null factor law" is the standard term in the Australian curriculum. In the US, this is almost exclusively referred to as the "Zero Product Property". Verifier: The term "null factor law" is specific to the Australian curriculum; the US equivalent is the "Zero Product Property". |
c4rImr55uNbSvyLvaKJY |
Localize | Units (simple) | Question
Maria runs a bakery selling strawberry cakes at a profit of $\$10$ each and Belgian cakes at $\$14$ each.
Each strawberry cake requires 1 kg of flour and 1.5 hours to prepare, while each Belgian cake requires 1.5 kg of flour and 1 hour.
Maria works a maximum of 8 hours daily and buys no more than 10 kg of flour. Let:
$x = $ number of strawberry cakes
$y = $ number of Belgian cakes
Write an expression for the objective function for the bakery's profit.
Options:
|
Question
Maria runs a bakery selling strawberry cakes at a profit of $\$10$ each and Belgian cakes at $\$14$ each.
Each strawberry cake requires 1 lb of flour and 1.5 hours to prepare, while each Belgian cake requires 1.5 lbs of flour and 1 hour.
Maria works a maximum of 8 hours daily and buys no more than 10 lbs of flour. Let:
$x = $ number of strawberry cakes
$y = $ number of Belgian cakes
Write an expression for the objective function for the bakery's profit.
Options:
|
Classifier: The text contains metric units (kg) which require conversion for US localization. Although the objective function itself is unitless, the problem context is defined using metric units. Verifier: The text contains metric units (kg) which require conversion. Although the final answer is an expression, the constraints in the problem description are provided in metric units. |
cPpzZQdFAd4EAiDpWGAc |
Localize | Units (simple) | Question
The displacement function of a particle is $s(t)=2t^2-4$ mm for $0\leq t\leq2$ s.
Find its initial displacement.
Hint: The initial displacement is the displacement at $t=0$
Answer:
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Question
The displacement function of a particle is $s(t)=2t^2-4$ in for $0\leq t\leq2$ s.
Find its initial displacement.
Hint: The initial displacement is the displacement at $t=0$
Answer:
|
Classifier: The text contains the metric unit "mm" (millimetres), which requires localization to US customary units or a decision on metric usage in science contexts. Per rule 1, any metric unit disqualifies GREEN. Verifier: The question contains the metric unit "mm" (millimetres). Per rule 1 and 3, any metric unit requires RED classification. Since it is a simple displacement value, simple_conversion is appropriate. |
cTuVIsh5GfxekAdopiTb |
Localize | Spelling (AU-US) | Multiple Choice
What is $x^6-4$ in fully factorised form?
Options:
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Multiple Choice
What is $x^6-4$ in fully factored form?
Options:
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Classifier: Contains the AU spelling "factorised" and "factorised", which requires conversion to the US spelling "factorized". Verifier: Contains the AU spelling "factorised" in the content and "factorised" in the answer choices, which requires conversion to the US spelling "factorized". |
c33f84ca-a226-4c44-bc7e-796bd8cb3ecb |
Localize | Terminology | Question
Why does $\tan(\theta)$ give the gradient of a straight line passing through the origin with angle $\theta$ to the positive x-axis?
Hint: Focus on how congruency ensures every corresponding part matches exactly.
Answer:
|
Question
Why does $\tan(\theta)$ give the slope of a straight line passing through the origin with angle $\theta$ to the positive x-axis?
Hint: Focus on how congruence ensures every corresponding part matches exactly.
Answer:
|
Classifier: The text uses the term "gradient" to refer to the slope of a line, which is the standard AU term. In a US context, "slope" is the standard term. Additionally, the hint contains the word "congruency," which typically maps to "congruence" in US English. Verifier: The term "gradient" is the standard AU term for "slope" in a US context. Additionally, "congruency" is used in the hint, which is more common in AU/UK than the US "congruence". |
cb35a216-1224-474b-9ea3-5f84c394673f |
Localize | Spelling (AU-US) | Question
How does understanding regions in a Venn diagram relate to counting set elements?
Answer:
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Question
How does understanding regions in a Venn diagram relate to counting set elements?
Answer:
|
Classifier: The text is bi-dialect neutral. "Recognising" is spelled with an 's' in AU, but the provided text uses "recognising" which is the AU spelling; however, the prompt instructions for GREEN require ZERO AU-specific spelling. Wait, "recognising" is AU spelling (US is "recognizing"). Therefore, it must be RED.spelling_only. Verifier: The answer text contains "recognising", which is AU/British spelling (US is "recognizing"). Per rule 1, any AU spelling disqualifies GREEN. |
catV0heFlAuLqmlSzpO0 |
Localize | Units (simple) | Question
Location coordinates are given as:
Point $X$ $=0^\circ,30^\circ{E}$
Point $Y$ $=0^\circ,120^\circ{W}$
What is the shortest distance between the two points (to the nearest kilometre), where the radius of the Earth is $6400$ km?
Answer:
|
Question
Location coordinates are given as:
Point $X$ $=0^\circ,30^\circ{E}$
Point $Y$ $=0^\circ,120^\circ{W}$
What is the shortest distance between the two points (to the nearest mile), where the radius of the Earth is $6400$ mi?
Answer:
|
Classifier: The text contains metric units ("kilometre", "km") and AU-specific spelling ("kilometre"). According to the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units ("kilometre", "km") and AU-specific spelling ("kilometre"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
csDFy73E9RGzlTSNQV79 |
Localize | Units (simple) | Question
Fill in the blank:
$123$ g $=[?]$ kg
Answer:
|
Question
Fill in the blank:
$123$ oz $=[?]$ lb
Answer:
|
Classifier: The question explicitly uses and requires conversion between metric units (grams and kilograms). Per decision rules, any metric unit requires RED classification. Verifier: The question involves metric units (grams and kilograms), which requires RED classification per rule 3. It is a simple conversion. |
cf311b11-b999-4f41-9182-7a52942cfc9d |
Localize | Units (simple) | Question
How are kilograms and grams related?
Answer:
|
Question
How are pounds and ounces related?
Answer:
|
Classifier: The text explicitly uses and discusses metric units ("kilograms" and "grams"). Per the decision rules, any metric unit found anywhere requires classification into a units category. Verifier: The text explicitly uses and discusses metric units ("kilograms" and "grams"). Per the decision rules, any metric unit found anywhere requires classification into a units category. |
cwFV7KCUoefi1zxh9KK3 |
Localize | Units (simple) | Question
How many litres are there in $0.5$ kL ?
Answer:
|
Question
How many gallons are there in $0.5$ kgals ?
Answer:
|
Classifier: Contains metric units (litres, kL, L) and AU spelling ("litres"). Per decision rules, any metric unit requires at least simple conversion classification. Verifier: Contains metric units ("litres", "kL", "L") and AU spelling ("litres"). Per decision rules, any metric unit requires at least simple conversion classification. |
cb8f7006-dd96-4df1-a5cd-7911b83c2ec7 |
Localize | Spelling (AU-US) | Question
What makes conjugates useful when rationalising?
Hint: Multiplying by the conjugate simplifies the expression.
Answer:
|
Question
What makes conjugates useful when rationalizing?
Hint: Multiplying by the conjugate simplifies the expression.
Answer:
|
Classifier: Contains the AU spelling "rationalising" (US: "rationalizing"). Verifier: Contains the AU spelling "rationalising" (US: "rationalizing") in both the question and the answer. |
ced518c8-07d9-429b-bddb-9b26fe7dda8e |
Localize | Spelling (AU-US) | Question
Why do we want to eliminate radicals from denominators by rationalising?
Hint: Rational denominators are preferred in standard form.
Answer:
|
Question
Why do we want to eliminate radicals from denominators by rationalizing?
Hint: Rational denominators are preferred in standard form.
Answer:
|
Classifier: The content contains the AU spelling "rationalising", which needs to be converted to the US spelling "rationalizing". Verifier: The content contains the AU spelling "rationalising", which needs to be converted to the US spelling "rationalizing". |
cfvbhPW9jWlA8ZQ6KFbP |
Localize | Units (simple) | Multiple Choice
Which of the following is equal to $2$ m?
Options:
|
Multiple Choice
Which of the following is equal to $2$ ft?
Options:
|
Classifier: The question and answers are entirely based on metric unit conversions (m, cm, mm, km), which requires localization to US customary units or a specific pedagogical decision for the US market. Verifier: The question is entirely based on metric unit conversions (m, cm, mm, km), which requires RED classification per rule 3. |
ce336a57-e5f2-440e-945a-539ef9c0342a |
Localize | Spelling (AU-US) | Question
Why does a quadratic equation have exactly one real solution when its discriminant equals zero?
Hint: Visualise how splitting a number into place values makes multiplication easier.
Answer:
|
Question
Why does a quadratic equation have exactly one real solution when its discriminant equals zero?
Hint: Visualize how splitting a number into place values makes multiplication easier.
Answer:
|
Classifier: The hint contains the AU spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint contains the AU spelling "Visualise", which requires conversion to the US spelling "Visualize". |
d5uWdyL2AmlomIE8qv1E |
Localize | Terminology | Question
Sumaira has an investment of $\$6500$ that pays her $5.4\%$ simple interest per annum.
The situation can be modelled using the recurrence relation:
$V_{0}=6500;$ $V_{n+1}=V_{n}+351$ where $n$ is the number of years
What is the value of Sumaira's investment after $5$ year?
Answer:
|
Question
Sumaira has an investment of $\$6500$ that pays her $5.4\%$ simple interest per year.
The situation can be modeled using the recurrence relation:
$V_{0}=6500;$ $V_{n+1}=V_{n}+351$ where $n$ is the number of years
What is the value of Sumaira's investment after $5$ years?
Answer:
|
Classifier: The text uses the term "per annum", which is standard in AU financial contexts but is typically localized to "per year" or "annually" in US K-12/undergraduate math contexts. More importantly, it uses "modelling" (implied by "modelled" which is the US spelling, but the phrasing "per annum" is a strong AU indicator). However, the primary trigger is "per annum" in a school context. Note: "5 year" in the question is a grammatical error ("5 years") but not a localization issue. Verifier: The term "per annum" is a strong indicator of AU/UK financial math context and is typically localized to "per year" or "annually" in US school contexts. |
d8GIga2NtPXUznuZbOqe |
Localize | Units (simple) | Question
What is the minimum number of complete rotations required for a wheel of radius $25$ cm to cover a distance of at least $10$ m?
Answer:
|
Question
What is the minimum number of complete rotations required for a wheel of radius $25$ in to cover a distance of at least $10$ ft?
Answer:
|
Classifier: Contains metric units "cm" and "m". Requires conversion to US customary units (e.g., inches and feet/yards) for US localization. Verifier: Contains metric units "cm" and "m". Requires conversion to US customary units for US localization. |
dm4EwsuC0RNG5bScRWpL |
Localize | Spelling (AU-US) | Question
How many equal triangles can be formed in the centre of a pentagon?
Answer:
|
Question
How many equal triangles can be formed in the center of a pentagon?
Answer:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: Contains "centre", which is the AU/UK spelling of "center". |
dgDEMPluuvy8aZSIgH1O |
Localize | Units (simple) | Question
Sam travelled $6$ km by bus and $3$ km by bicycle.
How far did he travel in total?
Answer:
|
Question
Sam traveled $6$ mi by bus and $3$ mi by bicycle.
How far did he travel in total?
Answer:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles) for localization. Verifier: The text uses "km" (kilometres), which is a metric unit requiring conversion for US localization. It is a simple addition problem, so simple_conversion is correct. |
d878035a-5ec1-497e-8a05-b6a68b0b6a86 |
Localize | Units (simple) | Question
Why must both quantities in the ratio $3$ km$:$ $600$ m be written in the same units before simplifying?
Answer:
|
Question
Why must both quantities in the ratio $3$ mi$:$ $600$ ft be written in the same units before simplifying?
Answer:
|
Classifier: Contains metric units "km" and "m". Per decision rules, any metric unit requires classification into a units category. This is a simple conversion/pedagogy question about units. Verifier: Contains metric units "km" and "m". Per decision rules, any metric unit requires classification into a units category. |
dcvjQCSe8Nb5mHQilsyr |
Localize | Terminology | Multiple Choice
Which type of triangle always has an altitude that perpendicularly bisects its base?
Options:
|
Multiple Choice
Which type of triangle always has an altitude that perpendicularly bisects its base?
Options:
|
Classifier: Contains the AU-specific term "Right angled triangle", which should be localized to "Right triangle" for US audiences. Verifier: The term "Right angled triangle" is the standard AU/UK term, whereas the US standard is "Right triangle". This requires localization. |
dStF6jDx4bRAfIN83wWl |
Localize | Spelling (AU-US) | Question
Factorise $P(x)=8x^3-64$.
Express your answer in the form $a(x+b)(x^2+cx+d)$.
Answer:
|
Question
Factor $P(x)=8x^3-64$.
Express your answer in the form $a(x+b)(x^2+cx+d)$.
Answer:
|
Classifier: Contains the AU spelling "Factorise", which must be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU/British spelling. US spelling is "Factorize". |
d8e15e96-d591-4496-b7e5-b2c7c9360d84 |
Localize | Spelling (AU-US) | Question
How can you tell which suffix to use for ordinal numbers above $20$?
Hint: Visualise how patterns determine suffixes.
Answer:
|
Question
How can you tell which suffix to use for ordinal numbers above $20$?
Hint: Visualize how patterns determine suffixes.
Answer:
|
Classifier: The hint field contains the AU spelling "Visualise", which needs to be converted to the US spelling "Visualize". Verifier: The hint contains "Visualise", which is the AU spelling of "Visualize". |
d85e85b2-b62f-4a6a-892a-e37308d0cd77 |
Localize | Terminology | Question
Why does BODMAS prioritise brackets first?
Answer:
|
Question
Why does PEMDAS prioritize parentheses first?
Answer:
|
Classifier: Contains "BODMAS", which is the standard acronym in AU/UK/NZ, whereas the US typically uses "PEMDAS". This is a school-context terminology difference. Verifier: Contains "BODMAS", which is the standard acronym in AU/UK/NZ, whereas the US typically uses "PEMDAS". This is a school-context terminology difference. |
d75ed144-35e8-442c-80ef-b4c7d3abbbd7 |
Localize | Spelling (AU-US) | Question
Why does calculating the total surface area involve summing the areas of all the faces?
Hint: Visualise how each face contributes to the total.
Answer:
|
Question
Why does calculating the total surface area involve summing the areas of all the faces?
Hint: Visualize how each face contributes to the total.
Answer:
|
Classifier: The word "Visualise" uses the AU/UK 's' spelling. Verifier: The word "Visualise" in the hint field uses the AU/UK 's' spelling. |
d8d75870-74c4-4ec4-8ba1-c57dfd91b8dc |
Localize | Spelling (AU-US) | Question
Why is it important to understand the mean when solving problems with data?
Answer:
|
Question
Why is it important to understand the mean when solving problems with data?
Answer:
|
Classifier: The answer content contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: The answer contains "centre", which is the AU spelling of "center". |
dmiR3tKnxIGSGpMU3AAT |
Localize | Spelling (AU-US) | Question
Find the distance between the co-ordinates $A(1,-2,4)$ and $B(0,-2,0)$.
Answer:
|
Question
Find the distance between the coordinates $A(1,-2,4)$ and $B(0,-2,0)$.
Answer:
|
Classifier: The term "co-ordinates" (with hyphen) is common in AU/UK but also accepted in US, though "coordinates" is more frequent. However, it does not violate the strict RED/GREEN rules as it is not a metric unit or a specific school term like "maths". The suffix "units" is generic. Verifier: The word "co-ordinates" is the hyphenated AU/UK spelling. In US English, "coordinates" is the standard form without a hyphen. Per rule 1, AU spelling requires RED classification. |
dpBtZ9WDXNyF0KDeTU1W |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Seasonal indices are used to deseasonalise the seasonal data for proper analysis.
Options:
|
Multiple Choice
True or false:
Seasonal indices are used to deseasonalize the seasonal data for proper analysis.
Options:
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Classifier: The word "deseasonalise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("deseasonalize"). Verifier: The word "deseasonalise" uses the AU/UK 's' spelling and requires localization to the US 'z' spelling ("deseasonalize"). |
e0cfbfcc-ced0-442d-8403-3c04fcf3c53a |
Localize | Spelling (AU-US) | Question
How can mastering exponential graph transformations simplify solving problems in finance or biology?
Hint: Visualise how transformations adjust the graph.
Answer:
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Question
How can mastering exponential graph transformations simplify solving problems in finance or biology?
Hint: Visualize how transformations adjust the graph.
Answer:
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Classifier: The text contains the AU spelling 'visualise' and 'behaviours', which require conversion to US spelling ('visualize' and 'behaviors'). Verifier: The text contains AU spellings "visualise" (in the hint) and "behaviours" (in the answer), which require localization to US English. |
d94a4a23-3bc7-408f-8a4f-1f336b401ec2 |
Localize | Spelling (AU-US) | Question
How can recognising patterns in adding sequences help predict future numbers?
Answer:
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Question
How can recognizing patterns in adding sequences help predict future numbers?
Answer:
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Classifier: The question contains the AU spelling "recognising", which needs to be converted to the US spelling "recognizing". Verifier: The question contains "recognising", which is the AU spelling of "recognizing". |
d9dcKtVR7vKr9puwuZs4 |
Localize | Terminology | Question
Find the $y$-coordinate of the turning point of the parabola $y=x^2-\frac{2x}{3}-\frac{8}{3}$.
Options:
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Question
Find the $y$-coordinate of the vertex of the parabola $y=x^2- rac{2x}{3}- rac{8}{3}$.
Options:
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Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is specific AU/UK terminology for the vertex of a parabola. |
dKiNgvsIvDXQHMOhiIgB |
Localize | Terminology | Multiple Choice
In $\triangle ABC$ and $\triangle DEF$, $\angle A\cong\angle D$, $AB\cong DE$, and $\angle B\cong\angle E$.
Which congruency test proves $\triangle ABC \cong \triangle DEF$?
Options:
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Multiple Choice
In $\triangle ABC$ and $\triangle DEF$, $\angle A\cong\angle D$, $AB\cong DE$, and $\angle B\cong\angle E$.
Which congruence theorem proves $\triangle ABC \cong \triangle DEF$?
Options:
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Classifier: The term "congruency" is used, which typically maps to "congruence" in US geometry curriculum. Verifier: The term "congruency" is used multiple times (including "congruency test" and "congruency rule"). In the US geometry curriculum, the standard term is "congruence". |
d63f69da-872f-4731-8748-b0d8dfaeb0a4 |
Localize | Spelling (AU-US) | Question
Why is the transformation $y=kf(x)$ considered a vertical stretch when $|k|>1$?
Hint: Visualise how the digits shift one place to the right.
Answer:
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Question
Why is the transformation $y=kf(x)$ considered a vertical stretch when $|k|>1$?
Hint: Visualize how the digits shift one place to the right.
Answer:
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Classifier: The word "Visualise" uses the AU/UK 's' spelling instead of the US 'z' spelling. Verifier: The word "Visualise" in the hint field uses the AU/UK 's' spelling, which requires localization to 'z' for US English. |
deYf7HFtvrJZ2Y6oddwT |
Localize | Units (simple) | Multiple Choice
Farmers are fighting a fungal growth, which can cause crop failure.
$8000$ hectares of farmland are infected right now and this infected area decreases by $5\%$ every year.
How much farmland will be infected in $15$ years?
Options:
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Multiple Choice
Farmers are fighting a fungal growth, which can cause crop failure.
$8000$ acres of farmland are infected right now and this infected area decreases by $5\%$ every year.
How much farmland will be infected in $15$ years?
Options:
|
Classifier: The text uses "hectares", which is a metric unit of area. This requires localization to US customary units (e.g., acres) or at least flags the content as metric-based. Verifier: The text uses "hectares", which is a metric unit of area. This requires localization to US customary units (e.g., acres). |
dGtAFlpD6ZpXNzlc4oXk |
Localize | Spelling (AU-US) | Question
Factorise $x^3+216$.
Express your answer in the form $(x+a)(x^2+bx+c)$.
Options:
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Question
Factor $x^3+216$.
Express your answer in the form $(x+a)(x^2+bx+c)$.
Options:
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Classifier: Contains the AU spelling "Factorise", which must be localized to "Factorize" for a US audience. Verifier: The text contains "Factorise", which is AU spelling. Per rule 1, this requires RED classification. |
duEviwqlq2L8JRg3ipXW |
Localize | Terminology | Multiple Choice
Convert the equation $y = 2x^2 - 8x + 9$ to turning point form.
Options:
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Multiple Choice
Convert the equation $y = 2x^2 - 8x + 9$ to vertex form.
Options:
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Classifier: The term "turning point form" is the standard AU/UK term for what is known as "vertex form" in the US. This requires localization for a US school context. Verifier: "Turning point form" is the AU/UK equivalent of the US "vertex form", requiring localization for school context. |
e39ZpWKZuHRZzrCGCeEw |
Localize | Units (simple) | Question
Find the area of an equilateral triangle with a side length of $10$ cm.
Answer:
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Question
Find the area of an equilateral triangle with a side length of $10$ in.
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question uses metric units (cm and cm^2) which require conversion to US customary units. It is a simple conversion as it involves a single side length and a standard area formula. |
e308c1cf-8bee-425f-be80-51167c6da023 |
Localize | Terminology | Question
Why is identifying turning points important for analysing graph symmetry?
Answer:
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Question
Why is identifying turning points important for analyzing graph symmetry?
Answer:
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Classifier: Contains "analysing" (AU spelling) and "turning points" (AU terminology for vertex). Per rule 6, terminology/spelling signals make it RED. "Turning point" is a specific AU school term mapping to US "vertex". Verifier: The text contains "analysing" (AU spelling) and "turning points" (AU terminology for vertex). Per rule 1 and 5, these require RED classification. |
e87e8aa2-1f27-4561-a8d0-3bc48923d422 |
Localize | Spelling (AU-US) | Question
Why do you separate numerical from categorical data?
Answer:
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Question
Why do you separate numerical from categorical data?
Answer:
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Classifier: Contains the AU spelling "organise", which requires conversion to the US spelling "organize". Verifier: The answer text contains the AU spelling "organise", which must be localized to "organize". |
e4624dcd-92bb-4d28-9e1a-9400980caf88 |
Localize | Terminology | Question
Why must we verify that triangles are right before using Pythagoras’ theorem?
Answer:
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Question
Why must we verify that triangles are right before using the Pythagorean theorem?
Answer:
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Classifier: The answer contains the AU-specific term "right-angled", which should be localized to "right" (as in "right triangle") for a US audience. Verifier: The answer uses the term "right-angled", which is the standard AU/UK term for what is called a "right triangle" in the US. |
eQj0zOQqVNmvjg3YzRWb |
Localize | Terminology | Question
Write $\sqrt{3}\times\sqrt{7}$ as a single surd.
Answer:
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Question
Write $\sqrt{3}\times\sqrt{7}$ as a single radical.
Answer:
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Classifier: The term 'surd' is standard in AU/UK curriculum but is almost exclusively referred to as a 'radical' or 'radical expression' in US school mathematics. Verifier: The term "surd" is specific to AU/UK/Commonwealth curricula; in the US, "radical" or "radical expression" is used. |
eJTflSZ6ManxLwAfZGem |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
A small circle can pass through the centre of the Earth.
Options:
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Multiple Choice
True or false:
A small circle can pass through the center of the Earth.
Options:
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Classifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". Verifier: The text contains "centre", which is the AU/British spelling of "center". |
eKRFa2Y7oMV50mIkdKFB |
Localize | Spelling (AU-US) | Question
Five ice-cream flavours are available: vanilla, strawberry, chocolate, mango and raspberry.
A boy wants two different scoops of ice cream.
How many different combinations of ice cream flavours can he choose, assuming that the order matters?
Answer:
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Question
Five ice-cream flavors are available: vanilla, strawberry, chocolate, mango and raspberry.
A boy wants two different scoops of ice cream.
How many different combinations of ice cream flavors can he choose, assuming that the order matters?
Answer:
|
Classifier: Contains the AU spelling "flavours" (used twice), which requires conversion to the US spelling "flavors". Verifier: The text contains "flavours" (twice), which is the AU/British spelling of "flavors". |
eNt1nXtGocNA18IZ8bys |
Localize | Units (simple) | Question
The length of a rectangular training area is $10$ m and the width is $8.5$ m.
What is the total training area?
Answer:
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Question
The length of a rectangular training area is $10$ ft and the width is $8.5$ ft.
What is the total training area?
Answer:
|
Classifier: The text contains the metric unit "m" (metres) and "m^2", which requires conversion to US customary units (e.g., feet/yards). Verifier: The question uses metric units ("m" for metres and "m^2"), which requires conversion to US customary units. |
e882ab67-0b22-4f9e-8187-226b34a51a4e |
Localize | Spelling (AU-US) | Question
How does understanding the unit circle relate to predicting sine curve behaviour?
Hint: Use the y-coordinate of points on the unit circle.
Answer:
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Question
How does understanding the unit circle relate to predicting sine curve behavior?
Hint: Use the y-coordinate of points on the unit circle.
Answer:
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Classifier: Contains the AU spelling "behaviour", which requires conversion to the US spelling "behavior". Verifier: The question text contains the AU spelling "behaviour", which must be localized to "behavior". |
f1524e6d-7799-42f1-9b45-e93b9be9b754 |
Localize | Terminology | Question
Why is finding the highest common factor useful when writing fractions in simpler form?
Answer:
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Question
Why is finding the greatest common factor useful when writing fractions in simplest form?
Answer:
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Classifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US equivalent is "greatest common factor" (GCF). Verifier: The term "highest common factor" is the standard AU/UK term, whereas "greatest common factor" is used in the US. This requires localization for school context. |
f77b1ce8-827b-4437-bcc5-5ef89c669216 |
Localize | Units (simple) | Question
What makes height numerical data?
Answer:
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Question
What makes height numerical data?
Answer:
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Classifier: The answer text contains metric units ("cm"), which triggers a mandatory RED classification for units conversion. Verifier: The answer text contains metric units ("cm"), which requires localization for a US audience. |
f9faa71b-ec6c-48b0-834a-c1e5f0abe26c |
Localize | Spelling (AU-US) | Question
How does understanding the behaviour near asymptotes help predict values of $y$ for very large $x$ values in a rectangular hyperbola?
Answer:
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Question
How does understanding the behavior near asymptotes help predict values of $y$ for very large $x$ values in a rectangular hyperbola?
Answer:
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Classifier: The text contains the AU spelling "behaviour", which requires conversion to the US spelling "behavior". Verifier: The text contains the AU spelling "behaviour", which requires conversion to the US spelling "behavior". |
f6cbccb6-b22b-43fc-a0b6-7f9ac897296c |
Localize | Spelling (AU-US) | Question
How does understanding conjugates relate to simplifying radicals?
Hint: Multiply by the conjugate to rationalise the denominator.
Answer:
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Question
How does understanding conjugates relate to simplifying radicals?
Hint: Multiply by the conjugate to rationalize the denominator.
Answer:
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Classifier: The hint contains the AU spelling "rationalise", which requires conversion to the US spelling "rationalize". Verifier: The hint contains the AU spelling "rationalise", which requires localization to "rationalize". |
e8qG9E4IR6WHckXpdtuW |
Localize | Units (simple) | Multiple Choice
The displacement function of a particle is given by $s(t)=t^2+6t+8$ m for $t\geq0$ in seconds.
How many times does the given particle change its direction?
Options:
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Multiple Choice
The displacement function of a particle is given by $s(t)=t^2+6t+8$ ft for $t\geq0$ in seconds.
How many times does the given particle change its direction?
Options:
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Classifier: The text contains the metric unit 'm' (metres) for displacement, which requires localization to US customary units (e.g., feet). Verifier: The text contains the metric unit 'm' (metres) for displacement. Although it is part of a function $s(t)$, the conversion is simple as it only labels the output unit and does not require re-calculating coefficients within the quadratic expression to maintain physical meaning in a different system (unlike gravity-based equations). |
f8mmJrbC6NJGIE6xZoX3 |
Localize | Units (simple) | Question
An object moves with the velocity function $v(t)=7t+5$ cm s$^{-1}$, $t\geq0$.
Find the average acceleration of the object from $t=3$ to $t=8$ seconds.
Answer:
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Question
An object moves with the velocity function $v(t)=7t+5$ in s$^{-1}$, $t\geq0$.
Find the average acceleration of the object from $t=3$ to $t=8$ seconds.
Answer:
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Classifier: The text contains metric units ("cm s^-1" and "cm/s^2") which require localization to US customary units or a decision on metric usage in US physics/math contexts. Per decision rules, any metric unit triggers a RED category. Verifier: The text contains metric units ("cm s^-1" and "cm/s^2"). While it involves a linear function, the conversion is a simple numeric change to the coefficient and suffix, fitting simple_conversion. |
f9ddbce9-8cd2-4682-b8b3-571f20d2c22d |
Localize | Spelling (AU-US) | Question
What makes log scales different from regular scales in histograms?
Hint: Visualise how the scale transforms data.
Answer:
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Question
What makes log scales different from regular scales in histograms?
Hint: Visualize how the scale transforms data.
Answer:
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Classifier: The text uses "visualise" in the hint, but wait—actually, looking closely at the source value: "Visualise how the scale transforms data." This is AU spelling. However, the heuristic bucket suggested GREEN and I must check the source text carefully. "Visualise" is AU spelling (US is "visualize"). Correction: The source value for the hint is "Visualise how the scale transforms data." This contains AU spelling. Verifier: The primary classifier correctly identified "Visualise" as AU spelling in its rationale but incorrectly assigned the GREEN category leaf. "Visualise" requires localization to "Visualize". |
f994d6bb-3d8d-4791-b936-044c7f630791 |
Localize | Spelling (AU-US) | Question
What makes $r^2$ represent the squared radius in the circle $(x-h)^2+(y-k)^2=r^2$?
Answer:
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Question
What makes $r^2$ represent the squared radius in the circle $(x-h)^2+(y-k)^2=r^2$?
Answer:
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Classifier: The answer content contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The answer content contains the AU spelling "centre", which needs to be localized to the US spelling "center". |
fEGtu5fe6XKnZQsjspIn |
Localize | Units (simple) | Multiple Choice
What are the correct dimensions of a rectangle with an area of $36$ cm$^2$ and a perimeter of $40$ cm?
Options:
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Multiple Choice
What are the correct dimensions of a rectangle with an area of $36$ in$^2$ and a perimeter of $40$ in?
Options:
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Classifier: The text contains metric units ("cm" and "cm^2") which require conversion to US customary units (e.g., inches). Verifier: The text contains metric units ("cm" and "cm^2") which require conversion to US customary units. The conversion is a straightforward numeric change for dimensions, fitting simple_conversion. |
fV4azUe8igSyK8DyoiEI |
Localize | Answer set | Multiple Choice
Which of the following is a season?
Options:
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Multiple Choice
Which of the following is a season?
Options:
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Classifier: The answer set contains "Autumn", which is the standard AU term. In a US context, "Fall" is the preferred/standard term for the season, requiring localization for consistency with US curriculum standards. Verifier: The answer choice "Autumn" is the standard term in AU, whereas "Fall" is the primary term used in US educational contexts for seasons. This requires localization for consistency. |
fbfe5830-6290-4672-987c-a92acf21261a |
Localize | Answer set | Question
How does knowing the area formula for a trapezium help in solving geometry problems?
Answer:
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Question
How does knowing the area formula for a trapezoid help in solving geometry problems?
Answer:
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Classifier: The text uses the term "trapezium". In the US, this shape is called a "trapezoid". This is a specific terminology difference in a school geometry context. Verifier: The term "trapezium" is used, which is the standard term in Australia/UK, whereas "trapezoid" is used in the US. This requires localization in a school geometry context. |
gFDnXertBVJgKsLGweqT |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
$(x-3)(x^2+3x+9)=0$ is a cubic equation in factorised form.
Options:
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Multiple Choice
True or false:
$(x-3)(x^2+3x+9)=0$ is a cubic equation in factored form.
Options:
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Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
fv4JKnsZu7WQPZPnFDjH |
Localize | Units (simple) | Question
An object moves in a straight line and its displacement function is given by $s(t)=t^2-t$ m for $0\leq t\leq 12$ s.
Find the instantaneous velocity at $t=3$ seconds.
Answer:
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Question
An object moves in a straight line and its displacement function is given by $s(t)=t^2-t$ ft for $0\leq t\leq 12$ s.
Find the instantaneous velocity at $t=3$ seconds.
Answer:
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Classifier: The question explicitly uses metric units "m" (metres) and "m/s" (metres per second). Per the decision rules, any metric unit requires classification as RED.units_simple_conversion at minimum. Verifier: The question contains metric units "m" (metres) and "m/s" (metres per second). According to the decision rules, any metric unit requires at least RED.units_simple_conversion. |
ff9b3df8-20ff-499f-b1ef-b7ec5fb86691 |
Localize | Spelling (AU-US) | Question
Why must a perpendicular bisector cross a line segment at its midpoint and at a $90^\circ$ angle?
Hint: Visualise the line splitting into halves at a right angle.
Answer:
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Question
Why must a perpendicular bisector cross a line segment at its midpoint and at a $90^\circ$ angle?
Hint: Visualize the line splitting into halves at a right angle.
Answer:
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Classifier: The hint contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint contains the AU/UK spelling "Visualise", which requires localization to the US spelling "Visualize". |
hxdGgjkgHAmwjuxg1JCN |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Activity networks do not have any labelled vertices.
Options:
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Multiple Choice
True or false:
Activity networks do not have any labeled vertices.
Options:
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Classifier: The word "labelled" contains the AU/UK double-l spelling; the US standard is "labeled". Verifier: The word "labelled" is the AU/UK spelling; the US standard is "labeled". Per rule 1, AU spelling requires RED classification. |
gK9Bb6JpPNPuDsKVg2XQ |
Localize | Units (simple) | Question
A sector-shaped garden has a curved path of $40$ m and a radius of $18$ m.
What is its perimeter?
Answer:
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Question
A sector-shaped garden has a curved path of $40$ ft and a radius of $18$ ft.
What is its perimeter?
Answer:
|
Classifier: The text contains the metric unit "m" (metres) in the context of measurement, which requires conversion to US customary units (feet/yards). Verifier: The text contains the metric unit "m" (metres) in the context of measurement (garden path and radius), which requires conversion to US customary units. The calculation is a simple sum (Perimeter = path + 2*radius), so simple conversion is appropriate. |
gx2Ojm7A8yZjnmOhsmdk |
Localize | Units (simple) | Question
Find the area of a circle whose circumference is $44$ cm.
Answer:
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Question
Find the area of a circle whose circumference is $44$ in.
Answer:
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Classifier: Contains metric units ("cm" and "cm^2") which require localization for a US audience. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. This is a simple conversion as it involves a single geometric calculation. |
h3WcvzLHdfodAcbgLgIm |
Localize | Spelling (AU-US) | Question
Fill in the blank.
The angle measured anti-clockwise from the positive $x$-axis to the point $(0,1)$ on the unit circle is $[?]$ degrees.
Answer:
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Question
Fill in the blank.
The angle measured counterclockwise from the positive $x$-axis to the point $(0,1)$ on the unit circle is $[?]$ degrees.
Answer:
|
Classifier: The term "anti-clockwise" is the standard AU/UK spelling and terminology; the US equivalent is "counterclockwise". Verifier: The term "anti-clockwise" is the standard AU/UK spelling/terminology; the US equivalent is "counterclockwise". Per rule 1, AU spelling/terminology requires RED classification. |
gT3zC5dJk403ZrmgQkkD |
Localize | Answer set | Multiple Choice
Which statement is true about a trapezium?
Options:
|
Multiple Choice
Which statement is true about a trapezoid?
Options:
|
Classifier: The term "trapezium" in AU/UK refers to a quadrilateral with one pair of parallel sides. In the US, this is called a "trapezoid". This requires a terminology change in both the question and the logic of the answer set. Verifier: The term "trapezium" (AU/UK) refers to a shape with one pair of parallel sides, which is called a "trapezoid" in the US. This is a significant terminology difference that affects the logic of the question and answer set. |
ggYamrprfoBXfgBrFJIH |
Localize | Units (simple) | Question
A circular pizza has a diameter of $30$ cm. There is a circular hole at the centre of the pizza with a diameter of $4$ cm.
What is the area of the pizza, excluding the hole?
Answer:
|
Question
A circular pizza has a diameter of $30$ in. There is a circular hole at the center of the pizza with a diameter of $4$ in.
What is the area of the pizza, excluding the hole?
Answer:
|
Classifier: Contains metric units (cm, cm^2) and AU spelling (centre). Units conversion is the higher priority classification. Verifier: The text contains the metric unit "cm" and the AU spelling "centre". Per rule 5, units conversion is the higher priority classification. |
gNhCXJ8fEiBMx3uY7xwg |
Localize | Units (simple) | Multiple Choice
What is the radius of a circle with a circumference of $4$ cm, rounded to one decimal place?
Options:
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Multiple Choice
What is the radius of a circle with a circumference of $4$ in, rounded to one decimal place?
Options:
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Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units (e.g., inches) or a change in pedagogy for a US audience. Verifier: The text contains the metric unit "cm" (centimetres) in both the question and the answers, which requires conversion for US localization. |
hK61rDKUGeN0VIO8kFEU |
Localize | Units (simple) | Multiple Choice
Choose the correct metric unit with its corresponding measure.
Options:
|
Multiple Choice
Choose the correct US customary unit with its corresponding measure.
Options:
|
Classifier: The text explicitly mentions "metric unit" and "grams". While it also mentions US customary units (miles, yards, pound), the presence of "grams" and the pedagogical focus on identifying metric units requires localization review for US standards. Verifier: The question explicitly uses the term "metric unit" and includes "grams" as an answer choice. While it also lists US customary units, the pedagogical focus on identifying metric units requires localization review for US standards. |
gmRr9ulNURXZDtniezqI |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
The prime factorisation of $12$ is $[?]$.
Options:
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Multiple Choice
Fill in the blank:
The prime factorization of $12$ is $[?]$.
Options:
|
Classifier: Contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: Contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". |
i2pk7uC7PQMi6Waj1QHP |
Localize | Units (complex) | Question
A particle has velocity function $v(t)=6t^2+4t+1$ cm/s for time $t\geq 0$.
Find the change in position of the particle from $t=4$ to $t=8$ seconds.
Answer:
|
Question
A particle has velocity function $v(t)=6t^2+4t+1$ in/s for time $t\geq 0$.
Find the change in position of the particle from $t=4$ to $t=8$ seconds.
Answer:
|
Classifier: Contains metric units "cm/s" in the question and "m" in the suffix field. This requires conversion to US customary units. Verifier: The question defines a velocity function v(t) in metric units (cm/s) and asks for a change in position (integration). Per rule 4, equations defining quantities in metric require RED.units_complex_converted classification. Additionally, there is a unit mismatch in the source (cm/s vs m) which further necessitates complex review. |
grfkxpc2oNHt1Qcn24SH |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following correctly splits the middle term in $2x^2 - 5x -3$ so it can be factorised by grouping?
Options:
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Multiple Choice
Which of the following correctly splits the middle term in $2x^2 - 5x -3$ so it can be factored by grouping?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains the AU spelling "factorised", which requires localization to the US spelling "factorized". |
gPEo1ww70EW5eHswUqiS |
Localize | Units (simple) | Question
Location coordinates are given as:
Point $X$ $=42^\circ{N},170^\circ{E}$
Point $Y$ $=60^\circ{N},170^\circ{E}$
What is the shortest distance between the two points, where the radius of the Earth is $6400$ km?
Answer:
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Question
Location coordinates are given as:
Point $X$ $=42^\circ{N},170^\circ{E}$
Point $Y$ $=60^\circ{N},170^\circ{E}$
What is the shortest distance between the two points, where the radius of the Earth is $6400$ miles?
Answer:
|
Classifier: The text uses "km" (kilometres) for the radius of the Earth and the resulting distance, which is a metric unit requiring conversion for US localization. Verifier: The question uses "km" (kilometres) for the radius of the Earth and the distance, which is a metric unit requiring conversion. |
hqgS58xZ5NEXyM0xPGEq |
Localize | Units (simple) | Multiple Choice
What are the correct dimensions of a rectangle that has an area of $36$ cm$^2$ and a perimeter of $26$ cm?
Options:
|
Multiple Choice
What are the correct dimensions of a rectangle that has an area of $36$ in$^2$ and a perimeter of $26$ in?
Options:
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Classifier: The text contains metric units (cm and cm^2) which require conversion to US customary units (e.g., inches) for US localization. Verifier: The question and answers contain metric units (cm and cm^2) which require conversion for US localization. |
ghgkvlKn4lODiXUhEKXc |
Localize | Units (complex) | Multiple Choice
An object starts from point $O$ and moves with velocity $v(t)=5t^2+4$ m/s.
Find the position of the object with respect to point $O$ at $t=1$ s.
Hint: Find the instantaneous velocity at $t=6$ s and use its sign to find its position.
Options:
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Multiple Choice
An object starts from point $O$ and moves with velocity $v(t)=5t^2+4$ ft/s.
Find the position of the object with respect to point $O$ at $t=1$ s.
Hint: Find the instantaneous velocity at $t=6$ s and use its sign to find its position.
Options:
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Classifier: Contains metric units (m/s). Any metric unit requires at least simple conversion category. Verifier: The question contains a velocity function defined in metric units: v(t)=5t^2+4 m/s. According to rule 4, equations defining quantities in metric require RED.units_complex_converted rather than simple conversion. |
hRlTtN0kwjxfZsBJyGLt |
Localize | Spelling (AU-US) | Multiple Choice
Which among the following semicircles does not have its centre at $(-5,3)$ and a radius of $5$ units?
Options:
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Multiple Choice
Which of the following semicircles does not have its center at $(-5,3)$ and a radius of $5$ units?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to "center" for a US audience. Verifier: The text contains the AU spelling "centre", which requires localization to "center" for the US locale. |
h4O362IR6OnLddmGvSHG |
Localize | Units (simple) | Multiple Choice
A rectangle is $4$ cm wide and $3x - 2$ cm long.
The area of the rectangle must be $18$ cm$^2$ or less.
What are the possible values of $x$ in cm, for $x > 1$?
Options:
|
Multiple Choice
A rectangle is $4$ in wide and $3x - 2$ in long.
The area of the rectangle must be $18$ in$^2$ or less.
What are the possible values of $x$ in in, for $x > 1$?
Options:
|
Classifier: The question uses metric units ("cm" and "cm^2") which require localization to US customary units (e.g., inches). Verifier: The question uses metric units ("cm" and "cm^2") which require localization to US customary units. It is a simple conversion as it involves a basic rectangle area calculation. |
heyZnueOxdwB73wulapT |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
$100x^2y-50y^2x+10xy$ in fully factorised form is given by $[?]$.
Options:
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Multiple Choice
Fill in the blank:
$100x^2y-50y^2x+10xy$ in fully factored form is given by $[?]$.
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: Contains the AU spelling "factorised", which requires localization to "factorized". |
goi0xwcKRzaz8kTJAew9 |
Localize | Units (simple) | Question
A city had $1050$ mm of rainfall in $2020$.
Due to climate change, rainfall in $2030$ is expected to increase by $456$ mm.
What is the total expected rainfall in $2030$?
Answer:
|
Question
A city had $1050$ in of rainfall in $2020$.
Due to climate change, rainfall in $2030$ is expected to increase by $456$ in.
What is the total expected rainfall in $2030$?
Answer:
|
Classifier: The text contains the metric unit "mm" (millimetres) for rainfall, which requires localization for a US audience. Verifier: The text contains the metric unit "mm" (millimetres), which requires localization for a US audience. |
i2QUB4EkBZvFNVgjFdYx |
Localize | Units (complex) | Multiple Choice
An object moves with the velocity function $v(t)=7t^4+5t^3$ cm s$^{-1}$, $t\geq0$.
Find the acceleration function for this object.
Options:
|
Multiple Choice
An object moves with the velocity function $v(t)=7t^4+5t^3$ in s$^{-1}$, $t\geq0$.
Find the acceleration function for this object.
Options:
|
Classifier: Contains metric units "cm" and "m" in the context of velocity and acceleration functions. Verifier: The question involves a velocity function v(t) defined in metric units (cm s^-1). According to rule 4, equations defining quantities in metric or requiring the derivation of related functions (acceleration from velocity) in metric should be classified as RED.units_complex_converted to ensure human review of the mathematical consistency after unit conversion. |
gbDTGY9y4pE9KDY9NFYv |
Localize | Terminology | Question
Write the equation $24x - 15y = 8$ in gradient-intercept form.
Simplify where possible.
Options:
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Question
Write the equation $24x - 15y = 8$ in slope-intercept form.
Simplify where possible.
Options:
|
Classifier: The term "gradient-intercept form" is the standard AU term for what is called "slope-intercept form" in the US. Verifier: The term "gradient-intercept form" is the specific Australian curriculum terminology for what is known as "slope-intercept form" in the US. |
iQngfsrQIsrSjhmR0DvU |
Localize | Spelling (AU-US) | Multiple Choice
Write the number $8546$ in words.
Options:
|
Multiple Choice
Write the number $8546$ in words.
Options:
|
Classifier: The answer choice "Eight thousand five hundred and forty-six" uses the "and" conjunction after "hundred", which is standard in AU/UK English but typically omitted in US English number-to-word conversion (e.g., "Eight thousand five hundred forty-six"). While often considered a stylistic preference, in a school context, this is a specific dialectal difference in how numbers are written out. Verifier: The answer choice "Eight thousand five hundred and forty-six" includes the conjunction "and" after "hundred", which is a specific convention in AU/UK English for writing numbers in words, whereas US English typically omits it. This constitutes a dialectal spelling/formatting difference. |
iED0J9qo03IJIYinLFOT |
Localize | Terminology | Question
At a birthday party, there were $63$ fizzers, $52$ sour straps and $71$ snake lollies.
How many lollies were there in total?
Answer:
|
Question
At a birthday party, there were $63$ pieces of taffy, $52$ sour strips and $71$ gummy snakes.
How many pieces of candy were there in total?
Answer:
|
Classifier: The term "lollies" is highly specific to Australian/British English for candy. Additionally, "fizzers" and "sour straps" are specific types of confectionery common in AU but not standard in US math problems. Verifier: The term "lollies" is a distinct Australian/British term for candy/sweets. "Fizzers", "sour straps", and "snake lollies" are also specific confectionery items common in the AU school/social context. |
iOqIkjvWv0MjasGqIuy4 |
Localize | Terminology | Multiple Choice
True or false:
The cubic equation $(x-1)^3+9=0$ is written in point of inflection form.
Options:
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Multiple Choice
True or false:
The cubic equation $(x-1)^3+9=0$ is written in inflection point form.
Options:
|
Classifier: The term "point of inflection form" for a cubic equation is specific to the Australian curriculum (referring to $y = a(x-h)^3 + k$). In the US, this is typically referred to as "vertex form" or "standard form" of a transformed cubic, or simply described by its transformations. Verifier: The phrase "point of inflection form" is a specific pedagogical term used in the Australian curriculum for cubic functions. In the US, this is typically referred to as "vertex form" or described via transformations. |
iSk9YFdplf7VamyIRNgx |
Localize | Units (simple) | Question
The radioactive material Thorium decays at a rate of $5\%$ per minute.
How much of $20$ grams of Thorium would remain after $5$ minutes?
Answer:
|
Question
The radioactive material Thorium decays at a rate of $5\%$ per minute.
How much of $20$ ounces of Thorium would remain after $5$ minutes?
Answer:
|
Classifier: The text contains the metric unit "grams". According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "grams". Per the decision rules, any metric unit requires a RED classification. Since it is a single value used in a simple decay formula, simple_conversion is appropriate. |
iY6j4FtKe3PZR4FQeBHl |
Localize | Terminology | Multiple Choice
True or false:
The turning point form of $y=5x^2-10x+13$ is given by $y=5(x-1)^2-18$.
Options:
|
Multiple Choice
True or false:
The vertex form of $y=5x^2-10x+13$ is given by $y=5(x-1)^2-18$.
Options:
|
Classifier: The term "turning point form" is standard in AU/UK curricula, whereas the US equivalent is "vertex form". Verifier: The term "turning point form" is the standard Australian/UK term for what is known as "vertex form" in the US. This requires localization for terminology. |
ioT3v5PNvJgGtYEM3LTd |
Localize | Units (simple) | Question
Express $15$ g in kilograms.
Answer:
|
Question
Express $15$ oz in pounds.
Answer:
|
Classifier: The question explicitly asks for a conversion between metric units (grams to kilograms). Per the decision rules, any metric unit requires classification into a RED.units category. Verifier: The question involves metric units ("g", "kilograms", "kg"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. Since it is a straightforward numeric conversion, simple_conversion is correct. |
iakYDSQHM7rsG2mepvuz |
Review | Uncertain | Question
Kate takes a holiday loan of $\$3500$ which has to be paid back in fortnightly installments for 3 years.
Calculate the flat interest rate to be paid per annum if she pays a total interest of $\$1575$.
Answer:
|
Question
Kate takes a vacation loan of $\$3500$ which has to be paid back in biweekly installments for 3 years.
Calculate the flat interest rate to be paid per year if she pays a total interest of $\$1575$.
Answer:
|
Classifier: The term "fortnightly" is very common in AU but rare in US educational contexts (where "every two weeks" or "bi-weekly" is preferred). Additionally, "flat interest rate" is a specific financial term that may require pedagogical alignment, though the math is universal. Verifier: The term "fortnightly" is highly characteristic of AU/UK English and is rarely used in US educational contexts, where "every two weeks" is preferred. "Flat interest rate" is also a specific term that may vary in pedagogical usage. |
iy32HskmTn8HwJhkDv2E |
Localize | Spelling (AU-US) | Question
What is $x(x-1)-1(x-1)$ in factorised form?
Options:
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Question
What is $x(x-1)-1(x-1)$ in factored form?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
ih6g0NtAtL6Nqq37E4Xd |
Localize | Units (simple) | Question
An object moves in a straight line and its velocity after $t$ seconds is given by $v(t)=t^2+t$ m/s for $0\leq t\leq 12$ s.
Find the average acceleration for the first four seconds.
Answer:
|
Question
An object moves in a straight line and its velocity after $t$ seconds is given by $v(t)=t^2+t$ ft/s for $0\leq t\leq 12$ s.
Find the average acceleration for the first four seconds.
Answer:
|
Classifier: The text contains multiple metric units (m/s, s, m/s^2) which require conversion for US localization. Verifier: The question contains metric units (m/s, s, m/s^2) which require conversion for US localization. Although it contains a function v(t), the conversion is a simple numeric change to the coefficients/result rather than a complex re-derivation of a physical constant like gravity. |
iyCJzk7VbWRqbTVsD7j4 |
Localize | Units (simple) | Question
$4$ equal wires are joined to make a new wire of length $44$ cm.
What is the length of each smaller wire?
Answer:
|
Question
$4$ equal wires are joined to make a new wire of length $44$ in.
What is the length of each smaller wire?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) in both the content and the suffix, which requires conversion to US customary units. Verifier: The question contains the metric unit "cm" (centimetres) in the content and suffix, requiring conversion to US customary units. |
j8AUkymHXdXDw9sljw4M |
Localize | Units (simple) | Question
A wheel of radius $35$ cm is rolled.
How far will it move after $10$ rotations?
Answer:
|
Question
A wheel of radius $35$ in is rolled.
How far will it move after $10$ rotations?
Answer:
|
Classifier: The question contains the metric unit 'cm' (centimetres), which requires conversion for US localization. Verifier: The question contains the metric unit 'cm' (centimetres) in both the content and the suffix, which requires conversion for US localization. It is a simple conversion as it involves a single unit-bearing value and a straightforward calculation. |
jYj7RiA0CskRQn2VzSWo |
Localize | Spelling (AU-US) | Question
Factorise $5x+15$
Answer:
|
Question
Factor $5x+15$
Answer:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling. In the US, "Factorize" is used (though often just "Factor" is preferred in this context, the spelling change is the primary trigger). Verifier: The word "Factorise" uses the AU/UK 's' spelling, which requires localization to "Factor" or "Factorize" for the US locale. |
iwUGORdgXKojB2JDjbxP |
Localize | Units (simple) | Question
I travel at an average speed of $60$ km/h for $2.5$ hours.
What is my total distance travelled?
Answer:
|
Question
I travel at an average speed of $60$ mph for $2.5$ hours.
What is my total distance traveled?
Answer:
|
Classifier: Contains metric units "km/h" and "km" which require conversion to US customary units (mph and miles) and also contains the AU spelling "travelled" (US: traveled). Per decision rules, units conversion takes precedence. Verifier: The question contains metric units "km/h" and "km" which require conversion to US customary units. It also contains the AU spelling "travelled". Units conversion is the most impactful change. |
jSLowtmMhDYknqokmM0S |
Localize | Terminology | Multiple Choice
If $f(x)=x(x-a)^2$, then $x=-a$ is a turning point.
Options:
|
Multiple Choice
If $f(x)=x(x-a)^2$, then $x=-a$ is a vertex.
Options:
|
Classifier: The term "turning point" is used, which is standard AU/UK terminology for what is typically called a "vertex" or "critical point" in US school mathematics. Verifier: The term "turning point" is used, which is standard AU/UK terminology for what is typically called a "vertex" or "critical point" in US school mathematics. |
j0QiI09coGfhZPErNq2d |
Localize | Spelling (AU-US) | Question
Factorise $x^3 + 9 x^2 + 27 x + 27$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Question
Factor $x^3 + 9 x^2 + 27 x + 27$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Classifier: The text uses the AU/UK spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU/UK spelling. Rule 1 states AU spelling ALWAYS requires RED classification. |
jFz03fxClHctdd03PqIf |
Localize | Units (simple) | Question
Annabella is making a rectangular storage room in her attic. The storage room has a length of $10$ m, a width of $9$ m, and a height of $8$ m.
What is the volume of the storage room?
Answer:
|
Question
Annabella is making a rectangular storage room in her attic. The storage room has a length of $10$ ft, a width of $9$ ft, and a height of $8$ ft.
What is the volume of the storage room?
Answer:
|
Classifier: The text contains multiple instances of metric units ("m" for meters and "m$^3$" for cubic meters) which require conversion for US localization. Verifier: The question contains metric units (m, m^3) which require conversion for US localization. The conversion is a simple volume calculation. |
jKaBT3AUeRW6cVL1jJMx |
Localize | Spelling (AU-US) | Multiple Choice
Write $41002$ in words.
Options:
|
Multiple Choice
Write $41002$ in words.
Options:
|
Classifier: The use of "and" in the word form of numbers (e.g., "thousand and two") is standard in AU/UK English but typically omitted in US English pedagogy for whole numbers. While often considered a style choice, in a school context, US students are taught not to use "and" except for the decimal point. Verifier: The use of "and" in whole number word forms (e.g., "thousand and two") is a specific convention taught in AU/UK schools that differs from US pedagogy (where "and" is reserved for decimals). This constitutes a spelling/convention change for the target locale. |
jnRoXq5liHZEy9UJSef9 |
Localize | Cultural refs | Question
How many $10$ cents coins are there in $\$3.20$ ?
Answer:
|
Question
How many dimes are there in $\$3.20$ ?
Answer:
|
Classifier: The question uses "10 cents coins". While the dollar sign is shared, the phrasing and specific denomination context often refers to the Australian 10-cent piece. In a US context, this would typically be referred to as a "dime". However, since it is a currency context and not a metric unit, RED.cultural_reference is the most appropriate fit. Verifier: The phrasing "10 cents coins" refers to a specific denomination context (AU 10-cent piece) which differs from the US "dime". |
jiakDWyKF7ow7mzmrafN |
Localize | Terminology | Multiple Choice
Which of the following is the equation of a quartic with turning point $(0,1)$?
Options:
|
Multiple Choice
Which of the following is the equation of a quartic with vertex $(0,1)$?
Options:
|
Classifier: The term "turning point" is standard AU terminology for what is referred to as a "vertex" in US mathematics curriculum. Verifier: The term "turning point" is the standard AU term for what is called a "vertex" in the US curriculum. This requires localization for terminology. |
jo9ErLkHqJeVvQBdRep0 |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
The expression $x^{2}+2x-24$ can be factorised by completing the square.
Options:
|
Multiple Choice
True or false:
The expression $x^{2}+2x-24$ can be factored by completing the square.
Options:
|
Classifier: The text contains the AU spelling "factorised", which requires conversion to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
jmUTB4ICp2BambtbD5kJ |
Localize | Units (simple) | Question
A solid is formed by removing a $90^\circ$ section from a cylinder with a $5$ m radius and a $2$ m height.
What is the volume of the solid, correct to one decimal place?
Answer:
|
Question
A solid is formed by removing a $90^\circ$ section from a cylinder with a $5$ ft radius and a $2$ ft height.
What is the volume of the solid, correct to one decimal place?
Answer:
|
Classifier: The question contains metric units ("m" for meters and "m^3" for cubic meters) which require conversion to US customary units. Verifier: The question contains metric units ("m" and "m^3") which require conversion to US customary units. |
kTxUxUwlLKnxfVMc0zUi |
Localize | Units (simple) | Question
A $6$ m ladder leans against a wall and makes an angle of $60^\circ$ with the ground.
Calculate the distance between the foot of the ladder and the wall.
Answer:
|
Question
A $6$ ft ladder leans against a wall and makes an angle of $60^\circ$ with the ground.
Calculate the distance between the foot of the ladder and the wall.
Answer:
|
Classifier: The text contains the metric unit "m" (metres) in the context of a measurement ("6 m ladder"), which requires conversion for US localization. Verifier: The question uses "m" (metres) as a unit of measurement for the ladder length and distance, which requires conversion for US localization. |
kYghW5qSG0Nv0CUQIb8s |
Localize | Spelling (AU-US) | Question
Given the number $111$, find the number of distinct prime factors it has using its prime factorisation.
Answer:
|
Question
Given the number $111$, find the number of distinct prime factors it has using its prime factorization.
Answer:
|
Classifier: Contains the AU spelling "factorisation", which needs to be converted to the US spelling "factorization". Verifier: Contains "factorisation", which is the AU/UK spelling. US spelling is "factorization". |
jrNn5L5sK9ctQaPdkVZj |
Localize | Units (simple) | Question
A box has a length of $12$ m and a breadth that is $5$ m less than its height.
What is the volume $V$ of the box?
Options:
|
Question
A box has a length of $12$ ft and a width that is $5$ ft less than its height.
What is the volume $V$ of the box?
Options:
|
Classifier: The question contains metric units ("m" for metres and "m^3" for cubic metres) and the term "breadth" (often "width" in US, though breadth is used). Per rule 1, any metric unit prevents a GREEN classification. Verifier: The question uses metric units ("m" and "m^3"), which requires RED classification. The conversion is simple as it involves algebraic expressions rather than complex re-derivation of coefficients. |
kjjJYELwFhEi4ViHsJoh |
Localize | Spelling (AU-US) | Question
Sarah has $6$ pairs of earrings and $5$ watches.
If she wears both a pair of earrings and a watch, how many jewellery combinations can she wear?
Answer:
|
Question
Sarah has $6$ pairs of earrings and $5$ watches.
If she wears both a pair of earrings and a watch, how many jewelry combinations can she wear?
Answer:
|
Classifier: Contains the AU spelling "jewellery", which must be localized to the US spelling "jewelry". Verifier: The word "jewellery" is the AU/British spelling and must be localized to "jewelry" for the US. |
lNZL2CZiiZ7Gbd8t4rYV |
Localize | Units (simple) | Question
$5$ identical squares are to be made from a $60$ cm string.
What is the length of each side of the square?
Answer:
|
Question
$5$ identical squares are to be made from a $60$ in string.
What is the length of each side of the square?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) in both the content and the suffix field, which requires conversion for US localization. Verifier: The question contains the metric unit "cm" (centimetres) in both the content and the suffix, requiring simple conversion for US localization. |
mHcABKUAfKMfwASmlVNY |
Localize | Units (simple) | Question
Convert $3.9$ kg into grams.
Answer:
|
Question
Convert $3.9$ lb into ounces.
Answer:
|
Classifier: Contains metric units "kg" and "grams" which require conversion or localization for a US audience. Verifier: Contains metric units "kg" and "grams" (and "g" in suffix) which require conversion for US localization. |
mJi8m2CQXiXsbRhA6Mjk |
Localize | Units (simple) | Question
Find the smallest distance between the centre of the circle of radius $12$ cm and a chord of length $18$ cm.
Answer:
|
Question
Find the smallest distance between the center of the circle of radius $12$ in and a chord of length $18$ in.
Answer:
|
Classifier: Contains both AU spelling ("centre") and metric units ("cm"). Units conversion takes precedence over spelling. Verifier: Contains both AU spelling ("centre") and metric units ("cm"). Per rule 5, units conversion takes precedence. |
kcMl4c6nVDOcBhIzkXCy |
Localize | Units (simple) | Question
An island on a map is shaped like a sector of a circle with a radius of $1$ cm and a central angle of $60^\circ$.
What is the area of the island on the map?
Answer:
|
Question
An island on a map is shaped like a sector of a circle with a radius of $1$ in and a central angle of $60^\circ$.
What is the area of the island on the map?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2") which require localization to US customary units or a decision on metric usage in US curriculum. Per rules, any metric unit triggers a RED category. Verifier: The question contains metric units ("cm" and "cm^2"), which requires RED classification per the decision rules. |
lK3WOLvYKeksHr2IfRj8 |
Localize | Terminology | Question
Find the gradient of the line segment joining the points $(2,5)$ and $(-3,6)$.
Express the answer as a fraction in its simplest form.
Options:
|
Question
Find the slope of the line segment joining the points $(2,5)$ and $(-3,6)$.
Express the answer as a fraction in its simplest form.
Options:
|
Classifier: In Australian mathematics, "gradient" is the standard term for the steepness of a line, whereas the US curriculum almost exclusively uses "slope" in this context. Verifier: The term "gradient" is the standard AU term for the steepness of a line, whereas "slope" is used in the US. |
mYgxUpJR3rGK14nGUcsU |
Localize | Terminology | Multiple Choice
Fill in the blank:
The highest or lowest point on the graph of a parabola is called the $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The highest or lowest point on the graph of a parabola is called the $[?]$.
Options:
|
Classifier: The text uses "Turning point" as a primary answer choice for the vertex of a parabola, which is a specific AU/UK school term. Additionally, the answer choice "Centre" uses AU spelling. Terminology takes precedence over spelling. Verifier: Contains AU spelling "Centre" and the specific AU/UK school term "Turning point" for the vertex of a parabola. |
lR3KBHQC6cV5vz2qh4JI |
Localize | Units (simple) | Question
Two cuboids of lengths and widths $5$ cm each are placed over one another.
If the height of each cuboid is $2.5$ cm, what is the total surface area of the resulting shape?
Answer:
|
Question
Two rectangular prisms of lengths and widths $5$ in each are placed over one another.
If the height of each rectangular prism is $2.5$ in, what is the total surface area of the resulting shape?
Answer:
|
Classifier: Contains metric units ("cm" and "cm^2") which require conversion to US customary units. Verifier: The question uses metric units ("cm" and "cm^2") which require conversion for a US audience. The conversion is simple as it involves basic geometric dimensions and a single numeric answer. |
lQMSGe2LttoYESAhRN9E |
Localize | Spelling (AU-US) | Question
In a neighbourhood of $40$ households, $13$ own only a cat and $7$ own both a cat and a dog.
If $10$ households own neither a cat nor a dog, how many own only a dog?
Answer:
|
Question
In a neighborhood of $40$ households, $13$ own only a cat and $7$ own both a cat and a dog.
If $10$ households own neither a cat nor a dog, how many own only a dog?
Answer:
|
Classifier: Contains the AU spelling "neighbourhood", which needs to be converted to the US spelling "neighborhood". Verifier: The text contains the AU spelling "neighbourhood", which requires localization to the US spelling "neighborhood". |
l73yN60t4EV6StZpB0pE |
Localize | Spelling (AU-US) | Question
Susan has an $18\%$ stake in an organisation that earned a profit of $\$75620$ in a year.
How much of the organisation's profit is Susan entitled to?
Give your answer to the nearest dollar.
Answer:
|
Question
Susan has an $18\%$ stake in an organization that earned a profit of $\$75620$ in a year.
How much of the organization's profit is Susan entitled to?
Give your answer to the nearest dollar.
Answer:
|
Classifier: The text contains the AU spelling "organisation" which needs to be converted to the US spelling "organization". While it contains a dollar sign, the currency symbol is shared and no specific AU cultural reference or metric unit is present to trigger a higher category. Verifier: The text contains "organisation" and "organisation's", which are AU/UK spellings requiring localization to "organization" and "organization's" for the US. |
ksGmGhoNFY7j7thsmoOu |
Localize | Units (simple) | Multiple Choice
What are the correct dimensions of a rectangle where the numerical value of its perimeter equals twice its area?
Options:
|
Multiple Choice
What are the correct dimensions of a rectangle where the numerical value of its perimeter equals twice its area?
Options:
|
Classifier: The answer choices contain the metric unit "cm" (centimetres), which requires localization to US customary units or generic units. Verifier: The answer choices contain the metric unit "cm" (centimetres), which requires localization. |
mNR6WmDFUx0NwQx12gd5 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following correctly shows the factorised form of
$4a^{2}+ab+4a+b$ ?
Options:
|
Multiple Choice
Which of the following correctly shows the factored form of
$4a^{2}+ab+4a+b$ ?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/British spelling. It must be localized to "factorized" for the US market. |
lCDsdvfsGDxIS9N8xAQb |
Localize | Terminology | Question
Find the highest common factor of the following algebraic terms.
$12x^2y^3,\space{6x^3y}$ and $21x^2y^4$
Options:
|
Question
Find the greatest common factor of the following algebraic terms.
$12x^2y^3,\space{6x^3y}$ and $21x^2y^4$
Options:
|
Classifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US equivalent is typically "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US uses "greatest common factor" (GCF). |
lHKDeGuKIBFKUrNHlzSN |
Localize | Terminology | Multiple Choice
Express $\frac{8}{33}$ as a recurring decimal.
Options:
|
Multiple Choice
Express $\frac{8}{33}$ as a repeating decimal.
Options:
|
Classifier: The term "recurring decimal" is the standard Australian/British term for what is called a "repeating decimal" in the United States. Verifier: The term "recurring decimal" is the standard Australian/British terminology, whereas "repeating decimal" is used in the US. |
lDdIXsTBSYHXrQ8JLyfb |
Localize | Terminology | Multiple Choice
Which of the following infinite geometric series has a limiting sum of $\frac{2}{3}$?
Options:
|
Multiple Choice
Which of the following infinite geometric series has a sum of $\frac{2}{3}$?
Options:
|
Classifier: The term "limiting sum" is frequently used in AU curriculum for the sum to infinity of a geometric series; US curriculum typically uses "sum of an infinite geometric series" or "sum to infinity". Verifier: "Limiting sum" is a specific terminology used in the Australian curriculum for the sum of an infinite geometric series. |
lqrvDhpZoNcW2lDEy6ez |
Localize | Units (simple) | Question
How many litres are there in $7$ m$^3$ ?
Answer:
|
Question
How many gallons are there in $7$ ft$^3$ ?
Answer:
|
Classifier: The text contains the metric unit "litres" (AU spelling) and "m^3" (cubic metres). According to the decision rules, any metric unit found anywhere in the text requires at least this category. Verifier: The text contains metric units "litres" and "m^3". "Litres" is also the AU/British spelling. Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
mYwP4gIAmxGPaRzUETQi |
Localize | Cultural refs | Question
A candy shop offers snakes, gumballs, liquorice, chocolate, sour worms, and lollipops.
How many different lolly bag combinations are possible when choosing $4$ types from these $6$?
Answer:
|
Question
A candy shop offers gummy snakes, gumballs, licorice, chocolate, sour worms, and lollipops.
How many different candy bag combinations are possible when choosing $4$ types from these $6$?
Answer:
|
Classifier: Contains AU-specific spelling ("liquorice") and cultural terms for candy ("snakes", "lolly bag"). In the US, "lolly" is "candy" or "goodie", and "liquorice" is "licorice". Verifier: Contains AU-specific spelling "liquorice" (US: licorice) and cultural terms like "lolly bag" (US: candy bag/goodie bag) and "snakes" (referring to a specific type of gummy candy). |
mqn_01J5J7KYFXR5SRQRJJ1FK6YQ7J |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
If two chords in a circle are equal in length, then they subtend equal angles at the centre of the circle.
Options:
|
Multiple Choice
True or false:
If two chords in a circle are equal in length, then they subtend equal angles at the center of the circle.
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: Contains the AU spelling "centre", which requires localization to "center". |
mm0oZmqfWS3zzwayQwgS |
Localize | Units (simple) | Multiple Choice
Carlos ran an $800$ m race in $348$ seconds.
Which option matches Carlos' time?
Options:
|
Multiple Choice
Carlos ran an $800$ ft race in $348$ seconds.
Which option matches Carlos' time?
Options:
|
Classifier: The text contains a metric unit ("m" for metres) in the context of a race distance, which requires localization for a US audience. Verifier: The text contains the metric unit "m" (metres) in the context of a race distance, which requires localization for a US audience. |
mqn_01J5MMYHEG59F3EW038P9PG1VC |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following pairs of variables is not suitable for a scatterplot?
Options:
|
Multiple Choice
Which of the following pairs of variables is not suitable for a scatterplot?
Options:
|
Classifier: The text contains the Australian spelling "favourite colour", which requires localization to "favorite color" for a US audience. Verifier: The answer choice contains "favourite colour", which are AU/British spellings of "favorite color". |
mqn_01HW9XFBG9ZBJ6Z8WXR7JJH1T5 |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $x^2+2x-6$ by completing the square.
Options:
|
Multiple Choice
Factor $x^2+2x-6$ by completing the square.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
mqn_01HW4E4508G9NSKQTH87ENZKH6 |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $x^2-8x+3$ by completing the square.
Options:
|
Multiple Choice
Factor $x^2-8x+3$ by completing the square.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
mqn_01HW9XJ2X6BWYZ9QG095N22E16 |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $2x^2 - 12x - 12$ by completing the square.
Options:
|
Multiple Choice
Factor $2x^2 - 12x - 12$ by completing the square.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
mqn_01J6C4QREMH969JYBAYCGQEZRG |
Localize | Spelling (AU-US) | Multiple Choice
What is $3y(2y - 4) + 5(2y - 4)$ in factorised form?
Options:
|
Multiple Choice
What is $3y(2y - 4) + 5(2y - 4)$ in factored form?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/British spelling. US spelling is "factorized". |
mqn_01J6C4N6HS88SVP6YV6MQQ8WJ8 |
Localize | Spelling (AU-US) | Multiple Choice
What is $2a^2(3a + 1) + 4(3a + 1)$ in factorised form?
Options:
|
Multiple Choice
What is $2a^2(3a + 1) + 4(3a + 1)$ in factored form?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/British spelling. US spelling is "factorized". |
mqn_01J6EG1CZ0S8Q8YPGM8QX455RM |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $y^2 - 9$.
Options:
|
Multiple Choice
Factor the polynomial $y^2 - 9$.
Options:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". Verifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". |
mqn_01J6C4KBF07V826CMSM8GCYR3T |
Localize | Spelling (AU-US) | Multiple Choice
What is $3x(2x - 4) + 5(2x - 4)$ in factorised form?
Options:
|
Multiple Choice
What is $3x(2x - 4) + 5(2x - 4)$ in factored form?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/British spelling. US spelling is "factorized". |
mqn_01J6EG3H44M0761ZHBMQ6R4VFM |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $z^2 - 25$.
Options:
|
Multiple Choice
Factor the polynomial $z^2 - 25$.
Options:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". Verifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". |
mqn_01J6EF7KJ9X6TQ62NNVXT14E9M |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(2x - 5y)(2x + 5y)(4x^2 + 25y^2)$?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(2x - 5y)(2x + 5y)(4x^2 + 25y^2)$?
Options:
|
Classifier: The text uses the AU spelling "factorised", which needs to be localized to the US spelling "factorized". Verifier: The text uses "factorised", which is the AU/UK spelling. US English requires "factorized". |
mqn_01J6EEXN6625TCEXVPW0JAWJHX |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $16a^6 - 81b^6$.
Options:
|
Multiple Choice
Factor $16a^6 - 81b^6$.
Options:
|
Classifier: The text uses the AU spelling "Factorise", which needs to be localized to the US spelling "Factorize". Verifier: The text uses "Factorise", which is the AU/UK spelling. US English requires "Factorize". |
mqn_01J6SCT2SHKHC96BYWF3AE5Z0A |
Localize | Units (simple) | Multiple Choice
True or false:
The total surface area of a cube of side length $0.2$ cm is $2.4$ cm$^2$
Options:
|
Multiple Choice
True or false:
The total surface area of a cube of side length $0.2$ in is $2.4$ in$^2$
Options:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion for US localization. Per decision rules, any metric unit triggers a RED category. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion to US customary units for localization. This is a simple conversion as it involves a single geometric object and a basic calculation. |
mqn_01J6EGCAH24AZ0WX784VTKWV4R |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $p^2 - 36$.
Options:
|
Multiple Choice
Factor the polynomial $p^2 - 36$.
Options:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". Verifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be "Factorize". |
mqn_01J6EFAXAN27PXVXJ7HE2SHGY6 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(3m - 2n)(3m + 2n)(9m^2 + 4n^2)$?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(3m - 2n)(3m + 2n)(9m^2 + 4n^2)$?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling. In US English, this must be "factorized". Verifier: The word "factorised" uses the AU/UK 's' spelling. In US English, this must be "factorized". |
mgvw2QkHjYGPmk3M1O2H |
Localize | Units (simple) | Multiple Choice
In a swimming race, Maithili covered $5$ m in the first $1.5$ minutes of the race.
As a part of her strategy to win, she covered the remaining $3$ m in just the next $0.48$ minutes.
Represent the distance covered by Maithili as a function $f(x).$
Options:
|
Multiple Choice
In a swimming race, Maithili covered $5$ ft in the first $1.5$ minutes of the race.
As a part of her strategy to win, she covered the remaining $3$ ft in just the next $0.48$ minutes.
Represent the distance covered by Maithili as a function $f(x).$
Options:
|
Classifier: The text contains metric units ("m" for metres) which require conversion to US customary units. Per rule 1, any metric unit disqualifies GREEN. Verifier: The text contains metric units ("m" for metres) which require conversion. The conversion is simple as it involves a few discrete values and the resulting function coefficients change linearly. |
mqn_01J6TT1YD8N5GHSCC76T9MY541 |
Localize | Units (simple) | Multiple Choice
True of false:
A parallelogram with a perpendicular height of $2$ cm and a base length $5$ cm has an area of $10$ cm$^2$
Options:
|
Multiple Choice
True or false:
A parallelogram with a perpendicular height of $2$ in and a base length $5$ in has an area of $10$ in$^2$
Options:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require localization to US customary units or a decision on metric pedagogy. Per decision rules, any metric unit triggers a RED units category. Verifier: The text contains metric units ("cm" and "cm^2") which require conversion for US localization. |
mqn_01J6EF180NC4C1PFQ8P0R3605G |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $49m^8 - 64n^{10}$.
Options:
|
Multiple Choice
Factor $49m^8 - 64n^{10}$.
Options:
|
Classifier: The text uses the AU spelling "Factorise", which needs to be localized to the US spelling "Factorize". Note: the variable 'm' is algebraic, not a metric unit. Verifier: The text uses "Factorise", which is the AU/UK spelling. US English requires "Factorize". The variable 'm' is algebraic and not a unit. |
mqn_01J6TTSXT071Y59PE43C44XGDD |
Localize | Units (simple) | Multiple Choice
Which of the following represents the radius of a circle with diameter $d$ cm?
Options:
|
Multiple Choice
Which of the following represents the radius of a circle with diameter $d$ in?
Options:
|
Classifier: The text and answer choices contain the metric unit "cm", which requires localization. Verifier: The text and answer choices contain the metric unit "cm", which requires conversion for US localization. |
mqn_01J6X1X2E4KJJXJ6B7QHER8E4D |
Localize | Terminology | Multiple Choice
Which of the following lines has a gradient of $0$?
Options:
|
Multiple Choice
Which of the following lines has a slope of $0$?
Options:
|
Classifier: The term "gradient" is standard in AU/UK curriculum for the steepness of a line, whereas the US curriculum almost exclusively uses "slope" in this context. Verifier: The term "gradient" is the standard AU/UK term for the steepness of a line, whereas US curriculum uses "slope". This requires localization. |
mqn_01J6X282DSXV9ZHS94S40WN62N |
Localize | Terminology | Multiple Choice
A horizontal line passes through the point $(10, -4)$.
What is the gradient of this line?
Options:
|
Multiple Choice
A horizontal line passes through the point $(10, -4)$.
What is the slope of this line?
Options:
|
Classifier: Uses the term "gradient", which requires localization to "slope" for US audiences. Verifier: Uses the term "gradient", which is specific to AU/UK school context and requires localization to "slope" for US audiences. |
mqn_01J6X24C397NRZRB0PZ8YEMSVY |
Localize | Terminology | Multiple Choice
A vertical line passes through the point $(2, -5)$.
What is the gradient of this line?
Options:
|
Multiple Choice
A vertical line passes through the point $(2, -5)$.
What is the slope of this line?
Options:
|
Classifier: Uses the term "gradient", which requires localization to "slope" for US audiences. Verifier: Uses the term "gradient", which is specific to AU/UK school context and requires localization to "slope" for US audiences. |
mqn_01J6X3Z97QTH7A4X8BRHCR7Q6T |
Localize | Terminology | Multiple Choice
A vertical line passes through the point $(0,0)$.
What is the gradient of this line?
Options:
|
Multiple Choice
A vertical line passes through the point $(0,0)$.
What is the slope of this line?
Options:
|
Classifier: Uses the term "gradient", which requires localization to "slope" for US audiences. Verifier: Uses the term "gradient", which is specific to AU/UK school context and requires localization to "slope" for US audiences. |
mqn_01J6TVDCB8Q3RK7JY53GR52MBP |
Localize | Units (simple) | Multiple Choice
A circular disc has a radius that is $0.4$ times the diameter of a larger circular disc.
If the diameter of the smaller disc is $24$ cm, what is the diameter of the larger disc?
Options:
|
Multiple Choice
A circular disk has a radius that is $0.4$ times the diameter of a larger circular disk.
If the diameter of the smaller disk is $24$ in, what is the diameter of the larger disk?
Options:
|
Classifier: The text contains the metric unit "cm" (centimetres) multiple times in both the question and the answer choices, which requires conversion to US customary units (inches) or a change in the problem's unit context. Verifier: The text contains the metric unit "cm" (centimetres) in the question and all answer choices, which requires conversion to US customary units (inches) or a change in unit context. |
mqn_01J6YSSAY3JZGR5ZJ9WY2PS7A0 |
Localize | Terminology | Multiple Choice
Which of the following is true for the turning point of the parabola $y=ax^2+bx+c$ ?
Options:
|
Multiple Choice
Which of the following is true for the vertex of the parabola $y=ax^2+bx+c$ ?
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard Australian/UK curriculum term for the vertex of a parabola. In the US, "vertex" is the standard term. |
mqn_01J6YTNMWPPJ65ZVRNKKQESGZY |
Localize | Terminology | Multiple Choice
Which of the following represents the turning point of the parabola $y=(x-3)(x+4)$ ?
Options:
|
Multiple Choice
Which of the following represents the vertex of the parabola $y=(x-3)(x+4)$ ?
Options:
|
Classifier: Contains the AU school math term "turning point", which should be localized to "vertex" for US audiences. Verifier: Contains "turning point", which is a specific AU/UK school math term for "vertex". |
mqn_01J82R8CNH7VEVRVFWHZ9S98X0 |
Localize | Units (textual) | Multiple Choice
True or false:
Cubic centimetres is an appropriate unit to measure the volume of a wooden plank.
Options:
|
Multiple Choice
True or false:
Cubic inches is an appropriate unit to measure the volume of a wooden plank.
Options:
|
Classifier: The text contains the metric unit "Cubic centimetres" which also uses the AU spelling "centimetres". This requires conversion to US customary units or at least spelling localization, but per rules, units take precedence. Since it is a conceptual question about the appropriateness of a unit, it is a textual conversion. Verifier: The text contains the metric unit "centimetres" (AU spelling) in a conceptual context. Per rule 3, any metric unit requires RED classification. Since it's a qualitative question about unit appropriateness, textual conversion is the correct leaf. |
mqn_01J8S9Z91RH3SBM14ARFZJAFWT |
Localize | Terminology | Multiple Choice
True or false:
A line with a gradient of zero is a vertical line.
Options:
|
Multiple Choice
True or false:
A line with a slope of zero is a vertical line.
Options:
|
Classifier: Uses the term "gradient". As noted in Group 5, while "slope" is more common in the US, "gradient" is a standard mathematical term. No other AU-specific markers are present. Verifier: The term "gradient" is used in a school geometry context where "slope" is the US equivalent. This requires localization. |
mqn_01J70ZR1YH9S1YF3VMV6MBHG0R |
Localize | Units (simple) | Multiple Choice
True or false:
The volume of a rectangular prism with base area $a$ cm$^2$ and height $b$ cm is $(a\times b)$ cm$^3$
Options:
|
Multiple Choice
True or false:
The volume of a rectangular prism with base area $a$ in$^2$ and height $b$ in is $(a\times b)$ in$^3$
Options:
|
Classifier: The text contains metric units (cm, cm^2, cm^3) which require localization to US customary units or a general units-neutral format. Verifier: The text contains metric units (cm, cm^2, cm^3) which require localization for a US audience. It is a simple conversion/replacement of units. |
mqn_01J735QCHWMS6KX03ZCQ8XWGSB |
Localize | Answer set | Multiple Choice
True or false:
A trapezium cannot have a right angle.
Options:
|
Multiple Choice
True or false:
A trapezoid cannot have a right angle.
Options:
|
Classifier: The term "trapezium" in AU refers to a quadrilateral with at least one pair of parallel sides, which is called a "trapezoid" in the US. Verifier: The term "trapezium" has different definitions in AU/UK vs US (where it is called a "trapezoid"). This requires localization to ensure the mathematical property being tested is accurate for the target locale. |
mqn_01J8QHKCB1FQ5NA657ZM2TQJZR |
Localize | Terminology | Multiple Choice
True or false:
The $y$-coordinate of the turning point of the parabola $y=2(x+1)^2-3$ is $3$.
Options:
|
Multiple Choice
True or false:
The $y$-coordinate of the vertex of the parabola $y=2(x+1)^2-3$ is $3$.
Options:
|
Classifier: The term "turning point" is used to describe the vertex of a parabola, which is an AU-specific mathematical term requiring localization to "vertex" for US audiences. Verifier: The term "turning point" is used, which requires localization to "vertex" for the US context. |
mqn_01J8QHGQEHN4GVBVCJPCS6J5BZ |
Localize | Terminology | Multiple Choice
True or false:
The turning point of the parabola $y=(x-2)^2+2$ is $(2,2)$.
Options:
|
Multiple Choice
True or false:
The vertex of the parabola $y=(x-2)^2+2$ is $(2,2)$.
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US school mathematics. |
mqn_01J6ZSZV1TWR87KWXD863W5VJJ |
Localize | Terminology | Multiple Choice
A line has a gradient of $2$.
What is the gradient of the line perpendicular to it?
Options:
|
Multiple Choice
A line has a slope of $2$.
What is the slope of the line perpendicular to it?
Options:
|
Classifier: While "gradient" is very common in AU/UK and "slope" is more common in the US, "gradient" is still mathematically valid and understood in US high school/college contexts. However, per the strict rules, there are no AU-specific spellings or metric units. If "gradient" were considered a restricted term it would be RED, but it is generally accepted as bi-dialect neutral in coordinate geometry. Verifier: While the classifier argued "gradient" is mathematically valid in the US, in the context of school-level coordinate geometry, "gradient" is the standard AU/UK term whereas "slope" is the standard US term. Following the logic applied to "turning point" in Groups 5 and 6, this should be classified as RED.terminology_school_context for localization to the US market. |
mqn_01J87493CB5JVJAXJZWWGK2Y13 |
Localize | Units (textual) | Multiple Choice
Which of the following is an example of categorical data?
Options:
|
Multiple Choice
Which of the following is an example of categorical data?
Options:
|
Classifier: The text contains a reference to "degrees Celsius", which is a metric unit. Per decision rules, any metric unit requires localization. Since it is a descriptive reference in a list of data types, it is classified as textual conversion. Verifier: The text contains "degrees Celsius", which is a metric unit. Per decision rule 3, any metric unit requires at least RED classification. Since it is a textual reference in a list of examples, units_textual_conversion is appropriate. |
mqn_01J7VQ06Y7F690FJJ0MT6VJR5X |
Localize | Terminology | Multiple Choice
True or false:
A true bearing of $000^\circ T$ means the object is located to the east.
Options:
|
Multiple Choice
True or false:
A true bearing of $000^\circ$ means the object is located to the east.
Options:
|
Classifier: Uses "true bearing" and the specific Australian notation "$000^\circ T$". In the US, bearings are often expressed as quadrant bearings (e.g., N 0 E) or simple degrees clockwise from North without the "T" suffix. Verifier: The use of "true bearing" combined with the specific notation "$000^\circ T$" (three digits followed by T) is highly specific to the Australian curriculum and navigation standards, differing from US conventions. |
mqn_01J8J49AYYYGAM8G4EXCN2N2MD |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following nominal rates has the lowest effective interest rate?
Options:
|
Multiple Choice
Which of the following nominal rates has the lowest effective interest rate?
Options:
|
Classifier: The text contains typos/misspellings ("quaterly", "monthy") but more importantly, "half-yearly" is the standard AU term for what is typically called "semiannually" in US financial contexts. However, per the decision rules, the presence of "quaterly" and "monthy" are likely typos, but "half-yearly" is a distinct terminology preference. Given the options, RED.spelling_only or terminology applies; "half-yearly" is the primary indicator for localization. Verifier: The text contains spelling errors ("quaterly", "monthy") and the term "half-yearly" which is the preferred Australian term over "semiannually". Per rule 5, spelling/typos and terminology both trigger RED. |
mqn_01J7XDANVAX5VEWW52XSG0MHK3 |
Localize | Terminology | Multiple Choice
True or false:
While evaluating the given expression, subtraction is performed before solving the brackets.
$18-[6 + {4 + (8\times9)}]$
Options:
|
Multiple Choice
True or false:
While evaluating the given expression, subtraction is performed before solving the parentheses.
$18-[6 + {4 + (8\times9)}]$
Options:
|
Classifier: The term "brackets" is the standard AU/UK term for grouping symbols in order of operations. In a US school context, "parentheses" is the primary term used for ( ), and "brackets" usually refers specifically to [ ]. Localization to "parentheses" or "grouping symbols" is required for US alignment. Verifier: The term "brackets" is the standard AU/UK term for grouping symbols. In US pedagogy, "parentheses" is used for ( ) and "brackets" for [ ]. Since the expression contains both, the use of "brackets" as a general term is a terminology difference requiring localization. |
mqn_01J8SA197K4DXDXRVNSRC28V92 |
Localize | Terminology | Multiple Choice
True or false:
A line with a gradient of $5$ is steeper than a line with a gradient of $2$.
Options:
|
Multiple Choice
True or false:
A line with a slope of $5$ is steeper than a line with a slope of $2$.
Options:
|
Classifier: Uses "gradient". No AU spelling, metric units, or specific school level terminology (like Year 7) found. Verifier: The term "gradient" is used in a school geometry context where "slope" is the US equivalent. This requires localization. |
mqn_01J847ZF5865XG4ABSMB7C7NJ9 |
Localize | Terminology | Multiple Choice
What does the D stand for in BODMAS?
Options:
|
Multiple Choice
What does the D stand for in PEMDAS?
Options:
|
Classifier: The acronym "BODMAS" is the standard Australian/UK term for order of operations. In the US, the equivalent acronym is "PEMDAS". This requires localization of the term itself and the corresponding question context. Verifier: The term "BODMAS" is the standard Australian/UK acronym for order of operations, whereas "PEMDAS" is used in the US. This is a clear case of school-context terminology requiring localization. |
mqn_01J72SWKCKHHK9CSTGFVQGXN2J |
Localize | Terminology | Multiple Choice
Which type of triangle does the RHS congruence rule apply to?
Options:
|
Multiple Choice
Which type of triangle does the HL congruence rule apply to?
Options:
|
Classifier: Contains "RHS" (AU terminology for HL) and "Right-angled" (AU terminology for Right triangle). Verifier: The question uses "RHS" (AU/UK terminology for HL) and the answer choice "Right-angled" (AU/UK terminology for Right triangle). |
mqn_01J8MAP3BFPWPV3T72QHKVFZV8 |
Localize | Terminology | Multiple Choice
Which of the following events are mutually exclusive?
A) Drawing a club and drawing a spade from a deck of cards
B) Rolling a $3$ and rolling an odd number on a die
C) Selecting a student who studies both maths and science
D) Choosing a student who plays soccer or basketball
Options:
|
Multiple Choice
Which of the following events are mutually exclusive?
A) Drawing a club and drawing a spade from a deck of cards
B) Rolling a $3$ and rolling an odd number on a die
C) Selecting a student who studies both math and science
D) Choosing a student who plays soccer or basketball
Options:
|
Classifier: Contains the term "maths", which is the standard AU term for the US "math". Verifier: The text contains the term "maths", which is the standard Australian/British term for the US "math". This requires localization. |
mqn_01J8S9W8PS1C5NKSAN15EAE03G |
Localize | Terminology | Multiple Choice
What does a positive gradient indicate about a line on a graph?
A) The line is horizontal
B) The line is sloping upwards from left to right
C) The line is sloping downwards from left to right
D) The line is vertical
Options:
|
Multiple Choice
What does a positive slope indicate about a line on a graph?
A) The line is horizontal
B) The line is sloping upward from left to right
C) The line is sloping downward from left to right
D) The line is vertical
Options:
|
Classifier: While "gradient" is very common in AU/UK and "slope" is more common in the US, "gradient" is still mathematically valid and understood in US high school/college calculus and vector contexts. However, per the specific decision rules, there are no AU-specific spellings or metric units. If "gradient" were considered a strictly AU school term, it would be RED, but it is often treated as bi-dialect neutral in higher math. Given the strict "ZERO AU-specific" rule for GREEN, and "gradient" not being explicitly listed in the RED.terminology examples (unlike "maths" or "turning point"), it is classified as GREEN. Verifier: In the context of school-level coordinate geometry (sloping lines on a graph), "gradient" is the standard AU term, whereas "slope" is the standard US term. Following the precedent of "turning point" being RED, "gradient" in this pedagogical context should also be RED. |
mqn_01J8SAGVEJP6SJNB1PB4WRPYQ8 |
Localize | Terminology | Multiple Choice
True or false:
A line that rises quickly from left to right has a steeper gradient than a line that rises slowly.
Options:
|
Multiple Choice
True or false:
A line that rises quickly from left to right has a steeper slope than a line that rises slowly.
Options:
|
Classifier: Uses "gradient". No AU-specific spelling or metric units. Verifier: The term "gradient" is used in a school geometry context where "slope" is the US equivalent. This requires localization. |
mqn_01J8SAKGW688DGW5KT0A0S82HD |
Localize | Terminology | Multiple Choice
True or false:
A line with a positive gradient rises when moving from left to right on a graph.
Options:
|
Multiple Choice
True or false:
A line with a positive slope rises when moving from left to right on a graph.
Options:
|
Classifier: Uses "gradient". No AU-specific spelling or metric units. Verifier: The term "gradient" is used in a school geometry context where "slope" is the US equivalent. This requires localization. |
mqn_01J8T1TRN83EQSK8P7DD0YT0BG |
Localize | Terminology | Multiple Choice
True or false:
The $x$-coordinate of the turning point of the quartic $y=(x-1)^4-1$ is $1$
Options:
|
Multiple Choice
True or false:
The $x$-coordinate of the vertex of the quartic $y=(x-1)^4-1$ is $1$
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for what is referred to as the "vertex" in US curriculum for parabolas and higher-order polynomials. Verifier: The term "turning point" is the standard AU/UK term for the "vertex" of a parabola or higher-order polynomial in the US curriculum. |
mqn_01J8T20F8F0RH1FP53H2PMTRZA |
Localize | Terminology | Multiple Choice
True or false:
The turning point of the quartic $y=(x-1)^4-1$ is $(1,-1)$
Options:
|
Multiple Choice
True or false:
The vertex of the quartic $y=(x-1)^4-1$ is $(1,-1)$
Options:
|
Classifier: Contains "turning point", a term used in AU/UK math contexts that maps to "vertex" in the US. Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J8T2CEXRJ8ABCS8860DYKKEH |
Localize | Terminology | Multiple Choice
Fill in the blank:
The quartic equation $y=x^4+4$ has a turning point at $[?]$
Options:
|
Multiple Choice
Fill in the blank:
The quartic equation $y=x^4+4$ has a vertex at $[?]$
Options:
|
Classifier: Contains "turning point", which requires localization to "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J8SA64TFJ6YANHV4G6FR2SZ1 |
Localize | Terminology | Multiple Choice
What does the gradient of a line describe on a graph?
Options:
|
Multiple Choice
What does the slope of a line describe on a graph?
Options:
|
Classifier: Uses "gradient". No AU-specific spelling or metric units. Verifier: The term "gradient" is used in a school geometry context where "slope" is the US equivalent. This requires localization. |
mqn_01J8VJGW0PDE0125N2SQCNDW4H |
Localize | Terminology | Multiple Choice
True or false:
$y=x^2-1$ is the turning point form of the quadratic equation $y=(x+1)(x+1)$
Options:
|
Multiple Choice
True or false:
$y=x^2-1$ is the vertex form of the quadratic equation $y=(x+1)(x+1)$
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This requires localization for the US school context. Verifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This is a school-context terminology difference. |
mqn_01J8VJB82KF1PK1334XQ34ZEH2 |
Localize | Terminology | Multiple Choice
True or false:
The quadratic equation $y=x^2-2x+1$ in turning point form is $y=(x-1)^2+1$
Options:
|
Multiple Choice
True or false:
The quadratic equation $y=x^2-2x+1$ in vertex form is $y=(x-1)^2+1$
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This requires localization for the US school context. Verifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This is a school-context terminology difference. |
mqn_01J8VJPH07K9T9J23W3M1ZKADH |
Localize | Terminology | Multiple Choice
True or false:
$y=(x+1)^2-2$ is the turning point form of the quadratic equation $y=x^2+2x-1$ .
Options:
|
Multiple Choice
True or false:
$y=(x+1)^2-2$ is the vertex form of the quadratic equation $y=x^2+2x-1$ .
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This requires localization for the US school context. Verifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. This is a school-context terminology difference. |
mqn_01J8T2PJ82610SR5E5W3T8FD29 |
Localize | Terminology | Multiple Choice
What is the turning point of the quartic equation $y=2(x-1)^4+3$?
Options:
|
Multiple Choice
What is the vertex of the quartic equation $y=2(x-1)^4+3$?
Options:
|
Classifier: Contains "turning point", which requires localization to "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J948XZ5V4ATGFCXCQ4ZQGMQJ |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
$2x^3-4x^2+3x-8=0$ is a cubic equation in $[?]$ form.
Options:
|
Multiple Choice
Fill in the blank:
$2x^3-4x^2+3x-8=0$ is a cubic equation in $[?]$ form.
Options:
|
Classifier: The answer choice "Factorised" uses the AU/UK 's' spelling, which requires conversion to the US 'z' spelling ("Factorized"). Verifier: The answer choice "Factorised" uses the AU/UK spelling (with 's') which requires localization to the US spelling "Factorized" (with 'z'). |
mqn_01J99PARJGS123S88G46AWF0A1 |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
The centre of the rectangular hyperbola $y=\frac{2}{x-1}+1$ is $(1,1)$.
Options:
|
Multiple Choice
True or false:
The center of the rectangular hyperbola $y=\frac{2}{x-1}+1$ is $(1,1)$.
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to "center" for a US audience. Verifier: Contains the AU spelling "centre", which requires localization to "center" for the US locale. |
mqn_01J90TKQ567ET6CKXQ4PFH8BWN |
Localize | Spelling (AU-US) | Multiple Choice
Which statement about a regression line is false?
Options:
|
Multiple Choice
Which statement about a regression line is false?
Options:
|
Classifier: The word "minimises" uses the Australian/British 's' spelling instead of the US 'z' spelling ("minimizes"). Verifier: The word "minimises" in the final answer choice is the Australian/British spelling. Under Rule 1, any AU spelling requires RED classification. |
mqn_01J8VK0S43XMH7T68MN5QKQETK |
Localize | Terminology | Multiple Choice
Which of the following is the turning point form of the quadratic equation $y=-2x^2+16x-37$ ?
Options:
|
Multiple Choice
Which of the following is the vertex form of the quadratic equation $y=-2x^2+16x-37$ ?
Options:
|
Classifier: The term "turning point form" is the standard Australian/UK term for what is called "vertex form" in the United States. Verifier: The term "turning point form" is the standard Australian/UK terminology for what is known as "vertex form" in the US. This requires localization to the specific curriculum terminology. |
mqn_01J9JPS3340K15HQQSQCXJ8K19 |
Localize | Terminology | Multiple Choice
True or false:
The cosine rule can be used to find a missing side of a right-angled triangle.
Options:
|
Multiple Choice
True or false:
The law of cosines can be used to find a missing side of a right triangle.
Options:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" for a US audience. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is the standard US term. This requires localization. |
mqn_01J912DY9BVP2QPWHP1KHZYCD5 |
Localize | Spelling (AU-US) | Multiple Choice
What is the primary purpose of a scatterplot?
A) To compare different categories of data
B) To display the frequency of a single variable
C) To explore the relationship between two numerical variables
D) To summarise data with averages and medians
Options:
|
Multiple Choice
What is the primary purpose of a scatterplot?
A) To compare different categories of data
B) To display the frequency of a single variable
C) To explore the relationship between two numerical variables
D) To summarize data with averages and medians
Options:
|
Classifier: The word "summarise" uses the Australian/British 's' spelling instead of the US 'z' spelling ("summarize"). Verifier: The word "summarise" in option D uses the Australian/British 's' spelling. Under Rule 1, this must be classified as RED. |
mqn_01J8T34XQW86MSDG4RF05FSV1B |
Localize | Terminology | Multiple Choice
What is the turning point of the quartic equation $y=0.2\left(x-0.1\right)^4-0.4$?
Options:
|
Multiple Choice
What is the vertex of the quartic equation $y=0.2\left(x-0.1\right)^4-0.4$?
Options:
|
Classifier: Contains "turning point", which requires localization to "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J8T3F1DQBKR5A14GTT3RSHG6 |
Localize | Terminology | Multiple Choice
Which of the following quartic equations has a turning point at $(0.2, -1.25)$?
Options:
|
Multiple Choice
Which of the following quartic equations has a vertex at $(0.2, -1.25)$?
Options:
|
Classifier: Contains "turning point", which requires localization to "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J9JEQFDC8PJ7G3AWEH01XB99 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following represents numerical data?
Options:
|
Multiple Choice
Which of the following represents numerical data?
Options:
|
Classifier: The text contains the Australian/British spellings "Colours" and "Favourite", which require localization to US English ("Colors" and "Favorite"). Verifier: The text contains "Colours" and "Favourite", which are AU/British spellings. These require localization to US English ("Colors" and "Favorite"). |
mqn_01J8T2WZ6R9VT1CG15T4G8MJP3 |
Localize | Terminology | Multiple Choice
What is the turning point of the quartic equation $y=\sqrt{2}\left(x+\frac{1}{2}\right)^4-\frac{1}{2}$?
Options:
|
Multiple Choice
What is the vertex of the quartic equation $y=\sqrt{2}\left(x+\frac{1}{2}\right)^4-\frac{1}{2}$?
Options:
|
Classifier: Contains "turning point", which requires localization to "vertex". Verifier: The term "turning point" is used, which requires localization to "vertex" for the US market. |
mqn_01J9MMGBBEQ02JAY0FRW0Y153Z |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
If $M$ and $N$ are two points on the circumference of a circle and $O$ represents the centre of the circle, then $\angle{OMN}$ is subtended by the arc $OM$.
Options:
|
Multiple Choice
True or false:
If $M$ and $N$ are two points on the circumference of a circle and $O$ represents the center of the circle, then $\angle{OMN}$ is subtended by the arc $OM$.
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: Contains the AU spelling "centre", which requires localization to "center". |
mqn_01J9K36JAG3106C4EH4PG438NE |
Localize | Units (textual) | Multiple Choice
Which of the following is an example of categorical data?
Options:
|
Multiple Choice
Which of the following is an example of categorical data?
Options:
|
Classifier: Contains the metric unit "centimetres" in a descriptive context. This requires conversion to a US customary unit (e.g., inches) and also contains AU spelling ("centimetres" vs "centimeters"). Verifier: Contains the metric unit "centimetres" which uses AU spelling and requires conversion to US customary units for localization. |
mqn_01J9MYWERZ3DQNRAZSJ2M7T5KB |
Localize | Terminology | Multiple Choice
Which of the following is the correct sequence of operations to solve the given expression?
$24-(15-3)+ 2$
Options:
|
Multiple Choice
Which of the following is the correct sequence of operations to solve the given expression?
$24-(15-3)+ 2$
Options:
|
Classifier: The term "Brackets" is used in the context of order of operations. In the US, "Parentheses" is the standard term used in PEMDAS, whereas "Brackets" (BODMAS/BIDMAS) is the standard AU/UK term for this context. Verifier: The use of "Brackets" in the context of order of operations is a specific AU/UK terminology (BODMAS/BIDMAS) whereas the US standard is "Parentheses" (PEMDAS). |
mqn_01JB8SSKBYR5WWQ9N2BBSPJ096 |
Localize | Terminology | Multiple Choice
Which of the following parabolas has a turning point closest to the origin?
Options:
|
Multiple Choice
Which of the following parabolas has a vertex closest to the origin?
Options:
|
Classifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
mqn_01JB8R8701CWAEP0HG5KQ925GT |
Localize | Terminology | Multiple Choice
Which of the following equations represents a parabola with the same turning point as the parabola given by $y = -\frac{3}{4} \left( x - \frac{5}{2} \right)^2 + \frac{7}{3}$?
Options:
|
Multiple Choice
Which of the following equations represents a parabola with the same vertex as the parabola given by $y = -\frac{3}{4} \left( x - \frac{5}{2} \right)^2 + \frac{7}{3}$?
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian/British term for the vertex of a parabola. In the US context, "vertex" is used. |
01JVJ7085RPT9JVGAX7S7700AK |
Localize | Units (simple) | Question
How many centimetres are in $2$ metres?
Answer:
|
Question
How many inches are in $2$ feet?
Answer:
|
Classifier: Contains metric units ("centimetres", "metres", "cm") and AU-specific spelling of those units ("metres", "centimetres"). Metric units require conversion for US localization. Verifier: Contains metric units ("centimetres", "metres", "cm") and AU-specific spelling of those units ("metres", "centimetres"). Metric units require conversion for US localization. |
01JVJ7085S8EW2TWTSMT8SJ1KX |
Localize | Units (simple) | Question
Find the total length, in metres, of the following:
$1.25$ km, $38\ 500$ cm and $72\ 000$ mm
Answer:
|
Question
Find the total length, in feet, of the following:
$1.25$ mi, $38\ 500$ in and $72\ 000$ in
Answer:
|
Classifier: Contains multiple metric units (km, cm, mm, m) and AU-specific spelling ("metres"). Metric units require conversion for US localization. Verifier: Contains multiple metric units (km, cm, mm, m) and AU-specific spelling ("metres"). Metric units require conversion for US localization. While there are multiple values, it is a simple sum of lengths, not a complex equation or re-derivation of coefficients, so simple_conversion is appropriate. |
01JVJ7AJWS6N0B3MP1ACSF3B63 |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Using the cross method, $x^2 + x - 2$ factorises to $(x+2)(x-1)$.
Options:
|
Multiple Choice
True or false:
Using the cross method, $x^2 + x - 2$ factors to $(x+2)(x-1)$.
Options:
|
Classifier: Contains the AU spelling "factorises", which needs to be converted to the US spelling "factorizes". Verifier: Contains the AU spelling "factorises", which requires localization to "factorizes" for the US locale. |
01JVMK685QEG1205XWCZPDKMTR |
Localize | Units (simple) | Question
A radioactive substance has a half-life of $10$ days.
If you start with $200$ grams, how much will remain after $30$ days?
Answer:
|
Question
A radioactive substance has a half-life of $10$ days.
If you start with $200$ ounces, how much will remain after $30$ days?
Answer:
|
Classifier: The text contains the metric unit "grams". According to the decision rules, any metric unit found anywhere in the text triggers at least the units_simple_conversion category. Verifier: The text contains the metric unit "grams", which requires localization per the decision rules. |
01JVJ7085W2Y7A0C9MMCFZAWXN |
Localize | Spelling (AU-US) | Question
Use the cross method to factorise $x^2 + 4x + 3$.
Write your answer in the form $(x+a)(x+b)$.
Options:
|
Question
Use the cross method to factor $x^2 + 4x + 3$.
Write your answer in the form $(x+a)(x+b)$.
Options:
|
Classifier: Contains the AU spelling "factorise", which needs to be converted to "factorize" for US localization. Verifier: Contains the AU spelling "factorise", which needs to be converted to "factorize" for US localization. |
01JVM2N7B6MPPAVG8Y8F38Z4KX |
Localize | Units (simple) | Multiple Choice
Which units are most appropriate for measuring a small amount of cooking oil in a recipe?
Options:
|
Multiple Choice
Which units are most appropriate for measuring a small amount of cooking oil in a recipe?
Options:
|
Classifier: The text contains metric units ("Millilitres", "Litres", "Kilograms") with AU/UK spellings. Verifier: The text contains metric units (Millilitres, Litres, Kilograms) with AU/UK spellings. |
01JVM2N7B10JKJDTESCBVMXQN3 |
Localize | Units (simple) | Multiple Choice
What units are typically used on road signs or maps to measure long distances between cities?
Options:
|
Multiple Choice
What units are typically used on road signs or maps to measure long distances between cities?
Options:
|
Classifier: The text contains multiple metric units ("Kilometres", "Metres", "Centimetres", "Litres") all using AU/UK spellings. Verifier: The text contains multiple metric units (Kilometres, Metres, Centimetres, Litres) all using AU/UK spellings. |
01JVM2N7B4BFZ96JX2H6J3F8E3 |
Localize | Units (simple) | Multiple Choice
What units would a builder most commonly use to measure the length of a large room?
Options:
|
Multiple Choice
What units would a builder most commonly use to measure the length of a large room?
Options:
|
Classifier: The text contains metric units ("Centimetres", "Kilometres", "Metres") with AU/UK spellings. Verifier: The text contains metric units (Centimetres, Kilometres, Metres) with AU/UK spellings. |
01JVM2N7B0DZ4MP5FQ838FG3WR |
Localize | Units (simple) | Multiple Choice
Which list shows common liquid volume units in order from smallest to largest?
Options:
|
Multiple Choice
Which list shows common liquid volume units in order from smallest to largest?
Options:
|
Classifier: The text contains the metric unit "Litre", which uses AU/UK spelling and is a metric unit requiring localization/review in a US context. Verifier: The text contains the metric unit "Litre" with AU/UK spelling. |
01JVHFV5252C43GFETZFPHFKMV |
Localize | Units (simple) | Question
A capsule-shaped object is made from a cylinder of radius $3$ cm and height $8$ cm, with a hemisphere of the same radius on each end. The total mass is $1.870$ kg.
Find its density.
Answer:
|
Question
A capsule-shaped object is made from a cylinder of radius $3$ in and height $8$ in, with a hemisphere of the same radius on each end. The total mass is $1.870$ lb.
Find its density.
Answer:
|
Classifier: The question contains multiple metric units (cm, kg, g/cm^3) which require localization to US customary units or at least classification as a units-based change. Verifier: The question contains metric units (cm, kg, g/cm^3) which require localization for a US audience. |
01JVM2N7AYWWS87S6GHBXNKMH9 |
Localize | Units (simple) | Multiple Choice
Which of the following units of length is the longest?
Options:
|
Multiple Choice
Which of the following units of length is the longest?
Options:
|
Classifier: The text contains metric units ("metre", "kilometre") which require localization. Additionally, these use AU/UK spelling ("metre" vs "meter"). Verifier: The text contains metric units "metre" and "kilometre" which use AU/UK spelling and require localization to US units/spelling. |
01JVHFV528V09PEHY8B2YYR0FC |
Localize | Units (simple) | Question
An alloy is formed by mixing $1.25$ kg of Metal A, with a density of $7.5$ g/cm$^3$, and $500$ cm$^3$ of Metal B, with a density of $9.2$ g/cm$^3$.
Assuming the total volume remains unchanged, calculate the density of the alloy.
Answer:
|
Question
An alloy is formed by mixing $1.25$ lb of Metal A, with a density of $7.5$ lb/in$^3$, and $500$ in$^3$ of Metal B, with a density of $9.2$ lb/in$^3$.
Assuming the total volume remains unchanged, calculate the density of the alloy.
Answer:
|
Classifier: The question contains metric units (kg, g/cm^3, cm^3) which require localization. Verifier: The question contains metric units (kg, g/cm^3, cm^3) which require localization. |
01JVHFV5278RXEQZ9PYY2JNHNM |
Localize | Units (simple) | Question
A rectangular prism has dimensions $x$ cm, $x$ cm, and $(x+4)$ cm.
Its mass is $384$ g. If the density of the material is $3.0$ g/cm$^3$, find the value of $x$.
Answer:
|
Question
A rectangular prism has dimensions $x$ in, $x$ in, and $(x+4)$ in.
Its mass is $384$ oz. If the density of the material is $3.0$ oz/in$^3$, find the value of $x$.
Answer:
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Classifier: The question contains metric units (cm, g, g/cm^3) which require localization. Verifier: The question contains metric units (cm, g, g/cm^3) which require localization. |
01JVJ6TJEN4X1Q6W4R218MD3BZ |
Localize | Units (simple) | Question
Mixture $X$ contains substances $P$, $Q$, and $R$ in a $3:4:2$ mass ratio.
$180$ g of $X$ is prepared. Then, $45$ g of $P$ and $20$ g of $R$ are added.
What is the new ratio of $Q$ to the total mass?
Express your answer as a fraction in simplest form.
Answer:
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Question
Mixture $X$ contains substances $P$, $Q$, and $R$ in a $3:4:2$ mass ratio.
$180$ oz of $X$ is prepared. Then, $45$ oz of $P$ and $20$ oz of $R$ are added.
What is the new ratio of $Q$ to the total mass?
Express your answer as a fraction in simplest form.
Answer:
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Classifier: The text contains metric units ("g" for grams). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "g" (grams) multiple times ("180 g", "45 g", "20 g"). According to rule 3, any metric unit requires at least RED.units_simple_conversion. |
01JVJ7AJWR20KT7WJS9KP8KD9Q |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $x^2 + 6x + 8$ using the cross method.
Options:
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Multiple Choice
Factor $x^2 + 6x + 8$ using the cross method.
Options:
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Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize" for the US locale. |
01JVM2N7C04SAB8Q4ZTR4J3RC9 |
Localize | Terminology | Multiple Choice
Let $M = \{\text{letters in MATHS\}}$ and $N = \{\text{letters in STATS\}}$.
What is $M \cap N$?
Options:
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Multiple Choice
Let $M = \{\text{letters in MATH\}}$ and $N = \{\text{letters in STATS\}}$.
What is $M \cap N$?
Options:
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Classifier: The text uses the term "MATHS", which is the standard AU/UK term for the subject. In the US, this is localized to "MATH". Because the set elements are the letters of the word itself, this requires a terminology change that affects the mathematical logic of the set intersection. Verifier: The text uses the term "MATHS", which is the standard AU/UK term for the subject. In the US, this is localized to "MATH". Because the set elements are the letters of the word itself, this requires a terminology change that affects the mathematical logic of the set intersection. |
01JVMK5ATMEY3Z030ZFM5FW5V7 |
Localize | Units (simple) | Multiple Choice
In an equilateral triangle $ABC$ with side length $10$ cm, the angle bisector from $A$ meets $BC$ at point $D$.
What is the length of $BD$?
Options:
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Multiple Choice
In an equilateral triangle $ABC$ with side length $10$ in, the angle bisector from $A$ meets $BC$ at point $D$.
What is the length of $BD$?
Options:
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Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units or a change in context for US localization. Verifier: The text contains the metric unit "cm" (centimetres) in both the question and the answers, requiring conversion for US localization. |
01JVJ7AJWEZQYSN0R2F26DVZF8 |
Localize | Units (simple) | Multiple Choice
A delivery route has three segments.
The first segment is $2.8$ km, the next is $1550$ m, and the last is $35000$ cm.
What is the total length of the route in kilometres?
Options:
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Multiple Choice
A delivery route has three segments.
The first segment is $2.8$ mi, the next is $1550$ ft, and the last is $35000$ in.
What is the total length of the route in miles?
Options:
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Classifier: The question contains multiple metric units (km, m, cm) and the AU spelling 'kilometres'. Per decision rules, any metric unit requires at least simple conversion category. Verifier: The question contains multiple metric units (km, m, cm) and the AU spelling 'kilometres'. Per decision rules, any metric unit requires at least simple conversion category. |
01JVJ2GWQ4MEF66XT12GPG0V92 |
Localize | Units (complex) | Multiple Choice
The function $h(t) = -4.9t^2 + 20t + 1.5$ describes the height of a projectile in metres, $t$ seconds after launch.
What is the instantaneous rate of change of height at $t=2$ seconds?
Options:
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Multiple Choice
The function $h(t) = -16t^2 + 20t + 1.5$ describes the height of a projectile in feet, $t$ seconds after launch.
What is the instantaneous rate of change of height at $t=2$ seconds?
Options:
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Classifier: The text contains the AU spelling "metres" and the metric units "metres" and "m/s", which require conversion to US customary units (feet/meters) or at least spelling correction, but per rule 6, units conversion is the higher priority category. Verifier: The question contains a physics equation $h(t) = -4.9t^2 + 20t + 1.5$ where the coefficient -4.9 is derived from the metric constant for gravity (9.8 m/s^2). Converting this to US Customary (feet) requires changing the formula coefficients (to -16t^2), which qualifies as RED.units_complex_converted per decision rule 4. |
01JVJ7AY7K6AZV096V7AHX3N6G |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
A perfect cube is a number you get by multiplying a whole number by itself three times.
If a positive integer $N$ is a perfect cube, every exponent in its prime factorisation is a multiple of $3$.
Options:
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Multiple Choice
True or false:
A perfect cube is a number you get by multiplying a whole number by itself three times.
If a positive integer $N$ is a perfect cube, every exponent in its prime factorization is a multiple of $3$.
Options:
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Classifier: The text contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: The text contains "factorisation", which is the AU spelling. US English uses "factorization". |
01JVPPE42A88N1E06M9HSJFMHZ |
Localize | Terminology | Multiple Choice
True or false:
$y=(x-2)^2+5$ is the turning point form of the quadratic equation $y=x^2-4x-1$ .
Options:
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Multiple Choice
True or false:
$y=(x-2)^2+5$ is the vertex form of the quadratic equation $y=x^2-4x-1$ .
Options:
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Classifier: The term "turning point form" is the standard Australian/UK term for what is called "vertex form" in the United States. Verifier: The term "turning point form" is the standard Australian/UK terminology for what is called "vertex form" in the US. This requires localization for a US audience. |
01JVQ0CA5ZGZD0A31S584JFKA0 |
Review | Review | Question
How many $50$c coins make $\$10.50$?
Answer:
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Question
How many $50$¢ coins make $\$10.50$?
Answer:
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Classifier: The question uses "50c" and "$10.50". While the dollar sign is shared, the "c" suffix for cents and the specific denominations (50c coin) are highly characteristic of the Australian currency system. Localization to US currency (quarters/dimes) or simply verifying if "50c" is acceptable in a US context is required. It does not fit neatly into spelling or units (metric). Verifier: The use of "50c" (cents suffix) and the specific reference to a "50c coin" is a regional currency convention (AU/UK/NZ) that differs from US conventions (where "50-cent piece" or "half dollar" is used, and the 'c' suffix is rare in formal math problems compared to the dollar sign or 'cents' word). This falls under regional terminology/context. |
01JVQ0CA6F93XVSY6J0VKBYQQW |
Localize | Terminology | Question
The numbers $16$ and $30$ are the two shorter sides of a right-angled triangle.
What is the length of the hypotenuse if these form a Pythagorean triple?
Answer:
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Question
The numbers $16$ and $30$ are the two shorter sides of a right triangle.
What is the length of the hypotenuse if these form a Pythagorean triple?
Answer:
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Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" for a US audience. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is the standard US term. This requires localization. |
01JVPPE42M62MD4W1ZZRKH7HRD |
Localize | Units (simple) | Multiple Choice
True or false:
$0.005$ kL + $50000$ mL is greater than $0.1$ m$^3$.
Options:
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Multiple Choice
True or false:
$0.005$ gal + $50000$ fl oz is greater than $0.1$ ft$^3$.
Options:
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Classifier: The question involves metric units of volume and capacity (kL, mL, m^3). These require localization/conversion for US curriculum alignment. Verifier: The question involves metric units of volume and capacity (kL, mL, m^3), which requires localization for US curriculum alignment. |
01JVPPE42M62MD4W1ZZRAE3PBD |
Localize | Units (simple) | Multiple Choice
True or false:
$350$ g $+ \ 1.2$ kg $+ \ 50000$ mg = $1.6$ kg
Options:
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Multiple Choice
True or false:
$350$ oz $+ \ 1.2$ lb $+ \ 50000$ mg = $1.6$ lb
Options:
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Classifier: The question is entirely based on metric unit conversions (g, kg, mg). Per decision rules, any metric unit requires RED classification. Verifier: The question is a direct comparison/addition of metric units (g, kg, mg), which requires localization to US customary units or a specific flag for metric-only content. |
01JVMK685RZFR1GJSRW8XB9ZXY |
Localize | Units (complex) | Question
The temperature of a liquid is given by $T(t) = T_s + (T_0 - T_s)\times 2.72^{-kt}$, where $T_s$ is the surrounding temperature as a constant.
If $T_s=20^\circ C$, $T_0=100^\circ C$ and $k=0.1$ per minute, what is the temperature after 10 minutes?
Answer:
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Question
The temperature of a liquid is given by $T(t) = T_s + (T_0 - T_s)\times 2.72^{-kt}$, where $T_s$ is the surrounding temperature as a constant.
If $T_s=20^\circ F$, $T_0=100^\circ F$ and $k=0.1$ per minute, what is the temperature after 10 minutes?
Answer:
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Classifier: The text contains metric units for temperature (degrees Celsius). Per the decision rules, the presence of metric units requires localization. Verifier: The question contains a mathematical formula (Newton's Law of Cooling style) where the variables and constants are defined in metric units (degrees Celsius). Per rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients should be classified as units_complex_converted. |
01JW5QPTNTS9QYVD8H2MC7MQSV |
Localize | Terminology | Question
For the parabola $y = -2x^2 + 8x - 3$, what is the product of the coordinates of the turning point?
Answer:
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Question
For the parabola $y = -2x^2 + 8x - 3$, what is the product of the coordinates of the vertex?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian/British term for the "vertex" of a parabola. This requires localization for a US context. |
01JVPPJRZN0WN1931GHY9XC84N |
Localize | Terminology | Question
Express $y = \dfrac{1}{2}x^2 - 3x + \dfrac{5}{2}$ in turning point form $y = a(x - h)^2 + k$.
What is the value of $h \times k$?
Answer:
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Question
Express $y = \dfrac{1}{2}x^2 - 3x + \dfrac{5}{2}$ in vertex form $y = a(x - h)^2 + k$.
What is the value of $h \times k$?
Answer:
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Classifier: The term "turning point form" is the standard AU/UK terminology for what is called "vertex form" in the US. This requires localization to be consistent with US school context. Verifier: The term "turning point form" is specific to AU/UK/NZ curricula; the US equivalent is "vertex form". This requires localization for the US context. |
01JVQ0CA69QMC0GATGY86H47ZW |
Localize | Units (simple) | Question
In a right-angled triangle, the side adjacent to angle $\theta$ is $4.5$ cm and the opposite side is $6.0$ cm.
Calculate $\theta$ to the nearest degree.
Answer:
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Question
In a right triangle, the side adjacent to angle $\theta$ is $4.5$ in and the opposite side is $6.0$ in.
Calculate $\theta$ to the nearest degree.
Answer:
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Classifier: The text contains both a metric unit ("cm") and AU-specific terminology ("right-angled triangle"). Per the decision rules, units conversion is the most impactful change. Verifier: The text contains the metric unit "cm", which requires conversion for US localization. It also uses "right-angled triangle" (AU/UK) vs "right triangle" (US), but units conversion is the higher priority classification. |
01JW5QPTMABJT4NDPQ29J75976 |
Localize | Terminology | Question
Three items cost $\$2.35$, $\$1.90$, and $\$4.55$. A $\$20$ note is used to pay.
How much is the change?
Answer:
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Question
Three items cost $\$2.35$, $\$1.90$, and $\$4.55$. A $\$20$ bill is used to pay.
How much is the change?
Answer:
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Classifier: The term "note" in the context of currency ($20 note) is standard in AU/UK, whereas the US uses "bill" ($20 bill). Verifier: The term "note" is used for currency ($20 note), which is standard in Australia/UK but would be "bill" in the US. This requires localization. |
01JW5QPTNGT5TBD5ET79KBJ2D4 |
Localize | Units (simple) | Question
A right-angled trapezium has parallel sides of length $10$ cm and $18$ cm.
The perpendicular side is $x$ cm, and the other non-parallel side is $10$ cm.
Find the area of the trapezium.
Answer:
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Question
A right trapezoid has parallel sides of length $10$ in and $18$ in.
The perpendicular side is $x$ in, and the other non-parallel side is $10$ in.
Find the area of the trapezoid.
Answer:
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Classifier: The text contains metric units ("cm") and AU-specific terminology ("trapezium" and "right-angled"). Per rule 6, units conversion is the primary classification. "Trapezium" maps to "trapezoid" and "right-angled" maps to "right". Verifier: The text contains metric units ("cm") and AU-specific terminology ("trapezium" and "right-angled"). Per rule 5, units conversion is the primary classification. |
01JW5QPTMDRW309R7H81B7XC9E |
Localize | Terminology | Question
Items cost $\$1.10$, $\$0.90$, and $\$2.05$. A $\$5$ note is used to pay.
How much is the change, rounded to the nearest $5$ cents?
Answer:
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Question
Items cost $\$1.10$, $\$0.90$, and $\$2.05$. A $\$5$ bill is used to pay.
How much is the change, rounded to the nearest $5$ cents?
Answer:
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Classifier: Contains the term "note" for currency ($5 note), which should be "bill" in US English. Additionally, rounding to the nearest 5 cents is a specific pedagogical/practical context related to the removal of 1 and 2 cent coins in Australia, though the terminology "note" is the primary driver for localization here. Verifier: The term "note" is used for currency ($5 note). Additionally, the instruction to round to the nearest 5 cents reflects Australian currency practice (where 1 and 2 cent coins are out of circulation), which is a school/pedagogical context difference from the US. |
01JW5QPTNH6VX6KFDSRXMD7EHZ |
Localize | Units (textual) | Question
What factor does the SI prefix ‘kilo-’ represent in terms like kilogram or kilometre?
Options:
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Question
What factor does the SI prefix ‘kilo-’ represent in terms like kilogram or kilometer?
Options:
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Classifier: The question refers to metric units ("kilogram", "kilometre") conceptually/descriptively to explain a prefix, rather than using them as measurements for a calculation. It also contains AU spelling "kilometre". Verifier: The question refers to metric units ("kilogram", "kilometre") conceptually to explain a prefix. It also contains the AU spelling "kilometre". |
01JW5QPTNH6VX6KFDSRTYE42VK |
Localize | Units (simple) | Question
In rectangle $ABCD$, sides $AB$ and $CD$ are marked with a single dash, and sides $BC$ and $AD$ are marked with a double dash.
If $AB = 10$ cm, what is the length of $CD$?
Answer:
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Question
In rectangle $ABCD$, sides $AB$ and $CD$ are marked with a single dash, and sides $BC$ and $AD$ are marked with a double dash.
If $AB = 10$ in, what is the length of $CD$?
Answer:
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Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm". |
01JVPPE42C2YKQXXC3V3Z96Z4N |
Localize | Terminology | Multiple Choice
Express $y = -\frac{1}{2}x^2 + 3x - \frac{7}{2}$ in turning point form.
Options:
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Multiple Choice
Express $y = -\frac{1}{2}x^2 + 3x - \frac{7}{2}$ in vertex form.
Options:
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Classifier: The term "turning point form" is used, which requires localization to "vertex form" for a US audience. Verifier: The term "turning point form" is used, which is the Australian equivalent of the US "vertex form". |
01JW5QPTNTS9QYVD8H2MNJY9FF |
Localize | Terminology | Question
The parabola $y = 0.5x^2 + 2x + 7$ has a turning point $(h,k)$.
Find $h+k$.
Answer:
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Question
The parabola $y = 0.5x^2 + 2x + 7$ has a vertex $(h,k)$.
Find $h+k$.
Answer:
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Classifier: The term "turning point" is used to describe the vertex of the parabola, which requires localization to "vertex" for US audiences. Verifier: The term "turning point" is used instead of the US standard "vertex". |
01JW5QPTNDHHNQGZDWZF3XJCHP |
Localize | Units (simple) | Question
A rhombus with diagonals $12$ cm and $16$ cm has an area of $96$ cm$^2$.
What is the area of a kite with the same diagonal lengths as the rhombus?
Answer:
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Question
A rhombus with diagonals $12$ in and $16$ in has an area of $96$ in$^2$.
What is the area of a kite with the same diagonal lengths as the rhombus?
Answer:
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Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion for US localization. Verifier: The text contains metric units ("cm" and "cm$^2$") which require conversion for US localization. |
01JW5QPTNV3GK9WG44596G3R6V |
Localize | Terminology | Question
For the parabola $y = x^2 + 10x$, what is the sum of the coordinates of its turning point?
Answer:
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Question
For the parabola $y = x^2 + 10x$, what is the sum of the coordinates of its vertex?
Answer:
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Classifier: Contains "turning point", which is the AU term for "vertex". Verifier: The term "turning point" is used instead of the US standard "vertex". |
01JW5QPTNV3GK9WG445AWM2D54 |
Localize | Terminology | Question
Find the turning point of $y = -x^2 + 5x$.
Express numbers in decimal form.
Answer:
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Question
Find the vertex of $y = -x^2 + 5x$.
Express numbers in decimal form.
Answer:
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Classifier: Contains "turning point", which should be localized to "vertex" in the US. Verifier: The term "turning point" is used instead of the US standard "vertex". |
01JW5QPTNZJWHHK0050TWMZ718 |
Localize | Terminology | Question
A parabola has $x$-intercepts at $x=2$ and $x=6$.
Find the $x$-coordinate of its turning point.
Answer:
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Question
A parabola has $x$-intercepts at $x=2$ and $x=6$.
Find the $x$-coordinate of its vertex.
Answer:
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Classifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. Verifier: The term "turning point" is used, which is the AU/UK equivalent of the US term "vertex". |
01JW5QPTNXTBAXRQ7VWG45R75Z |
Localize | Terminology | Question
A parabola has its turning point at $(2, 3)$ and passes through the point $(0, 7)$.
Find its equation in the form $y = a(x-h)^2+k$.
Answer:
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Question
A parabola has its vertex at $(2, 3)$ and passes through the point $(0, 7)$.
Find its equation in the form $y = a(x-h)^2+k$.
Answer:
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Classifier: Contains "turning point", which is the AU term for "vertex". Verifier: The term "turning point" is used instead of the US standard "vertex". |
01JW5QPTNZJWHHK0050XAXTDK7 |
Localize | Terminology | Question
The parabola $y = 3x(x-k)$ has its turning point at $x=2$.
What is the value of $k$?
Answer:
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Question
The parabola $y = 3x(x-k)$ has its vertex at $x=2$.
What is the value of $k$?
Answer:
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Classifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. Verifier: The term "turning point" is used, which is the AU/UK equivalent of the US term "vertex". |
01JW5QPTNY0DDKJBGBF46DPK7T |
Localize | Terminology | Question
The turning point of a parabola is $(h, k)$. The parabola passes through the point $(h - 3, k + 27)$.
What is the value of $a$ in $y = a(x - h)^2 + k$?
Answer:
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Question
The vertex of a parabola is $(h, k)$. The parabola passes through the point $(h - 3, k + 27)$.
What is the value of $a$ in $y = a(x - h)^2 + k$?
Answer:
|
Classifier: Contains "turning point", which is the AU term for "vertex". Verifier: The term "turning point" is used instead of the US standard "vertex". |
01JW5QPTNY0DDKJBGBF6RME70T |
Localize | Terminology | Question
The turning point of a parabola is $(h, k)$. The parabola passes through $(h+2, k+12)$.
What is the value of $a$ in $y=a(x-h)^2+k$?
Answer:
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Question
The vertex of a parabola is $(h, k)$. The parabola passes through $(h+2, k+12)$.
What is the value of $a$ in $y=a(x-h)^2+k$?
Answer:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian/British term for what is called the "vertex" in US mathematics. This requires localization. |
01K0RMVPSJS067DY2XRTRN56DA |
Localize | Units (simple) | Question
The roof of a gazebo is a hexagonal pyramid.
The area of the hexagonal base is $42$ m$^2$ and the height of the roof is $3$ m.
What is the volume of the roof?
Answer:
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Question
The roof of a gazebo is a hexagonal pyramid.
The area of the hexagonal base is $42$ ft$^2$ and the height of the roof is $3$ ft.
What is the volume of the roof?
Answer:
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Classifier: The text contains the metric unit "m", "m$^2$", and "m$^3$". Verifier: The text contains metric units "m$^2$", "m", and "m$^3$". Heuristics failed to flag them, but they are present in the source text. |
01K0RMY545F1HWZY0VB6MTSAS4 |
Localize | Units (simple) | Question
Convert $25$ millilitres to cubic centimetres.
Answer:
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Question
Convert $25$ fluid ounces to cubic inches.
Answer:
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Classifier: The text contains metric units ("millilitres", "centimetres") and AU-specific spelling ("millilitres", "centimetres"). Verifier: The text contains metric units ("millilitres", "centimetres") and AU spelling ("millilitres", "centimetres"). |
01K0RMY544KYWARHGYBDFZD8R6 |
Localize | Units (simple) | Question
A swimming pool has a capacity of $120$ kilolitres.
How many litres is this?
Answer:
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Question
A swimming pool has a capacity of $120$ kilogallons.
How many gallons is this?
Answer:
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Classifier: The text contains metric units ("kilolitres", "litres") and AU-specific spelling ("litres"). Per rule 6, units conversion is the most impactful change. Verifier: The text contains metric units ("kilolitres", "litres") and AU spelling ("litres"). Per rule 5, units conversion is the most impactful change. |
01K0RMY54829EQTTSGB46XQC1M |
Localize | Units (simple) | Question
Convert $0.025$ cubic metres to millilitres.
Answer:
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Question
Convert $0.025$ cubic feet to fluid ounces.
Answer:
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Classifier: The text contains metric units ("metres", "millilitres") and AU-specific spelling ("metres", "millilitres"). Verifier: The text contains metric units ("metres", "millilitres") and AU spelling ("metres"). |
01K0RMY54390PNYWZFGJXQA7PR |
Localize | Units (simple) | Question
Convert $3.75$ litres to millilitres.
Answer:
|
Question
Convert $3.75$ gallons to fluid ounces.
Answer:
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Classifier: Contains AU-specific spelling ("litres") and metric units ("litres", "millilitres", "mL"). Verifier: The question contains AU spelling ("litres") and metric units ("litres", "millilitres", "mL"). |
01K0RMVPT2WXFVHAA5WS394QKS |
Localize | Units (simple) | Question
A rectangular prism has a square base with sides of $4$ cm.
Its total surface area is $112$ cm$^2$.
Find its height.
Answer:
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Question
A rectangular prism has a square base with sides of $4$ in.
Its total surface area is $112$ in$^2$.
Find its height.
Answer:
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Classifier: The text contains metric units ("cm", "cm$^2$") which require localization. Verifier: The question contains metric units (cm, cm^2) which require localization. The math involves solving for a single dimension (height) given surface area and base side length, which is a simple numeric conversion. |
01K0RMY54390PNYWZFGMY0QC65 |
Localize | Units (simple) | Question
A container has a volume of $4500$ cm$^3$.
What is its volume in litres?
Answer:
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Question
A container has a volume of $4500$ in$^3$.
What is its volume in gallons?
Answer:
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Classifier: Contains AU-specific spelling ("litres") and metric units ("cm$^3$", "litres", "L"). Verifier: The question contains AU spelling ("litres") and metric units ("cm$^3$", "litres", "L"). |
01K0RMY5479RTN8VGRK5BCN9CS |
Localize | Units (simple) | Question
Convert $500000$ mL to kilolitres.
Answer:
|
Question
Convert $500000$ fl oz to gallons.
Answer:
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Classifier: The text contains metric units ("mL", "kilolitres", "kL"). Verifier: The text contains metric units ("mL", "kilolitres", "kL"). |
01K0RMY546ZDXR77TDT9276BR3 |
Localize | Units (simple) | Question
A large jug holds $2.25$ L.
How many $250$ mL cups can be filled from the jug?
Answer:
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Question
A large jug holds $2.25$ gal.
How many $250$ fl oz cups can be filled from the jug?
Answer:
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Classifier: The text contains metric units ("L", "mL"). Any metric unit requires localization. Verifier: The text contains metric units ("L", "mL"). Any metric unit requires RED classification. |
01K0RMY540HM4AYRCP1AYNZRR0 |
Localize | Units (simple) | Question
Convert $1$ cubic metre to litres.
Answer:
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Question
Convert $1$ cubic foot to gallons.
Answer:
|
Classifier: Contains AU-specific spelling ("metre", "litres") and metric units. Verifier: The question contains AU spelling ("metre", "litres") and metric units. |
01JW5QPTPTD6WF9NWMK5PKSSQ7 |
Localize | Units (simple) | Question
The mean height of $6$ children is $1.42$ m. A seventh child who is $1.55$ m tall joins the group.
What is the new mean height of all $7$ children?
Answer:
|
Question
The mean height of $6$ children is $1.42$ ft. A seventh child who is $1.55$ ft tall joins the group.
What is the new mean height of all $7$ children?
Answer:
|
Classifier: The text contains the metric unit "m" (metres) in both the content and the suffix field, which requires conversion for US localization. Verifier: The question contains the metric unit "m" (metres) in the content and suffix, requiring conversion to US customary units. |
01K0RMVPSHQPZJA3GPD8CEW7ZS |
Localize | Units (simple) | Question
A square pyramid has a volume of $24$ cm$^3$.
Its perpendicular height is equal to the length of its base side.
Find the height of the pyramid.
Answer:
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Question
A square pyramid has a volume of $24$ in$^3$.
Its perpendicular height is equal to the length of its base side.
Find the height of the pyramid.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^3$". Verifier: The text contains metric units "cm$^3$" and "cm". |
01K0RMY53XJ5XQ65CCAZ0THE7V |
Localize | Units (simple) | Question
Convert $2$ litres to millilitres.
Answer:
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Question
Convert $2$ gallons to fluid ounces.
Answer:
|
Classifier: Contains both AU-specific spelling ("litres") and metric units ("litres", "millilitres", "mL"). Units conversion/localization is the higher priority change. Verifier: The question contains AU spelling ("litres") and metric units ("litres", "millilitres", "mL"). Per rule 5, units conversion is the primary classification. |
01K0RMY542X6KW1BG67B01EY8H |
Localize | Units (simple) | Question
Convert $1.5$ kL to L.
Answer:
|
Question
Convert $1.5$ gal to fl oz.
Answer:
|
Classifier: Contains metric unit abbreviations ("kL", "L"). Even though no AU-specific spelling is present, the presence of metric units requires localization. Verifier: The question contains metric unit abbreviations ("kL", "L") which require localization. |
01K0RMVPT03H53P0TEJHPSAAE7 |
Localize | Units (simple) | Question
An open-topped box in the shape of a rectangular prism has a length of $12$ cm, a width of $10$ cm, and a height of $5$ cm.
Find its total surface area.
Answer:
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Question
An open-topped box in the shape of a rectangular prism has a length of $12$ in, a width of $10$ in, and a height of $5$ in.
Find its total surface area.
Answer:
|
Classifier: The text contains metric units ("cm", "cm$^2$") which require localization to US customary units or a decision on metric usage in US curriculum. Per rule 1, any metric unit disqualifies GREEN. Verifier: The question contains metric units (cm, cm^2) which require localization to US customary units. The calculation is a simple surface area calculation with a single numeric answer, fitting simple conversion. |
01K0RMY541PZ5ATD2ASD0XT01W |
Localize | Units (simple) | Question
How many millilitres are in $1$ cubic centimetre?
Answer:
|
Question
How many fluid ounces are in $1$ cubic inch?
Answer:
|
Classifier: Contains metric units ("millilitres", "centimetre", "mL"). Verifier: The question contains metric units ("millilitres", "centimetre", "mL") which require localization. |
01JW5QPTPH7QBNPE07HF8KMNAF |
Localize | Units (simple) | Question
The area of a segment of a circle is $A_{seg}$.
The area of the corresponding sector is $A_{sec}$, and the area of the triangle formed by the radii and the chord is $A_{tri}$.
If $A_{sec} = 2 A_{tri}$ and $A_{tri} = 25 \text{ cm}^2$, what is $A_{seg}$?
Answer:
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Question
The area of a segment of a circle is $A_{seg}$.
The area of the corresponding sector is $A_{sec}$, and the area of the triangle formed by the radii and the chord is $A_{tri}$.
If $A_{sec} = 2 A_{tri}$ and $A_{tri} = 25 \text{ in}^2$, what is $A_{seg}$?
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm^2", which requires conversion for US localization. Verifier: The text contains the metric unit "cm" and "cm^2", which requires conversion for US localization. |
01JW5QPTPH7QBNPE07HJW1TP9M |
Localize | Units (simple) | Question
The area of a minor segment of a circle is $\left ( \dfrac{25\pi}{6} - \dfrac{25\sqrt{3}}{4} \right)$ cm$^2$.
The central angle $\theta$, subtended by the chord of this segment, is $60^\circ$.
What is the radius $r$ of the circle?
Answer:
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Question
The area of a minor segment of a circle is $\left ( \dfrac{25\pi}{6} - \dfrac{25\sqrt{3}}{4} \right)$ in$^2$.
The central angle $\theta$, subtended by the chord of this segment, is $60^\circ$.
What is the radius $r$ of the circle?
Answer:
|
Classifier: The text contains the metric units "cm^2" and "cm", which require conversion for US localization. Verifier: The text contains the metric units "cm^2" and "cm", which require conversion for US localization. |
01K0RMY54991JHG1S5Y8JDG8QS |
Localize | Units (simple) | Question
A fish tank has dimensions $80$ cm $\times$ $50$ cm $\times$ $40$ cm.
What is its volume in litres?
Answer:
|
Question
A fish tank has dimensions $80$ in $\times$ $50$ in $\times$ $40$ in.
What is its volume in gallons?
Answer:
|
Classifier: The text contains metric units ("cm", "litres"). Verifier: The text contains metric units ("cm", "litres") and AU spelling ("litres"). |
01JW5RGMEHNHG353823HGS38KF |
Localize | Terminology | Multiple Choice
The equation $px - qy = r$ is given, where $p$, $q$, and $r$ are non-zero, and $q \ne 0$.
Which of the following shows this equation in gradient-intercept form?
Options:
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Multiple Choice
The equation $px - qy = r$ is given, where $p$, $q$, and $r$ are non-zero, and $q \ne 0$.
Which of the following shows this equation in slope-intercept form?
Options:
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Classifier: The term "gradient-intercept form" is the standard AU term for what is known as "slope-intercept form" in the US. This requires terminology localization. Verifier: The term "gradient-intercept form" is the standard Australian curriculum term for what is called "slope-intercept form" in the US. This is a clear terminology localization requirement. |
01K0RMY54WWYC6F1Z65F5TBF96 |
Localize | Terminology | Question
A line is parallel to the $x$-axis.
What is its gradient?
Answer:
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Question
A line is parallel to the $x$-axis.
What is its slope?
Answer:
|
Classifier: The term "gradient" is standard in AU/UK school mathematics to refer to the steepness of a line, whereas US curriculum consistently uses "slope". Verifier: The term "gradient" is the standard AU/UK term for "slope" in a school mathematics context. |
01K0RMY54XBVPGJD20G3D3PPP2 |
Localize | Terminology | Question
Find the gradient of a line parallel to $3x + y = 6$.
Answer:
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Question
Find the slope of a line parallel to $3x + y = 6$.
Answer:
|
Classifier: The term "gradient" is used, which requires localization to "slope" for the US market. Verifier: The term "gradient" is the standard AU/UK term for "slope" in a school mathematics context. |
01K0RMY54AF6P8DEEA04GYK91J |
Localize | Units (simple) | Question
A box has a volume of $2$ m$^3$.
How many smaller boxes with a volume of $4000$ cm$^3$ can fit inside it?
Answer:
|
Question
A box has a volume of $2$ ft$^3$.
How many smaller boxes with a volume of $4000$ in$^3$ can fit inside it?
Answer:
|
Classifier: The text contains metric units ("m", "cm"). Verifier: The text contains metric units ("m$^3$", "cm$^3$"). |
01K0RMY54991JHG1S5Y8ZXS3D2 |
Localize | Units (simple) | Question
Convert $1.5$ kilolitres to cubic centimetres.
Answer:
|
Question
Convert $1.5$ gallons to cubic inches.
Answer:
|
Classifier: The text contains metric units ("kilolitres", "centimetres"). Verifier: The text contains metric units ("kilolitres", "centimetres") and AU spelling ("centimetres"). |
01K0RMY54BKTR0FKV14T9VD417 |
Localize | Units (simple) | Question
A rectangular prism-shaped container measures $0.5$ m by $20$ cm by $100$ mm.
Calculate its volume in litres.
Answer:
|
Question
A rectangular prism-shaped container measures $0.5$ ft by $20$ in by $100$ in.
Calculate its volume in gallons.
Answer:
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Classifier: The text contains metric units ("m", "cm", "mm", "litres"). Verifier: The text contains metric units ("m", "cm", "mm", "litres") and AU spelling ("litres"). |
01K0RMY5527RE7W5W2XNC6C547 |
Localize | Terminology | Question
Anna has $12$ sweets and eats $5$.
Write a number sentence to show how many sweets she has left.
Answer:
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Question
Anna has $12$ pieces of candy and eats $5$.
Write a number sentence to show how many pieces of candy she has left.
Answer:
|
Classifier: The term "sweets" is highly characteristic of AU/UK English; the US equivalent is "candies". Additionally, "number sentence" is a pedagogical term that, while used in the US, often maps to "equation" or "expression" depending on the specific grade level and standard, but "sweets" is the primary localization trigger. Verifier: The term "sweets" is a British/Australian term for "candy" or "candies". |
01K94XMXR1GFSXNQANQA0EWSTV |
Localize | Units (simple) | Question
An equilateral triangle has a perimeter of $36$ cm.
If the perpendicular height of the triangle is $10.4$ cm, what is its area?
Answer:
|
Question
An equilateral triangle has a perimeter of $36$ in.
If the perpendicular height of the triangle is $10.4$ in, what is its area?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. It is a simple conversion as it involves a basic geometric area calculation. |
01K94XMXRFXE3ME6D3H5KV2VBD |
Localize | Terminology | Question
A parabola has its vertex at $(4, 5)$ and passes through the point $(6, -3)$.
What is its equation in turning point form?
Answer:
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Question
A parabola has its vertex at $(4, 5)$ and passes through the point $(6, -3)$.
What is its equation in vertex form?
Answer:
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Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in US curriculum. Verifier: The term "turning point form" is a specific AU/UK curriculum term for what is known as "vertex form" in the US. |
01K94XMXSZGAD7K2TQMREEZ9DX |
Localize | Terminology | Question
A pie chart shows students' favourite subjects.
'Maths' represents $25\%$ and 'Science' represents $20\%$.
If there are $15$ more students who prefer Maths over Science, what is the total number of students surveyed?
Answer:
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Question
A pie chart shows students' favorite subjects.
'Math' represents $25\%$ and 'Science' represents $20\%$.
If there are $15$ more students who prefer Math over Science, what is the total number of students surveyed?
Answer:
|
Classifier: Contains the term 'Maths' and 'favourite'. 'Maths' is the standard AU/UK term for the US 'Math'. 'Favourite' is the AU spelling for 'favorite'. Per decision rules, terminology/spelling requires RED classification. Verifier: The text contains 'favourite' (AU spelling) and 'Maths' (AU terminology). Per rule 5, terminology is the more impactful change. |
01K94XMXSAV78XBX04518RZPPQ |
Localize | Units (simple) | Question
A rectangular garden has a length that is $3$ metres longer than its width.
If the area of the garden is $50$ m$^2$, what is its width?
Answer:
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Question
A rectangular garden has a length that is $3$ feet longer than its width.
If the area of the garden is $50$ ft$^2$, what is its width?
Answer:
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Classifier: The text contains the metric unit "metres" (AU spelling) and "m^2". Per the decision rules, any metric unit requires at least this category. Verifier: The text contains the metric unit "metres" (AU spelling) and "m^2". Per rule 1 and 3, metric units and AU spelling require RED classification. Simple conversion is appropriate as it is a basic area/length problem. |
01K9CJKKY648M8JNEJYKJ9V5T8 |
Localize | Spelling (AU-US) | Question
How can you confirm a shape has been rotated $90^\circ$ clockwise around a specific point?
Answer:
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Question
How can you confirm a shape has been rotated $90^\circ$ clockwise around a specific point?
Answer:
|
Classifier: The answer text contains the AU spelling "centre" twice, which requires conversion to the US spelling "center". Verifier: The answer text contains the AU spelling "centre" twice, which requires localization to the US spelling "center". |
01K94WPKW8SKGEY1ZRCYM4AVN0 |
Localize | Terminology | Multiple Choice
What are the equations of the vertical and horizontal asymptotes for the truncus $y = \frac{2}{(x-5)^2} + 3$?
Options:
|
Multiple Choice
What are the equations of the vertical and horizontal asymptotes for the function $y = \frac{2}{(x-5)^2} + 3$?
Options:
|
Classifier: The term "truncus" is a specific term used in the Australian (specifically Victorian VCE) curriculum to describe a functional graph of the form y=a/(x-h)^2 + k. In the US, this is typically referred to as a "rational function" or described by its equation without a specific name like "truncus". Verifier: The term "truncus" is specific to the Australian (specifically Victorian VCE) curriculum and is not standard terminology in other locales like the US. |
01K94WPKQTPDYHPDRSEQEBFREN |
Localize | Units (simple) | Multiple Choice
Calculate the sum of $15.24$ cm, $0.51$ cm, and $102.1$ cm.
Express the answer to the correct number of significant figures.
Options:
|
Multiple Choice
Calculate the sum of $15.24$ in, $0.51$ in, and $102.1$ in.
Express the answer to the correct number of significant figures.
Options:
|
Classifier: The text contains the metric unit "cm" (centimetres/centimeters), which requires localization to US customary units. Verifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units (e.g., inches). |
01K94WPKSFSXWCEWXC360XQTC3 |
Localize | Units (simple) | Multiple Choice
A solid cylinder has a total surface area of $130\pi$ m$^2$ and a radius of $5$ m.
What is its height in metres?
Options:
|
Multiple Choice
A solid cylinder has a total surface area of $130\pi$ ft$^2$ and a radius of $5$ ft.
What is its height in feet?
Options:
|
Classifier: The text contains the metric unit "metres" (and its abbreviation "m"), which requires conversion to US customary units or at least spelling localization. Per rule 1, any metric unit prevents GREEN classification. Per rule 6, units conversion is the highest priority RED category. Verifier: The text contains the metric unit "metres" and "m", which requires conversion to US customary units. The conversion is a simple numeric change based on the surface area formula. |
01K94WPKV70A3YKR05T033QTSK |
Localize | Terminology | Multiple Choice
The graph of $y=a(x-h)^4+k$ has a turning point at $(-3, 5)$ and opens downwards.
Which of the following could be its equation?
Options:
|
Multiple Choice
The graph of $y=a(x-h)^4+k$ has a vertex at $(-3, 5)$ and opens downward.
Which of the following could be its equation?
Options:
|
Classifier: The term "turning point" is standard in AU/UK curricula for the vertex of a parabola or higher-order polynomial. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is typically called the "vertex" in US curricula. This requires localization for the US market. |
01K94WPKT5P7CS27RYYCW20ZZE |
Localize | Spelling (AU-US) | Multiple Choice
Circle A has the equation $(x - 2)^2 + (y + 3)^2 = 16$.
Circle B has the same centre as Circle A, but its radius is half as large.
What is the equation of Circle B?
Options:
|
Multiple Choice
Circle A has the equation $(x - 2)^2 + (y + 3)^2 = 16$.
Circle B has the same center as Circle A, but its radius is half as large.
What is the equation of Circle B?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: Contains the AU spelling "centre", which needs to be localized to the US spelling "center". |
01K9CJKKYFEXB42G1EQAY0Z2W2 |
Localize | Terminology | Question
Using a right-angled triangle, explain why $\sin(\theta) = \cos(90^\circ - \theta)$.
Answer:
|
Question
Using a right triangle, explain why $\sin(\theta) = \cos(90^\circ - \theta)$.
Answer:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" for a US audience. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is the standard US term. This requires localization. |
01K94WPKT895RAHVAE791RQ487 |
Localize | Spelling (AU-US) | Multiple Choice
Circle M has the equation $(x + 6)^2 + (y - 2)^2 = 81$.
Circle N has the same radius as Circle M but its centre is shifted $4$ units right and $3$ units up.
What is the equation of Circle N?
Options:
|
Multiple Choice
Circle M has the equation $(x + 6)^2 + (y - 2)^2 = 81$.
Circle N has the same radius as Circle M but its center is shifted $4$ units right and $3$ units up.
What is the equation of Circle N?
Options:
|
Classifier: The text contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The text contains "centre", which is the AU/British spelling. Per rule 1, this requires RED classification. |
01K94WPKR59BNKS5D970M6V8V0 |
Localize | Units (simple) | Multiple Choice
The temperature in a city was $-5^\circ\text{C}$ in the morning.
It rose by $12^\circ\text{C}$ by noon, then dropped by $9^\circ\text{C}$ by evening.
What was the evening temperature?
Options:
|
Multiple Choice
The temperature in a city was $-5^\circ\text{F}$ in the morning.
It rose by $12^\circ\text{F}$ by noon, then dropped by $9^\circ\text{F}$ by evening.
What was the evening temperature?
Options:
|
Classifier: The text contains metric temperature units (degrees Celsius), which requires conversion to Fahrenheit for US localization. Verifier: The question contains temperature in degrees Celsius ($^\circ\text{C}$), which is a metric unit requiring conversion to Fahrenheit for US localization. The conversion is a simple numeric change in a word problem context. |
01K94WPKSW7ZND3MRYKG4AEXKF |
Localize | Units (simple) | Multiple Choice
In a right triangle, one leg is $7$ cm shorter than the other leg, and the hypotenuse is $13$ cm.
If $x$ represents the longer leg, which equation could be used to solve for $x$?
Options:
|
Multiple Choice
In a right triangle, one leg is $7$ in shorter than the other leg, and the hypotenuse is $13$ in.
If $x$ represents the longer leg, which equation could be used to solve for $x$?
Options:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units (inches) for localization. Verifier: The text contains the metric unit "cm" (centimetres), which requires conversion. It is a simple conversion as the units are used as labels for side lengths in a standard Pythagorean theorem setup. |
01K9CJKKZX1JC9CYDSNA58S8EX |
Localize | Spelling (AU-US) | Question
When would you choose a histogram over a bar chart to display data?
Answer:
|
Question
When would you choose a histogram over a bar chart to display data?
Answer:
|
Classifier: The answer contains the AU/UK spelling "favourite colour", which requires localization to US spelling "favorite color". Verifier: The answer contains "favourite colour", which is AU/UK spelling and requires localization to US "favorite color". |
01K9CJV85XDD878ZTR37KWD9Z3 |
Localize | Spelling (AU-US) | Question
Why do consecutive sequences naturally form pairs that balance each other, regardless of the actual numbers involved?
Answer:
|
Question
Why do consecutive sequences naturally form pairs that balance each other, regardless of the actual numbers involved?
Answer:
|
Classifier: The answer contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: The answer contains the AU spelling "centre", which requires localization to the US spelling "center". |
01K9CJV86RH9BRH4NBFYHZTW96 |
Localize | Spelling (AU-US) | Question
Why does the cross method work for factorising a quadratic like $ax^2+bx+c$?
Answer:
|
Question
Why does the cross method work for factoring a quadratic like $ax^2+bx+c$?
Answer:
|
Classifier: The text contains the AU spelling "factorising", which needs to be converted to the US spelling "factorizing". Verifier: The text contains the AU spelling "factorising", which requires localization to "factorizing". |
01K9CJV867NKEXV0XTE729MVEZ |
Localize | Terminology | Question
In any right-angled triangle, why is the sine of one acute angle equal to the cosine of the other?
Answer:
|
Question
In any right triangle, why is the sine of one acute angle equal to the cosine of the other?
Answer:
|
Classifier: The term "right-angled triangle" is the standard AU/UK term. The US equivalent is "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas the US uses "right triangle". This is a terminology difference requiring localization. |
01K9CJKKZ43R7CA6TCGWHX0DD4 |
Localize | Spelling (AU-US) | Question
When trying to factorise $2x^3 - 5x^2 + x + 2$, what values should you test as possible rational roots?
Answer:
|
Question
When trying to factor $2x^3 - 5x^2 + x + 2$, what values should you test as possible rational roots?
Answer:
|
Classifier: Contains the AU spelling "factorise", which needs to be converted to the US spelling "factorize". Verifier: Contains the AU spelling "factorise", which requires conversion to US spelling "factorize". |
01K9CJV86Y07XR57ZKQPV5AQ9N |
Localize | Spelling (AU-US) | Question
What makes the form $y=a(x-h)^3+k$ useful for graphing cubics?
Answer:
|
Question
What makes the form $y=a(x-h)^3+k$ useful for graphing cubics?
Answer:
|
Classifier: The answer contains the AU spelling 'centre', which requires localization to the US spelling 'center'. Verifier: The answer contains the AU spelling "centre", which requires localization to "center" for the US market. |
01K9CJV87CR0DKJXM3VZA6TJMG |
Localize | Spelling (AU-US) | Question
What does the line of best fit represent in bivariate data?
Answer:
|
Question
What does the line of best fit represent in bivariate data?
Answer:
|
Classifier: The answer text contains the AU spelling "minimising", which requires conversion to the US spelling "minimizing". Verifier: The answer text contains "minimising", which is the AU/UK spelling. US English uses "minimizing". |
12767c89-5fd9-4315-b4ff-4edbf637d58e |
Localize | Units (textual) | Question
Why do we need different units to measure weight?
Answer:
|
Question
Why do we need different units to measure weight?
Answer:
|
Classifier: The text explicitly mentions metric units ("grams", "kilograms") in a descriptive/conceptual context regarding measurement. Per decision rules, any metric unit requires RED classification. Verifier: The text contains metric units "grams" and "kilograms". Even in a conceptual context, the presence of metric units requires RED classification. |
17c12875-49b5-45dd-a055-67dbd5fca574 |
Localize | Spelling (AU-US) | Question
Why must we know the data type before we look at the data?
Answer:
|
Question
Why must we know the data type before we look at the data?
Answer:
|
Classifier: The answer contains the AU spelling "organise", which needs to be converted to the US spelling "organize". Verifier: The answer contains the AU spelling "organise", which requires localization to "organize". |
1NpzMbjPnfrLVv6lokbc |
Localize | Terminology | Multiple Choice
What are the two parts of an angle called?
Options:
|
Multiple Choice
What are the two parts of an angle called?
Options:
|
Classifier: The term "arms" of an angle is standard AU/UK terminology; in the US, these are almost exclusively referred to as "sides" of an angle. Verifier: The term "arms" of an angle is specific to AU/UK pedagogy; US curriculum uses "sides". |
0adce98c-644f-49e3-8f1d-ef9dd6fa4714 |
Localize | Units (simple) | Question
Why do we multiply by $1000$ when changing cubic metres into litres?
Answer:
|
Question
Why do we multiply by $7.48$ when changing cubic feet into gallons?
Answer:
|
Classifier: The text contains metric units ("cubic metres", "litres") and AU-specific spellings ("metres", "litres"). Per the decision rules, any metric unit requires at least simple conversion classification. Verifier: The text contains metric units ("cubic metres", "litres") and AU-specific spellings ("metres", "litres"). This requires conversion to US customary units (e.g., cubic feet/gallons) for the US locale. |
06402f57-3b96-439c-b9d3-1b0b640e9c64 |
Localize | Terminology | Question
What makes substituting $x = \frac{-b}{2a}$ into $y = ax^2 + bx + c$ find the turning point?
Answer:
|
Question
What makes substituting $x = \frac{-b}{2a}$ into $y = ax^2 + bx + c$ find the vertex?
Answer:
|
Classifier: The term "turning point" is standard AU terminology for the vertex of a parabola. In a US context, "vertex" is the required term. Verifier: The term "turning point" is the standard AU curriculum term for the vertex of a parabola, whereas "vertex" is the standard US term. This requires localization for school context. |
144d5dba-dfef-4a2e-9904-6f6e9aef584c |
Localize | Spelling (AU-US) | Question
Why is organising data into frequency tables useful for solving real-world problems like surveys?
Hint: Consider how frequency tables make data interpretation efficient.
Answer:
|
Question
Why is organizing data into frequency tables useful for solving real-world problems like surveys?
Hint: Consider how frequency tables make data interpretation efficient.
Answer:
|
Classifier: The text contains the AU spelling "organising" (used twice), which requires conversion to the US spelling "organizing". Verifier: The text contains "organising" (in both content and answer), which is the AU spelling. US English uses "organizing". |
0287890a-131d-4c91-bd3a-7d7ef1de3852 |
Localize | Spelling (AU-US) | Question
How is $e$ used to calculate continuously compounded interest?
Hint: Visualise how $e$ models compounding.
Answer:
|
Question
How is $e$ used to calculate continuously compounded interest?
Hint: Visualize how $e$ models compounding.
Answer:
|
Classifier: The hint contains the AU spelling "Visualise", which should be "Visualize" in US English. Verifier: The hint contains the AU spelling "Visualise", which requires localization to "Visualize". |
0dab4a12-515d-4432-8f8a-07e1d27f9c1d |
Localize | Spelling (AU-US) | Question
Why does a periodic function repeat itself at regular intervals?
Hint: Visualise the repeating nature of the function on a graph.
Answer:
|
Question
Why does a periodic function repeat itself at regular intervals?
Hint: Visualize the repeating nature of the function on a graph.
Answer:
|
Classifier: The word "Visualise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Visualize"). Verifier: The word "Visualise" in the hint uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Visualize"). |
0sUp7zhU0ehKrQKrQSFV |
Localize | Units (simple) | Multiple Choice
Convert $1000$ mL to m$^3$.
Options:
|
Multiple Choice
Convert $1000$ fl oz to ft$^3$.
Options:
|
Classifier: The question explicitly requires conversion between metric units (mL to m^3). All metric units trigger a RED classification. |
0fa1fae9-c9f6-4436-900f-429fa0587716 |
Localize | Spelling (AU-US) | Question
What makes a tree diagram a good way to show all the possible outcomes?
Answer:
|
Question
What makes a tree diagram a good way to show all the possible outcomes?
Answer:
|
Classifier: The word "organises" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("organizes"). Verifier: The word "organises" in the answer content is AU/UK spelling and requires localization to "organizes". |
02053a1b-12b8-4df7-b8b1-4d9bdb832690 |
Localize | Spelling (AU-US) | Question
How does understanding grouping relate to factorising expressions?
Answer:
|
Question
How does understanding grouping relate to factoring expressions?
Answer:
|
Classifier: Contains the AU spelling "factorising" and "factorise", which should be "factorizing" and "factorize" in US English. Verifier: The text contains "factorising" and "factorise", which are AU/British spellings. |
1NgFYFPfIvt2bbEKNbJC |
Localize | Spelling (AU-US) | Question
Steffi has deposited $\$800$ in her bank account that pays her $2.5\%$ per annum, compounded monthly.
As she has received an increment in her salary, she is now adding $\$70$ monthly to that account.
Steffi's saving s can be modelled using recurrecnce relation: $V_{n+1}=RV_{n}+D$ where $n$ is the number of additional deposits made by her.
What is the value of $D$ here?
Answer:
|
Question
Steffi has deposited $\$800$ in her bank account that pays her $2.5\%$ per year, compounded monthly.
As she has received a raise in her salary, she is now adding $\$70$ monthly to that account.
Steffi's savings can be modeled using the recurrence relation: $V_{n+1}=RV_{n}+D$ where $n$ is the number of additional deposits made by her.
What is the value of $D$ here?
Answer:
|
Classifier: Contains AU-specific spelling "modelled" (US: modeled) and "recurrecnce" (typo, but in a context requiring review) and "per annum" (though used in US, often localized in school contexts, but "modelled" is a definitive spelling trigger). Also contains a typo "saving s". Verifier: Contains AU spelling "modelled" (US: modeled). Also contains typos "saving s" and "recurrecnce" which require review. |
19a71161-bd7d-428e-b8b2-2e16a07dd086 |
Localize | Spelling (AU-US) | Question
What makes negative bases unique in exponents?
Hint: The behaviour depends on whether the exponent is odd or even.
Answer:
|
Question
What makes negative bases unique in exponents?
Hint: The behavior depends on whether the exponent is odd or even.
Answer:
|
Classifier: Contains the AU spelling "behaviour", which needs to be converted to the US spelling "behavior". Verifier: Contains the AU spelling "behaviour", which requires localization to "behavior". |
04wGWjPRJyiNn2USXZws |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $100x^2-10x-10x+1$ by grouping.
Options:
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Multiple Choice
Factor $100x^2-10x-10x+1$ by grouping.
Options:
|
Classifier: Contains the AU spelling "Factorise", which must be localized to "Factorize" for a US audience. Verifier: Contains the AU spelling "Factorise", which must be localized to "Factorize" for a US audience. |
1851e896-f566-4492-9809-4052d654c64f |
Localize | Spelling (AU-US) | Question
Why do box plots use the median and interquartile range to summarise data?
Answer:
|
Question
Why do box plots use the median and interquartile range to summarize data?
Answer:
|
Classifier: The answer contains the AU spelling "centre", which needs to be converted to the US spelling "center". The question also uses "summarise", which needs to be "summarize". Verifier: The text contains AU spellings "summarise" and "centre", which require localization to "summarize" and "center". |
120c51b2-8035-4e7d-8d0a-806751e2965f |
Localize | Spelling (AU-US) | Question
Why do we need multiple measurements to fully describe a wave?
Hint: Consider how amplitude, wavelength, and period provide a complete description.
Answer:
|
Question
Why do we need multiple measurements to fully describe a wave?
Hint: Consider how amplitude, wavelength, and period provide a complete description.
Answer:
|
Classifier: The text contains the AU/UK spelling "behaviour", which needs to be converted to the US spelling "behavior". Verifier: The answer text contains the AU spelling "behaviour", which requires localization to "behavior". |
0yaUKB8lSyJ1yB2kHaxg |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the equation of a semicircle that corresponds to the upper half of a circle with centre at $(4,4)$ and radius $2$ units with its base on the $x-$axis ?
Options:
|
Multiple Choice
Which of the following is the equation of a semicircle that corresponds to the upper half of a circle with center at $(4,4)$ and radius $2$ units with its base on the $x-$axis?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to "center" for US localization. Verifier: Contains the AU spelling "centre", which needs to be converted to "center" for US localization. |
1RJRg2RQjRRxvsVRNg3c |
Localize | Terminology | Multiple Choice
True or false:
The gradients of the lines $y=2$ and $x=2$ are equal.
Options:
|
Multiple Choice
True or false:
The slopes of the lines $y=2$ and $x=2$ are equal.
Options:
|
Classifier: The term "gradients" is the standard AU term for what is referred to as "slope" in US school mathematics. Verifier: The term "gradients" is the standard AU term for what is referred to as "slope" in US school mathematics. This requires localization for a US audience. |
1d262a4a-5b3c-4b64-a62c-d1df621bf39a |
Localize | Terminology | Question
Why is the difference of squares useful for solving quadratic equations?
Answer:
|
Question
Why is the difference of squares useful for solving quadratic equations?
Answer:
|
Classifier: The text uses the term "brackets" to refer to the parts of a factored quadratic equation. In a US educational context, "parentheses" is the standard term for $(x-a)(x-b)$. While "brackets" is understood, it is a distinct regional preference in mathematical terminology. Verifier: The use of "brackets" to refer to parentheses in a factoring context is a regional terminology difference (AU/UK vs US). |
1a677062-dbf1-4610-9fc8-61cef20e8d51 |
Localize | Terminology | Question
Why is understanding orders (exponents) important in solving BODMAS problems?
Answer:
|
Question
Why is understanding exponents important in solving PEMDAS problems?
Answer:
|
Classifier: The text uses "BODMAS", which is the standard acronym in AU/UK, whereas the US uses "PEMDAS". Verifier: Uses "BODMAS", which is the standard acronym in AU/UK, whereas the US uses "PEMDAS". This is a school-context terminology difference. |
1f8c99a6-3863-4510-aeab-d220a960b13e |
Localize | Spelling (AU-US) | Question
Why do we use two-way tables for calculating probabilities?
Answer:
|
Question
Why do we use two-way tables for calculating probabilities?
Answer:
|
Classifier: Contains the AU spelling "organise", which needs to be converted to the US spelling "organize". Verifier: The answer text contains the AU spelling "organise", which must be localized to the US spelling "organize". |
1s0bwttwE87jXq4bbrTQ |
Localize | Units (simple) | Question
Find the area of kite $PQRS$ with diagonals $PR = 10$ m and $QS = 12$ m.
Answer:
|
Question
Find the area of kite $PQRS$ with diagonals $PR = 10$ ft and $QS = 12$ ft.
Answer:
|
Classifier: The text contains metric units ("m" for meters and "m^2" for square meters) which require conversion to US customary units. Verifier: The question contains metric units ("m" and "m^2") which require conversion to US customary units. The calculation is a simple area of a kite, fitting simple conversion. |
1f39c7dc-2d43-43a9-bc62-ffead0478950 |
Localize | Terminology | Question
Why is $(h,k)$ the turning point in the equation $y=a(x-h)^2+k$?
Answer:
|
Question
Why is $(h,k)$ the vertex in the equation $y=a(x-h)^2+k$?
Answer:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term used for the (h, k) point of a quadratic function. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US mathematics curricula. This requires localization for a US audience. |
1hwgLgDADCp6dduoYUMI |
Localize | Terminology | Multiple Choice
Which graph would best display the growth of a puppy over time?
Options:
|
Multiple Choice
Which graph would best display the growth of a puppy over time?
Options:
|
Classifier: The terms "Picture graph" and "Column graph" are standard in the Australian curriculum (ACARA), whereas the US equivalents are typically "Pictograph" and "Bar graph". Verifier: The terms "Picture graph" and "Column graph" are specific to the Australian curriculum (ACARA). In the US, "Pictograph" and "Bar graph" are the standard terms. |
2BheiAJOYmPuFtqdh6LM |
Localize | Units (complex) | Question
A body starts at rest and its velocity is given by $v(t)=3t^2-4t$ m/s.
Find its change in displacement in the first $6$ seconds.
Answer:
|
Question
A body starts at rest and its velocity is given by $v(t)=3t^2-4t$ ft/s.
Find its change in displacement in the first $6$ seconds.
Answer:
|
Classifier: The question contains metric units ("m/s" and "m") which require localization to US customary units (e.g., ft/s and ft) according to the decision rules. Verifier: The question contains metric units ("m/s" and "m"). However, the velocity is defined by a function v(t) = 3t^2 - 4t. According to rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients (calculus-based displacement from velocity) should be classified as RED.units_complex_converted. |
21xytvQKgEMY6SMBKB3Q |
Localize | Spelling (AU-US) | Question
Rationalise the fraction ${\Large\frac{2}{\sqrt{7}}}$.
Express your answer as a fraction in simplest form.
Options:
|
Question
Rationalize the fraction ${\Large\frac{2}{\sqrt{7}}}$.
Express your answer as a fraction in simplest form.
Options:
|
Classifier: Contains the AU spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: The word "Rationalise" uses AU/UK spelling (ending in -ise) and must be localized to the US spelling "Rationalize". |
2CnG2FYUhBZiZ2vGdh9c |
Localize | Units (simple) | Question
A rectangle has a perimeter of $28$ cm and a length of $10$ cm.
What is its width?
Answer:
|
Question
A rectangle has a perimeter of $28$ in and a length of $10$ in.
What is its width?
Answer:
|
Classifier: The question uses "cm" (centimetres), which is a metric unit requiring localization to US customary units (e.g., inches). Verifier: Contains metric unit "cm" in a simple geometric context, requiring straightforward conversion. |
24b0f43f-35c9-455b-9ce9-e2f9dba1dcec |
Localize | Units (simple) | Question
Why is it important to understand decimal shifts when solving measurement problems?
Answer:
|
Question
Why is it important to understand decimal shifts when solving measurement problems?
Answer:
|
Classifier: The text contains metric units ("metres" and "centimetres") and AU-specific spelling ("metres"). Per the decision rules, any metric unit found anywhere requires classification into a units category. Since it involves a simple conversion example, it is classified as units_simple_conversion. Verifier: The text contains metric units ("metres", "centimetres") and AU spelling ("metres"). This requires a RED classification. Since it is a simple conceptual example of unit conversion, units_simple_conversion is appropriate. |
1hgQAN7rL9YjWHtWGmvn |
Localize | Terminology | Multiple Choice
In Melbourne, $120$ schools are randomly surveyed to study the effects of remote learning.
Which group is the population?
Options:
|
Multiple Choice
In New York City, $120$ schools are randomly surveyed to study the effects of remote learning.
Which group is the population?
Options:
|
Classifier: The text contains specific Australian geographic references ("Melbourne", "Victoria") used to define the population and sample in a statistics problem. These should be localized to a US context (e.g., a US city and state) to be relevant to the target audience. Verifier: The text contains specific Australian geographic references ("Melbourne", "Victoria") which are used to define the population and sample in a statistics context. These require localization to a US context. |
273734d9-801c-4edf-ba93-81f37ac8710f |
Localize | Spelling (AU-US) | Question
How do asymptotes relate to understanding graphs?
Answer:
|
Question
How do asymptotes relate to understanding graphs?
Answer:
|
Classifier: Contains the AU spelling "behaviour", which requires conversion to US "behavior". Verifier: The answer text contains the AU spelling "behaviour", which requires localization to US "behavior". |
2Sqnhf02oGKhraaZpt17 |
Localize | Spelling (AU-US) | Question
Lauren wants to choose three scoops of ice cream from $5$ different flavours, with each flavour used only once.
How many combinations of three scoops can she make?
Answer:
|
Question
Lauren wants to choose three scoops of ice cream from $5$ different flavors, with each flavor used only once.
How many combinations of three scoops can she make?
Answer:
|
Classifier: Contains the AU/UK spelling "flavours" (US: "flavors"). Verifier: The text contains "flavours", which is the AU/UK spelling. US spelling is "flavors". Per rule 1, this requires RED classification. |
1tvtKJdYX8ODIEe8tmKy |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(x-3a)(x+3a)(x^{2}+{9a}^{2})$ ?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(x-3a)(x+3a)(x^{2}+{9a}^{2})$ ?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The word "factorised" is used, which is the AU/UK spelling. US spelling is "factorized". |
1vnRx5dh5msyp72IubB1 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following correctly splits the middle term in $x^2 + 5x +6$ so it can be factorised by grouping?
Options:
|
Multiple Choice
Which of the following correctly splits the middle term in $x^2 + 5x +6$ so it can be factored by grouping?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The word "factorised" uses the AU/UK 's' spelling; US spelling is "factorized". |
1w568hYaXMjFqGF5HOa8 |
Localize | Units (complex) | Multiple Choice
Find the velocity function $v(t)$ if the displacement function is $s(t)=4t^2+5t$ m for $t\geq 0$ s.
Options:
|
Multiple Choice
Find the velocity function $v(t)$ if the displacement function is $s(t)=4t^2+5t$ ft for $t\geq 0$ s.
Options:
|
Classifier: The text contains metric units ("m" for meters, "s" for seconds, and "m/s" for meters per second) which require conversion to US customary units. Verifier: While the primary classifier correctly identified metric units ("m", "s", "m/s"), this involves a displacement function s(t) and a velocity function v(t). Per rule 4, equations defining quantities in metric or functions where units are interlinked with the algebraic expression should be classified as RED.units_complex_converted to ensure human review of the functional context. |
1ZZfCpJHcJvQ9dZtrhq1 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the general equation of a semicircle with centre $(a,b)$ and radius $r$ units?
Options:
|
Multiple Choice
Which of the following is the general equation of a semicircle with center $(a,b)$ and radius $r$ units?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be localized to "center" for a US audience. Verifier: Contains the AU spelling "centre", which requires localization to "center". |
2ZHueD0MmDY7zD3OFJJq |
Localize | Units (simple) | Question
Fill in the blank:
$24$ kilograms $+[?]$ megagrams $=10024$ kilograms
Answer:
|
Question
Fill in the blank:
$24$ pounds $+[?]$ kilopounds $=10024$ pounds
Answer:
|
Classifier: Contains metric units "kilograms" and "megagrams" which require localization to US customary units or a specific metric-pedagogy handling for the US market. Verifier: The question contains metric units "kilograms" and "megagrams". According to rule 3, any metric unit requires at least RED classification. This is a simple conversion/arithmetic problem. |
2PbodiWsCdlQXaQB5dmR |
Localize | Spelling (AU-US) | Question
Steffi has deposited $\$800$ in her bank account that pays her $2.5\%$ per annum, compounded monthly.
As she has received an increment in her salary, she is now adding $\$70$ monthly to that account.
Steffi's savings can be modelled using recurrence relation: $V_{n+1}=1.002V_{n}+70$ where $n$ is the number of additional deposits made by her.
How much will she save after $3$ months?
Answer:
|
Question
Steffi has deposited $\$800$ in her bank account that pays her $2.5\%$ per year, compounded monthly.
As she has received a raise in her salary, she is now adding $\$70$ monthly to that account.
Steffi's savings can be modeled using the recurrence relation: $V_{n+1}=1.002V_{n}+70$ where $n$ is the number of additional deposits made by her.
How much will she save after $3$ months?
Answer:
|
Classifier: The text contains the AU/UK spelling "modelled" (US: "modeled"). While the currency symbol is neutral ($), the spelling requires localization. Verifier: The text contains "modelled", which is the AU/UK spelling. US spelling is "modeled". Per rule 1, any AU spelling requires RED classification. |
1jJrYIuZ70vvGXtFA7gx |
Localize | Terminology | Multiple Choice
Find the maximal domain of the quotient function $(\frac{f}{g})(x)$ for $f(x)=\ln(x)$ and $g(x)=\sin(x)$ where $x\in [-2\pi,2\pi]$.
Options:
|
Multiple Choice
Find the maximum domain of the quotient function $(\frac{f}{g})(x)$ for $f(x)=\ln(x)$ and $g(x)=\sin(x)$ where $x\in [-2\pi,2\pi]$.
Options:
|
Classifier: The term "maximal domain" is a specific phrasing common in the Australian (VCE) curriculum. In a US context, this is almost always referred to simply as the "domain" or "implied domain". Verifier: The term "maximal domain" is a specific phrasing used in the Australian (VCE) curriculum. In the US, "domain" or "implied domain" is used. |
2a24ec8d-51f2-4e12-a6d5-14f19c4cbcdd |
Localize | Terminology | Question
What makes turning points special coordinates when writing parabola equations?
Answer:
|
Question
What makes vertices special coordinates when writing parabola equations?
Answer:
|
Classifier: The text uses the term "turning points", which is the standard AU term for the "vertex" of a parabola. While the answer mentions "vertex" as an explanation, the primary question uses "turning points", which is a specific terminology mapping. Verifier: The term "turning points" is the standard Australian curriculum term for the vertex of a parabola, whereas "vertex" is the standard US term. This is a terminology mapping issue. |
2dce154f-cc8e-49e1-90e5-4099d55758f5 |
Localize | Spelling (AU-US) | Question
Why can data without an order not be arranged from lowest to highest?
Answer:
|
Question
Why can data without an order not be arranged from lowest to highest?
Answer:
|
Classifier: The answer contains the AU spelling "colours", which needs to be converted to the US spelling "colors". Verifier: The answer contains the AU spelling "colours", which must be localized to "colors". |
2a005ee3-8f53-4557-83cd-cafb1ab5ec92 |
Localize | Units (simple) | Question
How can changing units of length make solving real-world problems, like measuring distances, easier?
Answer:
|
Question
How can changing units of length make solving real-world problems, like measuring distances, easier?
Answer:
|
Classifier: The text contains metric units ("km", "m") and the AU spelling "metres". Per the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units (km, m) and the AU spelling "metres", which requires localization for a US audience. |
2abc3908-4e42-4f98-8ab5-f595c42edde4 |
Localize | Units (simple) | Question
Why do we use different units to measure liquids and solids?
Answer:
|
Question
Why do we use different units to measure liquids and solids?
Answer:
|
Classifier: The text contains the metric unit "litres", which also uses AU spelling. This requires conversion to US customary units (e.g., gallons/quarts) or at least spelling/unit localization. Verifier: The text uses the metric unit "litres", which is both a metric unit and an AU spelling. This requires localization to US customary units or at least spelling/unit adjustment. |
2cce3326-5707-4bdd-80bd-c96b4bc6752c |
Localize | Spelling (AU-US) | Question
Why must every point on a circle be exactly $r$ units (the radius) from the centre $(h,k)$?
Answer:
|
Question
Why must every point on a circle be exactly $r$ units (the radius) from the center $(h,k)$?
Answer:
|
Classifier: The text contains the AU spelling "centre", which requires conversion to the US spelling "center". While it mentions "units", they are abstract algebraic units ("r units") rather than metric units. Verifier: The text contains the AU spelling "centre", which requires localization to "center". |
2klsyZIzAQKmjVDHEOKr |
Localize | Units (simple) | Question
Find the total surface area of a rectangular prism with dimensions $1.5$ cm $\times$ $2.1$ cm $\times$ $5$ cm.
Answer:
|
Question
Find the total surface area of a rectangular prism with dimensions $1.5$ in $\times$ $2.1$ in $\times$ $5$ in.
Answer:
|
Classifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. It is a simple conversion as it involves a basic geometric shape with few values. |
2f82c786-b789-4f90-a9d1-135342de80f9 |
Localize | Terminology | Question
Why does the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ work for finding distances?
Answer:
|
Question
Why does the distance formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ work for finding distances?
Answer:
|
Classifier: The answer contains the term "right triangle" which is US-neutral, but it also uses "Pythagoras’ theorem". In US contexts, this is almost exclusively referred to as the "Pythagorean theorem". Additionally, "right-angled triangle" is the standard AU term, though "right triangle" appears here, the theorem name requires localization. Verifier: The text uses "Pythagoras’ theorem", which is the standard term in AU/UK, whereas "Pythagorean theorem" is the standard US term. This requires localization for the US market. |
39d70f13-7750-4da0-a751-447a5594be36 |
Localize | Spelling (AU-US) | Question
Why is analysing the strength of data relationships important for making accurate conclusions?
Answer:
|
Question
Why is analyzing the strength of data relationships important for making accurate conclusions?
Answer:
|
Classifier: The text uses the US spelling "analysing" (wait, "analysing" is actually AU/UK; US is "analyzing"). Correction: The word "analysing" in the source value is the AU/UK spelling. US spelling is "analyzing". Verifier: The text contains the word "analysing", which is the AU/UK spelling. The US spelling is "analyzing". Per rule 1, any AU spelling requires RED classification. |
3IlvafO33ogKxbjZXNw2 |
Localize | Spelling (AU-US) | Question
Fill in the blank.
Seasonal indices$=[?]$
Actual value$=6000$
Deseasonalised value$=5000$
Answer:
|
Question
Fill in the blank.
Seasonal indices$=[?]$
Actual value$=6000$
Deseasonalized value$=5000$
Answer:
|
Classifier: Contains the AU/UK spelling "Deseasonalised", which requires conversion to the US spelling "Deseasonalized". Verifier: Contains "Deseasonalised", which is the AU/UK spelling (US: Deseasonalized). |
3YXgNxA1mefDLaNoLq6P |
Localize | Spelling (AU-US) | Question
It is observed that $20\%$ of cars entering a car park are red.
What is the probability that the next three cars entering are all red?
Assume each car's colour is independent.
Answer:
|
Question
It is observed that $20\%$ of cars entering a parking lot are red.
What is the probability that the next three cars entering are all red?
Assume each car's color is independent.
Answer:
|
Classifier: Contains the AU spelling "colour", which needs to be converted to "color" for US localization. Verifier: Contains "colour", which is AU spelling and requires localization to "color". |
3775c733-0444-4acd-864e-32b5689fb856 |
Localize | Spelling (AU-US) | Question
How do frequency tables relate to understanding categorical variables?
Answer:
|
Question
How do frequency tables relate to understanding categorical variables?
Answer:
|
Classifier: Contains the AU spelling "summarise" in the answer content, which needs to be converted to "summarize" for US localization. Verifier: Contains the AU spelling "summarise" in the answer content, which needs to be converted to "summarize" for US localization. |
32339cad-6de2-4201-859c-f342b2bcd6f3 |
Localize | Spelling (AU-US) | Question
Why must we understand number structure to simplify square roots effectively?
Hint: We break the expression into factors for easier calculation.
Answer:
|
Question
Why must we understand number structure to simplify square roots effectively?
Hint: We break the expression into factors for easier calculation.
Answer:
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Classifier: The word "recognising" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("recognizing"). Verifier: The answer text contains the word "recognising", which is the AU/UK spelling. US English requires "recognizing". |
3LDZmZPsTEJ3mb1LWrjW |
Localize | Units (simple) | Question
How many cubic centimetres are there in $2$ cubic metres ?
Answer:
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Question
How many cubic inches are there in $2$ cubic feet ?
Answer:
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Classifier: The question is specifically about converting between metric units ("cubic centimetres" and "cubic metres") and contains AU spelling ("centimetres", "metres"). Per rule 6, units conversion is the most impactful change. Verifier: The question specifically asks for a conversion between metric units and uses AU spelling ("centimetres", "metres"). |
3ADaU3MnxdNVQQd83mdG |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
The expression $9x^2+84x+171$ can be factorised by completing the square.
Options:
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Multiple Choice
True or false:
The expression $9x^2+84x+171$ can be factored by completing the square.
Options:
|
Classifier: Contains the AU spelling "factorised" which needs to be converted to the US spelling "factorized". Verifier: The text contains the AU spelling "factorised", which must be localized to the US spelling "factorized". |
35CwtKThCwlKmkATOFvr |
Localize | Units (simple) | Question
Sandra's sandbox has dimensions $3$ m $\times$ $2$ m $\times$ $0.5$ m. Sand costs $\$6.50$ per m$^3$.
How much will it cost to fill the sandbox?
Answer:
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Question
Sandra's sandbox has dimensions $3$ ft $\times$ $2$ ft $\times$ $0.5$ ft. Sand costs $\$6.50$ per ft$^3$.
How much will it cost to fill the sandbox?
Answer:
|
Classifier: The text contains metric units (m, m^3) which require conversion for US localization. Verifier: The question contains metric units (m, m^3) which require conversion for US localization. It is a simple conversion as it involves basic volume and cost calculation. |
31c70609-0dc6-43e6-9bc6-dded9c2944fa |
Localize | Spelling (AU-US) | Question
How can creating a frequency table simplify analysing patterns in data?
Hint: Focus on how organised data reveals trends.
Answer:
|
Question
How can creating a frequency table simplify analyzing patterns in data?
Hint: Focus on how organized data reveals trends.
Answer:
|
Classifier: The text contains the AU spellings "analysing" and "organised", which require conversion to US "analyzing" and "organized". Verifier: The text contains AU spellings "analysing" (in content and answer) and "organised" (in hint), which require localization to US spelling. |
3bDxmjth6VbTlNAiNzIq |
Localize | Units (simple) | Question
The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$.
If the container initially has $10$ litres of water, what is the volume after $4$ hours?
Answer:
|
Question
The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$.
If the container initially has $10$ gallons of water, what is the volume after $4$ hours?
Answer:
|
Classifier: The text contains the metric unit "litres", which requires both spelling localization ("liters") and unit conversion to US customary units (e.g., gallons or quarts) per the hierarchy where unit conversion is the most impactful change. Verifier: The text contains "litres", which is both a metric unit requiring conversion and an AU/UK spelling. Per rule 5, unit conversion is the most impactful change. |
37Y9Hazm2jsIyAFw9B56 |
Localize | Units (simple) | Question
The velocity function of an object is given by $v(t)=2t-6$ m/s for $t\geq0$.
Find the average speed between $t=2$ to $t=4$ seconds.
Hint: Remember to consider the change in direction of the object.
Answer:
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Question
The velocity function of an object is given by $v(t)=2t-6$ ft/s for $t\geq0$.
Find the average speed between $t=2$ to $t=4$ seconds.
Hint: Remember to consider the change in direction of the object.
Answer:
|
Classifier: Contains the metric unit "m/s" (metres per second). Even though "m" is used in a rate, it represents a metric unit of length. Verifier: Contains the metric unit "m/s" (metres per second). Even though "m" is used in a rate, it represents a metric unit of length and requires localization. |
37567cf3-ce3d-4ad8-86c0-6e17aa198102 |
Localize | Spelling (AU-US) | Question
What makes $x \in \mathbb{R}$ describe all real numbers for a domain?
Hint: Visualise how the set encompasses all numbers.
Answer:
|
Question
What makes $x \in \mathbb{R}$ describe all real numbers for a domain?
Hint: Visualize how the set encompasses all numbers.
Answer:
|
Classifier: Contains the AU spelling "Visualise" in the hint field, which needs to be converted to "Visualize" for US localization. Verifier: Contains the AU spelling "Visualise" in the hint field, which needs to be converted to "Visualize" for US localization. |
37b74f8d-319f-44bb-b230-e8d1bd0239ed |
Localize | Units (simple) | Question
How can knowing SI prefixes make unit conversions easier?
Answer:
|
Question
How can knowing SI prefixes make unit conversions easier?
Answer:
|
Classifier: Contains metric units ("kilometres", "metres") and AU-specific spelling ("kilometres", "metres"). This is a metric-pedagogy question. Verifier: Contains metric units ("kilometres", "metres") and AU-specific spelling ("kilometres", "metres"). This is a metric-pedagogy question requiring localization. |
3CCCqXTQGIW333h0F8S8 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is not categorical data?
Options:
|
Multiple Choice
Which of the following is not categorical data?
Options:
|
Classifier: The text contains the AU spelling "colour" which requires conversion to the US spelling "color". While "cricketer" is more common in AU/UK, it is a valid noun in the US and does not strictly require localization compared to the spelling error. Verifier: The text contains the AU spelling "colour" in one of the answer choices, which requires localization to "color". |
345a4f08-16d6-49c9-b8a9-c5849bbd4f72 |
Localize | Spelling (AU-US) | Question
Why do exponential functions always have horizontal asymptotes?
Hint: The asymptote reflects the function's limiting behaviour.
Answer:
|
Question
Why do exponential functions always have horizontal asymptotes?
Hint: The asymptote reflects the function's limiting behavior.
Answer:
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Classifier: Contains the AU spelling "behaviour", which requires conversion to the US spelling "behavior". Verifier: The text contains the AU spelling "behaviour" in the hint field, which requires localization to "behavior". |
36B4IujuAFBmsiOOJ3vK |
Localize | Units (simple) | Question
What is the distance along $26^\circ$N between ($26^\circ$N, $150^\circ$W) and ($26^\circ$N, $112^\circ$W), rounded to two significant figures?
Hint: Take the Earth's radius to be $6371$ km
Answer:
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Question
What is the distance along $26^\circ$N between ($26^\circ$N, $150^\circ$W) and ($26^\circ$N, $112^\circ$W), rounded to two significant figures?
Hint: Take the Earth's radius to be $3959$ miles
Answer:
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Classifier: The text contains metric units (km) for Earth's radius and the final answer, requiring conversion to miles for US localization. Verifier: The question uses kilometers (km) for Earth's radius and the answer, which requires conversion to miles for US localization. |
37e69e04-d21b-429b-8a8f-5c94bf49440b |
Localize | Units (simple) | Question
Why do metric measurements use powers of $10$?
Hint: Think about how moving the decimal point left or right converts between units like metres and centimetres.
Answer:
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Question
Why do metric measurements use powers of $10$?
Hint: Think about how moving the decimal point left or right converts between units like meters and centimeters.
Answer:
|
Classifier: The text contains metric units ("metres" and "centimetres") and AU-specific spelling ("metres"). According to the decision rules, any metric unit found anywhere results in at least RED.units_simple_conversion. Verifier: The text contains the metric units "metres" and "centimetres". "Metres" also uses AU/British spelling. Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
33miRD3Z2m2GJn0mzilh |
Localize | Units (simple) | Multiple Choice
An object starts from point $O$ and is moving in a straight line with the displacement function $s(t)=-2t^2+4t+2$ m for $0\leq t \leq 10$ s.
When and where does the object change its direction?
Options:
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Multiple Choice
An object starts from point $O$ and is moving in a straight line with the displacement function $s(t)=-2t^2+4t+2$ ft for $0\leq t \leq 10$ s.
When and where does the object change its direction?
Options:
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Classifier: The text contains metric units ("m" for metres and "s" for seconds) used in a physics/calculus context. Per decision rules, any metric unit requires classification as a units conversion category. Verifier: The text contains metric units ("m" for metres and "s" for seconds). Per decision rule 3, any metric unit requires RED classification. Simple conversion is appropriate as the values are straightforward and do not require re-deriving complex coefficients. |
37e4f9a5-efe5-47cc-b5cc-4b2a08b88ece |
Localize | Spelling (AU-US) | Question
Why are two-way frequency tables used to analyse potential associations between two categorical variables?
Answer:
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Question
Why are two-way frequency tables used to analyze potential associations between two categorical variables?
Answer:
|
Classifier: Contains the AU spelling "analyse", which needs to be converted to "analyze" for US localization. Verifier: Contains the AU spelling "analyse", which needs to be converted to "analyze" for US localization. |
3K2jMMgvKm8MEBj9tCQK |
Localize | Units (simple) | Multiple Choice
A particle moves in a straight line with velocity function $v(t) =6t^2+4t$ m s$^{-1}$.
Describe the motion of the particle at $t=2$ s given that it was initially at rest.
Options:
|
Multiple Choice
A particle moves in a straight line with velocity function $v(t) =6t^2+4t$ ft s$^{-1}$.
Describe the motion of the particle at $t=2$ s given that it was initially at rest.
Options:
|
Classifier: The text contains multiple metric units ("m s^{-1}", "m", "s") which require conversion to US customary units for localization. Verifier: The text contains metric units (m, s, m/s) which require conversion to US customary units. The conversion is simple as it involves substituting values into a given function or interpreting results. |
3e9f6d11-fca5-4918-a320-ed4edf243092 |
Localize | Spelling (AU-US) | Question
Why do we count categories in a frequency table?
Answer:
|
Question
Why do we count categories in a frequency table?
Answer:
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Classifier: The word "organise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("organize"). Verifier: The word "organise" in the answer content is AU/UK spelling and requires localization to "organize" for the US. |
3rFFqBId5tPsrgnPkFDD |
Localize | Terminology | Question
There are $16$ maths books, $31$ science books and $46$ English books on a bookshelf.
What fraction of total books are science books?
Express your answer in the simplest form.
Answer:
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Question
There are $16$ math books, $31$ science books and $46$ English books on a bookshelf.
What fraction of total books are science books?
Express your answer in the simplest form.
Answer:
|
Classifier: Contains the term "maths", which is the standard AU/UK term; the US equivalent is "math". Verifier: The term "maths" is the standard AU/UK term for the subject, whereas the US uses "math". This is a terminology difference in a school context. |
3o8hF5jljnITTzKcxWkh |
Localize | Units (simple) | Question
How much area is covered by the minute hand of a clock in $50$ minutes, given that the length of the minute hand is $13$ cm?
Answer:
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Question
How much area is covered by the minute hand of a clock in $50$ minutes, given that the length of the minute hand is $13$ in?
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. |
3bf2b459-659d-4dbd-a8b9-f8b985d4dea0 |
Localize | Spelling (AU-US) | Question
How can understanding negative bases help solve problems involving patterns?
Hint: Visualise how exponents change the outcome of negatives.
Answer:
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Question
How can understanding negative bases help solve problems involving patterns?
Hint: Visualize how exponents change the outcome of negatives.
Answer:
|
Classifier: The word "Visualise" in the hint field uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Visualize"). Verifier: The word "Visualise" in the hint field is AU/UK spelling and requires localization to "Visualize". |
3vDPfrjhkAFSOUEjrLIY |
Localize | Units (simple) | Question
A cyclist rides $10$ km in an easterly direction and then travels $23$ km south.
She then travels $50$ km on a bearing of $240^\circ \text{T}$.
After the journey, how far south is the cyclist from her starting point?
Answer:
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Question
A cyclist rides $10$ mi in an easterly direction and then travels $23$ mi south.
She then travels $50$ mi on a bearing of $240^\circ$.
After the journey, how far south is the cyclist from her starting point?
Answer:
|
Classifier: Contains metric units ("km") which require conversion for US localization. Verifier: The question uses "km" (kilometres), which is a metric unit requiring conversion to US customary units (miles). The conversion is a straightforward distance calculation, fitting simple conversion. |
461cd49f-77fb-4ce1-ab11-650ea64d7e7c |
Localize | Spelling (AU-US) | Question
Why do timetables use columns to show different times and locations?
Answer:
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Question
Why do schedules use columns to show different times and locations?
Answer:
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Classifier: Contains the AU spelling "organise", which requires conversion to the US spelling "organize". Verifier: The answer text contains the AU spelling "organise", which requires localization to the US spelling "organize". |
3v6zX3d2t2s1TQUyEg5v |
Localize | Terminology | Question
Write the equation $6x+3y=3$ in gradient-intercept form.
Simplify where possible.
Options:
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Question
Write the equation $6x+3y=3$ in slope-intercept form.
Simplify where possible.
Options:
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Classifier: The term "gradient-intercept form" is the standard AU term for what is typically called "slope-intercept form" in the US. Verifier: The term "gradient-intercept form" is the standard AU term for what is called "slope-intercept form" in the US. |
4IXiiZCIqFuV68EbLkyD |
Localize | Units (simple) | Question
If Naruto can run a distance of $600$ m in $8$ sec, what is his average speed?
Answer:
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Question
If Naruto can run a distance of $600$ ft in $8$ sec, what is his average speed?
Answer:
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Classifier: The question contains metric units ("m" for metres and "m/s"), which require localization to US customary units or a decision on metric usage in US curriculum. Verifier: The question contains metric units ("m" and "m/s") which require conversion for US localization. It is a simple conversion as it involves a single calculation and straightforward units. |
4IroUAd4Luq2k58Wj28p |
Localize | Units (simple) | Question
How many mL are there in $0.1$ L ?
Answer:
|
Question
How many fl oz are there in $0.1$ gal ?
Answer:
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Classifier: The question is specifically about converting between metric units (mL and L), which is a metric-pedagogy question requiring localization. Verifier: This is a metric-pedagogy question (converting mL to L). While it is a conversion within the metric system, the policy requires RED classification for metric units. |
435cf9a2-bf87-49c9-ae4f-6eb7d51064f7 |
Localize | Spelling (AU-US) | Question
How does understanding geometric sequences relate to modelling exponential growth?
Hint: Use the formula $a_n = a \times r^{n-1}$ to model growth.
Answer:
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Question
How does understanding geometric sequences relate to modeling exponential growth?
Hint: Use the formula $a_n = a \times r^{n-1}$ to model growth.
Answer:
|
Classifier: The word "modelling" is the AU/UK spelling; the US spelling is "modeling". Verifier: The word "modelling" is the AU/UK spelling; the US spelling is "modeling". This requires localization. |
4ac4843c-5aad-4583-ad20-98e2fcf0f810 |
Localize | Spelling (AU-US) | Question
Why is it important to organise $x$ and $y$ values in a table?
Answer:
|
Question
Why is it important to organize $x$ and $y$ values in a table?
Answer:
|
Classifier: Contains the AU spelling "organise", which needs to be converted to the US spelling "organize". Verifier: The text contains "organise", which is the AU spelling. US spelling is "organize". |
4630ee2b-405a-4f8a-b465-e43b1ee5251a |
Localize | Terminology | Question
How can you verify your turning point form by expanding back to standard form?
Hint: Expand $(x-h)^2+k$ and compare it to the original equation.
Answer:
|
Question
How can you verify your vertex form by expanding back to standard form?
Hint: Expand $(x-h)^2+k$ and compare it to the original equation.
Answer:
|
Classifier: The term "turning point form" is the standard AU term for what is called "vertex form" in the US. This requires terminology localization. Verifier: The term "turning point form" is the standard AU term for what is called "vertex form" in the US. This is a terminology localization requirement. |
43LMeMoEktOg3YsHoqdh |
Localize | Terminology | Multiple Choice
In $\triangle XYZ$ and $\triangle UVW$, $\angle X \cong \angle U$, $XZ \cong UW$, and $\angle Z \cong \angle W$.
Which congruency test proves $\triangle XYZ \cong \triangle UVW$?
Options:
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Multiple Choice
In $\triangle XYZ$ and $\triangle UVW$, $\angle X \cong \angle U$, $XZ \cong UW$, and $\angle Z \cong \angle W$.
Which congruence postulate proves $\triangle XYZ \cong \triangle UVW$?
Options:
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Classifier: The term "congruency" is typically used in AU/UK contexts, whereas "congruence" is the standard US term. Additionally, "congruency test" or "congruency rule" often maps to "congruence theorem" or "congruence postulate" in US curricula. Verifier: The term "congruency test" and "congruency rule" are specific to AU/UK curriculum contexts, whereas US contexts typically use "congruence theorem", "congruence postulate", or simply "congruence". |
4FBgpdcXtPFO9GJtlPFX |
Localize | Terminology | Multiple Choice
Fill in the blank:
If a straight line makes an angle of $\theta$ with the $[?]$, its gradient is given by the equation $m=\tan{\theta}$.
Options:
|
Multiple Choice
Fill in the blank:
If a straight line makes an angle of $\theta$ with the $[?]$, its slope is given by the equation $m=\tan{\theta}$.
Options:
|
Classifier: While "gradient" is often a signal for AU/UK (vs US "slope"), it is widely used in US high school and college calculus/geometry contexts as well. However, looking at the decision rules, "gradient" is not explicitly listed as a RED terminology mapping in the prompt (unlike "right-angled triangle" or "maths"). Given the prompt's specific examples, this is likely acceptable as GREEN, though "slope" is more common in US K-12. Verifier: The term "gradient" is the standard Australian/British term for what is called "slope" in US K-12 mathematics. While used in US higher education, in the context of "straight lines" and "m = tan(theta)", it is a primary indicator of AU/UK curriculum terminology and requires localization for a US audience. |
3pS8646kLiVdLam9P363 |
Localize | Spelling (AU-US) | Multiple Choice
Which of these equations is true when minimising the vertical distance between each data point and the regression line?
Options:
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Multiple Choice
Which of these equations is true when minimizing the vertical distance between each data point and the regression line?
Options:
|
Classifier: The word "minimising" uses the AU/UK 's' spelling instead of the US 'z' spelling ("minimizing"). Verifier: The word "minimising" is the AU/UK spelling. US English uses "minimizing". Per rule 1, AU spelling always requires RED classification. |
49df7953-1a29-4c56-9e5d-a0bd6e3a469b |
Localize | Spelling (AU-US) | Question
Why does a geometric sequence grow faster than an arithmetic one?
Hint: Visualise how multiplication accelerates growth.
Answer:
|
Question
Why does a geometric sequence grow faster than an arithmetic one?
Hint: Visualize how multiplication accelerates growth.
Answer:
|
Classifier: The word "Visualise" in the hint field uses the AU/UK 's' spelling and requires conversion to the US 'z' spelling ("Visualize"). Verifier: The word "Visualise" in the hint field is the AU/UK spelling and requires localization to "Visualize" for the US locale. |
4KnsrJS2uEpR3q9O4nTP |
Localize | Spelling (AU-US) | Multiple Choice
Choose the correct option concerning the unit circle.
Options:
|
Multiple Choice
Choose the correct option concerning the unit circle.
Options:
|
Classifier: The text contains the AU spelling "centre" multiple times, which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre" in all four answer choices, which requires localization to the US spelling "center". |
4c1340f8-3e7c-4f5e-9811-2d5ef2ecbb0a |
Localize | Spelling (AU-US) | Question
Why group terms in pairs when factorising?
Answer:
|
Question
Why group terms in pairs when factoring?
Answer:
|
Classifier: Contains the AU spelling "factorising", which must be localized to "factorizing" for a US audience. Verifier: The text contains the AU spelling "factorising", which requires localization to "factorizing" for the US. |
4dcee162-1c81-4f43-975f-152bf3e71b0e |
Localize | Spelling (AU-US) | Question
How can analysing context help identify non-causal explanations for an association?
Answer:
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Question
How can analyzing context help identify non-causal explanations for an association?
Answer:
|
Classifier: Contains the AU spelling "analysing", which must be converted to the US spelling "analyzing". Verifier: Contains "analysing" which is the AU/UK spelling; US spelling is "analyzing". |
4eHkC1KPxO9sDNXKLD8X |
Localize | Terminology | Multiple Choice
True or false:
When an item is bought and regular payments of an agreed amount are made to pay its price, the payment is called a hire-purchase payment.
Options:
|
Multiple Choice
True or false:
When an item is bought and regular payments of an agreed amount are made to pay its price, the payment is called an installment loan payment.
Options:
|
Classifier: The term "hire-purchase" is a specific British/Commonwealth term for what is typically called "installment plan" or "rent-to-own" in the US. This requires terminology localization. Verifier: "Hire-purchase" is a Commonwealth term for installment plans/rent-to-own, requiring localization for a US audience. |
4gh1E1MKv38FbaGONBWK |
Localize | Spelling (AU-US) | Question
The seasonal index for an educational institute's fee is $0.94$.
If the total fees collected were $\$25000$, what is the deseasonalised fee?
Answer:
|
Question
The seasonal index for an educational institute's fee is $0.94$.
If the total fees collected were $\$25000$, what is the deseasonalized fee?
Answer:
|
Classifier: Contains the AU spelling "deseasonalised", which requires conversion to the US spelling "deseasonalized". While it uses the "$" sign, this is common to both locales and does not trigger a units conversion. Verifier: Contains the AU spelling "deseasonalised", which requires localization to "deseasonalized". |
53e4ff0e-94d4-48d5-bc66-faa69d3edcfb |
Localize | Spelling (AU-US) | Question
Why do we use $x$ and $y$ tables when working with equations?
Answer:
|
Question
Why do we use $x$ and $y$ tables when working with equations?
Answer:
|
Classifier: Contains the AU spelling "organise", which needs to be converted to the US spelling "organize". Verifier: The answer contains "organise", which is the AU spelling. US spelling is "organize". |
545eaa72-a6ee-4c6e-b8ef-8a6420471825 |
Localize | Spelling (AU-US) | Question
Why is identifying independence important in interpreting experimental results?
Hint: Consider how recognising independence avoids misinterpretation.
Answer:
|
Question
Why is identifying independence important in interpreting experimental results?
Hint: Consider how recognizing independence avoids misinterpretation.
Answer:
|
Classifier: The hint contains the AU spelling "recognising", which requires conversion to the US spelling "recognizing". Verifier: The hint contains "recognising", which is the AU spelling. US spelling is "recognizing". |
5bLowuLwxs4vbeIBuB6m |
Localize | Spelling (AU-US) | Question
How many different arrangements are possible if the colour red must always come first?
$\text{RED}\,$ $\text{BLUE}\,$ $\text{YELLOW}\,$ $\text{GREEN}\,$ $\text{PINK}$
Answer:
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Question
How many different arrangements are possible if the color red must always come first?
$\text{RED}\,$ $\text{BLUE}\,$ $\text{YELLOW}\,$ $\text{GREEN}\,$ $\text{PINK}$
Answer:
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Classifier: Contains the AU spelling "colour", which needs to be converted to "color" for US localization. Verifier: Contains the AU spelling "colour", which requires localization to "color". |
5uejCNWf7o8qONkQELba |
Localize | Units (simple) | Question
The perimeter of a square is $130$ cm.
What is the length of one of its sides?
Answer:
|
Question
The perimeter of a square is $130$ in.
What is the length of one of its sides?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units or a different unit context per the decision rules. Verifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units. It is a simple conversion as it involves a single value and a basic geometric property (perimeter of a square). |
59SnMKfVCgaYxdUDAIee |
Localize | Units (simple) | Question
A shopkeeper completely fills a carton with $15$ boxes of biscuits. Each box has dimensions $13$ cm $\times$ $5$ cm $\times$ $5$ cm.
What is the volume of the carton?
Answer:
|
Question
A shopkeeper completely fills a carton with $15$ boxes of cookies. Each box has dimensions $13$ in $ imes$ $5$ in $ imes$ $5$ in.
What is the volume of the carton?
Answer:
|
Classifier: The question contains metric units ("cm" and "cm^3") which require conversion or localization for a US audience. Verifier: The question contains metric units ("cm" and "cm^3") which require conversion for a US audience. The calculation is a simple volume product, so simple conversion is appropriate. |
64b41fed-e154-417a-87e7-46664d4a8bdc |
Localize | Spelling (AU-US) | Question
Why do stem-and-leaf plots organise data using stems and leaves?
Answer:
|
Question
Why do stem-and-leaf plots organize data using stems and leaves?
Answer:
|
Classifier: Contains the AU spelling 'organise', which needs to be converted to the US spelling 'organize'. Verifier: Contains "organise", which is the AU spelling; US English uses "organize". |
653a117f-87d8-42c2-b226-2a60ac93489a |
Localize | Units (simple) | Question
Why is it important to choose the right unit when measuring volume of large containers?
Answer:
|
Question
Why is it important to choose the right unit when measuring volume of large containers?
Answer:
|
Classifier: The text contains metric units ('litres', 'mL') and AU-specific spelling ('litres'). Per the decision rules, any metric unit found anywhere results in at least a units conversion category. Verifier: The text contains metric units ("litres", "mL") and AU spelling ("litres"), requiring conversion to US units (gallons/quarts or similar) and spelling ("liters"). |
5f50dd1c-84de-4210-8953-4340638dbb5a |
Localize | Terminology | Question
Why must we find the highest common factor when simplifying ratios?
Answer:
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Question
Why must we find the greatest common factor when simplifying ratios?
Answer:
|
Classifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US equivalent is typically "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard AU/UK terminology, whereas "greatest common factor" (GCF) is used in the US. This requires localization for the US market. |
5e4b04ec-d1ac-4a44-a461-5cf3a50d074e |
Localize | Terminology | Question
Why do horizontal lines always have zero gradient?
Answer:
|
Question
Why do horizontal lines always have zero slope?
Answer:
|
Classifier: The term "gradient" is the standard AU/UK term for what is almost exclusively called "slope" in US school mathematics. While "gradient" is used in higher-level US math (calculus/vectors), in the context of "rise over run" and horizontal lines, "slope" is the required US localization. Verifier: The term "gradient" is the standard AU/UK term for what is called "slope" in US school mathematics. In the context of "rise over run", "slope" is the required US localization. |
5rjruVT4e43mpNudxgVq |
Localize | Spelling (AU-US) | Question
Fully factorise the following expression:
$-2x^6y^7z^3-4x^3y^3z$
Answer:
|
Question
Fully factor the following expression:
$-2x^6y^7z^3-4x^3y^3z$
Answer:
|
Classifier: Contains the AU spelling "factorise", which needs to be converted to the US spelling "factorize". Verifier: The text contains "factorise", which is the AU/British spelling. US spelling is "factorize". |
5OykxIcMvmqzHxo9H0zp |
Localize | Terminology | Multiple Choice
Fill in the blank:
Co-interior angles are always $[?]$.
Options:
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Multiple Choice
Fill in the blank:
Consecutive interior angles are always $[?]$.
Options:
|
Classifier: The term "Co-interior angles" is standard in AU/UK geometry but is typically referred to as "Same-side interior angles" or "Consecutive interior angles" in US curriculum. Verifier: The term "Co-interior angles" is specific to AU/UK/International curricula; the US equivalent is "Same-side interior" or "Consecutive interior" angles. |
5tjKdCnyW99zRAJwUFuK |
Localize | Terminology | Question
Find the simple interest rate per annum at which the principal amount $\$2300$ earns $\$80.50$ interest in $6$ months.
Hint: Convert the time in years.
Answer:
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Question
Find the simple interest rate per year at which the principal amount $2300 earns $80.50 interest in 6 months.
Hint: Convert the time to years.
Answer:
|
Classifier: The abbreviation "p.a." (per annum) is much more common in AU/UK curricula. While "per annum" is understood in the US, US school math typically uses "per year" or simply "annual interest rate". More importantly, the suffix "p.a." is a specific notation style that usually requires localization to "per year" or removal in favor of "annual" in the question stem for US audiences. Verifier: The use of "p.a." (per annum) is a specific AU/UK curriculum convention for interest rates. US curricula typically use "per year" or "annual". |
5bd3379c-8968-4e24-9ae6-182d788fc390 |
Localize | Spelling (AU-US) | Question
Why is a tally chart a good way to show and organise things?
Answer:
|
Question
Why is a tally chart a good way to show and organize things?
Answer:
|
Classifier: Contains the AU spelling "organise", which needs to be converted to "organize" for US localization. Verifier: Contains the AU spelling "organise", which requires localization to "organize". |
5oO2pQI9qWO4GnNDqYq4 |
Localize | Spelling (AU-US) | Multiple Choice
How is $987$ written in words?
Options:
|
Multiple Choice
How is $987$ written in words?
Options:
|
Classifier: The text uses the British/Australian convention of including "and" after "hundred" when writing numbers in words (e.g., "Nine hundred and eighty-seven"). In US English, the "and" is typically omitted for whole numbers (reserved for decimals). This is a stylistic/spelling-adjacent localization requirement. Verifier: The use of "and" in "Nine hundred and eighty-seven" is a specific AU/UK convention for whole numbers that differs from US English (where "and" is omitted or reserved for decimals). This falls under spelling/stylistic localization. |
55e6e4c0-33ae-463b-84bf-61c7c9413345 |
Localize | Spelling (AU-US) | Question
How can interpreting histograms simplify analysing large datasets?
Answer:
|
Question
How can interpreting histograms simplify analyzing large datasets?
Answer:
|
Classifier: The word "analysing" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("analyzing"). Verifier: The word "analysing" in the question is the AU/UK spelling and requires localization to "analyzing". |
5LsperWJSPjr8YHAu8DZ |
Localize | Units (simple) | Question
A triangle has a base length of $15$ cm and a height of $8$ cm.
Find the area of the triangle.
Answer:
|
Question
A triangle has a base length of $15$ in and a height of $8$ in.
Find the area of the triangle.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2") which require conversion to US customary units (e.g., inches) for US localization. Verifier: The text contains metric units "cm" and "cm^2" which require conversion to US customary units (inches/square inches). This is a simple numeric conversion. |
63e01ce8-0a76-4076-bdb1-0b77a8b2d70c |
Localize | Terminology | Question
Why is it important to understand parallelograms in maths or in real-life designs?
Answer:
|
Question
Why is it important to understand parallelograms in math or in real-life designs?
Answer:
|
Classifier: Contains the term 'maths', which is the standard AU term for the US 'math'. Verifier: The term "maths" is the standard AU term and requires localization to "math" for US context. |
5u9r1bGo09kVFGStPwx6 |
Localize | Terminology | Question
A cumulative distribution function $F(x)$ for a continuous random variable $X$ is defined as:
$F(x)=\begin{cases} 0&,x<-3 \\ \frac{(x^2+3x+3)(x+3)}{217} &, -3\le x\le 4 \\ 1 &, x>4 \end{cases} $
Find $Pr(X<2)$.
Answer:
|
Question
A cumulative distribution function $F(x)$ for a continuous random variable $X$ is defined as:
$F(x)=\begin{cases} 0&,x<-3 \\ \frac{(x^2+3x+3)(x+3)}{217} &, -3\le x\le 4 \\ 1 &, x>4 \end{cases} $
Find $P(X<2)$.
Answer:
|
Classifier: The notation "Pr(X<2)" for probability is standard in Australia (VCE/HSC), whereas US curricula almost exclusively use "P(X<2)". Verifier: The notation "Pr(X<2)" is the standard AU convention for probability, whereas US curricula almost exclusively use "P(X<2)". |
5H5rsr6SMH7AYoEKJEYV |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the equation of a semicircle with centre at $(1,1)$ and radius $2$ units with its base on $y-$axis ?
Options:
|
Multiple Choice
Which of the following is the equation of a semicircle with center at $(1,1)$ and radius $2$ units with its base on the $y$-axis?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to "center" for US localization. Verifier: Contains the AU spelling "centre", which requires localization to "center" for the US market. |
6608a805-4ae5-4f98-b423-cbf63a084e03 |
Localize | Spelling (AU-US) | Question
Why do we use exponents in the formula for the $n\text{th}$ term?
Hint: Visualise how exponents simplify progression.
Answer:
|
Question
Why do we use exponents in the formula for the $n\text{th}$ term?
Hint: Visualize how exponents simplify progression.
Answer:
|
Classifier: The hint contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The hint contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". |
5KuDMRdEGxu5xcXP3nDJ |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $x^3 - 15 x^2 + 74 x - 120$.
Options:
|
Multiple Choice
Factor $x^3 - 15 x^2 + 74 x - 120$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to "Factorize" for US localization. Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize" for the US market. |
6PExikd1iftJjMKciCxW |
Localize | Spelling (AU-US) | Question
Find the number of distinct prime factors that $126$ has using prime factorisation.
Answer:
|
Question
Find the number of distinct prime factors that $126$ has using prime factorization.
Answer:
|
Classifier: Contains the AU spelling "factorisation", which needs to be converted to the US spelling "factorization". Verifier: Contains the AU spelling "factorisation", which needs to be converted to the US spelling "factorization". |
6FTa7AohDXNnenlS8VwJ |
Localize | Spelling (AU-US) | Question
How many pizza combinations are there if a shop offers $3$ sizes, $5$ flavours, and the choice of thick or thin crust?
Answer:
|
Question
How many pizza combinations are there if a shop offers $3$ sizes, $5$ flavors, and the choice of thick or thin crust?
Answer:
|
Classifier: Contains the AU spelling "flavours", which needs to be converted to the US spelling "flavors". Verifier: Contains the AU spelling "flavours", which must be localized to "flavors" for the US locale. |
67i7naTB08h912laD6PA |
Localize | Terminology | Question
What is the $x$-coordinate of the turning point of the parabola $y=-4x^2-28x+35$ ?
Answer:
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Question
What is the $x$-coordinate of the vertex of the parabola $y=-4x^2-28x+35$ ?
Answer:
|
Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In the US, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian curriculum term for the vertex of a parabola. In the US, "vertex" is used almost exclusively. |
693fc6a1-10f1-4fc4-abc8-d01c93800be0 |
Localize | Units (simple) | Question
Why do grams change to kilograms the same way millilitres change to litres?
Answer:
|
Question
Why do grams change to kilograms the same way milliliters change to liters?
Answer:
|
Classifier: The text contains multiple metric units (grams, kilograms, millilitres, litres) and uses AU-specific spelling for "millilitres" and "litres". Per rule 6, units conversion is the most impactful change. Verifier: The text contains multiple metric units (grams, kilograms, millilitres, litres) and uses AU-specific spelling for "millilitres" and "litres". Per rule 5, units conversion is the most impactful change. |
6c03ffb9-446b-437b-af89-4d97485fc593 |
Localize | Terminology | Question
Why is it important to know coins and notes when using money?
Answer:
|
Question
Why is it important to know coins and bills when using money?
Answer:
|
Classifier: The term "notes" in the context of money is the standard AU/UK term for what is called "bills" in the US. Verifier: The term "notes" refers to paper currency, which is called "bills" in the US. This is a terminology difference. |
6c7454c1-6d34-44a4-8b26-00bfa1fbe696 |
Localize | Terminology | Question
What makes zero special in the null factor law?
Answer:
|
Question
What makes zero special in the zero product property?
Answer:
|
Classifier: The "null factor law" is the standard AU term for what is known as the "Zero Product Property" in the US. Verifier: The "null factor law" is the standard Australian term for what is called the "Zero Product Property" in the US. |
6fe26b81-0629-433f-9ddf-4544a4aea010 |
Localize | Spelling (AU-US) | Question
Why do some expressions need grouping to be factorised?
Answer:
|
Question
Why do some expressions need grouping to be factored?
Answer:
|
Classifier: Contains the AU spelling 'factorised', which needs to be converted to the US spelling 'factorized'. Verifier: Contains the AU spelling "factorised", which requires localization to "factorized". |
6tVO2liCKAXes1HNMjRN |
Localize | Units (simple) | Question
Find the height of a rectangular prism whose base area is $24$ cm$^2$ and its volume is $268.8$ cm$^3$.
Answer:
|
Question
Find the height of a rectangular prism whose base area is $24$ in$^2$ and its volume is $268.8$ in$^3$.
Answer:
|
Classifier: The text contains metric units ("cm", "cm^2", "cm^3") which require conversion for US localization. Verifier: The text contains metric units ("cm", "cm^2", "cm^3") which require conversion for US localization. The conversion is a simple numeric change. |
6b79a761-f56d-449c-8cb3-f58ddc1d5665 |
Localize | Spelling (AU-US) | Question
Why do geometric sequences grow differently from arithmetic ones?
Hint: Visualise how multiplication results in faster growth compared to addition.
Answer:
|
Question
Why do geometric sequences grow differently from arithmetic ones?
Hint: Visualize how multiplication results in faster growth compared to addition.
Answer:
|
Classifier: Contains the AU spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: The word "Visualise" in the hint is the AU spelling; the US spelling is "Visualize". |
6a6f81c6-c669-4649-8df7-1f78251b872b |
Localize | Spelling (AU-US) | Question
Why do we need to identify which variable depends on the other?
Hint: Focus on how recognising these roles clarifies the data and its patterns.
Answer:
|
Question
Why do we need to identify which variable depends on the other?
Hint: Focus on how recognizing these roles clarifies the data and its patterns.
Answer:
|
Classifier: Contains the AU/UK spelling "recognising", which requires conversion to the US spelling "recognizing". Verifier: The hint field contains the AU/UK spelling "recognising", which requires localization to the US spelling "recognizing". |
6d157ff9-3e2b-462c-9f87-783811b98dd4 |
Localize | Terminology | Question
Why do triangles need both angle and side measurements for classification?
Answer:
|
Question
Why do triangles need both angle and side measurements for classification?
Answer:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" in a US context. Verifier: The answer contains "right-angled triangle", which is the standard AU/UK term. In a US context, this is typically "right triangle". This falls under terminology_school_context. |
6GcJyq9lylEi2Ns8Skfw |
Localize | Terminology | Multiple Choice
Express $y=-3 x^2 - 12 x - 11$ in turning point form.
Options:
|
Multiple Choice
Express $y=-3 x^2 - 12 x - 11$ in vertex form.
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is known as "vertex form" in the US. Verifier: "Turning point form" is the AU/UK equivalent of the US "vertex form". |
6PzLml8hSoeCmlzTw7Zs |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $P(x)=x^3 + x^2 - x - 1$.
Options:
|
Multiple Choice
Factor $P(x)=x^3 + x^2 - x - 1$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". |
71Lun8ZEmp4pQsmHtyWi |
Localize | Units (simple) | Question
A trapezium has an area of $44$ cm$^2$ and one parallel side measuring $12$ cm.
If its height is $4$ cm, find the length of the other parallel side.
Answer:
|
Question
A trapezoid has an area of $44$ in$^2$ and one parallel side measuring $12$ in.
If its height is $4$ in, find the length of the other parallel side.
Answer:
|
Classifier: The text contains metric units (cm, cm^2) and the AU terminology "trapezium" (which is "trapezoid" in the US). Per decision rules, units conversion is the most impactful change. Verifier: The text contains metric units (cm, cm^2) and the AU terminology "trapezium" (US: "trapezoid"). Units conversion is the primary classification. |
6hklepJ3BpL9vbfiAdbr |
Localize | Spelling (AU-US) | Question
The population of a town after $n$ years can be modelled using the recurrence relation:
$P_{n+1}=1.4P_{n}-500;$ $P_{0}=10000$
For what value of $n$ will the population of the town be $35060$ ?
Answer:
|
Question
The population of a town after $n$ years can be modeled using the recurrence relation:
$P_{n+1}=1.4P_{n}-500;$ $P_{0}=10000$
For what value of $n$ will the population of the town be $35060$ ?
Answer:
|
Classifier: The word "modelled" is the AU/UK spelling; the US spelling is "modeled". Verifier: The word "modelled" is the AU/UK spelling; the US spelling is "modeled". Per rule 1, AU spelling always requires RED classification. |
6CM0WEc0cZR6lffJjzzv |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $P(x)=2 x^3 + 5 x^2 - 18 x - 45$.
Hint: Use the Rational Root Theorem.
Options:
|
Multiple Choice
Factor the polynomial $P(x)=2 x^3 + 5 x^2 - 18 x - 45$.
Hint: Use the Rational Root Theorem.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize" for the US locale. |
70c18fcf-f371-4834-ad56-2a7b9beb304d |
Localize | Spelling (AU-US) | Question
Why is understanding quadratic inequalities important for solving problems in algebra or optimisation?
Hint: Focus on how inequalities apply to real-world constraints.
Answer:
|
Question
Why is understanding quadratic inequalities important for solving problems in algebra or optimization?
Hint: Focus on how inequalities apply to real-world constraints.
Answer:
|
Classifier: Contains the AU/UK spelling "optimisation", which requires conversion to the US spelling "optimization". Verifier: The text contains "optimisation", which is the AU/UK spelling. US spelling is "optimization". |
7106846c-5610-4ee7-be7b-c13be0fa34f0 |
Localize | Spelling (AU-US) | Question
How does understanding the shape of cosine relate to modelling periodic motion?
Hint: Identify the amplitude and period of the cosine wave.
Answer:
|
Question
How does understanding the shape of cosine relate to modeling periodic motion?
Hint: Identify the amplitude and period of the cosine wave.
Answer:
|
Classifier: Contains the AU/UK spelling "modelling", which requires conversion to the US spelling "modeling". Verifier: The text contains "modelling", which is the AU/UK spelling. US spelling is "modeling". |
73b0dab5-8f4c-45c4-beee-9b854922d107 |
Localize | Spelling (AU-US) | Question
Why are non-planar graphs impossible to draw on a flat surface without edges crossing?
Hint: Visualise how edge arrangement affects planarity.
Answer:
|
Question
Why are non-planar graphs impossible to draw on a flat surface without edges crossing?
Hint: Visualize how edge arrangement affects planarity.
Answer:
|
Classifier: The word "visualise" is the AU/UK spelling; the US spelling is "visualize". Verifier: The word "visualise" in the hint is the AU/UK spelling; the US spelling is "visualize". |
755c45e6-6cf4-435b-8a3e-d53bb20ee09f |
Localize | Spelling (AU-US) | Question
What makes tree diagrams useful for multi-step probability problems?
Hint: Each branch represents a possible path for events.
Answer:
|
Question
What makes tree diagrams useful for multi-step probability problems?
Hint: Each branch represents a possible path for events.
Answer:
|
Classifier: The word "organise" is used in the answer field, which is the AU spelling. The US spelling is "organize". Verifier: The answer contains "organise", which is the AU spelling (US: organize). |
758129f6-9fab-457a-a10e-a081edb28b32 |
Localize | Spelling (AU-US) | Question
Why does changing the centre angle affect both the sector and triangle areas differently?
Answer:
|
Question
Why does changing the center angle affect both the sector and triangle areas differently?
Answer:
|
Classifier: The word "centre" is used in the question, which is the AU spelling. The US spelling is "center". Verifier: The question contains "centre", which is the AU spelling (US: center). |
7563cc71-0ad3-402e-8693-8e51ac042492 |
Localize | Spelling (AU-US) | Question
Why do non-planar graphs not satisfy Euler’s formula?
Hint: Visualise how crossings disrupt the structure.
Answer:
|
Question
Why do non-planar graphs not satisfy Euler’s formula?
Hint: Visualize how crossings disrupt the structure.
Answer:
|
Classifier: The word "Visualise" is used in the hint, which is the AU spelling. The US spelling is "Visualize". Verifier: The hint contains "Visualise", which is the AU spelling (US: Visualize). |
7654f513-c911-428a-800b-042007d4e1e2 |
Localize | Answer set | Question
Why do trapeziums and parallelograms need different names?
Answer:
|
Question
Why do trapezoids and parallelograms need different names?
Answer:
|
Classifier: The term "trapezium" (used in AU/UK) must be converted to "trapezoid" for US learners. This is a high-impact terminology change where the answer set/definitions differ between locales. Verifier: The term "trapezium" is the standard AU/UK term for what is called a "trapezoid" in the US. This requires terminology localization. |
788a315a-0df4-4c39-b707-339956f9406d |
Localize | Terminology | Question
Why is it important to understand place value?
Answer:
|
Question
Why is it important to understand place value?
Answer:
|
Classifier: The text uses the term "maths", which is the standard AU/UK term and must be localized to "math" for a US audience. Verifier: The text uses the term "maths", which is the standard AU/UK term and must be localized to "math" for a US audience. |
7b65b051-4e24-4356-9f6f-3dc54006ebcb |
Localize | Spelling (AU-US) | Question
Why is analysing subgraphs useful in solving problems like social or transport networks?
Answer:
|
Question
Why is analyzing subgraphs useful in solving problems like social or transportation networks?
Answer:
|
Classifier: The word "analysing" is the AU/UK spelling; the US spelling is "analyzing". Verifier: The word "analysing" is the AU/UK spelling; the US spelling is "analyzing". |
78ac2ae8-ad30-415b-b011-909f9ddb03b2 |
Localize | Spelling (AU-US) | Question
How can mastering transformations simplify solving problems in contexts like signal processing or wave modelling?
Hint: Consider how transformations adjust the graph to fit real-world data.
Answer:
|
Question
How can mastering transformations simplify solving problems in contexts like signal processing or wave modeling?
Hint: Consider how transformations adjust the graph to fit real-world data.
Answer:
|
Classifier: The text contains the AU spelling "behaviour" and "modelling", which require conversion to US spellings "behavior" and "modeling". Verifier: The text contains the AU spelling "behaviour" and "modelling", which require conversion to US spellings "behavior" and "modeling". |
7TaITDBr0vzY4cqSZcIr |
Localize | Terminology | Multiple Choice
Fill in the blank:
The longest side of a right-angled triangle is known as the $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The longest side of a right triangle is known as the $[?]$.
Options:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" for a US audience. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is used in the US. This requires terminology localization. |
7bBJLsBHUWTfyION4sq8 |
Localize | Terminology | Question
George has $26$ lollies and Jacob has $5$.
How many more does George have?
Answer:
|
Question
George has $26$ pieces of candy and Jacob has $5$.
How many more does George have?
Answer:
|
Classifier: The term "lollies" is a specific AU/UK term for candy/sweets that is not typically used in US educational contexts. Verifier: The term "lollies" is a specific AU/UK term for candy/sweets that is not typically used in US educational contexts. |
8LcJIkXo572FKtJ5JECb |
Localize | Units (simple) | Question
Convert $0.2$ L to cm$^3$.
Answer:
|
Question
Convert $0.2$ gal to in$^3$.
Answer:
|
Classifier: Contains metric units "L" (litres) and "cm^3" (cubic centimeters). Per decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: Contains metric units "L" (litres) and "cm^3", which requires RED classification per rule 3. |
8JDkrUm86ZKzpvPFpsUL |
Localize | Units (simple) | Question
An observer on a hill at $50$ m above ground level observes a tree at the hill's base.
The angle of depression to the tree top is $30^\circ$ and to the bottom is $45^\circ$.
Calculate the tree's height.
Answer:
|
Question
An observer on a hill at $50$ ft above ground level observes a tree at the hill's base.
The angle of depression to the tree top is $30^\circ$ and to the bottom is $45^\circ$.
Calculate the tree's height.
Answer:
|
Classifier: Contains the metric unit "m" (metres) for height and distance, which requires conversion for US localization. Verifier: The text contains the metric unit "m" (metres), which requires conversion for US localization. |
7d7a1ff4-97f5-40ed-868b-593e77966a05 |
Localize | Units (simple) | Question
How do centimetres and metres help us measure small and big things?
Answer:
|
Question
How do inches and feet help us measure small and big things?
Answer:
|
Classifier: Contains metric units ("centimetres", "metres") and AU-specific spelling of those units. Per rule 1, any metric unit disqualifies GREEN. Verifier: Contains metric units ("centimetres", "metres") and AU-specific spelling of those units. Per rule 1 and 3, this requires RED classification. |
8INRs3AkosTg1zdmYyM3 |
Localize | Units (simple) | Question
A particle moves in a straight line and has the velocity function $v(t)=2t-t^2$ m/s for $t\geq0$.
Find the distance travelled by the particle from $t=6$ to $t=9$ seconds.
Answer:
|
Question
A particle moves in a straight line and has the velocity function $v(t)=2t-t^2$ ft/s for $t\geq0$.
Find the distance traveled by the particle from $t=6$ to $t=9$ seconds.
Answer:
|
Classifier: Contains metric units "m/s" and "m" which require localization to US customary units or a decision on metric usage in US physics contexts. Per rule 1, any metric unit disqualifies GREEN. Verifier: The text contains metric units "m/s" and "m", which require localization for the US market. |
8V3IQEtKrIP6R7jhRgTV |
Localize | Units (simple) | Question
A parallelogram has a length of $12$ cm and a height of $8$ cm.
What will be its area if the length is doubled?
Answer:
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Question
A parallelogram has a length of $12$ in and a height of $8$ in.
What will be its area if the length is doubled?
Answer:
|
Classifier: Contains metric units "cm" and "cm^2" which require conversion to US customary units. Verifier: The question uses metric units "cm" and "cm^2", which require conversion to US customary units. The conversion is simple as it involves a basic geometric calculation. |
8b36a186-8cef-431d-a1a1-a4c4a9a35a85 |
Localize | Spelling (AU-US) | Question
How does understanding decimal form relate to recognising irrational numbers?
Answer:
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Question
How does understanding decimal form relate to recognizing irrational numbers?
Answer:
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Classifier: The word "recognising" uses the AU/UK 's' spelling; the US equivalent is "recognizing". Verifier: The word "recognising" uses the AU/UK 's' spelling, which requires localization to "recognizing" for a US audience. |
7be5eed5-f527-43d1-807c-dbe8205e0d15 |
Localize | Spelling (AU-US) | Question
Why does a frequency table help organise data into categories?
Hint: Think about how categories make data easier to analyse.
Answer:
|
Question
Why does a frequency table help organize data into categories?
Hint: Think about how categories make data easier to analyze.
Answer:
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Classifier: Contains AU spellings "organise" and "analyse" which require conversion to "organize" and "analyze" for US localization. Verifier: Contains AU spellings "organise" and "analyse" which require conversion to "organize" and "analyze" for US localization. |
8054d5d8-4134-43f6-b1d7-2346c9d98def |
Localize | Spelling (AU-US) | Question
How does understanding bridges relate to analysing networks?
Answer:
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Question
How does understanding bridges relate to analyzing networks?
Answer:
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Classifier: Contains the AU spelling "analysing", which requires conversion to the US spelling "analyzing". Verifier: The word "analysing" is the AU/British spelling and requires localization to the US spelling "analyzing". |
86qTTCGGQzOmjuRZJAO6 |
Localize | Units (simple) | Question
An object travels in one dimension according to the displacement function $s(t)=8t^2+5t+3$ m for $0\leq t\leq12$ s.
Find the initial displacement of the object.
Answer:
|
Question
An object travels in one dimension according to the displacement function $s(t)=8t^2+5t+3$ ft for $0\leq t\leq12$ s.
Find the initial displacement of the object.
Answer:
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Classifier: The text contains the metric unit "m" (metres) for displacement. According to the decision rules, any metric unit requires classification into a units category. Verifier: The text contains the metric unit "m" (metres) for displacement. According to rule 3, any metric unit requires a RED classification. Since it is a simple numeric evaluation at t=0, simple_conversion is appropriate. |
8QPRA3el0DpU2qfbDQWU |
Localize | Units (simple) | Multiple Choice
Fill in the blank.
$745.98$ mL$=[?]$ cm$^3$
Options:
|
Multiple Choice
Fill in the blank.
$745.98$ fl oz$=[?]$ in$^3$
Options:
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Classifier: The question explicitly uses metric units (mL and cm^3) and tests the conversion between them. Per decision rules, any metric unit requires RED classification. Verifier: The question involves metric units (mL and cm^3) and their conversion, which requires RED classification per the decision rules. |
84115df6-2c4b-49de-a04b-2fe67ba75dc9 |
Localize | Spelling (AU-US) | Question
How do two-way tables help us understand relationships between categories of events?
Answer:
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Question
How do two-way tables help us understand relationships between categories of events?
Answer:
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Classifier: The word "organise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("organize"). Verifier: The word "organise" in the answer content is the AU/UK spelling and requires localization to "organize" for the US locale. |
8aPVY9dSFtWvUhTV9woj |
Localize | Units (simple) | Question
A man was driving a van at an acceleration of $a(t)=6t^2+4t-2$ km/h$^2$ for time $t\geq0$ in hours.
Find the instantaneous velocity at $t=2$ hours if the initial velocity was $65$ km/h.
Hint: Initial velocity is the velocity for $t=0$.
Answer:
|
Question
A man was driving a van at an acceleration of $a(t)=6t^2+4t-2$ mi/h$^2$ for time $t\geq0$ in hours.
Find the instantaneous velocity at $t=2$ hours if the initial velocity was $65$ mi/h.
Hint: Initial velocity is the velocity for $t=0$.
Answer:
|
Classifier: The text contains multiple instances of metric units ("km/h", "km/h^2") which require conversion to US customary units (mph) for US localization. Verifier: The question uses metric units (km/h and km/h^2) which require conversion for US localization. Although there is a function $a(t)$, it is a simple polynomial and the conversion of the final answer and the initial velocity constant is straightforward. |
7d94c1e2-1acb-415c-a669-7e9c1cd1d493 |
Localize | Terminology | Question
Why does the sign of $a$ in $y = ax^2 + bx + c$ affect the direction of the turning point?
Answer:
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Question
Why does the sign of $a$ in $y = ax^2 + bx + c$ affect the direction of the vertex?
Answer:
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Classifier: Uses the term "turning point", which is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: Uses the term "turning point", which is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. |
8a013401-4af3-4c8f-8d76-b1506702d81d |
Localize | Terminology | Question
Why does point-gradient form make finding equations of a line through points easier?
Answer:
|
Question
Why does point-slope form make finding equations of a line through points easier?
Answer:
|
Classifier: The text uses the term "gradient", which is the standard AU/UK term for "slope" in a US school context. Additionally, "point-gradient form" maps to "point-slope form" in the US. Verifier: The text uses "gradient" and "point-gradient form", which are standard AU/UK terms that map to "slope" and "point-slope form" in a US context. |
7fbe637e-df86-44fa-aa4a-f9e93747c292 |
Localize | Spelling (AU-US) | Question
Why do vertical transformations apply to the entire equation while horizontal transformations apply to $x$?
Hint: Visualise how each transformation modifies the graph.
Answer:
|
Question
Why do vertical transformations apply to the entire equation while horizontal transformations apply to $x$?
Hint: Visualize how each transformation modifies the graph.
Answer:
|
Classifier: Contains the AU/UK spelling "Visualise", which requires conversion to the US spelling "Visualize". Verifier: Contains the AU/UK spelling "Visualise" in the hint, which requires conversion to the US spelling "Visualize". |
8JRfuc4NJIEiofWY4k2x |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is wrong about activity networks?
Options:
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Multiple Choice
Which of the following is incorrect regarding activity networks?
Options:
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Classifier: Contains the AU spelling "labelled" (double 'l'), which should be "labeled" in US English. Verifier: The text contains the AU spelling "labelled" (double 'l') in multiple answer choices, which is "labeled" in US English. |
815CsuH474q6vFoDTWrX |
Localize | Terminology | Question
Make $y$ the subject of the formula.
$x = \frac{3-2y}{5}+2$
Options:
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Question
Solve the formula for $y$.
$x = \frac{3-2y}{5}+2$
Options:
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Classifier: The phrase "Make y the subject of the formula" is a common AU/UK mathematical convention. In the US, this is typically phrased as "Solve the literal equation for y" or "Solve for y in terms of x". Verifier: The phrase "Make y the subject of the formula" is a specific AU/UK mathematical convention. In the US, this is typically "Solve for y". |
8W0hkt21yJzDIhBJE4iC |
Localize | Units (simple) | Multiple Choice
A tank is $\Large\frac{2}{3}$ full of water.
After $12$ litres of water are removed, the tank is now $\Large\frac{1}{2}$ full.
Which equation represents the total capacity of the tank in litres, where $C$ is the total capacity?
Options:
|
Multiple Choice
A tank is $\Large\frac{2}{3}$ full of water.
After $12$ gallons of water are removed, the tank is now $\Large\frac{1}{2}$ full.
Which equation represents the total capacity of the tank in gallons, where $C$ is the total capacity?
Options:
|
Classifier: Contains the metric unit "litres" which uses AU spelling and requires conversion to US customary units (e.g., gallons). Verifier: The text contains the metric unit "litres" (AU spelling) which requires conversion to US customary units. The conversion is a straightforward numeric change in the context of a linear equation. |
8c3ce254-a286-4325-ba3b-172718b4e472 |
Localize | Spelling (AU-US) | Question
Why is the radius one unit for a unit circle?
Answer:
|
Question
Why is the radius one unit for a unit circle?
Answer:
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Classifier: The answer content contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The answer contains the AU spelling "centre", which requires localization to "center". |
8b8b9ba4-afec-48f9-921f-7446ba3c62cd |
Localize | Spelling (AU-US) | Question
How can understanding combined transformations help solve real-world problems involving graphs?
Hint: Visualise how transformations model complex scenarios.
Answer:
|
Question
How can understanding combined transformations help solve real-world problems involving graphs?
Hint: Visualize how transformations model complex scenarios.
Answer:
|
Classifier: The word "visualise" uses the AU/UK 's' spelling; the US equivalent is "visualize". Verifier: The word "Visualise" in the hint field uses the AU/UK 's' spelling; the US equivalent is "Visualize". |
8ox5ObDwR6mH6KlqrFzQ |
Localize | Units (simple) | Question
Maria walks from her house to school and back to her house. The total time it takes her is $2$ hours.
If she walks at $8$ km/hour, what is the distance between her house and school?
Answer:
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Question
Maria walks from her house to school and back to her house. The total time it takes her is $2$ hours.
If she walks at $8$ mi/hour, what is the distance between her house and school?
Answer:
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Classifier: The text contains metric units ("km/hour" and "km") which require conversion to US customary units (miles). Verifier: The question contains metric units "km/hour" and "km" which require conversion to US customary units (miles). |
8f17b4f1-1a40-47a5-a192-03194eb5f178 |
Localize | Units (simple) | Question
How does understanding both metric and imperial systems relate to solving real-world measurement problems?
Hint: Use conversion factors like $1\,\text{inch} = 2.54\,\text{cm}$.
Answer:
|
Question
How does understanding both metric and US customary systems relate to solving real-world measurement problems?
Hint: Use conversion factors like $1\,\text{inch} = 2.54\,\text{cm}$.
Answer:
|
Classifier: The text explicitly contains the metric unit "cm" in the hint. Per decision rules, any metric unit found anywhere requires classification into a units category. Verifier: The hint contains the metric unit "cm". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
92q61ta83pNYF2YLMaQe |
Localize | Units (complex) | Question
The velocity function of a particle is given by $v(t)=4t+5$ mm/s for $t\geq0$.
Find the average speed of the particle in the first $5$ seconds.
Answer:
|
Question
The velocity function of a particle is given by $v(t)=4t+5$ in/s for $t\geq0$.
Find the average speed of the particle in the first $5$ seconds.
Answer:
|
Classifier: The text contains the metric unit "mm/s" (millimetres per second), which requires localization/conversion according to the decision rules. Verifier: The question contains a metric unit "mm/s" within a velocity function equation v(t)=4t+5. According to rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients should be classified as RED.units_complex_converted. |
8cd31557-f7b0-4b8d-baf2-c2f4fd1195d7 |
Localize | Spelling (AU-US) | Question
How can the period of a periodic function help identify its behaviour?
Hint: Focus on how the period sets the function's rhythm.
Answer:
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Question
How can the period of a periodic function help identify its behavior?
Hint: Focus on how the period sets the function's rhythm.
Answer:
|
Classifier: The text contains the AU spelling "behaviour" in multiple fields, which requires conversion to the US spelling "behavior". Verifier: The text contains the AU spelling "behaviour" in the question and answer, which requires conversion to the US spelling "behavior". |
96cef9d9-b33a-4623-af8e-25d01de6cc40 |
Localize | Spelling (AU-US) | Question
Why do we group items in sets?
Answer:
|
Question
Why do we group items in sets?
Answer:
|
Classifier: Contains the AU spelling "organise", which requires conversion to the US spelling "organize". |
9MgJQNlf3RIrqvavsmtI |
Localize | Units (simple) | Question
How many cubic metres are there in $7$ kL?
Answer:
|
Question
How many cubic feet are there in $7$ kilogallons?
Answer:
|
Classifier: Contains metric units (kL, cubic metres) and AU spelling of "metres". Units conversion is the higher priority classification. Verifier: The text contains metric units (kL, cubic metres) and the AU spelling "metres". Per rule 5, units conversion is the primary classification. |
8qYKsHrD1nrXvfY8Wrxf |
Localize | Units (simple) | Question
An object moves in a straight line, and its position at time $t$ seconds is given by $s(t)=5(t^3-4t)$ m.
Find the average speed in the first $2$ seconds.
Hint: You can use its motion diagram.
Answer:
|
Question
An object moves in a straight line, and its position at time $t$ seconds is given by $s(t)=5(t^3-4t)$ ft.
Find the average speed in the first $2$ seconds.
Hint: You can use its motion diagram.
Answer:
|
Classifier: The text contains metric units ("m" for metres and "m/s" for metres per second) which require conversion to US customary units (feet or meters depending on specific curriculum, but usually flagged for conversion in US localization). Verifier: The text contains metric units "m" (metres) and "m/s" (metres per second). According to rule 3, any metric unit requires at least RED.units_simple_conversion. The conversion is straightforward (average speed over a time interval), so simple conversion is appropriate. |
9ZD0Xox5Jrt2Ex98RXwK |
Localize | Units (simple) | Question
Fill in the blank:
$2.60$ L $=[?]$ mL
Answer:
|
Question
Fill in the blank:
$2.60$ gal $=[?]$ fl oz
Answer:
|
Classifier: The question explicitly requires conversion between metric units (L to mL). All metric units trigger a RED classification. Verifier: The question involves metric units (L and mL), which requires RED classification per rule 3. |
9NpxM1LYBCQPcQUvBvPx |
Localize | Units (simple) | Question
How many mL are there in $40$ cm$^3$ ?
Answer:
|
Question
How many fl oz are there in $40$ in$^3$ ?
Answer:
|
Classifier: Contains metric units (mL, cm^3). Any metric unit requires at least simple conversion classification. Verifier: The question involves converting between metric units (mL and cm^3). Any metric unit requires at least RED.units_simple_conversion. |
99b2a379-7ef6-41dc-89bc-473793b51010 |
Localize | Spelling (AU-US) | Question
Why do we need to recognise conditional language in probability?
Answer:
|
Question
Why do we need to recognize conditional language in probability?
Answer:
|
Classifier: Contains the AU spelling "recognise" and "Recognising", which should be "recognize" and "Recognizing" in US English. Verifier: Contains AU spelling "recognise" and "Recognising" which require localization to "recognize" and "Recognizing". |
953536c0-54a0-4c50-a4c9-e86ea2c97194 |
Localize | Spelling (AU-US) | Question
Why do planar graphs help in designing network layouts like circuits?
Hint: Use planar graphs to create efficient designs.
Answer:
|
Question
Why do planar graphs help in designing network layouts like circuits?
Hint: Use planar graphs to create efficient designs.
Answer:
|
Classifier: The word "minimising" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("minimizing"). Verifier: The answer text contains "minimising", which is the AU/UK spelling. This requires localization to "minimizing". |
9305e79a-6194-4772-a3c4-fc6291c2d352 |
Localize | Spelling (AU-US) | Question
Why do we need to consider both horizontal and vertical stretches in periodic functions?
Hint: Visualise how stretches modify the graph’s appearance.
Answer:
|
Question
Why do we need to consider both horizontal and vertical stretches in periodic functions?
Hint: Visualize how stretches modify the graph’s appearance.
Answer:
|
Classifier: The text contains the AU spelling "Visualise", which needs to be converted to the US spelling "Visualize". Verifier: The hint contains the AU spelling "Visualise", which requires localization to "Visualize". |
965eaac3-324f-4fb6-b3c1-428c141fd7d2 |
Localize | Terminology | Question
What makes $(x-h)^2 + k$ the turning point form of a quadratic?
Hint: Identify $h$ and $k$ as the turning point of the parabola.
Answer:
|
Question
What makes $(x-h)^2 + k$ the vertex form of a quadratic?
Hint: Identify $h$ and $k$ as the vertex of the parabola.
Answer:
|
Classifier: The term "turning point form" is the standard AU term for what is known as "vertex form" in the US. The answer content even explicitly links "turning point form" to "vertex coordinates", confirming the mapping. Verifier: The term "turning point form" is the standard Australian curriculum term for what is called "vertex form" in the US. This is a terminology difference that requires localization. |
9aqQ7HlwRC1H7hu7XAF9 |
Localize | Metadata | Multiple Choice
Fill in the blank:
In Melbourne, $500$ randomly selected households are surveyed on income, expenditure, and family size.
The $[?]$ consists of $500$ households.
Options:
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Multiple Choice
Fill in the blank:
In Chicago, $500$ randomly selected households are surveyed on income, expenditure, and family size.
The $[?]$ consists of $500$ households.
Options:
|
Classifier: The text contains a specific AU city reference ("Melbourne") in a word problem context. While not a spelling or unit error, it is a locale-specific reference that typically requires localization to a US city for US-market alignment. Verifier: The text contains a specific Australian city reference ("Melbourne") which requires localization for the US market. |
9DowMF98bEapcoeS2k3J |
Localize | Terminology | Multiple Choice
Which of the following is the equation of a parabola with turning point $(1,3)$ ?
Options:
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Multiple Choice
Which of the following is the equation of a parabola with vertex $(1,3)$ ?
Options:
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Classifier: The term "turning point" is standard AU school terminology for the "vertex" of a parabola in US curriculum. Verifier: The term "turning point" is the standard AU curriculum term for what is called the "vertex" in the US. This requires localization for terminology. |
93d2b9ba-81da-42cf-b910-9bb459530b9b |
Localize | Spelling (AU-US) | Question
Why does the graph of the cosine function oscillate between $-1$ and $1$?
Hint: Visualise how the line crosses the parabola twice, creating two intersection points.
Answer:
|
Question
Why does the graph of the cosine function oscillate between $-1$ and $1$?
Hint: Visualize how the line crosses the parabola twice, creating two intersection points.
Answer:
|
Classifier: The text contains multiple AU-specific spellings: "Visualise" (US: Visualize) and "centre" (US: center). Verifier: The text contains AU-specific spellings: "Visualise" (US: Visualize) in the hint and "centre" (US: center) in the answer. |
9b1XIh4lHH4q7MnoYXkS |
Localize | Terminology | Multiple Choice
Which of the following is not a recurring decimal?
Options:
|
Multiple Choice
Which of the following is not a repeating decimal?
Options:
|
Classifier: The term "recurring decimal" is the standard AU/UK term, whereas the US equivalent is "repeating decimal". Verifier: The term "recurring decimal" is the standard AU/UK term; the US equivalent is "repeating decimal". |
9bRjh8wQRt3WdAVqnhSJ |
Localize | Units (simple) | Question
A wooden log has a circular cross-section with a diameter of $5.4$ cm.
What is its circumference to the nearest whole number?
Answer:
|
Question
A wooden log has a circular cross-section with a diameter of $5.4$ in.
What is its circumference to the nearest whole number?
Answer:
|
Classifier: The question contains the metric unit "cm" (centimetres), which requires conversion to US customary units (e.g., inches) for US localization. Verifier: The question contains the metric unit "cm" (centimetres), which requires conversion to US customary units for US localization. It is a simple conversion as it involves a single value and a basic geometric formula. |
9e1cd1bc-ae87-4685-b077-f18b2923a60a |
Localize | Terminology | Question
Why do you distribute the negative sign to each term within a bracket when multiplying?
Answer:
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Question
Why do you distribute the negative sign to each term within parentheses when multiplying?
Answer:
|
Classifier: The term "bracket" is predominantly used in AU/UK math contexts where US contexts use "parentheses". In the context of distributing a sign, "parentheses" is the standard US term. Verifier: The term "bracket" is the standard AU/UK term for what is referred to as "parentheses" in US math contexts. |
9naOeUGdmWhx3MkZWu8W |
Localize | Terminology | Multiple Choice
Fill in the blank:
Year levels in a school are considered $[?]$ data.
Options:
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Multiple Choice
Fill in the blank:
Grade levels in a school are considered $[?]$ data.
Options:
|
Classifier: The term "Year levels" is specific to the AU/UK school systems. In a US context, this is referred to as "Grade levels". Verifier: The term "Year levels" is specific to AU/UK/NZ school systems; the US equivalent is "Grade levels". This requires localization. |
9f3c68d5-1651-4046-9d6b-e9323bbce5d5 |
Localize | Spelling (AU-US) | Question
Why do we use hundreds, tens, and ones to show numbers up to $1000$?
Answer:
|
Question
Why do we use hundreds, tens, and ones to show numbers up to $1000$?
Answer:
|
Classifier: The answer contains the AU spelling "organised", which requires conversion to the US spelling "organized". Verifier: The answer contains "organised", which is the AU/UK spelling. US spelling is "organized". |
9ed2b544-4b31-443c-9d00-62d455631a0a |
Localize | Terminology | Question
Why do different quadrilaterals have different features?
Answer:
|
Question
Why do different quadrilaterals have different features?
Answer:
|
Classifier: The text uses the term "trapeziums". In the US, this shape is called a "trapezoid". This is a significant terminology difference in geometry. Verifier: The primary classifier correctly identified the terminology issue ("trapeziums" vs "trapezoids") but picked the wrong category leaf. Terminology differences in geometry belong in RED.terminology_school_context, not RED.answer_set_consistency_required. |
9e1c643c-8c9a-45e1-b9be-e319925a8528 |
Localize | Terminology | Question
How are index laws important for working with scientific notation?
Hint: Focus on how congruent triangles guarantee equality of their components.
Answer:
|
Question
How are exponent rules important for working with scientific notation?
Hint: Focus on how congruent triangles guarantee equality of their components.
Answer:
|
Classifier: The term "index laws" is the standard AU/UK term for what is referred to as "exponent rules" or "laws of exponents" in the US. While "scientific notation" is neutral, "index laws" is a specific school-context terminology difference. Verifier: The term "index laws" is the standard AU/UK term for what is referred to as "exponent rules" or "laws of exponents" in the US. This is a specific school-context terminology difference. |
9e646584-f28a-49b0-9edb-1a9b9f4c2394 |
Localize | Spelling (AU-US) | Question
How do key features of sine curves relate to modelling real-world patterns?
Hint: Focus on the height (amplitude) and cycle length (period).
Answer:
|
Question
How do key features of sine curves relate to modeling real-world patterns?
Hint: Focus on the height (amplitude) and cycle length (period).
Answer:
|
Classifier: Contains the AU spelling "modelling", which should be "modeling" in US English. Verifier: Contains the AU spelling "modelling", which should be "modeling" in US English. |
9ntjXTg3CfIXajZqb4QQ |
Localize | Units (simple) | Question
An object is moving with a velocity of $20$ m/s. It then accelerates at a rate of $a(t)=-5t$ m/s$^2$, $t\geq0$ where $t$ is in seconds.
Find the instantaneous velocity $v(t)$ of the object at $t=6$ s.
Answer:
|
Question
An object is moving with a velocity of $20$ ft/s. It then accelerates at a rate of $a(t)=-5t$ ft/s$^2$, $t\geq0$ where $t$ is in seconds.
Find the instantaneous velocity $v(t)$ of the object at $t=6$ s.
Answer:
|
Classifier: The text contains multiple metric units (m/s, m/s^2, s, m s^-1). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains multiple metric units (m/s, m/s^2, s). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Since the values are used in a basic calculus/kinematics context without complex interlinked unit systems or re-deriving coefficients, simple conversion is appropriate. |
9fb15a55-29a7-4ee0-aebc-4adda8422fcf |
Localize | Spelling (AU-US) | Question
Why is understanding subsets important for solving problems in set theory?
Hint: Think about how subsets help in organising and analysing sets.
Answer:
|
Question
Why is understanding subsets important for solving problems in set theory?
Hint: Think about how subsets help in organizing and analyzing sets.
Answer:
|
Classifier: The hint contains the AU spellings "organising" and "analysing", which require conversion to "organizing" and "analyzing". Verifier: The hint contains "organising" and "analysing", which are AU/UK spellings. US spellings are "organizing" and "analyzing". |
9ietkw19UGThlZRAaba0 |
Localize | Units (simple) | Multiple Choice
What are the correct dimensions of a rectangle with area $30$ cm$^2$ and perimeter $34$ cm?
Options:
|
Multiple Choice
What are the correct dimensions of a rectangle with area $30$ in$^2$ and perimeter $34$ in?
Options:
|
Classifier: The question and all answer choices contain the metric unit "cm" (centimetres), which requires localization to US customary units (e.g., inches). Verifier: The question and answers contain the metric unit "cm", which requires conversion to US customary units. |
9paSbM9LqPSFd85WBD9T |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Theoretical probability is given by the ratio of the number of favourable outcomes to the total number of possible outcomes.
Options:
|
Multiple Choice
True or false:
Theoretical probability is given by the ratio of the number of favorite outcomes to the total number of possible outcomes.
Options:
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Classifier: The text contains the AU spelling "favourable", which needs to be converted to the US spelling "favorable". Verifier: The text contains "favourable", which is AU spelling. Rule 1 states AU spelling always requires RED classification. |
AmcCiEHxX9DNEDnufSfr |
Localize | Terminology | Question
A line has a gradient of $-\frac{1}{3}$.
What is the gradient of the line perpendicular to it?
Answer:
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Question
A line has a slope of $-\frac{1}{3}$.
What is the slope of the line perpendicular to it?
Answer:
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Classifier: The term "gradient" is the standard AU term for the steepness of a line, whereas the US standard term is "slope". Verifier: The term "gradient" is the standard AU term for the steepness of a line, whereas the US standard term is "slope". |
A8I8IG2FwDnbWqITWY0u |
Localize | Units (simple) | Question
Fill in the blank:
$1$ gram $=[?]$ kilograms
Answer:
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Question
Fill in the blank:
$1$ ounce $=[?]$ pounds
Answer:
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Classifier: The text contains metric units ("gram" and "kilograms") which require conversion or localization to US customary units per the decision rules. Verifier: The text contains metric units "gram" and "kilograms". According to rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
B7Suq0836yVwuGcDrC5W |
Localize | Spelling (AU-US) | Question
If you draw lines from the vertices of a regular polygon to its centre, a number of angles are formed.
What is the sum of these angles?
Answer:
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Question
If you draw lines from the vertices of a regular polygon to its center, a number of angles are formed.
What is the sum of these angles?
Answer:
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Classifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: The text contains "centre", which is the AU/British spelling. It must be localized to "center" for the US locale. |
A77UNL41FfRYNNWhS8bt |
Localize | Terminology | Multiple Choice
Fill in the blank.
Suppose you are given a scatterplot whose line of regression has a negative gradient, then the correlation coefficient of that scatterplot is $[?]$.
Options:
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Multiple Choice
Fill in the blank.
Suppose you are given a scatterplot whose line of regression has a negative slope, then the correlation coefficient of that scatterplot is $[?]$.
Options:
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Classifier: The term "gradient" in the context of a line of regression is standard AU/UK terminology, whereas US curriculum typically uses "slope". Verifier: The use of "gradient" instead of "slope" in the context of a regression line is a specific terminology difference between AU/UK and US curricula. |
9xlqLQJ0LeI2dpXuH6aH |
Localize | Spelling (AU-US) | Question
Rationalise the denominator and simplify ${\Large\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}$.
Answer:
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Question
Rationalize the denominator and simplify ${\Large\frac{3+2\sqrt{2}}{3-2\sqrt{2}}}$.
Answer:
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Classifier: The word "Rationalise" uses the AU/UK "s" spelling; the US equivalent is "Rationalize". Verifier: The word "Rationalise" uses the AU/UK "s" spelling; the US equivalent is "Rationalize". Per rule 1, this requires RED classification. |
ApeLswsIA4DBcnObHBoE |
Localize | Spelling (AU-US) | Multiple Choice
How many prime factors are there in the prime factorisation of $770$ ?
Options:
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Multiple Choice
How many prime factors are there in the prime factorization of $770$ ?
Options:
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Classifier: The word "factorisation" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorization"). Verifier: Contains "factorisation", which is the AU/UK spelling. US spelling is "factorization". |
9vhKF0JOpjJck7XIGSXn |
Localize | Units (simple) | Question
A hall is in the shape of a parallelogram. The length of the hall is $60$ m and the height is $40$ m.
What is the area of the hall's floor?
Answer:
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Question
A hall is in the shape of a parallelogram. The length of the hall is $60$ ft and the height is $40$ ft.
What is the area of the hall's floor?
Answer:
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Classifier: The question uses metric units ("m" for metres and "m$^2$" for square metres), which requires conversion to US customary units (feet/yards). Verifier: The question uses metric units ("m" and "m$^2$"), which requires conversion to US customary units. It is a simple area calculation, so simple_conversion is appropriate. |
B4K9wToHQJL2rkxs88Gr |
Localize | Spelling (AU-US) | Multiple Choice
A company has to lay out a LAN network for their organisation. They used a minimum spanning tree to connect every building.
Will this help reduce the cost of the cable and the time needed to install the network?
Options:
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Multiple Choice
A company has to lay out a LAN network for their organization. They used a minimum spanning tree to connect every building.
Will this help reduce the cost of the cable and the time needed to install the network?
Options:
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Classifier: Contains the AU spelling "organisation", which needs to be converted to the US spelling "organization". Verifier: The text contains the AU/British spelling "organisation", which requires localization to the US spelling "organization". |
B1ebBhc7aE0G1lztOrwd |
Localize | Units (simple) | Question
Calculate the volume of a rectangular prism that has a base of $2$ m$\times4$ m, and a height of $6$ m.
Answer:
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Question
Calculate the volume of a rectangular prism that has a base of $2$ ft$\times4$ ft, and a height of $6$ ft.
Answer:
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Classifier: The question contains metric units ("m" for metres and "m^3" for cubic metres) which require conversion for US localization. Verifier: The question uses metric units ("m" and "m^3") which require conversion to US customary units. It is a simple conversion as it involves a basic volume calculation. |
Alt4GZyPeGUX9kbKP1Fx |
Localize | Spelling (AU-US) | Multiple Choice
How is $334$ written in words?
Options:
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Multiple Choice
How is $334$ written in words?
Options:
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Classifier: In US English, the word "and" is typically omitted when writing whole numbers (e.g., "Three hundred thirty-four" vs AU "Three hundred and thirty-four"). While often considered a stylistic or convention difference, in a school context, US curriculum standards (CCSS) explicitly teach writing whole numbers without "and" (which is reserved for the decimal point). Verifier: The answer choices use the AU/British convention of including "and" when writing whole numbers in words (e.g., "Three hundred and thirty-four"). In US English pedagogy, "and" is reserved for the decimal point and is omitted in whole numbers. |
A11P6MromhmO9gBRUKjk |
Localize | Units (simple) | Question
In triangle $\text{ABC}$, $\angle B=35^\circ,AB=6$ cm and $AC=3.5$ cm.
If $\angle C$ is an obtuse angle, then find the value of $\angle C$.
Answer:
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Question
In triangle $\text{ABC}$, $\angle B=35^\circ,AB=6$ in and $AC=3.5$ in.
If $\angle C$ is an obtuse angle, then find the value of $\angle C$.
Answer:
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Classifier: The text contains the metric unit "cm", which requires localization for a US audience. Verifier: The text contains the metric unit "cm", which requires localization for a US audience. |
ApulGCP3G15BrMzAw0I7 |
Localize | Terminology | Question
A man invested $\$100$ at the compound interest rate of $10\%$ p.a.
Find the amount at which the interest will be calculated for $2^{\text{nd}}$ year.
Answer:
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Question
A man invested $\$100$ at the compound interest rate of $10\%$ per year.
Find the amount at which the interest will be calculated for the $2^{\text{nd}}$ year.
Answer:
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Classifier: The term "p.a." (per annum) is common in AU financial mathematics but is typically replaced by "per year" or "annually" in US K-12 contexts. Additionally, while the dollar sign is used, the phrasing "amount at which the interest will be calculated" is slightly more common in Commonwealth curricula, though the "p.a." is the primary trigger for localization here. Verifier: The abbreviation "p.a." (per annum) is specific to Commonwealth financial mathematics and is not standard in US K-12 education, where "per year" or "annually" is used. |
AtYazjHG3qC3Af7l7qDm |
Localize | Spelling (AU-US) | Multiple Choice
What is $x^2(x+3)-5(2x+6)$ in factorised form?
Options:
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Multiple Choice
What is $x^2(x+3)-5(2x+6)$ in factored form?
Options:
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Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
AfEHunlNZwRLv4QrlhGe |
Localize | Units (simple) | Question
Jim yelled, "Hello!" near a cliff and heard an echo $0.1$ seconds later.
If the speed of sound is $340$ m/s, how far was Jim from the cliff?
Hint: Jim's distance from the cliff is equal to half the total distance travelled by the sound.
Answer:
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Question
Jim yelled, "Hello!" near a cliff and heard an echo $0.1$ seconds later.
If the speed of sound is $340$ ft/s, how far was Jim from the cliff?
Hint: Jim's distance from the cliff is equal to half the total distance traveled by the sound.
Answer:
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Classifier: The text contains metric units ('m/s' and 'm') which require conversion or localization for a US audience. Verifier: The question contains metric units ('m/s' and 'm') which require conversion for the US locale. |
BGbsN6mLDVci0Hysd6dZ |
Localize | Units (simple) | Multiple Choice
A wooden cylindrical log is $4$ m long and has a circumference of $ 44$ cm.
Find its volume.
Options:
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Multiple Choice
A wooden cylindrical log is $4$ ft long and has a circumference of $ 44$ in.
Find its volume.
Options:
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Classifier: The question contains multiple metric units ("m", "cm", "m$^3$", "cm$^3$") which require conversion to US customary units. Verifier: The question contains metric units (m, cm, m^3, cm^3) which require conversion to US customary units. The conversion is straightforward (simple). |
Asb5gTmIYVzrWYuIbKe9 |
Localize | Units (simple) | Multiple Choice
A particle starts at rest and is moving with an acceleration of $a(t)=6t+2$ m/s$^2$ at time $t$ seconds.
Find the velocity function $v(t)$.
Options:
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Multiple Choice
A particle starts at rest and is moving with an acceleration of $a(t)=6t+2$ ft/s$^2$ at time $t$ seconds.
Find the velocity function $v(t)$.
Options:
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Classifier: The text contains metric units "m/s^2" and "m/s" which require conversion or localization to US customary units in a physics/kinematics context. Verifier: The text contains metric units "m/s^2" and "m/s" which require conversion to US customary units (e.g., ft/s^2). |
AR2mCDyPagLkKdDxZ44y |
Localize | Terminology | Multiple Choice
Which of the following is a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Options:
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Multiple Choice
Which of the following is a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Options:
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Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" for a US audience. Verifier: The term "right-angled triangle" is the standard AU/British term, whereas "right triangle" is the standard US term. This requires localization. |
BLihQ0c3ui8Fnxb8zgXe |
Localize | Terminology | Question
What is the highest common factor of $28$ and $64$ ?
Answer:
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Question
What is the greatest common factor of $28$ and $64$ ?
Answer:
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Classifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US equivalent is typically "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard terminology in Australia/UK, whereas "greatest common factor" (GCF) is standard in the US. This is a terminology difference. |
BN0isIqxS0hX7VFx4gqv |
Localize | Units (simple) | Question
How many mL are there in $0.002$ cm$^{3}$ ?
Answer:
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Question
How many fl oz are there in $0.002$ in$^{3}$ ?
Answer:
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Classifier: The question explicitly uses and asks for conversion between metric units (mL and cm^3). Per rule 1, any metric unit requires classification as RED.units_*. Verifier: The question explicitly uses and asks for conversion between metric units (mL and cm^3). Per rule 3, any metric unit requires classification as RED.units_*. This is a simple conversion. |
BSzNY07Y5pSKcWpMgsil |
Localize | Units (simple) | Question
The perimeter of a rectangle is $40$ cm.
If the length of the rectangle is $4$ cm greater than its width, find its length.
Answer:
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Question
The perimeter of a rectangle is $40$ in.
If the length of the rectangle is $4$ in greater than its width, find its length.
Answer:
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Classifier: The text contains the metric unit "cm" multiple times, which requires conversion to US customary units (e.g., inches) for US localization. Verifier: The text contains the metric unit "cm" which requires conversion to US customary units. The math is a simple linear relationship, so simple_conversion is appropriate. |
BZO8SoaZIiXjSWuMoHox |
Localize | Units (simple) | Question
How many mL are there in $3.5$ L ?
Answer:
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Question
How many fl oz are there in $3.5$ gal ?
Answer:
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Classifier: The question explicitly uses and asks for conversions between metric units (mL and L). Per the decision rules, any metric unit requires classification into a RED.units category. Verifier: The question involves converting between metric units (L and mL), which requires RED classification per the decision rules. |
CLs8Nu6zAH6ClKpKZRb9 |
Localize | Spelling (AU-US) | Question
Factorise $3xz+6x$
Answer:
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Question
Factor $3xz+6x$
Answer:
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Classifier: The word "Factorise" uses the AU/UK 's' spelling. The US equivalent is "Factorize". Verifier: The word "Factorise" is the AU/UK spelling; the US spelling is "Factorize". Per rule 1, AU spelling always requires RED classification. |
Bjj7StjZWAr11ge755Di |
Localize | Units (simple) | Question
Convert $9800$ g into kilograms.
Answer:
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Question
Convert $9800$ oz into pounds.
Answer:
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Classifier: The question is a direct metric conversion task (grams to kilograms). This is explicitly covered under RED.units_simple_conversion. Verifier: The question is a direct metric conversion task (grams to kilograms), which requires localization to US customary units or a decision on metric usage. |
BNqZFSak9fav2qiK3XgM |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $x^2-4$.
Options:
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Multiple Choice
Factor the polynomial $x^2-4$.
Options:
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Classifier: The text uses the AU spelling "Factorise" and "factorised". In US English, these should be "Factorize" and "factorized". Verifier: The text contains "Factorise" and "factorised", which are AU/British spellings. US English uses "Factorize" and "factorized". |
BQj4pFULEiuz0Mc0oOt5 |
Localize | Units (simple) | Question
A farmer has a triangular field. The base of the field measures $150$ m. The perpendicular distance from the base to the opposite corner is $100$ m.
What is the area of the field?
Answer:
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Question
A farmer has a triangular field. The base of the field measures $150$ ft. The perpendicular distance from the base to the opposite corner is $100$ ft.
What is the area of the field?
Answer:
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Classifier: The question contains metric units ("m" for metres and "m^2" for square metres), which require conversion for US localization. Verifier: The question uses metric units ("m" for metres and "m^2" for square metres), which require conversion to US customary units. |
BKfoPZZVr72drrI2rEH3 |
Localize | Units (simple) | Multiple Choice
Which of the following is an imperial unit of area?
Options:
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Multiple Choice
Which of the following is a US customary unit of area?
Options:
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Classifier: The answer choices contain the AU/UK spelling "centimeters" and "meters" is actually spelled "centimeters" and "meters" in the source, but wait—looking closely at the source: "centimeters" and "meters" are already using US spelling in the provided text. However, "kilometers" is also US spelling. Wait, let me re-read the source values: "Square centimeters", "Square meters", "Square kilometers". These are actually US spellings. If the source already uses US spelling and there are no other AU markers, it might be GREEN. However, the prompt asks "Which of the following is an imperial unit of area?", and the distractors are metric units. Under the decision rules, any metric unit found anywhere (even if spelled in US English) triggers RED.units_simple_conversion. Verifier: The primary classifier correctly identified that the presence of metric units (centimeters, meters, kilometers) requires a RED classification per Rule 3, but it incorrectly labeled the leaf as RED.spelling_only in the JSON while arguing for units in the rationale. Since metric units are present, RED.units_simple_conversion is the correct classification. |
Bi1bJkYanbQAkHs9GyMZ |
Localize | Units (simple) | Question
The density of a substance decreases by $25\%$ upon boiling.
Find the density of the substance after boiling if the initial density is $12.38$ g/m$^3$.
Answer:
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Question
The density of a substance decreases by $25\%$ upon boiling.
Find the density of the substance after boiling if the initial density is $12.38$ oz/ft$^3$.
Answer:
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Classifier: Contains the metric unit 'g/m^3' (grams per cubic meter), which requires localization to US customary units or a decision on metric usage in science contexts. Per rule 1, any metric unit disqualifies GREEN. Verifier: The text contains the metric unit "g/m^3". According to Rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
CmfwAS8V6bDdOP0LJnoB |
Localize | Units (simple) | Question
How many millimetres are there in $16.5$ m?
Answer:
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Question
How many inches are there in $16.5$ ft?
Answer:
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Classifier: The question explicitly uses metric units ("millimetres", "m"). Additionally, "millimetres" uses the AU/UK spelling (US: millimeters). Per rule 1, any metric unit disqualifies GREEN. Verifier: The question uses metric units ("millimetres", "m"). "millimetres" is also the AU/UK spelling. Per rule 1 and 3, metric units require RED classification. |
Bd8FApKtmz3eGbVWAwpm |
Localize | Units (simple) | Question
An object moves in a straight line and its velocity after $t$ seconds is given by $v(t)=2t^2+t-2$ m/s for $0\leq t\leq 12$ s.
Find the average acceleration from $t=4$ to $t=6$ seconds.
Answer:
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Question
An object moves in a straight line and its velocity after $t$ seconds is given by $v(t)=2t^2+t-2$ ft/s for $0\leq t\leq 12$ s.
Find the average acceleration from $t=4$ to $t=6$ seconds.
Answer:
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Classifier: The text contains metric units of measurement ("m/s" and "m/s$^2$") which require localization to US customary units or a decision on metric usage in US physics contexts. Per rule 1, any metric unit disqualifies GREEN. Verifier: The text contains metric units "m/s" and "m/s$^2$". According to Rule 3, any metric unit requires at least RED.units_simple_conversion. Since these are simple units in a kinematics context without complex interlinked formulas requiring coefficient re-derivation, simple conversion is appropriate. |
BlQB6lPbEZRnyt7oOc8o |
Localize | Terminology | Multiple Choice
Find the turning point for the parabola $y=5(x-4)^2$
Options:
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Multiple Choice
Find the vertex for the parabola $y=5(x-4)^2$
Options:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian curriculum term for the vertex of a quadratic function. In the US, "vertex" is almost exclusively used in this context. |
CxVHppQpPVRK7EwG1vjG |
Review | Uncertain | Multiple Choice
True or false:
When hybrid functions are plotted, all the sections must join up.
Options:
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Multiple Choice
True or false:
When piecewise functions are plotted, all the sections must join up.
Options:
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Classifier: The term "hybrid functions" is commonly used in Australia (specifically Victoria/VCE) to refer to what is almost universally called "piecewise functions" in the US. While not a spelling error, it is a terminology difference that likely requires localization to "piecewise functions" for a US audience. Verifier: The term "hybrid functions" is a specific Australian curriculum term (VCE) for what is known as "piecewise functions" in the US. This is a terminology difference that requires localization. |
BeQ5BOiieyUCSH487Izg |
Localize | Spelling (AU-US) | Multiple Choice
In a shopping centre, $25$ people are randomly selected to rate a product.
Which group is the sample?
Options:
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Multiple Choice
In a shopping center, $25$ people are randomly selected to rate a product.
Which group is the sample?
Options:
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Classifier: Contains the AU spelling "centre" which needs to be converted to the US spelling "center". Verifier: The text contains the AU spelling "centre" (shopping centre), which requires localization to the US spelling "center" per Rule 1. |
CJTobAcycXzp9SI9cipR |
Localize | Terminology | Multiple Choice
What is the turning point of the parabola $y=2x^{2}-12x+12$ ?
Options:
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Multiple Choice
What is the vertex of the parabola $y=2x^{2}-12x+12$ ?
Options:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is referred to as the "vertex" in US curriculum. |
Cn0rVPgz9aiTovd3007u |
Localize | Units (simple) | Question
A circular cone has a height of $12$ m and a slant height of $25$ m.
Find the angle formed by the apex of the cone in degrees.
Answer:
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Question
A circular cone has a height of $12$ ft and a slant height of $25$ ft.
Find the angle formed by the apex of the cone in degrees.
Answer:
|
Classifier: The question uses the metric unit "m" (metres). Per rule 1, any metric unit requires localization to US customary units or at least classification as RED.units_simple_conversion. Verifier: The question uses the metric unit "m" (metres). Per rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
BoISR4ETcvuf4Oah2Yny |
Localize | Terminology | Question
The cost price of a television is $\$8,600$. It can be bought by a hire-purchase agreement with a deposit of $\$800$ and monthly instalments at the rate of $6\%$ p.a. for two years.
What is the total cost of buying the television?
Answer:
|
Question
The cost price of a television is $\$8,600$. It can be bought by an installment loan with a deposit of $\$800$ and monthly installments at the rate of $6\%$ p.a. for two years.
What is the total cost of buying the television?
Answer:
|
Classifier: The text contains several AU/UK specific financial terms: "hire-purchase agreement" (US: installment plan/financing), "instalments" (US spelling: installments), and "p.a." (per annum, less common in US K-12 than "per year" or "annually"). Verifier: The text contains "hire-purchase agreement" (US: installment plan), "instalments" (US: installments), and "p.a." (US: per year/annually). These are distinct AU/UK financial and spelling conventions. |
D22SDPMgvu5ERxagA5Nv |
Localize | Terminology | Question
A product originally costs $\$1200$ and is marked up by $\$150$.
It is then increased by another $20\%$ before GST is added.
What is the final price of the product?
Answer:
|
Question
A product originally costs $\$1200$ and is marked up by $\$150$.
It is then increased by another $20\%$ before sales tax is added.
What is the final price of the product?
Answer:
|
Classifier: Contains "GST" (Goods and Services Tax), which is a specific AU/Commonwealth tax term. In a US context, this would typically be "sales tax" or removed. Verifier: The term "GST" (Goods and Services Tax) is specific to AU/Commonwealth countries. In the US, "sales tax" is used. |
D3CvuWMFD6v32nwFdLgc |
Localize | Terminology | Question
An item costs $\$350$.
What is the total price including GST?
Answer:
|
Question
An item costs $\$350$.
What is the total price including sales tax?
Answer:
|
Classifier: The term "GST" (Goods and Services Tax) is the specific name for the value-added tax in Australia. In a US context, this would typically be referred to as "sales tax", or the problem would be framed differently as the US does not have a federal GST. Verifier: The term "GST" (Goods and Services Tax) is specific to the Australian tax system. In the US, this is referred to as "sales tax". This is a clear terminology difference requiring localization. |
DM6AmuMq76pGnPSoJfvP |
Localize | Units (simple) | Question
What is $0.0035$ m$^3$ in mm$^3$ ?
Answer:
|
Question
What is $0.0035$ ft$^3$ in in$^3$ ?
Answer:
|
Classifier: The question explicitly uses metric units (m^3 and mm^3) which requires localization to US customary units or a different pedagogical approach for a US audience. Verifier: The question involves converting between metric units (m^3 to mm^3), which requires localization for a US context. |
DSrhRg8Tl1RrDkrPW1kK |
Localize | Units (simple) | Question
Jason and his friend each drew a kite with diagonals of $9$ cm and $12$ cm.
What is the sum of the areas of both kites?
Answer:
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Question
Jason and his friend each drew a kite with diagonals of $9$ in and $12$ in.
What is the sum of the areas of both kites?
Answer:
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Classifier: Contains metric units ("cm" and "cm^2") which require conversion to US customary units (e.g., inches). Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for a US audience. |
DdIVgkD9BPFvRW7UFFJi |
Localize | Units (simple) | Question
A rectangular prism with dimensions $6$ cm $\times$ $4$ cm $\times$ $3$ cm is enlarged by a scale factor of $3$.
What is the volume of the new rectangular prism?
Answer:
|
Question
A rectangular prism with dimensions $6$ in $\times$ $4$ in $\times$ $3$ in is enlarged by a scale factor of $3$.
What is the volume of the new rectangular prism?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^3$") which require conversion to US customary units for localization. Verifier: The text contains metric units "cm" and "cm^3" which require conversion to US customary units. The conversion is a simple scaling of dimensions and volume, fitting the simple_conversion category. |
DUE7uAzUaWyPIMTVIz5Q |
Localize | Units (simple) | Question
A $10$ cm by $18$ cm photo is placed in a frame that is $4$ cm wide on all sides.
What is the outer perimeter of the frame?
Hint: It may help to draw a diagram of the photo and frame.
Answer:
|
Question
A $10$ in by $18$ in photo is placed in a frame that is $4$ in wide on all sides.
What is the outer perimeter of the frame?
Hint: It may help to draw a diagram of the photo and frame.
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times in the content and as a suffix. According to the decision rules, any metric unit requires classification as at least RED.units_simple_conversion. Verifier: The text contains the metric unit "cm" multiple times. According to rule 3, any metric unit requires at least RED.units_simple_conversion. The conversion is a straightforward perimeter calculation with a few values, so simple conversion is correct. |
DID3p1r44rvE5038iTMu |
Localize | Spelling (AU-US) | Multiple Choice
The company's actual sales are $\$6000$, their present sale is $\$5000$.
How can they correct their seasonality?
Options:
|
Multiple Choice
The company's actual sales are $\$6000$, their present sale is $\$5000$.
How can they correct their seasonality?
Options:
|
Classifier: The text contains the AU/UK spelling "deseasonalised", which requires conversion to the US spelling "deseasonalized". Verifier: The text contains "deseasonalised", which is the AU/UK spelling. The US spelling is "deseasonalized". |
DNvisT5cYgJPlHkLJjDq |
Localize | Units (simple) | Multiple Choice
Choose the correct statement:
Ron is $154$ cm tall, in a class with a mean height of $160$ cm and a standard deviation of $10$ cm.
Riya is $158$ cm tall, in a class with a mean height of $157$ cm and a standard deviation of $8$ cm.
Options:
|
Multiple Choice
Choose the correct statement:
Ron is $154$ in tall, in a class with a mean height of $160$ in and a standard deviation of $10$ in.
Riya is $158$ in tall, in a class with a mean height of $157$ in and a standard deviation of $8$ in.
Options:
|
Classifier: The text contains multiple instances of the metric unit "cm" used for height, which requires conversion for a US context. Verifier: The problem uses centimeters (cm) for height, which is a metric unit requiring localization. |
EHqO7OcXJHIenODlo4P2 |
Localize | Units (simple) | Question
Fill in the blank:
$0.12$ kg $=[?]$ g
Answer:
|
Question
Fill in the blank:
$0.12$ lb $=[?]$ oz
Answer:
|
Classifier: Contains metric units (kg and g). Per decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: Contains metric units (kg and g). Per decision rule 3, any metric unit requires at least RED.units_simple_conversion. |
EjBwl76HwHRDHOo6zaQc |
Localize | Units (simple) | Question
Fill in the blank:
$20060$ g $=20$ kg and $[?]$ g
Answer:
|
Question
Fill in the blank:
$20060$ oz $=20$ lb and $[?]$ oz
Answer:
|
Classifier: The text contains metric units "g" (grams) and "kg" (kilograms), which require conversion for US localization. Verifier: The question uses metric units (grams and kilograms) which require conversion for US localization. |
Ey42hWTC6vNqk0vSBA9M |
Localize | Terminology | Question
Find the highest common factor of $42$ and $27$.
Answer:
|
Question
Find the greatest common factor of $42$ and $27$.
Answer:
|
Classifier: "Highest common factor" (HCF) is used in both AU and US, though "Greatest common factor" (GCF) is more common in the US. However, HCF is not exclusively AU and is mathematically neutral. No AU-specific spelling or units are present. Verifier: While "Highest common factor" (HCF) is understood in the US, it is the primary term used in the AU curriculum, whereas "Greatest common factor" (GCF) is the standard term in the US curriculum. This falls under terminology school context. |
E3WzUfa0nRQfyrpgOFkz |
Localize | Spelling (AU-US) | Question
Fill in the blank:
The seasonal index for the institute’s fee is $[?]$, given that the total fee collected is $\$7265$ and the deseasonalised fee is $\$6604.54$.
Answer:
|
Question
Fill in the blank:
The seasonal index for the institute’s fee is $[?]$, given that the total fee collected is $\$7265$ and the deseasonalized fee is $\$6604.54$.
Answer:
|
Classifier: The term "deseasonalised" uses the AU/UK "s" spelling; the US equivalent is "deseasonalized". Verifier: The word "deseasonalised" is the AU/UK spelling; the US spelling is "deseasonalized". Per rule 1, AU spelling always requires RED classification. |
E4nvuxM9OXf8Qxrid1yG |
Localize | Spelling (AU-US) | Question
You have eight cubes of the same size but with different colours.
How many possible ways are there to arrange these cubes in a row?
Answer:
|
Question
You have eight cubes of the same size but with different colors.
How many possible ways are there to arrange these cubes in a row?
Answer:
|
Classifier: Contains the AU spelling "colours", which requires conversion to the US spelling "colors". Verifier: The text contains "colours", which is the AU/UK spelling. US spelling is "colors". Per rule 1, this requires RED classification. |
DzTqRJ3xgiWp4XVoHcv6 |
Localize | Units (simple) | Question
A sphere with a radius of $3$ cm is enlarged by a scale factor of $3$.
What is the volume of the new sphere?
Answer:
|
Question
A sphere with a radius of $3$ in is enlarged by a scale factor of $3$.
What is the volume of the new sphere?
Answer:
|
Classifier: The question uses metric units ("cm" and "cm$^3$"), which require localization for a US audience. Verifier: Contains metric units "cm" and "cm^3" which require conversion for US localization. |
EIcuDzfsFcqQNeJwJTbt |
Localize | Terminology | Multiple Choice
True or false:
The triangle formed by the sides of length $28$, $53$ and $45$ units is a right-angled triangle.
Options:
|
Multiple Choice
True or false:
The triangle formed by the sides of length $28$, $53$ and $45$ units is a right triangle.
Options:
|
Classifier: The term "right-angled triangle" is standard AU/UK terminology. In the US, this is typically referred to as a "right triangle". Verifier: The term "right-angled triangle" is the standard Australian/British term, whereas "right triangle" is used in the US. This requires localization for terminology. |
EUzDyVjgoyfMzwghexpQ |
Localize | Units (simple) | Question
What is the width of a rectangle with an area of $108$ m$^2$ and a length of $12$ m?
Answer:
|
Question
What is the width of a rectangle with an area of $108$ ft$^2$ and a length of $12$ ft?
Answer:
|
Classifier: The text contains metric units ("m" and "m$^2$") which require conversion for US localization. Verifier: The question contains metric units ("m" and "m$^2$") which require conversion to US customary units. This is a simple conversion as it involves a single geometric calculation. |
E1H4taxXVsPBJAjaRHtR |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
A regular polygon with $n$ sides can be divided into $[?]$ triangles by joining each vertex to the centre.
Options:
|
Multiple Choice
Fill in the blank:
A regular polygon with $n$ sides can be divided into $[?]$ triangles by joining each vertex to the center.
Options:
|
Classifier: The text contains the AU/UK spelling "centre", which needs to be converted to the US spelling "center". Verifier: The text contains "centre", which is the AU/UK spelling. It must be converted to "center" for US localization. |
DlQV2rYvTl9rArBmlai2 |
Localize | Terminology | Multiple Choice
Which of the following parabolas has a turning point at $(-1,8)$ and passes through $(0,15)$?
Options:
|
Multiple Choice
Which of the following parabolas has a vertex at $(-1,8)$ and passes through $(0,15)$?
Options:
|
Classifier: The term "turning point" is the standard AU term for what is referred to as the "vertex" in US mathematics curriculum. Verifier: The term "turning point" is the standard AU curriculum term for the "vertex" of a parabola. |
DuV4d0Til4v1jsHr7Cji |
Localize | Spelling (AU-US) | Question
$\text{Pr}(A)=0.6$, $\text{Pr}(B)=0.7$ and $\text{Pr}(A \cap B)= 0.5$ .
Given this information, find $\text{Pr}( A \cup B)$.
Hint: It may be helpful to use a Venn diagram to visualise this situation.
Answer:
|
Question
$\text{P}(A)=0.6$, $\text{P}(B)=0.7$ and $\text{P}(A \cap B)= 0.5$ .
Given this information, find $\text{P}( A \cup B)$.
Hint: It may be helpful to use a Venn diagram to visualize this situation.
Answer:
|
Classifier: The hint contains the AU spelling "visualise", which requires conversion to the US spelling "visualize". Verifier: Contains the AU spelling "visualise" in the hint field. |
EFHL9tIi7lcEl3OWNWTv |
Localize | Spelling (AU-US) | Question
Factorise $f(x)=27x^3+8$.
Express your answer in the form $(ax+b)(cx^2+dx+e)$.
Options:
|
Question
Factor $f(x)=27x^3+8$.
Express your answer in the form $(ax+b)(cx^2+dx+e)$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is AU/UK spelling. Per decision rule 1, AU spelling always requires RED classification. |
Efld6w6CBG6ODqtYLcuo |
Localize | Terminology | Multiple Choice
Fill in the blank:
The turning point of the parabola $y=a(x-h)^2+k$ is $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The vertex of the parabola $y=a(x-h)^2+k$ is $[?]$.
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: "Turning point" is the standard AU/UK term for the vertex of a parabola, whereas "vertex" is the standard US term. This requires localization. |
Ects3XLr5D9LhZe4TsX1 |
Localize | Units (simple) | Multiple Choice
True or false:
The displacement function of a particle is given by $s(t)=-2t^2-7t-5$ m for $t\geq0$ (seconds).
The speed of the particle is increasing at $t=2$ s.
Hint:
Recall that $a(t)=v'(t)=s''(t)$ and $v(t)=s'(t)$.
Options:
|
Multiple Choice
True or false:
The displacement function of a particle is given by $s(t)=-2t^2-7t-5$ ft for $t\geq0$ (seconds).
The speed of the particle is increasing at $t=2$ s.
Hint:
Recall that $a(t)=v'(t)=s''(t)$ and $v(t)=s'(t)$.
Options:
|
Classifier: The text contains the metric unit "m" (metres) for displacement and "s" (seconds). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "m" (metres). While it is part of a function, the question asks for a qualitative "True or false" check on speed increasing at a specific point, which is a simple application of the derivative rather than a complex multi-step metric conversion or formula re-derivation. |
FLWK5OKgJrHVriRQzkew |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is not true for a reducing balance loan in an amortising table containing information about payment number, payment amount, interest paid, principal reduction and balance of the loan?
Options:
|
Multiple Choice
Which of the following is not true for a reducing balance loan in an amortization table containing information about payment number, payment amount, interest paid, principal reduction and balance of the loan?
Options:
|
Classifier: The text contains the AU/UK spelling "amortising", which needs to be converted to the US spelling "amortizing". Verifier: The text contains "amortising", which is the AU/UK spelling. The US spelling is "amortizing". |
EVfj8CoYmFPj6IeC6rws |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $y^3+125$
Options:
|
Multiple Choice
Factor the polynomial $y^3+125$
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU spelling. US spelling is "Factorize". |
ExKkXRuCdF6xfNQYqGh6 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the general equation of a semicircle with a centre at the origin and radius $r$ units?
Options:
|
Multiple Choice
Which of the following is the general equation of a semicircle with a center at the origin and radius $r$ units?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: The text contains the AU spelling "centre", which requires localization to the US spelling "center". |
EEnCbbBYtqhQMwLFQanu |
Localize | Units (simple) | Multiple Choice
True or false:
A continuous random variable can represent the amount of iron contained in a beaker containing $250$ ml of water from a river.
Options:
|
Multiple Choice
True or false:
A continuous random variable can represent the amount of iron contained in a beaker containing $250$ fl oz of water from a river.
Options:
|
Classifier: The text contains the metric unit "ml" (millilitres), which requires localization to US customary units or US-style metric presentation (mL) depending on specific style guides, but the presence of a metric unit automatically triggers a RED classification per the decision rules. Verifier: The text contains the metric unit "ml" (millilitres). Per decision rule 3, any metric unit requires at least RED.units_simple_conversion. |
FxF4G8JocLAvepBu3B5x |
Localize | Units (simple) | Question
The scale factor between two similar figures is $\frac{3}{5}$.
The longer side of the smaller figure is $9$ cm.
What is the length of the corresponding side on the larger figure?
Answer:
|
Question
The scale factor between two similar figures is $\frac{3}{5}$.
The longer side of the smaller figure is $9$ in.
What is the length of the corresponding side on the larger figure?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion for US localization. Verifier: The question contains the metric unit "cm" (centimetres), which requires conversion to US customary units. It is a simple conversion as it involves a single value and a straightforward ratio. |
FxGQESBgNqTx5jKnRlgs |
Localize | Spelling (AU-US) | Question
The seasonal index of the sales in a restaurant is $0.78$, and the deseasonalised sales are $\$31500$.
What is the value of the actual sales?
Answer:
|
Question
The seasonal index of the sales in a restaurant is $0.78$, and the deseasonalized sales are $\$31500$.
What is the value of the actual sales?
Answer:
|
Classifier: The text contains the AU/UK spelling "deseasonalised", which needs to be converted to the US spelling "deseasonalized". Verifier: The word "deseasonalised" uses the AU/UK 's' spelling instead of the US 'z' spelling ("deseasonalized"). Per rule 1, any AU spelling requires RED classification. |
GkWf5IrjU5rtrmbcJoD1 |
Localize | Units (simple) | Question
Fill in the blank:
$15600$ kilograms $+[?]$ megagrams $=17900$ kilograms
Answer:
|
Question
Fill in the blank:
$15600$ pounds $+[?]$ tons $=17900$ pounds
Answer:
|
Classifier: The question explicitly uses metric units "kilograms" and "megagrams". According to the decision rules, any metric unit requires localization. Verifier: The question uses metric units "kilograms" and "megagrams". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
GaNUPrMkzZ7jB7UUc8of |
Localize | Units (simple) | Question
Find the radius of the circle in which the central angle of $\frac{\pi}{3}$ intercepts an arc of length $37.4$ cm.
Answer:
|
Question
Find the radius of the circle in which the central angle of $\frac{\pi}{3}$ intercepts an arc of length $37.4$ in.
Answer:
|
Classifier: Contains metric units ("cm") which require conversion to US customary units for localization. Verifier: The question contains the metric unit "cm" (centimetres), which requires conversion to US customary units. It is a simple conversion as it involves a single value and a standard geometric formula (s = r*theta). |
HCQ0MObVwbaIVtaoP3Md |
Localize | Units (simple) | Question
Convert $7$ kg and $409$ g into grams.
Answer:
|
Question
Convert $7$ lb and $409$ oz into ounces.
Answer:
|
Classifier: The question explicitly uses metric units "kg" (kilograms) and "g" (grams) for a unit conversion exercise. Metric units always require at least RED.units_simple_conversion. Verifier: The question uses metric units "kg" and "g". According to rule 3, any metric unit requires at least RED.units_simple_conversion. |
HJ4dtAWSKgRrL1sChntg |
Localize | Terminology | Question
The gradient of the line joining the points $(-3,[?])$ and $(0,2)$ is equal to $-2$.
Find the missing value.
Answer:
|
Question
The slope of the line joining the points $(-3,[?])$ and $(0,2)$ is equal to $-2$.
Find the missing value.
Answer:
|
Classifier: The term "gradient" is used to refer to the steepness of a line. In a US school context, "slope" is the standard term for the steepness of a line between two points. Verifier: The term "gradient" is used to describe the slope of a line, which is a standard AU/UK term that requires localization to "slope" for a US context. |
GNSdpHx9cROsMv9UwDBb |
Localize | Terminology | Multiple Choice
What is the turning point of the parabola $y=(x-2)(x-4)$ ?
Options:
|
Multiple Choice
What is the vertex of the parabola $y=(x-2)(x-4)$ ?
Options:
|
Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In the US, "vertex" is the standard term used in this context. Verifier: "Turning point" is the standard AU school term for what is called the "vertex" in the US. This requires localization for the US market. |
GJnbp7lOmATsKNyPipFu |
Localize | Units (complex) | Multiple Choice
The displacement function of a car is $s(t)=4t^3+5t+15$ km for $t\geq0$ hours.
Find the acceleration function for the car.
Options:
|
Multiple Choice
The displacement function of a car is $s(t)=4t^3+5t+15$ mi for $t\geq0$ hours.
Find the acceleration function for the car.
Options:
|
Classifier: The problem and its answer choices use metric units ("km" and "km/h^2"), which require conversion to US customary units (e.g., miles). Verifier: The question contains a displacement function s(t) defined in metric units (km). According to rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients should be classified as RED.units_complex_converted rather than simple conversion. |
Gqcf2MbpRL2uFUwJi1bn |
Localize | Metadata | Multiple Choice
Paris, France is $8$ hours behind Brisbane, Australia.
What time will it be in Brisbane if it is $3$:$00$ PM in Paris?
Options:
|
Multiple Choice
London, England is $5$ hours ahead of New York, USA.
What time will it be in London if it is $6$:$00$ AM in New York?
Options:
|
Classifier: The question is centered on an Australian city (Brisbane, Australia). While not a spelling or unit change, the context is highly locale-specific and typically requires localization to a US city/time zone for US students. Verifier: The question is centered on Brisbane, Australia. While the language is neutral, the geographic context is highly locale-specific and typically requires localization for US students. |
HPfvfeGcGqBcsDO0kqZt |
Localize | Units (simple) | Question
After $500$ rotations, a wheel has travelled $1.06$ km.
Find the diameter of the wheel in metres.
Answer:
|
Question
After $500$ rotations, a wheel has traveled $1.06$ mi.
Find the diameter of the wheel in feet.
Answer:
|
Classifier: The text contains metric units ("km", "metres") and the AU spelling "metres". According to the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units ("km", "metres") and the AU spelling "metres". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
Gr4r0jGhcZGCiBRksZTL |
Localize | Spelling (AU-US) | Question
Rationalise the denominator of ${\Large\frac{3}{5-\sqrt{4}}}$.
Express your answer as a fraction in simplest form.
Options:
|
Question
Rationalize the denominator of ${\Large\frac{3}{5-\sqrt{4}}}$.
Express your answer as a fraction in simplest form.
Options:
|
Classifier: Contains the AU spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: The text contains "Rationalise", which is the AU/British spelling. US spelling is "Rationalize". |
HFOXM4KEeEfGPKcaiZaw |
Localize | Spelling (AU-US) | Multiple Choice
Fully factorise the following expression:
$-5x^6+10x^4$
Options:
|
Multiple Choice
Completely factor the following expression:
$-5x^6+10x^4$
Options:
|
Classifier: Contains the AU spelling "factorise", which needs to be converted to the US spelling "factorize". Verifier: The text contains "factorise", which is AU spelling. Rule 1 states AU spelling always requires RED classification. |
H5cpw76dXFVFNy0xv9vN |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following statements defines a chord?
Options:
|
Multiple Choice
Which of the following statements defines a chord?
Options:
|
Classifier: Contains the AU spelling "centre" multiple times, which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre" in two of the answer choices, which requires localization to the US spelling "center". |
HO0jUVjQfmmLaVTPLedh |
Localize | Spelling (AU-US) | Multiple Choice
What is the prime factorisation of $420$ ?
Options:
|
Multiple Choice
What is the prime factorization of $420$ ?
Options:
|
Classifier: The text contains the AU spelling "factorisation", which needs to be converted to the US spelling "factorization". Verifier: The text contains "factorisation", which is the AU/British spelling. Per rule 1, this requires RED classification. |
HJWuHDaHJrmly8NYyC62 |
Localize | Units (simple) | Question
Maria runs a bakery and sells freshly baked strawberry cake at a profit of $\$10$ and Belgian cakes at a gain of $\$14$ each.
She uses $1$ kg of refined flour for a strawberry cake and $1.5$ kg for a Belgian cake.
A strawberry cake needs $1.5$ hours to prepare, while a Belgian cake gets ready in $1$ hour.
Maria cannot work for more than $8$ hours in a day and buys not more than $10$ kg of refined flour for cakes daily.
What is the maximum total profit she can make in a day?
Hint: Maximize the objective function!
Answer:
|
Question
Maria runs a bakery and sells freshly baked strawberry cake at a profit of $\$10$ and Belgian cakes at a gain of $\$14$ each.
She uses $1$ lb of refined flour for a strawberry cake and $1.5$ lbs for a Belgian cake.
A strawberry cake needs $1.5$ hours to prepare, while a Belgian cake gets ready in $1$ hour.
Maria cannot work for more than $8$ hours in a day and buys not more than $10$ lbs of refined flour for cakes daily.
What is the maximum total profit she can make in a day?
Hint: Maximize the objective function!
Answer:
|
Classifier: The problem uses "kg" (kilograms), which is a metric unit. Per the decision rules, any metric unit requires localization to US customary units (e.g., pounds) or at least classification as a units conversion. Verifier: The text contains the metric unit "kg" (kilograms) multiple times, which requires conversion/localization for the US market. |
HW8fMZvPPqJKyTB0CbdK |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $x^2-16$.
Options:
|
Multiple Choice
Factor the polynomial $x^2-16$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires conversion to US "Factorize" per rule 1. |
Hd2YLg6D0rRafkQJkZjO |
Localize | Units (simple) | Question
Find the total surface area of a hemisphere of radius $8$ cm.
Hint: Total surface area $=$ Curved surface area $+$ Base area
Answer:
|
Question
Find the total surface area of a hemisphere of radius $8$ in.
Hint: Total surface area $=$ Curved surface area $+$ Base area
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) and "cm$^2$", which requires conversion to US customary units (inches). Verifier: The question contains the metric unit "cm" (centimetres) which requires conversion to US customary units. It is a simple conversion as it involves a single geometric calculation with one radius value. |
GTgxSsV2ggyf9jeKHE3f |
Localize | Terminology | Multiple Choice
The Fibonacci sequence can be defined by which of the following recurrence relations?
Hint: Try to use these formulae to calculate $u_3$ and compare this to your knowledge of the sequence.
Options:
|
Multiple Choice
The Fibonacci sequence can be defined by which of the following recurrence relations?
Hint: Try to use these formulas to calculate $u_3$ and compare this to your knowledge of the sequence.
Options:
|
Classifier: Uses the term "formulae", which is the Latin/British plural. While sometimes used in US higher math, "formulas" is the standard US school-context plural. More importantly, the use of "u_n" notation for sequences is very common in AU/UK curricula, whereas US curricula predominantly use "a_n". Verifier: The use of "formulae" (plural) and the sequence notation "u_n" are characteristic of AU/UK school contexts, whereas US contexts typically use "formulas" and "a_n". |
HwJj9jn9eUDXivPhcIRq |
Localize | Units (simple) | Question
Find the perimeter of a semicircle with a diameter of $6$ m.
Answer:
|
Question
Find the perimeter of a semicircle with a diameter of $6$ ft.
Answer:
|
Classifier: The text contains the metric unit 'm' (metres) in the context of a measurement ("diameter of 6 m" and suffix "m"). Per decision rules, any metric unit counts as RED. Verifier: The text contains the metric unit 'm' (metres) in both the content and the suffix. Per rule 3, any metric unit requires RED classification. |
HtMxxGPGPWz5dRC7WTom |
Localize | Terminology | Multiple Choice
True or false:
The turning point form of $y=-4x^2-16x-21$ is given by $y=-4(x+2)^2-5$.
Options:
|
Multiple Choice
True or false:
The vertex form of $y=-4x^2-16x-21$ is given by $y=-4(x+2)^2-5$.
Options:
|
Classifier: The term "turning point form" is the standard Australian/UK term for what is called "vertex form" in the United States. Verifier: The term "turning point form" is the standard Australian/UK terminology for what is known as "vertex form" in the United States. This requires localization for the US market. |
HXlS3WlTk0NysRngkgu1 |
Localize | Units (simple) | Multiple Choice
Fill in the blank.
A rectangular park is enclosed by $250$ m of fencing, and one of the sides has a length of $x$ m.
The area enclosed by the park is given by $A=[?]$.
Options:
|
Multiple Choice
Fill in the blank.
A rectangular park is enclosed by $250$ ft of fencing, and one of the sides has a length of $x$ ft.
The area enclosed by the park is given by $A=[?]$.
Options:
|
Classifier: The text contains the metric unit 'm' (metres) and 'm^2' (square metres), which requires conversion for US localization. Verifier: The text contains metric units 'm' (metres) and 'm^2' (square metres), which require conversion for US localization. |
Hvk8LNgY0tb2d9vhS5Rq |
Localize | Units (simple) | Multiple Choice
Which of the following is a unit of measurement for volume?
Options:
|
Multiple Choice
Which of the following is a unit of measurement for volume?
Options:
|
Classifier: The question asks about units of volume, and the answer choices contain multiple metric units (mm^2, km, cm^2, mm^3). Any metric unit presence requires RED.units_simple_conversion. Verifier: The answer choices contain multiple metric units (mm, km, cm). According to rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
HgJ82r1PQisQQJ0RRZus |
Localize | Terminology | Multiple Choice
Fill in the blank:
If GST is applied to the price of a product then the customer pays $[?]$ in total.
Options:
|
Multiple Choice
Fill in the blank:
If sales tax is applied to the price of a product then the customer pays $[?]$ in total.
Options:
|
Classifier: The term "GST" (Goods and Services Tax) is specific to the Australian tax system (and others like NZ/Canada/India) but is not used in the US, where "sales tax" is the standard term. Verifier: The term "GST" (Goods and Services Tax) is a specific tax system terminology used in Australia, whereas the US uses "sales tax". |
HhUtcVwEdCaQBDJ0qiiZ |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following measures the centre of the curve of a normal distribution function?
Options:
|
Multiple Choice
Which of the following measures the center of the curve of a normal distribution function?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: Contains the AU spelling "centre", which needs to be converted to the US spelling "center". |
HwuX12OQwdLaMCDmBTc2 |
Localize | Units (simple) | Question
The displacement function of a particle is $s(t)=-3t^2+4t-7$ cm for $0\leq t\leq10$ s.
Find the displacement of the particle at $t=6$ s.
Answer:
|
Question
The displacement function of a particle is $s(t)=-3t^2+4t-7$ in for $0\leq t\leq10$ s.
Find the displacement of the particle at $t=6$ s.
Answer:
|
Classifier: The text contains metric units 'cm' (centimetres) and 's' (seconds). While 's' is bi-dialect, 'cm' is a metric unit requiring conversion. Verifier: The text contains the metric unit 'cm' (centimetres). Per rule 3, any metric unit requires RED classification. Although it involves a function, the conversion is a simple scalar change to the output unit, fitting simple_conversion. |
INHOEAtBlq9EfxXvFQWf |
Localize | Units (simple) | Question
How many mL are there in $0.2$ kL ?
Answer:
|
Question
How many fl oz are there in $0.2$ gal ?
Answer:
|
Classifier: The question explicitly uses metric units (mL and kL) and asks for a conversion between them. Any metric unit requires localization per the decision rules. Verifier: The question involves metric units (mL and kL), which requires RED classification. It is a simple conversion of a single value. |
IL6enDImVa2w0pNlPgbP |
Localize | Terminology | Multiple Choice
What is the gradient of a vertical line?
Options:
|
Multiple Choice
What is the slope of a vertical line?
Options:
|
Classifier: The term "gradient" is the standard AU/UK term for what is almost exclusively called "slope" in US K-12 mathematics. Verifier: The term "gradient" is the standard AU/UK term for "slope" in US K-12 mathematics, requiring localization. |
I6KzZJnvBDHcVTn1060S |
Localize | Terminology | Multiple Choice
Fill in the blank:
A team of talented maths students being selected to represent a school in an interschool maths competition is an example of $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
A team of talented math students being selected to represent a school in an interschool math competition is an example of $[?]$.
Options:
|
Classifier: The text uses the term "maths" twice, which is the standard AU term for the US "math". Per decision rules, terminology takes precedence over spelling. Verifier: The text uses "maths", which is the standard AU/British term for the US "math". This is a terminology difference in a school context. |
JQ7R1MlmQT12tWOfnQLN |
Localize | Spelling (AU-US) | Question
Factorise $2x^3y^2+6x^4y$
Answer:
|
Question
Factor $2x^3y^2+6x^4y$
Answer:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU/UK spelling. The US spelling is "Factorize". This requires a RED classification per rule 1. |
JdxsISI29t6FGqtOzFHD |
Localize | Spelling (AU-US) | Question
How many arrangements are possible when you arrange red, green, blue, white and yellow flags such that the white flag is always the first colour of the row?
Answer:
|
Question
How many arrangements are possible when you arrange red, green, blue, white and yellow flags such that the white flag is always the first color of the row?
Answer:
|
Classifier: The text contains the AU spelling "colour", which needs to be converted to the US spelling "color". Verifier: The text contains the AU spelling "colour", which must be localized to the US spelling "color". |
IcZjyJME0vebM9atCoSW |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
If an angle of $270^\circ$ is measured anticlockwise, then the value of angle $\theta=-270^\circ$.
Options:
|
Multiple Choice
True or false:
If an angle of $270^\circ$ is measured counterclockwise, then the value of angle $\theta=-270^\circ$.
Options:
|
Classifier: Contains the AU/UK spelling 'anticlockwise', which should be localized to 'counterclockwise' for a US audience. Verifier: Contains 'anticlockwise', which is the AU/UK spelling. US English uses 'counterclockwise'. |
JXWkwagEMuXmmQlScBSE |
Localize | Units (simple) | Question
How many cubic millimetres are there in $10$ cubic centimetres ?
Answer:
|
Question
How many cubic inches are there in $10$ cubic feet ?
Answer:
|
Classifier: The text contains metric units ("millimetres" and "centimetres") which require conversion or localization for a US audience. It also contains AU spelling ("millimetres", "centimetres"). Verifier: The text contains metric units ("millimetres" and "centimetres") and AU-specific spelling of those units, requiring localization for a US audience. |
IzZ9IQz9tUJJedPRyP77 |
Localize | Spelling (AU-US) | Multiple Choice
Write $4256$ in words.
Options:
|
Multiple Choice
Write $4256$ in words.
Options:
|
Classifier: The text uses the word "and" in the written form of a whole number ("four thousand two hundred and fifty-six"). In US English pedagogy, "and" is strictly reserved for the decimal point, and whole numbers should not include it. This is a common AU/UK vs US convention difference in elementary mathematics. Verifier: The primary classifier correctly identified the use of "and" in the written form of a whole number ("Four thousand two hundred and fifty-six"). In US English mathematics pedagogy, "and" is reserved for the decimal point, whereas in AU/UK English, it is standard to include "and" after the hundreds place. This constitutes a locale-specific convention difference. |
JVHsIFEn70OrXC8fYkTY |
Localize | Units (simple) | Question
A particle is moving, and its displacement function is $s(t)=2t^3+t-5$ m for $0\leq t\leq 4$ s.
Find the instantaneous velocity of the particle at $t=2$ seconds.
Answer:
|
Question
A particle is moving, and its displacement function is $s(t)=2t^3+t-5$ ft for $0\leq t\leq 4$ s.
Find the instantaneous velocity of the particle at $t=2$ seconds.
Answer:
|
Classifier: The text contains metric units ("m" for metres and "s" for seconds, as well as "m/s" in the suffix). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains metric units ("m" for metres and "s" for seconds, as well as "m/s" in the suffix). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Since it is a simple derivative calculation with one primary equation, simple_conversion is appropriate. |
K3hbwm3awPkGB8YKLj0G |
Localize | Units (simple) | Question
A $100$ m long rectangular soccer pitch has a perimeter of $350$ m.
Find the width of the pitch.
Answer:
|
Question
A $100$ ft long rectangular soccer field has a perimeter of $350$ ft.
Find the width of the field.
Answer:
|
Classifier: The question uses "m" (metres) as a unit of measurement for the dimensions of a soccer pitch. Metric units require localization. Verifier: The question uses the metric unit "m" (metres) for length and perimeter, which requires simple unit conversion for the US locale. |
IbWGOYG3VnnkekRWW4cK |
Localize | Units (simple) | Question
In a right-angled triangle, one side is $12$ cm and the hypotenuse is $37$ cm.
Find the length of the other side.
Answer:
|
Question
In a right triangle, one side is $12$ in and the hypotenuse is $37$ in.
Find the length of the other side.
Answer:
|
Classifier: The text contains the metric unit 'cm' and the AU-specific term 'right-angled triangle' (US: right triangle). Per the decision rules, the presence of a metric unit triggers the units conversion category as the most impactful change. Verifier: The text contains the metric unit 'cm' and the AU-specific term 'right-angled triangle' (US: right triangle). Metric units require RED classification. |
KD7dutgKDRqXFPN1maVq |
Localize | Units (simple) | Question
How many km$^2$ are there in $1$ m$^2$ ?
Answer:
|
Question
How many mi$^2$ are there in $1$ ft$^2$ ?
Answer:
|
Classifier: The question explicitly uses and asks for a conversion between metric units (km^2 and m^2). Verifier: The question involves a direct conversion between metric units (km^2 and m^2). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
JdP1bIHt7szYDPon0DRg |
Localize | Terminology | Multiple Choice
Find the highest common factor of $24$ and $60$.
Options:
|
Multiple Choice
Find the greatest common factor of $24$ and $60$.
Options:
|
Classifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US standard is "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is the standard AU/UK term, whereas the US standard is "greatest common factor" (GCF). This requires localization. |
JE9HIYQCp6jdWqng1f7B |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
The average speed of an object over the time interval $[t_1,t_2]$ is given by:
${\text{Average Speed}}$ = $\Large\frac{\text{Distance Travelled from }t_1 \text{ to } t_2}{t_2-t_1}$
Options:
|
Multiple Choice
True or false:
The average speed of an object over the time interval $[t_1,t_2]$ is given by:
${\text{Average Speed}}$ = $\Large\frac{\text{Distance Traveled from }t_1 \text{ to } t_2}{t_2-t_1}$
Options:
|
Classifier: Contains the AU spelling "Travelled", which requires conversion to the US spelling "Traveled". Verifier: The text contains "Travelled", which is the AU/UK spelling. US English uses "Traveled". |
ItIiZkqHZTj86hL7DqXD |
Localize | Answer set | Multiple Choice
Which of the following quadrilaterals has diagonals that perpendicularly bisect each other?
Options:
|
Multiple Choice
Which of the following quadrilaterals has diagonals that perpendicularly bisect each other?
Options:
|
Classifier: Contains the term "Trapezium", which in the US refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to a quadrilateral with at least one pair of parallel sides (which the US calls a "Trapezoid"). This requires localization of the answer set. Verifier: The term "Trapezium" is used in the answer set. In the US, this refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to what the US calls a "Trapezoid". This requires localization for the US market. |
J7mANtkS2ojspnwLcYND |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
The mass of a grain of sand is best measured in $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The weight of a grain of sand is best measured in $[?]$.
Options:
|
Classifier: The question specifically asks for the best unit of measurement for mass and provides metric options (mg, g, kg, t). Any presence of metric units requires localization to US customary units or a check against US science/math curriculum standards which typically favor US customary for general mass estimation. Verifier: The question and answers contain metric units of mass (mg, g, kg, t). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
IR2pNOWTivrZghVtMjic |
Localize | Units (simple) | Multiple Choice
Which of the following can be represented by a discrete random variable?
Options:
|
Multiple Choice
Which of the following can be represented by a discrete random variable?
Options:
|
Classifier: Contains the metric unit "mL" (millilitres) and the AU spelling "flavoured" and "lollies" (US: candies). Per rule 1, any metric unit or AU spelling disqualifies GREEN. Units conversion is the highest priority change. Verifier: The text contains the metric unit "mL" and AU spellings "flavoured" and "lollies". Per the decision rules, metric units and AU spelling require RED classification, with units conversion taking priority. |
J1o1O5vu0KPKxj1Qr4W4 |
Localize | Units (simple) | Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$2$ kg $:$ $400$ g $:$ $6$ kg
Options:
|
Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$2$ lb $:$ $400$ oz $:$ $6$ lb
Options:
|
Classifier: The question explicitly uses metric units (kg and g) and requires a ratio calculation based on those units. Per decision rules, any metric unit requires RED classification. Verifier: The question contains metric units ("kg" and "g"). According to the decision rules, any metric unit requires at least RED.units_simple_conversion. The conversion is simple (ratio of constants), so simple_conversion is correct. |
JK95oiAXE7tNCJGo05fT |
Localize | Units (simple) | Multiple Choice
Which of the following is equal to $67$ L ?
Options:
|
Multiple Choice
Which of the following is equal to $67$ gal ?
Options:
|
Classifier: The question and answers contain multiple metric units (L, ml, m^3, cm^3) which require localization to US customary units or a decision on metric pedagogy. Verifier: The question contains multiple metric units (L, ml, m^3, cm^3) which require localization. |
K3JcohBlrWaSiHVjJSTp |
Localize | Spelling (AU-US) | Multiple Choice
What is $2x(2x-1)+3(2x-1)$ in factorised form?
Options:
|
Multiple Choice
What is $2x(2x-1)+3(2x-1)$ in factored form?
Options:
|
Classifier: Contains the AU spelling "factorised", which needs to be converted to the US spelling "factorized". Verifier: The text contains the AU spelling "factorised", which requires localization to the US spelling "factorized". |
IYLzM9rTR3lQhl1HjBPc |
Localize | Answer set | Multiple Choice
Starting with summer, what is the correct order of the four seasons?
Options:
|
Multiple Choice
Starting with summer, what is the correct order of the four seasons?
Options:
|
Classifier: The term "Autumn" is the standard AU term for the season, whereas "Fall" is the standard US term. This requires localization for the answer set to be natural for a US audience. Verifier: The answer choices use "Autumn", which is the standard AU term. For US localization, this is typically changed to "Fall" to ensure the answer set is natural for the target audience. |
K0CjJuBbjRNps2l0yNub |
Localize | Units (simple) | Multiple Choice
Which of the following most reasonably represents the sample space for $Y$ if $Y$ is the weight of the students in a class in kilograms?
Options:
|
Multiple Choice
Which of the following most reasonably represents the sample space for $Y$ if $Y$ is the weight of the students in a class in pounds?
Options:
|
Classifier: The text explicitly uses "kilograms" as the unit of measurement, which requires localization to pounds for a US audience. Verifier: The text uses "kilograms", which is a metric unit requiring conversion to US customary units (pounds). |
KQv9DZLy75MXHXhq7PKY |
Localize | Units (simple) | Question
Fill in the blank:
$0.12$ kL $=[?]$ L
Answer:
|
Question
Fill in the blank:
$0.12$ gal $=[?]$ fl oz
Answer:
|
Classifier: The question explicitly uses and asks for conversion between metric units (kL and L). Verifier: The question involves metric units (kL and L), which requires RED classification per rule 3. It is a simple numeric conversion. |
KdaFnzNxjbwHAS9YFved |
Localize | Terminology | Multiple Choice
True or false:
Hire-purchase agreements never require a deposit at the beginning of the agreement.
Options:
|
Multiple Choice
True or false:
Installment loans never require a deposit at the beginning of the agreement.
Options:
|
Classifier: "Hire-purchase agreements" is a specific Commonwealth term for what is known in the US as "installment plans" or "rent-to-own". This requires terminology localization for a US audience. Verifier: "Hire-purchase agreements" is a specific Commonwealth/AU term for what is known in the US as "installment plans" or "rent-to-own". This requires terminology localization. |
KqSIeH4j2heupZfFGjeD |
Localize | Terminology | Question
Which number greater than $35$ completes the Pythagorean triple?
$\{12, 35, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Answer:
|
Question
Which number greater than $35$ completes the Pythagorean triple?
$\{12, 35, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Answer:
|
Classifier: The hint contains the term "right-angled triangle", which is the standard AU/UK term. The US equivalent is "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK terminology, whereas "right triangle" is used in the US. |
uPMROp2B5NZGMNJYXQVs |
Localize | Units (simple) | Question
What is $400000$ mm$^3$ in cm$^3$ ?
Answer:
|
Question
What is $400000$ in$^3$ in ft$^3$ ?
Answer:
|
Classifier: The question is specifically about converting between metric units (mm^3 to cm^3). Verifier: The question specifically involves converting between metric units (mm^3 and cm^3). |
uQv6K5UF0SOaSD19sDNc |
Localize | Units (simple) | Question
Find the area of a parallelogram with a height of $2$ cm and a base of $4$ cm.
Answer:
|
Question
Find the area of a parallelogram with a height of $2$ in and a base of $4$ in.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units per the decision rules. Verifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units. This is a simple numeric area calculation. |
KesWQLM27ButRypQczUr |
Localize | Terminology | Multiple Choice
Fill in the blank.
The calculations used to solve for annuities are the same as the calculations used for $[?]$.
Options:
|
Multiple Choice
Fill in the blank.
The calculations used to solve for annuities are the same as the calculations used for $[?]$.
Options:
|
Classifier: The term "Reducing-balance loans" is standard AU terminology for what is typically called an "amortized loan" or "declining balance loan" in the US. While "Compound interest" is neutral, the specific loan types listed are characteristic of the AU financial math curriculum. Verifier: "Reducing-balance loans" is standard AU terminology for "amortized loans" or "declining balance loans" in the US. This is a terminology-based localization requirement. |
ulN9i5Ews7JQ6HgraJ63 |
Localize | Spelling (AU-US) | Question
Rationalise ${\Large\frac{3-6\sqrt{3}}{3+2\sqrt{3}}}$ in the form of $a+b\sqrt{3}$ and then find the value of $b.$
Answer:
|
Question
Rationalize ${\Large\frac{3-6\sqrt{3}}{3+2\sqrt{3}}}$ in the form of $a+b\sqrt{3}$ and then find the value of $b.$
Answer:
|
Classifier: Contains the AU spelling "Rationalise", which should be "Rationalize" in US English. Verifier: Contains "Rationalise", which is the AU/UK spelling; US spelling is "Rationalize". |
KuD7gGrmzRxtMersX5bU |
Localize | Terminology | Multiple Choice
What is the turning point of the parabola $y=-(x+2)(x-4)$ ?
Options:
|
Multiple Choice
What is the vertex of the parabola $y=-(x+2)(x-4)$ ?
Options:
|
Classifier: The term "turning point" is standard in AU/UK curriculum for the vertex of a parabola. In the US, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK curriculum term for what is called the "vertex" in the US. |
KPZOY5vwFCQ7BYmjVhwj |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank.
If $v(t)$ is the velocity function of an object, then the distance travelled by the object in the time interval $[t_1,t_2]$ is $[?]$.
Options:
|
Multiple Choice
Fill in the blank.
If $v(t)$ is the velocity function of an object, then the distance traveled by the object in the time interval $[t_1,t_2]$ is $[?]$.
Options:
|
Classifier: The word "travelled" is the AU/UK spelling; the US spelling is "traveled". Verifier: The word "travelled" is the AU/UK spelling (US: "traveled"). Per rule 1, any AU spelling requires RED classification. |
ujrHDGSNU5MoTlHaEXja |
Localize | Terminology | Question
Which number greater than $63$ completes the Pythagorean triple?
$\{16, 63, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Answer:
|
Question
Which number greater than $63$ completes the Pythagorean triple?
$\{16, 63, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Answer:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" in a US context. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is used in the US. |
uOQH0epP78zvkVevWwL5 |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $2x^{2}+12x+18$
Options:
|
Multiple Choice
Factor $2x^{2}+12x+18$
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be localized to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which must be localized to "Factorize". |
ulfXf7fxTEqZIqjBjRZm |
Review | Review | Question
A university semester score of $270$ corresponds to the $69{\text{th}}$ percentile, with a total of $1200$ students.
How many students scored below $270$?
Answer:
|
Question
A college semester score of $270$ corresponds to the $69{\text{th}}$ percentile, with a total of $1200$ students.
How many students scored below $270$?
Answer:
|
Classifier: Contains the term "semester". While common in the US, its usage in this specific context (university scoring) may be subject to specific localization policies regarding academic terms. Verifier: The term "semester" is standard in both US and AU academic contexts. There are no other locale-specific markers (spelling, units, or currency). It does not meet the criteria for GRAY.term_semester_quarter_policy which usually applies to specific date/term alignments or school year structures not present here. |
udOTIRWteKBDDMkRe8R2 |
Localize | Units (simple) | Question
The average height of $5$ students in a class is $160$ cm.
What is the sum of their heights?
Answer:
|
Question
The average height of $5$ students in a class is $160$ in.
What is the sum of their heights?
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres) which requires conversion to US customary units (inches/feet) for US localization. Verifier: The question contains the metric unit "cm" (centimetres) in both the content and the suffix, which requires conversion to US customary units. |
uUUZ1jIoTvQs5tTG8S3b |
Localize | Terminology | Multiple Choice
Determine whether $\triangle ABC$ is scalene, isosceles, or equilateral given that $A=(-2,-2,-4)$, $B=(2,2,4)$ and $C=(6,-2,2)$.
Options:
|
Multiple Choice
Determine whether $\triangle ABC$ is scalene, isosceles, or equilateral given that $A=(-2,-2,-4)$, $B=(2,2,4)$ and $C=(6,-2,2)$.
Options:
|
Classifier: The answer set contains the term "Right angled triangle", which is the AU/UK standard. The US equivalent is "Right triangle". Verifier: The answer set contains "Right angled triangle", which is the AU/UK standard terminology. The US equivalent is "Right triangle". |
vRf0ytEYKgUOjU0NX1LP |
Localize | Units (simple) | Question
The perimeter of a square garden is $100$ m.
Find the length of each side.
Answer:
|
Question
The perimeter of a square garden is $100$ ft.
Find the length of each side.
Answer:
|
Classifier: The text contains the metric unit "m" (metres) which requires conversion to US customary units (feet/yards) or at least triggers the units classification. Verifier: The text contains the metric unit "m" (metres), which requires conversion to US customary units. |
uQW6lbjDxowhn8bVoerH |
Localize | Units (simple) | Multiple Choice
A $1000$ m long wire is bent into the shape of a rectangle.
Which expression represents the area of the rectangle in terms of $L$?
Options:
|
Multiple Choice
A $1000$ ft long wire is bent into the shape of a rectangle.
Which expression represents the area of the rectangle in terms of $L$?
Options:
|
Classifier: Contains the metric unit "m" (metres). Per decision rules, any metric unit found anywhere in the text triggers a units category. Verifier: Contains the metric unit "m" (metres), which triggers a units category per decision rules. |
unZOtAH0Ac77CqGQuvyE |
Localize | Units (simple) | Question
A driver travels at a fixed speed of $61$ km/h.
How much distance will they cover in $19$ hours?
Answer:
|
Question
A driver travels at a fixed speed of $61$ mph.
How much distance will they cover in $19$ hours?
Answer:
|
Classifier: The question contains metric units ("km/h", "km", "kilometres") which require conversion to US customary units (mph, miles). Verifier: The question uses metric units "km/h", "km", and "kilometres" which require conversion to US customary units. It is a simple conversion as it involves a single rate and a single time value to find distance. |
vY7PEOoqsuGaM5XxYwJ2 |
Localize | Terminology | Multiple Choice
Which type of graph is best for comparing five distinct metals?
Options:
|
Multiple Choice
Which type of graph is best for comparing five distinct metals?
Options:
|
Classifier: The term "Column graph" is the standard Australian term for what is typically called a "Bar graph" in US curriculum. Verifier: "Column graph" is the specific term used in the Australian curriculum (ACARA) where US curricula typically use "Bar graph". |
vT5GNGJNYmW1Gu4T1oEH |
Review | Policy | Multiple Choice
For the given situation, which of these options is correct?
The price of an electronic bicycle worth $\$900$ over time is represented using the regression equation:
Price$=900-10\times$quarter of a year
For the given situation, which of these options is correct?
Options:
|
Multiple Choice
For the given situation, which of these options is correct?
The price of an electric bicycle worth $\$900$ over time is represented using the regression equation:
Price$=900-10\times$quarter of a year
For the given situation, which of these options is correct?
Options:
|
Classifier: The text uses "quarter of a year" and "4 months". While "quarter" is used in the US, the logic in the answer choices (equating a quarter to 4 months) is mathematically unusual (a quarter is typically 3 months). This may be a specific curriculum convention or a typo, warranting a policy check or human review. Verifier: The use of "quarter of a year" equated to "4 months" is mathematically non-standard (a quarter is 3 months) and may reflect a specific curriculum convention or error that requires human review. |
v9Da3i9y961KuDWw2vQK |
Localize | Units (simple) | Multiple Choice
A body starts at $12$ m to the right of the point $O$ and then moves in a straight line with the velocity $v(t)=-8t+15$ m/s in time $t\geq0$.
Describe the position and the velocity of the body at $t=3$ s.
Options:
|
Multiple Choice
A body starts at $12$ ft to the right of the point $O$ and then moves in a straight line with the velocity $v(t)=-8t+15$ ft/s in time $t\geq0$.
Describe the position and the velocity of the body at $t=3$ s.
Options:
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Classifier: The text contains multiple metric units ("m", "m/s", "m s$^{-1}$") which require localization to US customary units. Verifier: The text contains metric units "m", "m/s", and "m s$^{-1}$" which require conversion to US customary units. The conversion is straightforward (simple). |
vuTmq5UdltkhqSHTkYn6 |
Localize | Terminology | Multiple Choice
True or false:
$-6x^3+1=0$ is a cubic equation in point of inflection form.
Options:
|
Multiple Choice
True or false:
$-6x^3+1=0$ is a cubic equation in inflection point form.
Options:
|
Classifier: The term "point of inflection form" for a cubic equation is a specific terminology used in Australian (specifically VCE/Victorian) curriculum. In the US, this is more commonly referred to as "vertex form" or "transformation form" of a cubic, or simply described via transformations. Verifier: The phrase "point of inflection form" is specific to the Australian (VCE) curriculum for cubic functions. In the US, this is typically called "vertex form" or "transformation form". |
vzai9WC72Y4nCMtInuxO |
Localize | Units (simple) | Question
Fill in the blank:
$2.36$ m$^2=[?]$ cm$^2$
Answer:
|
Question
Fill in the blank:
$2.36$ ft$^2=[?]$ in$^2$
Answer:
|
Classifier: The question involves a conversion between metric units (m² to cm²). Any presence of metric units triggers a RED classification. Verifier: The question involves metric units (m² and cm²), which requires RED classification. It is a simple numeric conversion. |
vziAuYcsQpfH30ayjaTy |
Localize | Units (simple) | Question
Fill in the blank:
$[?]$ cm$^{3}$ $=0.842$ litres
Answer:
|
Question
Fill in the blank:
$[?]$ in$^{3}$ $=0.842$ gallons
Answer:
|
Classifier: The question contains metric units (cm³ and litres). Per the decision rules, units conversion takes precedence over spelling ("litres"). Verifier: The question contains metric units (cm³ and litres). Units conversion takes precedence over the spelling of "litres". |
wDaRLTKJbPHUovjhPJN2 |
Localize | Terminology | Multiple Choice
True or false:
The triangle formed by the sides of length $35$, $615$ and $613$ units is a right-angled triangle.
Options:
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Multiple Choice
True or false:
The triangle formed by the sides of length $35$, $615$ and $613$ units is a right triangle.
Options:
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Classifier: The term "right-angled triangle" is the standard AU/UK term. In the US, this is typically referred to as a "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas the US uses "right triangle". This requires localization for the US market. |
vcBNdg7Y78ziaq7sHgPB |
Localize | Spelling (AU-US) | Multiple Choice
What is $x^{3}y-x^{2}y^{2}$ in factorised form?
Options:
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Multiple Choice
What is $x^{3}y-x^{2}y^{2}$ in factored form?
Options:
|
Classifier: The word "factorised" uses the Australian/British 's' spelling; the US equivalent is "factorized". Verifier: The word "factorised" is the Australian/British spelling. The US equivalent is "factorized". Per rule 1, AU spelling always requires RED classification. |
xJi52VrtMvZeZoDCzzzc |
Localize | Spelling (AU-US) | Multiple Choice
As part of a school project, a student counted the number of students on the schoolyard at recess.
Is this data discrete or continuous?
Options:
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Multiple Choice
As part of a school project, a student counted the number of students on the playground at recess.
Is this data discrete or continuous?
Options:
|
Classifier: The answer choice "Continous" is a misspelling of "Continuous". While not strictly an AU-specific spelling (like "metres"), it is a spelling error in the source that requires correction during localization. Additionally, "schoolyard" and "recess" are bi-dialectal, but the spelling error in the answer set triggers a RED classification. Verifier: The answer choice "Continous" is a spelling error (missing 'u') that requires correction. While not an AU-specific spelling variant, it is a spelling-based localization requirement. |
xmaJPdC6C5LG9TLYFLQB |
Localize | Units (simple) | Question
What is $10$ m$^{3}$ in litres?
Answer:
|
Question
What is $10$ ft$^{3}$ in gallons?
Answer:
|
Classifier: The text contains both metric units (m^3) and AU-specific spelling of a metric unit ("litres"). Units conversion takes precedence over spelling. Verifier: The text contains metric units (m^3) and the AU spelling "litres". Per Rule 5, units conversion takes precedence over spelling. It is a simple unit conversion question. |
x04Uubal9YbcWXD1ysL9 |
Localize | Units (simple) | Question
The cost of a $2$ litre can of paint is $\$6$.
What will the cost of $24$ litres of paint be?
Answer:
|
Question
The cost of a $2$ gallon can of paint is $\$6$.
What will the cost of $24$ gallons of paint be?
Answer:
|
Classifier: Contains metric units ("litre", "litres") which also use AU-specific spelling. Units conversion/localization takes precedence over spelling. Verifier: The text contains the metric unit "litre" and "litres", which uses AU/British spelling and is a metric unit, requiring RED classification. |
wUaX8BAXaWYgVbu6TIuH |
Localize | Units (simple) | Question
Tim ran for $5.8$ km yesterday and $2.3$ km today.
How far did he run in total over the two days?
Answer:
|
Question
Tim ran for $5.8$ mi yesterday and $2.3$ mi today.
How far did he run in total over the two days?
Answer:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles) for US localization. Verifier: The question uses "km" (kilometres), which is a metric unit requiring conversion for US localization. The math is a simple addition of two values, making it a simple conversion. |
wtGTKdnkpdzxL5FSsXGf |
Localize | Units (simple) | Question
Convert $0.065$ m$^2$ to cm$^2$.
Answer:
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Question
Convert $0.065$ ft$^2$ to in$^2$.
Answer:
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Classifier: The question specifically asks to convert between metric units (m^2 to cm^2). Any presence of metric units requires RED classification. Verifier: The question involves converting between metric units (m^2 and cm^2), which requires RED classification per rule 3. |
wnkZ9DoRul8M51N0aJVg |
Localize | Terminology | Question
Write $\sqrt{2}\times2\sqrt{3}$ as a single surd.
Options:
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Question
Write $\sqrt{2}\times2\sqrt{3}$ as a single radical.
Options:
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Classifier: The term "surd" is standard in AU/UK curriculum but is rarely used in US K-12 math, where "radical" or "radical expression" is the standard term. Verifier: The term "surd" is specific to AU/UK/Commonwealth curricula; the US equivalent is "radical". This is a terminology difference in a school context. |
wNsirv1cqCz3QfhP8ll3 |
Localize | Units (complex) | Question
Find the average velocity of a particle moving for $5$ hours with a velocity of $v(t)=5t-t^3$ km/hr, initially at rest.
Answer:
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Question
Find the average velocity of a particle moving for $5$ hours with a velocity of $v(t)=5t-t^3$ mi/hr, initially at rest.
Answer:
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Classifier: The text contains metric units ("km/hr") which require conversion to US customary units (e.g., mph). Verifier: The question contains a velocity function v(t) defined in metric units (km/hr). Per rule 4, equations defining quantities in metric or requiring re-deriving formula coefficients should be classified as RED.units_complex_converted. |
wG3ZXwNRFzuov5BTOMJj |
Localize | Units (simple) | Question
A tunnel runs for $46$ km on a bearing of $330^\circ \text{T}$.
How far north is the end of the tunnel from its starting point?
Hint: Use trigonometry to determine the distance travelled.
Answer:
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Question
A tunnel runs for $46$ mi on a bearing of $330^\circ \text{T}$.
How far north is the end of the tunnel from its starting point?
Hint: Use trigonometry to determine the distance traveled.
Answer:
|
Classifier: The text contains the metric unit "km" multiple times, which requires conversion for US localization. Verifier: The question contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles) for localization. It is a simple conversion as it involves a single distance value and a bearing. |
wMNi55hyhDLQJxUj786w |
Localize | Units (simple) | Question
Ali has $55$ kilograms of potatoes in his store. He sold $46$ kilograms of potatoes in a week.
How many grams of potatoes did he not sell?
Answer:
|
Question
Ali has $55$ pounds of potatoes in his store. He sold $46$ pounds of potatoes in a week.
How many ounces of potatoes did he not sell?
Answer:
|
Classifier: The text contains metric units ("kilograms", "grams") which require conversion to US customary units for localization. Verifier: Contains metric units "kilograms" and "grams" which require conversion to US customary units. |
xjwHYVmZ5RWW4sF4xIKG |
Localize | Spelling (AU-US) | Multiple Choice
Standardise the IQ score of $96$ when the mean of all the scores is $92$ and the standard deviation is $3$.
Options:
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Multiple Choice
Standardize the IQ score of $96$ when the mean of all the scores is $92$ and the standard deviation is $3$.
Options:
|
Classifier: The word "Standardise" uses the AU/UK "s" spelling instead of the US "Standardize". Verifier: The word "Standardise" uses the AU/UK spelling (ending in -ise) rather than the US "Standardize". |
xD0NECgcdNqQPVRld0Bq |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $x^2+4$.
Options:
|
Multiple Choice
Factor the polynomial $x^2+4$.
Options:
|
Classifier: Contains the AU/UK spelling "Factorise" and "factorised", which must be converted to "Factorize" and "factorized" for US localization. Verifier: Contains "Factorise" and "factorised", which are AU/UK spellings that require localization to US "Factorize/factorized". |
wrdXHxjufHiDH9eyXZkn |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
The total surface area of a closed cylinder with radius $r$ cm and height $h$ cm is given by $[?]$.
Options:
|
Multiple Choice
Fill in the blank:
The total surface area of a closed cylinder with radius $r$ in and height $h$ in is given by $[?]$.
Options:
|
Classifier: The text explicitly uses metric units ("cm" and "cm^2") which requires conversion or localization for a US audience. Verifier: The question and answers use metric units ("cm" and "cm^2"), which requires localization for the US market. |
xDCAj188IW215lMbm75w |
Localize | Terminology | Multiple Choice
Fill in the blank:
A quadratic equation in turning point form is generally written in the form $[?].$
Options:
|
Multiple Choice
Fill in the blank:
A quadratic equation in vertex form is generally written in the form $[?].$
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. Verifier: "Turning point form" is the AU/UK term for "vertex form" in the US. |
xlsaimxmC6XC8La6bFIs |
Localize | Units (simple) | Multiple Choice
The velocity function of a particle is $v(t)=t^2-t-20$ m/s at time $t\geq 0$.
How many times does the particle change its direction?
Options:
|
Multiple Choice
The velocity function of a particle is $v(t)=t^2-t-20$ ft/s at time $t\geq 0$.
How many times does the particle change its direction?
Options:
|
Classifier: The text contains the metric unit "m/s" (meters per second), which requires localization to US customary units or a decision on metric usage in US physics contexts. Per rule 1, any metric unit disqualifies the group from being GREEN. Verifier: The text contains the metric unit "m/s" (metres per second). According to Rule 3, any metric unit requires at least RED.units_simple_conversion. Since it is a single unit in a kinematics context without complex interlinked conversions or re-deriving coefficients, simple conversion is appropriate. |
xGEq9RvRwl4Dc71A27kF |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following equations represents a circle centred at $(-1,0)$ with a radius of $64$ units?
Options:
|
Multiple Choice
Which of the following equations represents a circle centered at $(-1,0)$ with a radius of $64$ units?
Options:
|
Classifier: Contains the AU spelling "centred", which needs to be localized to "centered" for a US audience. Verifier: Contains the AU spelling "centred", which requires localization to "centered" for US English. |
xTTdWqLehwQxgXBRyDAA |
Localize | Spelling (AU-US) | Multiple Choice
Which point on the unit circle corresponds to an angle $\theta$ measured anticlockwise from the positive $x$-axis?
Options:
|
Multiple Choice
Which point on the unit circle corresponds to an angle $\theta$ measured counterclockwise from the positive $x$-axis?
Options:
|
Classifier: Contains the AU/UK spelling "anticlockwise", which should be "counterclockwise" in US English. Verifier: Contains "anticlockwise", which is the AU/UK spelling. The US equivalent is "counterclockwise". |
x2AbFwoeIqj7w8goweyW |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank.
To rationalise the denominator of $\Large\frac{a}{\sqrt{b}}$ , we have to $[?]$.
Options:
|
Multiple Choice
Fill in the blank.
To rationalize the denominator of $\Large\frac{a}{\sqrt{b}}$ , we have to $[?]$.
Options:
|
Classifier: Contains the AU spelling "rationalise", which needs to be converted to the US spelling "rationalize". Verifier: Contains the AU spelling "rationalise", which requires localization to the US spelling "rationalize". |
xJyNMewyX0lDqFdIwPwi |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
To calculate the actual figure, we divide the seasonal index by the deseasonalised data.
Options:
|
Multiple Choice
True or false:
To calculate the actual figure, we divide the seasonal index by the deseasonalized data.
Options:
|
Classifier: Contains the AU/UK spelling "deseasonalised" (with an 's'), which should be "deseasonalized" (with a 'z') for US localization. |
y2BgBqm7nu2WyP40Celh |
Localize | Units (simple) | Question
A physicist finds that a radioactive sample decays by $20\%$ per year.
If $1.70$ g remains after $4$ years, what was the initial amount?
Answer:
|
Question
A physicist finds that a radioactive sample decays by $20\%$ per year.
If $1.70$ oz remains after $4$ years, what was the initial amount?
Answer:
|
Classifier: The text contains the metric unit "g" (grams). According to the decision rules, any metric unit found anywhere in the text triggers a units classification. Verifier: The question contains the metric unit "g" (grams), which requires conversion or localization for a US audience. |
xsgODqzw5NtWXeMVcffJ |
Localize | Units (simple) | Question
The velocity function of a particle is given by $v(t)=2t^2+7t-5$ m for $t\geq0$ s.
Find the average acceleration from $t=10$ to $t=20$ seconds.
Answer:
|
Question
The velocity function of a particle is given by $v(t)=2t^2+7t-5$ ft for $t\geq0$ s.
Find the average acceleration from $t=10$ to $t=20$ seconds.
Answer:
|
Classifier: The text contains metric units ("m" for meters and "s" for seconds) and the suffix uses metric notation (m s^-2). Per decision rules, any metric unit requires classification into a units category. Verifier: The question contains metric units (m, s, m s^-2) which requires a RED classification. Simple conversion is appropriate as it is a straightforward calculation of average acceleration. |
y6V8rGjzsK0y6ZeFAEmk |
Localize | Units (simple) | Question
A full bucket of water overflows when a metal ball with a density of $3.68$ g/cm$^3$ and a mass of $400$ g is dropped inside.
Find the volume of spilled water.
Answer:
|
Question
A full bucket of water overflows when a metal ball with a density of $3.68$ oz/in$^3$ and a mass of $400$ oz is dropped inside.
Find the volume of spilled water.
Answer:
|
Classifier: The text contains metric units "g/cm^3", "g", and "cm^3" which require conversion for US localization. Verifier: The text contains metric units "g/cm^3", "g", and "cm^3" which require conversion for US localization. The calculation is a simple density/mass/volume relationship, fitting simple conversion. |
y2Bd11icD98WdBuxtNtz |
Localize | Units (simple) | Question
A rectangular garden is under construction, and according to the architect, they need only $300$ m of fencing material to enclose it from three of its sides.
Find the maximum possible area $A$ of the garden.
Answer:
|
Question
A rectangular garden is under construction, and according to the architect, they need only $300$ ft of fencing material to enclose it from three of its sides.
Find the maximum possible area $A$ of the garden.
Answer:
|
Classifier: The text contains metric units ("m" for metres and "m$^2$" for square metres) which require conversion to US customary units (feet/yards). Verifier: The question contains metric units ("m" for metres and "m$^2$" for square metres) which require conversion to US customary units. |
y6IQb92FErQSlfoqU1UZ |
Localize | Units (simple) | Question
A scientist wants to calculate the density of a metal ball.
The ball has a mass of $250$ g and a volume of $25$ cm$^3$.
What is its density?
Answer:
|
Question
A scientist wants to calculate the density of a metal ball.
The ball has a mass of $250$ oz and a volume of $25$ in$^3$.
What is its density?
Answer:
|
Classifier: The text contains metric units (g, cm^3) which require localization for a US audience according to the decision rules. Verifier: The question contains metric units (g, cm^3) which require conversion for the US locale. The calculation is a simple division (250/25), making it a simple conversion. |
xz4ilAyLrs7OcrMa6Fol |
Localize | Terminology | Multiple Choice
Express $y=2x^2-4x+5$ in turning point form.
Options:
|
Multiple Choice
Express $y=2x^2-4x+5$ in vertex form.
Options:
|
Classifier: The term "turning point form" is the standard Australian/UK term for what is called "vertex form" in the United States. Verifier: The term "turning point form" is the standard Australian/UK terminology for what is known as "vertex form" in the US. This requires localization for the US market. |
xqt1rMLhuR1iLGUB2lRO |
Localize | Terminology | Multiple Choice
When we find payments on an interest-only loan, which of the following information is the one we aim to calculate on the finance solver?
Options:
|
Multiple Choice
When we find payments on an interest-only loan, which of the following information is the one we aim to calculate on the finance solver?
Options:
|
Classifier: The term "finance solver" and the specific notation in the answers (Cp/Y, Pp/Y) are highly characteristic of the Australian curriculum (specifically VCE General/Further Mathematics) and the use of TI-Nspire/Casio ClassPad calculators in that region. While the concepts are universal, the specific calculator terminology often requires localization to US-standard financial calculator or spreadsheet terminology. Verifier: The term "finance solver" and the specific notation (Cp/Y, Pp/Y) are specific to the Australian curriculum and calculator usage (TI-Nspire/Casio ClassPad). |
yUTxHJHliNtTrav4hqLa |
Localize | Terminology | Question
Fill in the missing information:
Rate, $r=[?]\%$ p.a.
Simple interest, $I=\$360$
Principal, $P=\$2000$
Time, $t=6$ years
Hint: p.a. means per annum
Answer:
|
Question
Fill in the missing information:
Rate, $r=[?]\%$ p.a.
Simple interest, $I=\$360$
Principal, $P=\$2000$
Time, $t=6$ years
Hint: p.a. means per year
Answer:
|
Classifier: The term "p.a." (per annum) is the standard abbreviation in Australian/British financial contexts. While understood in the US, "per year" or simply "annual" is significantly more common in US K-12 pedagogy. More importantly, the hint explicitly defines "p.a.", which is a strong indicator of locale-specific terminology needing alignment. Verifier: The use of "p.a." and the explicit definition "p.a. means per annum" in the hint are characteristic of AU/British financial mathematics pedagogy. In US K-12 contexts, "annual" or "per year" is the standard terminology. |
yZ2aalIFhBmAqxqe2ptv |
Localize | Units (simple) | Question
A cuboid-shaped tank has a length of $8$ m and a cross-sectional area of $7$ m$^2$.
Calculate the volume of the tank in litres.
Answer:
|
Question
A rectangular prism-shaped tank has a length of $8$ ft and a cross-sectional area of $7$ ft$^2$.
Calculate the volume of the tank in gallons.
Answer:
|
Classifier: The text contains metric units ("m", "m$^2$", "litres", "L") and specifically uses the AU spelling "litres". Per rule 6, units conversion takes precedence over spelling. Verifier: The question contains metric units (m, m^2, litres, L) and uses the AU spelling "litres". Per rule 5, units conversion takes precedence over spelling. It is a simple conversion (volume calculation and unit shift). |
yXoWPP8wMgTlrJH8IHMT |
Localize | Spelling (AU-US) | Question
The seasonal index for electronics sales in February is $1.25$.
If the deseasonalised sales were $\$18260$, what are the actual sales?
Answer:
|
Question
The seasonal index for electronics sales in February is $1.25$.
If the deseasonalized sales were $\$18260$, what are the actual sales?
Answer:
|
Classifier: Contains "deseasonalised" which uses the AU 's' instead of the US 'z'. Currency symbol ($) is neutral. Verifier: The word "deseasonalised" uses the AU/UK 's' spelling instead of the US 'z' (deseasonalized). |
yTVLJrrEHYgww6ZvqC5x |
Localize | Terminology | Question
Given that $A$ and $B$ are mutually exclusive events, where $\text{Pr}(A)=0.4$ and $\text{Pr}(B)=0.25$, find $\text{Pr}(A\cup B)$.
Express your answer as a percentage.
Answer:
|
Question
Given that $A$ and $B$ are mutually exclusive events, where $P(A)=0.4$ and $P(B)=0.25$, find $P(A\cup B)$.
Express your answer as a percentage.
Answer:
|
Classifier: The notation "Pr(A)" for probability is much more common in Australia/UK; US curriculum almost exclusively uses "P(A)". This falls under school terminology/notation context. Verifier: The notation "Pr(A)" is a specific school-context notation common in Australia/UK, whereas the US standard is "P(A)". |
xs3gDm7118BWNKyp0uw3 |
Localize | Terminology | Multiple Choice
Fill in the blank.
The absolute function $f(x)=|x|$ can be defined in the form of a hybrid function $[?]$
Options:
|
Multiple Choice
Fill in the blank.
The absolute value function $f(x)=|x|$ can be defined in the form of a piecewise function $[?]$
Options:
|
Classifier: The term "hybrid function" is the standard Australian term for what is called a "piecewise function" in the United States. Verifier: The term "hybrid function" is the standard Australian curriculum term for what is known as a "piecewise function" in the US. |
y9AhDxnu28jj1xGfODtd |
Localize | Terminology | Multiple Choice
Which of the following parabolas has a turning point at $(0,-5)$ and passes through $(-2.5,-30)$ ?
Options:
|
Multiple Choice
Which of the following parabolas has a vertex at $(0,-5)$ and passes through $(-2.5,-30)$ ?
Options:
|
Classifier: The term "turning point" is standard AU terminology for what is referred to as the "vertex" of a parabola in US curriculum. Verifier: The term "turning point" is the standard AU term for the "vertex" of a parabola in US curriculum. |
z3qFmopIHO74NyqZvZpp |
Localize | Units (simple) | Question
Find the arc length of a sector of radius $10$ cm with a central angle of $\frac{\pi}{4}$ radians.
Answer:
|
Question
Find the arc length of a sector of radius $10$ in with a central angle of $\frac{\pi}{4}$ radians.
Answer:
|
Classifier: The question contains the metric unit "cm" (centimetres), which requires conversion to US customary units or at least flags the content as non-neutral. Verifier: The question contains the metric unit "cm" (centimetres), which requires conversion for US localization. |
yPfxPlYgrxgIojeNArcx |
Localize | Cultural refs | Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$\$10$ $:$ $\$8.20$ $:$ $200c$
Options:
|
Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$\$10$ $:$ $\$8.20$ $:$ $200¢$
Options:
|
Classifier: The use of "200c" to represent cents is a specific currency notation style often associated with AU/UK contexts, and the problem involves converting between dollars and cents in a way that implies a specific currency system. While the dollar sign is shared, "c" for cents in this specific ratio format is a cultural/geographic convention. Verifier: The notation "200c" for cents is a specific convention often found in AU/UK contexts. In the US, cents are typically denoted with the cent sign (¢) or as decimals of a dollar ($0.02). This represents a cultural/geographic convention in currency notation. |
yh0KvhkJdCIBesclKtzW |
Localize | Units (simple) | Question
The temperature at $4$:$00$ pm was $15^\circ C$.
Five hours later, the temperature dropped by $21^\circ C$.
What was the temperature at $9$:$00$ pm?
Answer:
|
Question
The temperature at $4$:$00$ pm was $15^\circ F$.
Five hours later, the temperature dropped by $21^\circ F$.
What was the temperature at $9$:$00$ pm?
Answer:
|
Classifier: The question uses degrees Celsius, which is a metric unit requiring conversion to Fahrenheit for US localization. Verifier: The question uses degrees Celsius ($^\circ C$), which is a metric unit requiring conversion for US localization. It is a simple conversion involving a few numeric values. |
zEHUdZuMoZ5aMQiBQetQ |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Picking a red-coloured ball from a bag containing $3$ red and $2$ blue balls is a random event.
Options:
|
Multiple Choice
True or false:
Picking a red-colored ball from a bag containing $3$ red and $2$ blue balls is a random event.
Options:
|
Classifier: Contains the AU spelling "red-coloured". The US spelling is "colored". Verifier: Contains "red-coloured", which uses the AU/British spelling "coloured" instead of the US "colored". |
zRs2c8g8Y6Od0iDHVmXE |
Localize | Spelling (AU-US) | Multiple Choice
Which method is best for minimising the horizontal distance of each data point?
Options:
|
Multiple Choice
Which method is best for minimizing the horizontal distance of each data point?
Options:
|
Classifier: Contains the AU/UK spelling "minimising", which requires conversion to the US spelling "minimizing". Verifier: Contains "minimising", which is the AU/UK spelling. US spelling is "minimizing". |
znfgzQnHFh1idUPuqbLk |
Localize | Terminology | Question
A random survey of $500$ people was conducted, and their responses recorded, with $369$ people agreeing that maths was their favourite subject at school.
Find the margin of error of a $90\%$ confidence interval constructed from this data.
Answer:
|
Question
A random survey of $500$ people was conducted, and their responses recorded, with $369$ people agreeing that math was their favorite subject at school.
Find the margin of error of a $90\%$ confidence interval constructed from this data.
Answer:
|
Classifier: The text uses the term "maths", which is the standard Australian/British term for the subject. In the US, "math" is used. Verifier: The text uses "maths", which is the standard Australian/British term for the subject. In the US, "math" is used. This is a terminology difference in a school context. |
zusYZeupFqiuLMB5590e |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $x^2-x-p^2x+p^2$ by grouping.
Options:
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Multiple Choice
Factor $x^2-x-p^2x+p^2$ by grouping.
Options:
|
Classifier: Contains the AU spelling "Factorise", which requires conversion to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU/British spelling. US spelling is "Factorize". |
zUQlsrEjInHACYp3RQaF |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $2 x^3 - 6 x^2 - 10 x + 30$.
Hint: Use the Rational Root Theorem.
Options:
|
Multiple Choice
Factor $2 x^3 - 6 x^2 - 10 x + 30$.
Hint: Use the Rational Root Theorem.
Options:
|
Classifier: Contains the AU/UK spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains "Factorise", which is the AU/UK spelling. US spelling is "Factorize". |
zxqMyvS2P5ktVXvbwHTj |
Localize | Units (simple) | Multiple Choice
A rectangular garden has an area of $120$ m$^2$ and a perimeter of $52$ m, with length $𝑙$ metres and width $𝑤$ metres.
Which of the following pairs represents the correct values of $𝑙$ and $𝑤$ ?
Options:
|
Multiple Choice
A rectangular garden has an area of $120$ ft$^2$ and a perimeter of $52$ ft, with length $𝑙$ feet and width $𝑤$ feet.
Which of the following pairs represents the correct values of $𝑙$ and $𝑤$ ?
Options:
|
Classifier: The text contains metric units (m, m^2) and the AU spelling "metres". Per decision rules, any metric unit requires at least RED.units_simple_conversion, which takes precedence over spelling. Verifier: The text contains metric units (m, m^2) and the AU spelling "metres". Per decision rules, metric units require RED.units_simple_conversion. |
01JVJ695805K9000YX5A1KY6QQ |
Localize | Units (simple) | Question
A rectangular park is $120$ m long and $50$ m wide.
A person walks along the length, then the width, and returns along the diagonal path.
What is the total distance walked, to the nearest metre?
Answer:
|
Question
A rectangular park is $120$ ft long and $50$ ft wide.
A person walks along the length, then the width, and returns along the diagonal path.
What is the total distance walked, to the nearest foot?
Answer:
|
Classifier: The text contains metric units ("m") and the AU spelling of "metre". Per the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units ("m") and the AU spelling "metre". Per rule 3 and 5, this requires RED.units_simple_conversion. |
01JVJ695814BRSN1V380M72Y1E |
Localize | Units (simple) | Question
A $17$-metre ladder leans against a vertical wall, with its top $15$ metres above the ground.
The foot is then pulled $7$ metres farther from the wall. How many metres does the top of the ladder slide down the wall?
Answer:
|
Question
A $17$-foot ladder leans against a vertical wall, with its top $15$ feet above the ground.
The foot is then pulled $7$ feet farther from the wall. How many feet does the top of the ladder slide down the wall?
Answer:
|
Classifier: The text contains metric units ("metres", "m") and the AU spelling "metre". This requires conversion to US customary units or at least spelling localization, but units conversion is the higher priority category. Verifier: The text contains metric units ("metres", "m") and the AU spelling "metre". This requires conversion to US customary units. |
01JW7X7K5CBTFC10WE5ZFBDGTS |
Localize | Spelling (AU-US) | Multiple Choice
The longer hand on an analogue clock is the $\fbox{\phantom{4000000000}}$ hand.
Options:
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Multiple Choice
The longer hand on an analog clock is the $\fbox{\phantom{4000000000}}$ hand.
Options:
|
Classifier: Contains the AU spelling "analogue", which must be converted to the US spelling "analog". Verifier: Contains "analogue", which is the AU/UK spelling. US spelling is "analog". |
01JW7X7K5GMJ8N9TKK48R8YA24 |
Localize | Terminology | Multiple Choice
A surd is an $\fbox{\phantom{4000000000}}$ number.
Options:
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Multiple Choice
A radical is an $\fbox{\phantom{4000000000}}$ number.
Options:
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Classifier: The term "surd" is standard in AU/UK curriculum but is rarely used in US K-12 education, where "radical" or "irrational square root" is preferred. Verifier: The term "surd" is a specific AU/UK curriculum term; US curriculum typically uses "radical" or "irrational square root". |
01JW7X7K5ZN071CEJH7VBHXC1Q |
Localize | Terminology | Multiple Choice
Pythagoras' $\fbox{\phantom{4000000000}}$ relates the sides of a right-angled triangle.
Options:
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Multiple Choice
Pythagorean $\fbox{\phantom{4000000000}}$ relates the sides of a right triangle.
Options:
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Classifier: The text contains the term "right-angled triangle", which is the standard AU term. The US equivalent is "right triangle". Verifier: The term "right-angled triangle" is the standard AU term; the US equivalent is "right triangle". |
01JW7X7K63W4RR67C3HKJZ2FA5 |
Localize | Spelling (AU-US) | Multiple Choice
Index laws are used to $\fbox{\phantom{4000000000}}$ expressions with exponents.
Options:
|
Multiple Choice
Exponent rules are used to $\fbox{\phantom{4000000000}}$ expressions with exponents.
Options:
|
Classifier: The answer choice "factorise" uses the AU/UK 's' spelling, which requires conversion to the US 'z' spelling ("factorize"). Verifier: The answer choice "factorise" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("factorize"). |
01JW7X7K6KRP4T964WNGTB7APF |
Localize | Spelling (AU-US) | Multiple Choice
Mutual exclusivity and independence are distinct $\fbox{\phantom{4000000000}}$ in probability.
Options:
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Multiple Choice
Mutual exclusivity and independence are distinct $\fbox{\phantom{4000000000}}$ in probability.
Options:
|
Classifier: The answer set contains the word "formulae", which is the preferred AU/UK plural. In US English, "formulas" is the standard spelling. Verifier: The answer set contains "formulae", which is the AU/UK plural form. US English standardly uses "formulas". |
01JW7X7K6HH1ZDN4PK4HSGFVD4 |
Localize | Terminology | Multiple Choice
In a $\fbox{\phantom{4000000000}}$, the bars have no gaps between them to show that the data is continuous.
Options:
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Multiple Choice
In a $\fbox{\phantom{4000000000}}$, the bars have no gaps between them to show that the data is continuous.
Options:
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Classifier: Similar to Group 4, "column graph" is an AU-specific term for a bar graph. The presence of "column graph" in the answer set requires localization to "bar graph" to match US conventions. Verifier: The presence of "column graph" in the answer set as a distractor/option requires localization to "bar graph" to align with US terminology conventions. |
01JW7X7K5FD5VC39QYG08YD23N |
Localize | Terminology | Multiple Choice
$\fbox{\phantom{4000000000}}$ form is a way of writing a linear equation that shows the gradient and $y$-intercept.
Options:
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Multiple Choice
$\fbox{\phantom{4000000000}}$ form is a way of writing a linear equation that shows the slope and $y$-intercept.
Options:
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Classifier: The text uses the term "gradient", which is the standard AU/UK term for what is called "slope" in US mathematics. Verifier: The text uses "gradient", which is the standard AU/UK term for "slope" in US mathematics. |
01JW7X7K6G7C185R51YHJ9J9XN |
Localize | Terminology | Multiple Choice
Column graphs are used for $\fbox{\phantom{4000000000}}$ data, while histograms are used for continuous data.
Options:
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Multiple Choice
Bar graphs are used for $\fbox{\phantom{4000000000}}$ data, while histograms are used for continuous data.
Options:
|
Classifier: The term "Column graphs" is the standard AU term for what is almost exclusively called a "Bar graph" in US K-12 education, especially when contrasted with histograms. While "column graph" is understood, "bar graph" is the required localization for US school context. Verifier: The term "Column graphs" is the standard AU term for what is called a "Bar graph" in US K-12 education. This requires localization for the US school context. |
01JW7X7K5JJHHWPHGKJPYEJ1VZ |
Localize | Spelling (AU-US) | Multiple Choice
Polynomial long division can be used to $\fbox{\phantom{4000000000}}$ polynomials.
Options:
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Multiple Choice
Polynomial long division can be used to $\fbox{\phantom{4000000000}}$ polynomials.
Options:
|
Classifier: Contains the AU spelling "factorise", which requires conversion to the US spelling "factorize". Verifier: The answer choice contains "factorise", which is the AU spelling of the US "factorize". |
01JW7X7K69MM7TCW7AX8PPF7QQ |
Localize | Units (simple) | Multiple Choice
Area is measured in $\fbox{\phantom{4000000000}}$ units, such as square centimetres or square metres.
Options:
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Multiple Choice
Area is measured in $\fbox{\phantom{4000000000}}$ units, such as square inches or square feet.
Options:
|
Classifier: The text contains metric units ("centimetres", "metres") which require conversion to US customary units. These also contain AU-specific spellings ("metres" vs "meters"). Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains metric units "centimetres" and "metres", which require conversion to US customary units. These also use AU/British spelling. Per rule 5, units conversion takes precedence over spelling. |
01JW7X7K5B33YQDM3TCY5AEVFP |
Localize | Spelling (AU-US) | Multiple Choice
The shorter hand on an analogue clock is the $\fbox{\phantom{4000000000}}$ hand.
Options:
|
Multiple Choice
The shorter hand on an analog clock is the $\fbox{\phantom{4000000000}}$ hand.
Options:
|
Classifier: Contains the AU spelling "analogue", which must be converted to the US spelling "analog". Verifier: Contains "analogue", which is the AU/UK spelling. US spelling is "analog". |
01JW7X7K65M8G3RHZVRF0GGJBM |
Localize | Units (simple) | Multiple Choice
The metric system uses units like metres, litres, and $\fbox{\phantom{4000000000}}$
Options:
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Multiple Choice
The US customary system uses units like feet, gallons, and $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The text explicitly mentions metric units ("metres", "litres", "kilograms") and uses AU-specific spellings for them ("metres", "litres"). This requires both spelling correction and potentially a shift in focus for a US audience, though the category is driven by the presence of metric units and AU spelling. Verifier: The text contains metric units ("metres", "litres", "kilograms") and uses AU-specific spellings ("metres", "litres"). This requires localization. |
01JW7X7K5WA4AD1WXASQHZAHWN |
Localize | Terminology | Multiple Choice
$\fbox{\phantom{4000000000}}$ tests, such as SSS, SAS, and ASA, are used to determine if two triangles are the same.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ tests, such as SSS, SAS, and ASA, are used to determine if two triangles are the same.
Options:
|
Classifier: The term "Congruency" is used in the answer set. In US curriculum standards (CCSS), the preferred term is "Congruence". Additionally, "tests" for congruence are more commonly referred to as "criteria" or "postulates/theorems" in the US, though "Congruency" is the primary trigger for localization here. Verifier: The term "Congruency" and the use of "tests" for congruence (SSS, SAS, ASA) are characteristic of AU/UK curricula. In the US, "Congruence" is the standard noun, and these are typically called "criteria", "postulates", or "theorems". |
01JW7X7K5MGCGKBP69XFVSB3J4 |
Localize | Terminology | Multiple Choice
A $\fbox{\phantom{4000000000}}$ decimal has an infinite number of digits after the decimal point.
Options:
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Multiple Choice
A $\fbox{\phantom{4000000000}}$ decimal has an infinite number of digits after the decimal point.
Options:
|
Classifier: While "non-terminating" is neutral, "recurring decimal" is the primary AU term, whereas "repeating decimal" is the standard US term. Since "recurring" is an answer choice, it signals AU-centric terminology. Verifier: The term "recurring decimal" is standard in AU/UK pedagogy, whereas "repeating decimal" is the standard US term. |
01JW7X7K5NM7BDWTF7Q91RW8YJ |
Localize | Spelling (AU-US) | Multiple Choice
Equations can be $\fbox{\phantom{4000000000}}$, while expressions can be simplified or evaluated.
Options:
|
Multiple Choice
Equations can be $\fbox{\phantom{4000000000}}$, while expressions can be simplified or evaluated.
Options:
|
Classifier: Contains the AU spelling "factorised" in the answer set, which requires conversion to "factorized". Verifier: The answer choice contains "factorised", which is the AU spelling of the US "factorized". |
01JW7X7K58JZSZ2QR7GTVX5FWZ |
Localize | Terminology | Multiple Choice
$\fbox{\phantom{4000000000}}$ are also referred to as exponents or powers.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ are also referred to as exponents or powers.
Options:
|
Classifier: The term "Indices" is the standard AU/UK term for what is almost exclusively referred to as "Exponents" or "Powers" in US school mathematics. While "indices" is used in higher-level US math (e.g., index of a radical), in this context (synonym for exponents/powers), it is a distinct AU pedagogical term. Verifier: The term "Indices" is the standard pedagogical term in Australia for what is called "Exponents" in the US. This is a clear terminology difference in a school context. |
01JW7X7K5PF04FP0J216GF1FCD |
Localize | Spelling (AU-US) | Multiple Choice
Expanding brackets is often a step in $\fbox{\phantom{4000000000}}$ algebraic expressions.
Options:
|
Multiple Choice
Expanding parentheses is often a step in $\fbox{\phantom{4000000000}}$ algebraic expressions.
Options:
|
Classifier: The answer choice "factorising" uses the AU 's' spelling and needs to be converted to the US 'z' spelling "factorizing". Verifier: The answer choice "factorising" uses the AU/UK spelling (with 's'). US English requires "factorizing" (with 'z'). |
01JW7X7K6SSNRSTESM6785D339 |
Localize | Spelling (AU-US) | Multiple Choice
Prime factorisation is the process of breaking down a composite number into its $\fbox{\phantom{4000000000}}$ factors.
Options:
|
Multiple Choice
Prime factorization is the process of breaking down a composite number into its $\fbox{\phantom{4000000000}}$ factors.
Options:
|
Classifier: The word "factorisation" uses the AU/UK 's' spelling. In US English, this must be "factorization". Verifier: The word "factorisation" uses the AU/UK 's' spelling, which requires localization to "factorization" for a US audience. |
01JW7X7K7W1MKRWGD86J7FQA1G |
Localize | Spelling (AU-US) | Multiple Choice
A stem-and-$\fbox{\phantom{4000000000}}$ plot organises numerical data.
Options:
|
Multiple Choice
A stem-and-$\fbox{\phantom{4000000000}}$ plot organizes numerical data.
Options:
|
Classifier: The word "organises" uses the AU/UK 's' spelling instead of the US 'z' spelling ("organizes"). Verifier: The word "organises" is the AU/UK spelling; the US spelling is "organizes". Per rule 1, AU spelling requires RED classification. |
01JW7X7K7BBS7EE39QG1H6GW1Z |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ is the process of writing an expression as a product of factors.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ is the process of writing an expression as a product of factors.
Options:
|
Classifier: The answer choice "Factorising" uses the AU/UK 's' spelling. In US English, this must be "Factorizing". Verifier: The answer choice "Factorising" uses the AU/UK spelling (with an 's'). US English requires "Factorizing". This is a spelling-only change. |
01JW7X7K88RGX4GB6TRFY1G144 |
Localize | Terminology | Multiple Choice
How sharply a line rises or falls is called its $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
How sharply a line rises or falls is called its $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The term "gradient" is the standard AU term for the steepness of a line, whereas "slope" is the standard US term. This requires localization to the US curriculum context. Verifier: The term "gradient" is the standard AU term for the steepness of a line, whereas "slope" is the standard US term. This requires localization to the US curriculum context. |
01JW7X7K8SS00PQFYF2XK6HX36 |
Localize | Spelling (AU-US) | Multiple Choice
Multiplying terms inside brackets by terms outside is called $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
Multiplying terms inside parentheses by terms outside is called $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The answer set contains the AU spelling "factorising", which needs to be converted to the US spelling "factorizing". Verifier: The answer set contains "factorising", which is the AU spelling. US English uses "factorizing". Per rule 1, AU spelling requires RED classification. |
01JW7X7K8MYGN4CFFDJK5N9D84 |
Localize | Answer set | Multiple Choice
A quadrilateral with two pairs of adjacent equal sides is called a $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
A quadrilateral with two pairs of adjacent equal sides is called a $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The answer set contains the term "trapezium", which in the US refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to a quadrilateral with one pair of parallel sides (US: trapezoid). This requires localization for consistency. Verifier: The term "trapezium" has conflicting definitions between AU/UK and US English. In AU, it is a quadrilateral with one pair of parallel sides (US: trapezoid). In the US, a trapezium is a quadrilateral with no parallel sides. This requires localization for consistency. |
01JW7X7K8VE51B07V8VY7A509F |
Localize | Terminology | Multiple Choice
The point where a parabola changes direction is its $\fbox{\phantom{4000000000}}$ point.
Options:
|
Multiple Choice
The point where a parabola changes direction is its $\fbox{\phantom{4000000000}}$ point.
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In US curriculum, "vertex" is the primary term used in this context. Verifier: The primary classifier is correct. "Turning point" is the standard term in Australian and British curricula for the vertex of a parabola. In the US, "vertex" is the standard term. This requires terminology localization. |
01JW7X7K9HN674TBB9CTRJDZZJ |
Localize | Terminology | Multiple Choice
Rules for working with exponents are called $\fbox{\phantom{4000000000}}$ laws.
Options:
|
Multiple Choice
Rules for working with exponents are called $\fbox{\phantom{4000000000}}$ laws.
Options:
|
Classifier: The answer set includes "index", which in the context of "index laws" is the standard AU term for what the US calls "exponent rules" or "laws of exponents". While "exponent" is also an option, the presence of "index" as a distractor/alternative in an AU source often points to the need to ensure the US terminology (exponent) is prioritized or the AU term (index) is removed/replaced to avoid confusion. Verifier: The presence of "index" as a distractor for "exponent" indicates an AU source context (Index Laws vs Laws of Exponents). In a US context, "index" is rarely used this way, and the question should be reviewed to ensure US terminology is prioritized. |
01JW7X7KA3VZZ4BWT4E6AEDX1Z |
Localize | Spelling (AU-US) | Multiple Choice
The direction of rotation can be described as either clockwise or $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
The direction of rotation can be described as either clockwise or $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: Contains the AU/UK spelling "anticlockwise", which should be localized to "counterclockwise" for a US audience. Verifier: The term "anticlockwise" is the standard AU/UK term, whereas "counterclockwise" is used in the US. This requires localization. |
01JW7X7KA4X6S5TBJGTY0ZGXEG |
Localize | Terminology | Multiple Choice
Recurring fractions can be converted to $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
Repeating decimals can be converted to $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The terms "Recurring fractions", "whole numbers", "decimals", "percentages", and "mixed numbers" are standard in both AU and US English. While "repeating decimals" is more common in the US, "recurring" is understood and not strictly an AU-only spelling or terminology error requiring a RED classification under these rules. Verifier: The term "Recurring fractions" and "recurring" (in the context of decimals) is specific to AU/UK pedagogy. In the US, the standard terminology is "repeating decimals". While the classifier noted this, it incorrectly dismissed it as "understood"; under the provided rules, this terminology difference warrants a RED classification. |
01JW7X7KA21X6QBZAXTA032SZA |
Localize | Spelling (AU-US) | Multiple Choice
Identifying upcoming elements involves recognising the $\fbox{\phantom{4000000000}}$ in the pattern and applying it to determine subsequent terms.
Options:
|
Multiple Choice
Identifying upcoming elements involves recognizing the $\fbox{\phantom{4000000000}}$ in the pattern and applying it to determine subsequent terms.
Options:
|
Classifier: The word "recognising" uses the AU/UK 's' spelling and must be converted to the US 'z' spelling ("recognizing"). Verifier: The text contains "recognising", which is the AU/UK spelling. US English requires "recognizing". |
01JW7X7KAM6MKQAHSA5034HEWW |
Localize | Spelling (AU-US) | Multiple Choice
Conditional probability is used to analyse situations with $\fbox{\phantom{4000000000}}$ events.
Options:
|
Multiple Choice
Conditional probability is used to analyze situations with $\fbox{\phantom{4000000000}}$ events.
Options:
|
Classifier: Contains the AU spelling "analyse", which needs to be converted to the US spelling "analyze". Verifier: The text contains "analyse", which is the AU/UK spelling. The US spelling is "analyze". |
01JW7X7KB14FE3YRJHNTKE9GMR |
Localize | Terminology | Multiple Choice
The largest shared factor of two numbers is called their highest common $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
The largest shared factor of two numbers is called their greatest common $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US typically uses "greatest common factor" (GCF). Verifier: The term "highest common factor" (HCF) is standard in AU/UK, whereas the US typically uses "greatest common factor" (GCF). |
01JW7X7KBEH9MP724EDZA5XY2N |
Localize | Terminology | Multiple Choice
The turning point of a parabola is called its $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
The vertex of a parabola is called its $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The text uses the AU-specific term "turning point" to describe the vertex of a parabola. In US curriculum, "vertex" is the standard term used in this context. Verifier: The term "turning point" is the standard Australian curriculum term for the vertex of a parabola, whereas "vertex" is the primary term in the US. This requires localization for terminology. |
01K0RMP952AB1QWFAM1Y813FKF |
Localize | Units (simple) | Multiple Choice
Convert $0.8$ cubic metres to litres.
Options:
|
Multiple Choice
Convert $0.8$ cubic feet to gallons.
Options:
|
Classifier: Contains metric units ("metres", "litres") and AU-specific spelling of those units. Requires conversion to US customary units or at least spelling correction, but per rules, any metric unit triggers units_simple_conversion. Verifier: Contains metric units ("metres", "litres") and AU-specific spelling of those units. Per rule 3, any metric unit triggers at least RED.units_simple_conversion. |
01JW7X7KAP7E231Q506EBKZ119 |
Localize | Units (simple) | Multiple Choice
Square metres and square centimetres represent units of $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
Square feet and square inches represent units of $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The text contains metric units ("metres", "centimetres") and AU spelling ("metres", "centimetres" vs US "meters", "centimeters"). Per rule 6, units conversion is the most impactful change. Verifier: The text contains metric units ("metres", "centimetres") which require conversion to US customary units. The spelling is also AU-specific. |
01JW7X7KAYRZV0Z317PY4XMBEE |
Localize | Terminology | Multiple Choice
Triangles can be classified by their sides (equilateral, isosceles, $\fbox{\phantom{4000000000}}$ ) or angles (acute, obtuse, right-angled).
Options:
|
Multiple Choice
Triangles can be classified by their sides (equilateral, isosceles, $\fbox{\phantom{4000000000}}$ ) or angles (acute, obtuse, right).
Options:
|
Classifier: Contains the AU-specific term "right-angled", which should be localized to "right" (as in "right triangle") for a US audience. Verifier: Contains the AU-specific term "right-angled", which should be localized to "right" (as in "right triangle") for a US audience. |
01K0RMP953G0C2PWYEQQHRE9ME |
Localize | Units (simple) | Multiple Choice
Water is flowing at a rate of $300$ millilitres per second.
How many litres flow in one minute?
Options:
|
Multiple Choice
Water is flowing at a rate of $300$ fluid ounces per second.
How many gallons flow in one minute?
Options:
|
Classifier: Contains metric units ("millilitres", "litres") and AU spelling ("litres"). Verifier: Contains metric units ("millilitres", "litres") and AU spelling ("litres"). |
01K0RMSP8M5VW62QS7MFVDRX90 |
Localize | Units (simple) | Multiple Choice
A sphere has a surface area of $100\pi$ m$^2$.
What is its diameter?
Options:
|
Multiple Choice
A sphere has a surface area of $100\pi$ ft$^2$.
What is its diameter?
Options:
|
Classifier: The text contains the metric unit "m" (metres) and "m^2" (square metres), which requires conversion to US customary units (e.g., feet/inches) or at least triggers the units classification. Verifier: The text contains the metric unit "m" (metres) and "m^2", which requires conversion for US localization. |
01K0RMSP8PKNEPZ5ZK3711DFFJ |
Localize | Units (simple) | Multiple Choice
A sphere has a volume of $288\pi$ cm$^3$.
What is its surface area?
Options:
|
Multiple Choice
A sphere has a volume of $288\pi$ in$^3$.
What is its surface area?
Options:
|
Classifier: The text contains the metric unit "cm^3" and "cm^2", which requires localization for a US audience. Verifier: The text contains metric units "cm^3" and "cm^2", requiring conversion. |
01K0RMVPQE919RNF1GQGZ27K80 |
Localize | Units (simple) | Question
Calculate the surface area of a sphere with a radius of $10$ m to the nearest square metre.
Answer:
|
Question
Calculate the surface area of a sphere with a radius of $10$ ft to the nearest square foot.
Answer:
|
Classifier: Contains both a metric unit ("m") and AU-specific spelling ("metre"). Per decision rules, units conversion takes precedence over spelling. Verifier: The text contains the metric unit "m" and the AU spelling "metre". Per rule 5, units conversion takes precedence over spelling. |
01K0RMSP9Z6P7HSBAMHZD8Z5VF |
Localize | Units (simple) | Question
A rectangular prism has a length of $x$ cm, a width of $5$ cm, and a height of $8$ cm. Its total surface area is $292$ cm$^2$.
Find the value of $x$ to two decimal places.
Answer:
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Question
A rectangular prism has a length of $x$ in, a width of $5$ in, and a height of $8$ in. Its total surface area is $292$ in$^2$.
Find the value of $x$ to two decimal places.
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires localization to US customary units or a decision on metric usage in US curriculum. Verifier: The text contains the metric unit "cm" and "cm^2". This requires simple unit conversion for the US locale. |
01K0RMVPQKZ11RFSTHXPNE0EG8 |
Localize | Units (simple) | Question
The surface area of a sphere is $36\pi$ cm$^2$.
What is its radius?
Answer:
|
Question
The surface area of a sphere is $36\pi$ in$^2$.
What is its radius?
Answer:
|
Classifier: Contains the metric unit "cm". Verifier: The text contains the metric unit "cm" and "cm^2". |
01K0RMVPQGMF8BVHVNQ0Y04ZRE |
Localize | Units (simple) | Question
Find the surface area of a sphere with a radius of $2$ m to two decimal places.
Answer:
|
Question
Find the surface area of a sphere with a radius of $2$ ft to two decimal places.
Answer:
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Classifier: Contains the metric unit "m". Verifier: The text contains the metric unit "m" and "m^2". |
01K0RMVPQFKJE8HG1097BT29E4 |
Localize | Units (simple) | Question
The radius of a spherical asteroid is $10$ km.
Find its surface area in terms of $\pi$.
Answer:
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Question
The radius of a spherical asteroid is $10$ mi.
Find its surface area in terms of $\pi$.
Answer:
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Classifier: Contains the metric unit "km". Verifier: The text contains the metric unit "km" and "km^2". |
01K0RMVPQJ4GN170W59MPJ5VED |
Localize | Units (simple) | Question
The diameter of a sphere is $20$ mm.
Find its surface area in terms of $\pi$.
Answer:
|
Question
The diameter of a sphere is $20$ in.
Find its surface area in terms of $\pi$.
Answer:
|
Classifier: Contains the metric unit "mm". Verifier: The text contains the metric unit "mm" and "mm^2". |
01K0RMSP9EG4ZJ97A7ZKGPG4G2 |
Localize | Units (simple) | Multiple Choice
The volume of a sphere is $288\pi$ cm$^3$.
What is its radius?
Options:
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Multiple Choice
The volume of a sphere is $288\pi$ in$^3$.
What is its radius?
Options:
|
Classifier: The text contains the metric unit "cm" and "cm^3". Verifier: The text contains metric units "cm" and "cm^3", requiring conversion. |
01K0RMVPQHK6C8SBY89BG4TGTS |
Localize | Units (simple) | Question
A spherical ball has a radius of $1$ m.
What is its surface area in terms of $\pi$?
Answer:
|
Question
A spherical ball has a radius of $1$ ft.
What is its surface area in terms of $\pi$?
Answer:
|
Classifier: Contains the metric unit "m". Verifier: The text contains the metric unit "m" and "m^2". |
01K0RMSP9F5XGT368F8RZVX30Q |
Localize | Units (simple) | Multiple Choice
A solid metal sphere of radius $9$ cm is melted down and recast into smaller solid spheres of radius $1$ cm.
How many smaller spheres can be made?
Options:
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Multiple Choice
A solid metal sphere of radius $9$ in is melted down and recast into smaller solid spheres of radius $1$ in.
How many smaller spheres can be made?
Options:
|
Classifier: The text contains the metric unit "cm". Even though the final answer is a dimensionless ratio, the presence of metric units in the prompt requires localization. Verifier: The text contains the metric unit "cm". Even though the final answer is a ratio, the presence of metric units in the prompt triggers the requirement for localization. |
01K0RMSP9237E8RHBY3MGPKG1M |
Localize | Units (simple) | Multiple Choice
An ice cream cone has a height of $10$ cm and a diameter of $6$ cm.
Find the volume of the cone to the nearest cubic centimetre.
Options:
|
Multiple Choice
An ice cream cone has a height of $10$ in and a diameter of $6$ in.
Find the volume of the cone to the nearest cubic inch.
Options:
|
Classifier: The text contains metric units "cm" and the word "centimetre". Note that "centimetre" also contains AU spelling (re vs er), but units conversion is the higher priority classification. Verifier: The text contains metric units "cm" and the word "centimetre" (which also uses AU spelling). Units conversion is the primary reason for RED. |
01K0RMVPR3EBMKY6QF4A0XTKXB |
Localize | Units (simple) | Question
Find the total surface area of a cone with a perpendicular height of $4$ cm and a diameter of $6$ cm to one decimal place.
Answer:
|
Question
Find the total surface area of a cone with a perpendicular height of $4$ in and a diameter of $6$ in to one decimal place.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$"), which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm^2", which require conversion to US customary units. |
01K0RMVPQMN50B6WC4PQA028B7 |
Localize | Units (simple) | Question
Calculate the surface area of a sphere with a radius of $3.5$ cm to the nearest square centimetre.
Answer:
|
Question
Calculate the surface area of a sphere with a radius of $3.5$ in to the nearest square inch.
Answer:
|
Classifier: Contains metric units ("cm") and AU-specific spelling ("centimetre"). Units conversion is the primary classification. Verifier: The text contains the metric unit "cm" and the AU spelling "centimetre". Units conversion takes precedence. |
01K0RMVPQN9VZSHC01VX6MRY4V |
Localize | Units (simple) | Question
Find the surface area of the curved part of a hemisphere with a diameter of $12$ cm.
Answer:
|
Question
Find the surface area of the curved part of a hemisphere with a diameter of $12$ in.
Answer:
|
Classifier: Contains the metric unit "cm". Verifier: The text contains the metric unit "cm" and "cm^2". |
01K0RMVPQP1NEEZK8PKV8ZKPW7 |
Localize | Units (simple) | Question
The surface area of a sphere is approximately $616$ cm$^2$.
Find the radius of the sphere to the nearest centimetre.
Answer:
|
Question
The surface area of a sphere is approximately $616$ in$^2$.
Find the radius of the sphere to the nearest inch.
Answer:
|
Classifier: The text contains metric units ("cm") and the AU spelling of a metric unit ("centimetre"), which requires conversion to US customary units and US spelling ("centimeter"). Verifier: The text contains metric units ("cm", "cm^2") and the AU spelling "centimetre", both of which require localization to US customary units and US spelling ("centimeter"). |
01K0RMVPR12F2894S9MCA23SKW |
Localize | Units (simple) | Question
The total surface area of a cone is $90\pi$ cm$^2$.
If its radius is $5$ cm, what is its slant height?
Answer:
|
Question
The total surface area of a cone is $90\pi$ in$^2$.
If its radius is $5$ in, what is its slant height?
Answer:
|
Classifier: The text contains metric units ("cm$^2$" and "cm"), which require conversion to US customary units. Verifier: The text contains metric units "cm^2" and "cm", which require conversion to US customary units. |
01K0RMVPQTCMTPFNP2Z9N97058 |
Localize | Units (simple) | Question
The total surface area of a hemisphere is $75\pi$ m$^2$.
What is the radius of the hemisphere?
Answer:
|
Question
The total surface area of a hemisphere is $75\pi$ ft$^2$.
What is the radius of the hemisphere?
Answer:
|
Classifier: The text contains metric units ("m$^2$" and "m"), which require conversion to US customary units. Verifier: The text contains metric units "m^2" and "m", which require conversion to US customary units. |
01K0RMVPRAPRXRPS145GN2PQ4Z |
Localize | Units (simple) | Question
The area of the circular base of a cone is $20$ m$^2$ and its height is $9$ m.
Find the volume of the cone to the nearest cubic metre.
Answer:
|
Question
The area of the circular base of a cone is $20$ ft$^2$ and its height is $9$ ft.
Find the volume of the cone to the nearest cubic foot.
Answer:
|
Classifier: The text contains metric units ("m", "m$^2$") and the AU spelling "metre". Verifier: The text contains metric units ("m", "m$^2$") and the AU spelling "metre". |
01K0RMVPR8YJEWXTSVH2QFPATS |
Localize | Units (simple) | Question
A cone has a total surface area of $36\pi$ m$^2$.
The sum of its radius and slant height is $12$ m.
Find the radius of the cone.
Answer:
|
Question
A cone has a total surface area of $36\pi$ ft$^2$.
The sum of its radius and slant height is $12$ ft.
Find the radius of the cone.
Answer:
|
Classifier: The text contains the metric unit "m", which requires conversion to US customary units. Verifier: The text contains metric units "m^2" and "m", which require conversion to US customary units. |
01K0RMVPRFB8V1PFCB2BCKDD0H |
Localize | Units (simple) | Question
The circumference of the base of a cone is $10\pi$ cm and its height is $9$ cm.
Find the volume of the cone in terms of $\pi$.
Answer:
|
Question
The circumference of the base of a cone is $10\pi$ in and its height is $9$ in.
Find the volume of the cone in terms of $\pi$.
Answer:
|
Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm" and "cm$^3$". |
01K0RMVPRB7XRXSZJ3ZWH0B1S1 |
Localize | Units (simple) | Question
Find the volume, in exact form, of a cone with a radius of $2$ cm and a height of $3$ cm.
Answer:
|
Question
Find the volume, in exact form, of a cone with a radius of $2$ in and a height of $3$ in.
Answer:
|
Classifier: The text contains the metric unit "cm". Any metric unit triggers this classification. Verifier: The text contains the metric unit "cm". Any metric unit triggers this classification. |
01K0RMVPR4SKX4R1C91RVX8S9J |
Localize | Units (simple) | Question
An open-topped cone has a radius of $1.5$ m and a slant height of $4$ m.
What is the area of the material used to make the cone, in terms of $\pi$?
Answer:
|
Question
An open-topped cone has a radius of $1.5$ ft and a slant height of $4$ ft.
What is the area of the material used to make the cone, in terms of $\pi$?
Answer:
|
Classifier: The text contains metric units ("m" and "m$^2$"), which require conversion to US customary units. Verifier: The text contains metric units "m" and "m^2", which require conversion to US customary units. |
01K0RMVPRB7XRXSZJ4007T8427 |
Localize | Units (simple) | Question
A cone has a height of $5$ mm and a radius of $3$ mm.
Calculate its volume to one decimal place.
Answer:
|
Question
A cone has a height of $5$ in and a radius of $3$ in.
Calculate its volume to one decimal place.
Answer:
|
Classifier: The text contains the metric unit "mm". Verifier: The text contains the metric unit "mm" in both the content and the suffix. |
01K0RMVPQX6G4T56JB8898KBGF |
Localize | Units (simple) | Question
Calculate the total surface area of a cone with a radius of $10$ m and a slant height of $15$ m.
Answer:
|
Question
Calculate the total surface area of a cone with a radius of $10$ ft and a slant height of $15$ ft.
Answer:
|
Classifier: The text contains metric units ("m" and "m$^2$"), which require conversion to US customary units. Verifier: The text contains metric units "m" and "m^2", which require conversion to US customary units. |
01K0RMVPR6KJZ3JGTQXCMR1B08 |
Localize | Units (simple) | Question
In a cone, the perpendicular height is equal to the radius.
If the total surface area is $16\pi(1+\sqrt{2})$ cm$^2$, find the radius.
Answer:
|
Question
In a cone, the perpendicular height is equal to the radius.
If the total surface area is $16\pi(1+\sqrt{2})$ in$^2$, find the radius.
Answer:
|
Classifier: The text contains metric units ("cm$^2$" and "cm"), which require conversion to US customary units. Verifier: The text contains metric units "cm^2" and "cm", which require conversion to US customary units. |
01K0RMVPRGA2307YQE7YE88AR6 |
Localize | Units (simple) | Question
The height of a cone is equal to its radius.
If the volume of the cone is $9\pi$ cm$^3$, find its height.
Answer:
|
Question
The height of a cone is equal to its radius.
If the volume of the cone is $9\pi$ in$^3$, find its height.
Answer:
|
Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm" and "cm$^3$". |
01K0RMVPQQ2P59EJKS0EQS07K2 |
Localize | Units (simple) | Question
The volume of a sphere is $\frac{4}{3}\pi$ m$^3$.
What is its total surface area?
Answer:
|
Question
The volume of a sphere is $\frac{4}{3}\pi$ ft$^3$.
What is its total surface area?
Answer:
|
Classifier: The text contains metric units ("m$^3$" and "m$^2$"), which require conversion to US customary units. Verifier: The text contains metric units "m^3" and "m^2", which require conversion to US customary units. |
01K0RMVPR9QMJ3CZQNN6NE43QS |
Localize | Units (simple) | Question
Calculate the volume of a cone with a radius of $5$ m and a height of $6$ m to the nearest cubic metre.
Answer:
|
Question
Calculate the volume of a cone with a radius of $5$ ft and a height of $6$ ft to the nearest cubic foot.
Answer:
|
Classifier: The text contains the metric unit "m" (metres) and the AU-specific spelling "metre". According to the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains the metric unit "m" (metres) and the AU-specific spelling "metre". According to the decision rules, any metric unit requires at least RED.units_simple_conversion. |
01K0RMVPRDEAWHTPJ51ZMWF4NN |
Localize | Units (simple) | Question
The volume of a cone is $75\pi$ cm$^3$.
If its radius is $5$ cm, what is its perpendicular height?
Answer:
|
Question
The volume of a cone is $75\pi$ in$^3$.
If its radius is $5$ in, what is its perpendicular height?
Answer:
|
Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm" and "cm$^3$". |
01K0RMVPRFB8V1PFCB2DY4DRXJ |
Localize | Units (simple) | Question
A cone has a diameter of $16$ m and a slant height of $17$ m.
Find its volume in terms of $\pi$.
Answer:
|
Question
A cone has a diameter of $16$ ft and a slant height of $17$ ft.
Find its volume in terms of $\pi$.
Answer:
|
Classifier: The text contains the metric unit "m". Verifier: The text contains the metric unit "m" and "m$^3$". |
01K0RMVPREWXHJY6H3D39NV728 |
Localize | Units (simple) | Question
A cone has a height of $8.2$ m and a radius of $4.5$ m.
Calculate its volume, correct to two decimal places.
Answer:
|
Question
A cone has a height of $8.2$ ft and a radius of $4.5$ ft.
Calculate its volume, correct to two decimal places.
Answer:
|
Classifier: The text contains the metric unit "m". Verifier: The text contains the metric unit "m" and "m$^3$". |
01K0RMVPRK15PNF7HSBVKF6PF4 |
Localize | Units (simple) | Question
A cube with side length $3$ cm is placed centrally on top of a larger cube with side length $5$ cm.
Find the total exposed surface area.
Answer:
|
Question
A cube with side length $3$ in is placed centrally on top of a larger cube with side length $5$ in.
Find the total exposed surface area.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^2$" which require conversion to US customary units. |
01K0RMVPRNRF4GKQ263NZF47VY |
Localize | Units (simple) | Question
A solid is made by joining two cubes of side length $10$ cm along one full face.
What is the total surface area of the resulting solid?
Answer:
|
Question
A solid is made by joining two cubes of side length $10$ in along one full face.
What is the total surface area of the resulting solid?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^2$" which require conversion to US customary units. |
01K0RMVPS0W98A89QNH7WTDY24 |
Localize | Units (simple) | Question
A sphere has a diameter of $100$ cm.
What is its radius?
Answer:
|
Question
A sphere has a diameter of $100$ in.
What is its radius?
Answer:
|
Classifier: The text contains metric units ("cm") which require conversion to US customary units. Verifier: The text contains the metric unit "cm" which requires conversion to US customary units. |
01K0RMVPRY7MFC2FHQXG4TX8SS |
Localize | Units (simple) | Question
A sphere has a radius of $3$ cm.
Find its volume, leaving your answer in terms of $\pi$.
Answer:
|
Question
A sphere has a radius of $3$ in.
Find its volume, leaving your answer in terms of $\pi$.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^3$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^3$" which require conversion to US customary units. |
01K0RMVPRJFRV6HPZBQ7NZTHTK |
Localize | Units (simple) | Question
Two similar cones, A and B, have radii of $4$ cm and $6$ cm.
If the volume of cone A is $48\pi$ cm$^3$, what is the volume of cone B in exact form?
Answer:
|
Question
Two similar cones, A and B, have radii of $4$ in and $6$ in.
If the volume of cone A is $48\pi$ in$^3$, what is the volume of cone B in exact form?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^3$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^3$" which require conversion to US customary units. The math involves a simple ratio of similar solids, making it a simple conversion. |
01K0RMVPS0W98A89QNH70MW0Q9 |
Localize | Units (simple) | Question
Find the volume of a sphere with a radius of $6$ mm, leaving your answer in terms of $\pi$.
Answer:
|
Question
Find the volume of a sphere with a radius of $6$ in, leaving your answer in terms of $\pi$.
Answer:
|
Classifier: The text contains metric units ("mm" and "mm$^3$") which require conversion to US customary units. Verifier: The text contains metric units "mm" and "mm$^3$" which require conversion to US customary units. |
01K0RMVPS2AAMTEE48X1NMS84K |
Localize | Units (simple) | Question
Find the volume, in terms of $\pi$, of a hemisphere with a radius of $6$ m.
Answer:
|
Question
Find the volume, in terms of $\pi$, of a hemisphere with a radius of $6$ ft.
Answer:
|
Classifier: The text contains metric units ("m" and "m$^3$") which require conversion to US customary units. Verifier: The text contains metric units "m" and "m$^3$" which require conversion to US customary units. |
01K0RMVPS2AAMTEE48X3THC9AM |
Localize | Units (simple) | Question
A sphere has a diameter of $9$ cm.
Find its volume to the nearest cubic centimetre.
Answer:
|
Question
A sphere has a diameter of $9$ in.
Find its volume to the nearest cubic inch.
Answer:
|
Classifier: The text contains metric units ("cm", "cm$^3$") and the word "centimetre" which require conversion to US customary units and US spelling ("centimeter"). Verifier: The text contains metric units "cm" and "cm$^3$" as well as the AU/UK spelling "centimetre" (US: centimeter). Per rule 5, units conversion takes precedence over spelling. |
01K0RMVPS1G1KYKSH1WBNVTNEG |
Localize | Units (simple) | Question
A sphere has a diameter of $8$ cm.
Calculate its volume, leaving the answer in terms of $\pi$.
Answer:
|
Question
A sphere has a diameter of $8$ in.
Calculate its volume, leaving the answer in terms of $\pi$.
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^3$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^3$" which require conversion to US customary units. |
01K0RMVPS3BJSJ62F39B714AG0 |
Localize | Units (simple) | Question
A spherical water balloon has a radius of $5.5$ cm.
What is its volume, correct to two decimal places?
Answer:
|
Question
A spherical water balloon has a radius of $5.5$ in.
What is its volume, correct to two decimal places?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^3$") which require conversion to US customary units. Verifier: The text contains metric units "cm" and "cm$^3$" which require conversion to US customary units. |
01K0RMVPS3BJSJ62F39BR232X3 |
Localize | Units (simple) | Question
A hemisphere has a diameter of $18$ cm.
Find its volume in terms of $\pi$.
Answer:
|
Question
A hemisphere has a diameter of $18$ in.
Find its volume in terms of $\pi$.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^3$", which requires conversion for US localization. Verifier: The text contains metric units "cm" and "cm$^3$", which require conversion for US localization. This is a simple geometric calculation. |
01K0RMVPS7BK7VM8BV44S0X5ZB |
Localize | Units (simple) | Question
A hemisphere has a volume of $18\pi$ cm$^3$.
Find the radius of its flat base.
Answer:
|
Question
A hemisphere has a volume of $18\pi$ in$^3$.
Find the radius of its flat base.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^3$". Verifier: The text contains metric units "cm$^3$" and "cm". |
01K0RMVPS5KCHC19HS9YNDWPD0 |
Localize | Units (simple) | Question
A smaller solid sphere of radius $8$ cm is removed from inside a larger sphere of radius $10$ cm.
Find the exact volume of the remaining material.
Answer:
|
Question
A smaller solid sphere of radius $8$ in is removed from inside a larger sphere of radius $10$ in.
Find the exact volume of the remaining material.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^3$". Verifier: The text contains metric units "cm" and "cm$^3$". |
01K0RMVPS96GSCAYEWYNC6QH1G |
Localize | Units (simple) | Question
The base area of a pyramid is $30$ cm$^2$ and its height is $5$ cm.
What is its volume?
Answer:
|
Question
The base area of a pyramid is $30$ in$^2$ and its height is $5$ in.
What is its volume?
Answer:
|
Classifier: The text contains the metric unit "cm", "cm$^2$", and "cm$^3$". Verifier: The text contains metric units "cm$^2$", "cm", and "cm$^3$". |
01K0RMVPSXH2XX1EBYT5PMBQAS |
Localize | Units (simple) | Question
A cube has a total surface area of $24$ m$^2$.
What is the length of one of its sides?
Answer:
|
Question
A cube has a total surface area of $24$ ft$^2$.
What is the length of one of its sides?
Answer:
|
Classifier: The text contains the metric unit "m" and "m$^2$". Verifier: The text contains metric units "m$^2$" and "m". Heuristics failed to flag them, but they are present in the source text. |
01K0RMVPSE6J0VYX44K7AYNM47 |
Localize | Units (simple) | Question
A pyramid has a triangular base with a base length of $15$ cm and height $4$ cm.
The pyramid’s height perpendicular to the base is $9$ cm.
Find its volume.
Answer:
|
Question
A pyramid has a triangular base with a base length of $15$ in and height $4$ in.
The pyramid’s height perpendicular to the base is $9$ in.
Find its volume.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^3$". Verifier: The text contains metric units "cm" and "cm$^3$". |
s0BmCEvMV0dPB6Z8nWwC |
Localize | Units (simple) | Question
A man runs with velocity $v(t)=t-3t^2+4$ m/s at time $t$ seconds.
Find the man's average velocity from $t=2$ to $t=8$ seconds.
Answer:
|
Question
A man runs with velocity $v(t)=t-3t^2+4$ ft/s at time $t$ seconds.
Find the man's average velocity from $t=2$ to $t=8$ seconds.
Answer:
|
Classifier: Contains metric units "m/s" (metres per second) and "seconds". Per rule 1 and 9, any metric unit requires classification into a units category. Verifier: Contains metric units "m/s" (metres per second). While it contains a function, the conversion is a simple numeric scaling of the result/units rather than a complex re-derivation of coefficients. |
01K0RMVPSGEQW4QTG0FMFAWSMZ |
Localize | Units (simple) | Question
An office building is in the shape of a square pyramid.
Its base is $100$ m by $100$ m, and its height is $150$ m.
What is its volume?
Answer:
|
Question
An office building is in the shape of a square pyramid.
Its base is $100$ ft by $100$ ft, and its height is $150$ ft.
What is its volume?
Answer:
|
Classifier: The text contains the metric unit "m" and "m$^3$". Verifier: The text contains metric units "m" and "m$^3$". Heuristics failed to flag them, but they are present in the source text. |
s3kYuBFnWAXeUELXu0nB |
Localize | Units (simple) | Multiple Choice
Which of the following is a unit of length in the imperial system?
Options:
|
Multiple Choice
Which of the following is a unit of length in the US customary system?
Options:
|
Classifier: Contains multiple metric units ("Kilometres", "Millimetres", "Metres") and AU-specific spelling ("metres", "kilometres"). Units take precedence over spelling. Verifier: Contains multiple metric units ("Kilometres", "Millimetres", "Metres") and AU-specific spelling ("metres", "kilometres"). Under rule 5, units conversion takes precedence over spelling. |
sJ028ou4nsiIkjcMpJd2 |
Localize | Units (simple) | Multiple Choice
To boil between $10$ and $60$ litres of water, the time required is given by the equation:
$\text{time} = 2 + 2.5 \times \text{volume of water}$
Which of the following data represents an interpolation?
Options:
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Multiple Choice
To boil between $10$ and $60$ gallons of water, the time required is given by the equation:
$\text{time} = 2 + 2.5 \times \text{volume of water}$
Which of the following data represents an interpolation?
Options:
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Classifier: Contains the metric unit "litres" with AU-specific spelling. Per rule 1 and 5, any metric unit requires at least simple conversion. Verifier: The text contains the metric unit "litres" (AU spelling) and requires conversion of the volume range and the context of the problem to US customary units (gallons). Although an equation is present, it is a simple linear relationship and the conversion of the input range (10-60) is straightforward, fitting simple conversion. |
sPyQOUOKtb9TowBTfDFN |
Localize | Units (simple) | Question
Find the area of a rectangle with dimensions $19.78$ cm $\times$ $5$ cm.
Answer:
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Question
Find the area of a rectangle with dimensions $19.78$ in $\times$ $5$ in.
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require conversion to US customary units. Verifier: The question uses metric units "cm" and "cm^2" which require conversion to US customary units. |
sSHyeh9pwKhQAFADexDi |
Localize | Terminology | Multiple Choice
Kelly scored an $87\%$ in History with a class average of $85\%$ and a standard deviation of $8\%$.
In Maths, she scored a $75\%$ with a class average of $72\%$ and a standard deviation of $6\%$.
Using $z$-scores, in which class did she perform better in comparison to the other students?
Options:
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Multiple Choice
Kelly scored an $87\%$ in History with a class average of $85\%$ and a standard deviation of $8\%$.
In Math, she scored a $75\%$ with a class average of $72\%$ and a standard deviation of $6\%$.
Using $z$-scores, in which class did she perform better in comparison to the other students?
Options:
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Classifier: The text uses the term "Maths", which is the standard AU/UK term. The US equivalent is "Math". Verifier: The term "Maths" is the standard AU/UK term; the US equivalent is "Math". |
safYaR0wswsIe4syeJJS |
Localize | Cultural refs | Multiple Choice
Which of the following method is used to calculate the interest rate for a hire-purchase payment?
Options:
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Multiple Choice
Which of the following methods is used to calculate the interest rate for an installment loan payment?
Options:
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Classifier: "Hire-purchase" is a term primarily used in Commonwealth countries (UK/AU) for what is typically called "installment plan" or "rent-to-own" in the US. While it is a financial term, it functions as a cultural/regional terminology difference. Verifier: "Hire-purchase" is a specific Commonwealth term for installment plans/rent-to-own, representing a regional terminology difference. |
sRFh5JNNFoH3vs2Lxs4Q |
Localize | Units (simple) | Question
The latitude and longitude of Beijing, China is $40^\circ N$ and $116^\circ E$ respectively.
Find its distance from the North Pole.
Hint: Take Earth's radius to be $6371$ km
Answer:
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Question
The latitude and longitude of Beijing, China is $40^\circ N$ and $116^\circ E$ respectively.
Find its distance from the North Pole.
Hint: Take Earth's radius to be $6371$ miles
Answer:
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Classifier: The question uses "km" for Earth's radius and the final distance, which is a metric unit requiring conversion. Verifier: The question uses "km" for Earth's radius and the distance, which is a metric unit requiring conversion. |
sStEBos6NFBe53O18Jcr |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the equation of a semicircle with centre at $(3,2)$ and radius $4$ units?
Options:
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Multiple Choice
Which of the following is the equation of a semicircle with center at $(3,2)$ and radius $4$ units?
Options:
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Classifier: The text contains the AU spelling "centre", which needs to be converted to the US spelling "center". Verifier: The text uses the AU spelling "centre", which requires localization to the US spelling "center". |
sqn_01J6D0X0NCR8J97BGJH9Z7TPCP |
Localize | Spelling (AU-US) | Question
Rationalise the denominator of $\Large\frac{2\sqrt{7}}{5\sqrt{2}}$ and simplify the expression.
Answer:
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Question
Rationalize the denominator of $\Large\frac{2\sqrt{7}}{5\sqrt{2}}$ and simplify the expression.
Answer:
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Classifier: Contains the AU spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: The text contains "Rationalise", which is the AU/UK spelling. US English uses "Rationalize". This requires a spelling-only localization. |
snnrwRZdlpqH66gvLuDP |
Localize | Cultural refs | Question
In Alice Springs, for every day it rains, there are $19$ days without rain.
What percentage of the year experiences rain?
Answer:
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Question
In Phoenix, for every day it rains, there are $19$ days without rain.
What percentage of the year experiences rain?
Answer:
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Classifier: Contains a specific Australian geographic reference ("Alice Springs") which should be localized to a US context. No metric units are present, so cultural_reference is the correct leaf. Verifier: The question references "Alice Springs", which is a specific Australian geographic location, requiring localization to a US context. |
sqn_01J6C3XD2BF45DC5KVB9DGP3R2 |
Localize | Spelling (AU-US) | Question
Write $y^2 + 4y + 3y + 12$ in factorised form.
Answer:
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Question
Write $y^2 + 4y + 3y + 12$ in factored form.
Answer:
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Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The word "factorised" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("factorized"). |
sqn_01J6D0HD8GVTD8RW0AKH46QZZJ |
Localize | Spelling (AU-US) | Question
Rationalise the denominator of $\Large\frac{2\sqrt{5}}{\sqrt{5} + 2}$ and simplify the expression.
Options:
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Question
Rationalize the denominator of $\Large\frac{2\sqrt{5}}{\sqrt{5} + 2}$ and simplify the expression.
Options:
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Classifier: Contains the AU spelling "Rationalise", which needs to be converted to the US spelling "Rationalize". Verifier: The text contains "Rationalise", which is the AU/UK spelling. US English uses "Rationalize". This requires a spelling-only localization. |
sqn_01J6TTAWC5R25Q0FMRVRRMXV1C |
Localize | Units (simple) | Question
The base of a parallelogram is $4$ cm.
If the height is three times the base, what is its area?
Answer:
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Question
The base of a parallelogram is $4$ in.
If the height is three times the base, what is its area?
Answer:
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Classifier: The text contains the metric unit "cm", which requires conversion for US localization. Verifier: The question uses "cm" and "cm^2", which are metric units requiring conversion for US localization. |
sqn_01J6P2XT4C05S50NENBA955Q61 |
Localize | Units (simple) | Question
If a cyclist travels $250$ metres in $25$ seconds, what is their average speed in metres per second?
Answer:
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Question
If a cyclist travels $250$ feet in $25$ seconds, what is their average speed in feet per second?
Answer:
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Classifier: Contains metric units (metres) and AU spelling (metres). Units take precedence. Verifier: Contains metric units (metres) and AU spelling (metres). |
sqn_01J6P2RSBTWV4FZZ6D1YZG6QVP |
Localize | Units (simple) | Question
Farrel sprinted $1.8$ km in $3.2$ minutes.
What was his average speed in m/s?
Answer:
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Question
Farrel sprinted $1.8$ mi in $3.2$ minutes.
What was his average speed in ft/s?
Answer:
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Classifier: Contains metric units (km, m/s). Any metric unit requires localization to US customary units or a units-based classification. Verifier: Contains metric units (km, m/s). Any metric unit requires localization to US customary units. |
sqn_01J6TTZSHDWHZPKTPQJTSZYX8Q |
Localize | Units (simple) | Question
A wheel has a diameter that is $2.5$ times the radius of another wheel.
If the radius of the second wheel is $12$ cm, what is the diameter of the first wheel?
Answer:
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Question
A wheel has a diameter that is $2.5$ times the radius of another wheel.
If the radius of the second wheel is $12$ in, what is the diameter of the first wheel?
Answer:
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Classifier: The text contains the metric unit "cm", which requires conversion for US localization. Verifier: The question uses "cm", which is a metric unit requiring conversion for US localization. |
sqn_01J60RGBD25FD4HAS51GJ079N8 |
Localize | Units (simple) | Question
Find the area of a rectangular field with a length of $40.041$ m and width of $31.2$ m.
Answer:
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Question
Find the area of a rectangular field with a length of $40.041$ ft and width of $31.2$ ft.
Answer:
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Classifier: The text contains metric units ("m" for metres and "m^2" for square metres) which require conversion for US localization. Verifier: The question contains metric units ("m" and "m^2") which require conversion for US localization. The calculation is a simple area formula (length x width), making it a simple conversion. |
sqn_01J5GNA10HD78DF3JJ6HPX2H7K |
Localize | Units (simple) | Question
In a triangle, two adjacent sides are $8$ cm and $10$ cm long with an acute angle, $𝑥$, between them.
If the area is $32$ cm$^2$, calculate $x$ to the nearest degree.
Answer:
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Question
In a triangle, two adjacent sides are $8$ in and $10$ in long with an acute angle, $𝑥$, between them.
If the area is $32$ in$^2$, calculate $x$ to the nearest degree.
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. The conversion is simple as it involves substituting values into a standard area formula. |
speX7usYn8aDeDXY7obQ |
Localize | Units (simple) | Question
An object travels in one dimension according to the displacement function $s(t)=8t^2+5t-3$ m for $0\leq t\leq12$ s.
Find the displacement of the object at time $t=10$ s.
Answer:
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Question
An object travels in one dimension according to the displacement function $s(t)=8t^2+5t-3$ ft for $0\leq t\leq12$ s.
Find the displacement of the object at time $t=10$ s.
Answer:
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Classifier: The text contains metric units "m" (metres) and "s" (seconds) used in a physics/calculus context. According to the decision rules, any metric unit requires classification into a units category. Verifier: The text contains metric units "m" (metres) and "s" (seconds). While it contains a displacement function, the calculation required for the answer (t=10) is a simple substitution and evaluation, making simple_conversion appropriate. |
sqn_01J6P2KX98WH5Z7ZEG8E19D9XQ |
Localize | Units (simple) | Question
Kakashi covered $4$ kilometres in $7$ minutes while conducting a mission.
What was his average speed in metres per second?
Answer:
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Question
Kakashi covered $4$ miles in $7$ minutes while conducting a mission.
What was his average speed in feet per second?
Answer:
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Classifier: Contains metric units (kilometres, metres) and AU-specific spelling (metres, kilometres). Units conversion takes precedence over spelling. Verifier: Contains metric units (kilometres, metres) and AU-specific spelling (metres, kilometres). Simple conversion is appropriate as it is a basic speed calculation. |
sqn_01J6SBX1ZRPQPRQJ1B4BXGWWX2 |
Localize | Units (simple) | Question
The total surface area of a rectangular prism is equal to the total surface area of $2$ cubes, each with a side length of $2$ cm.
What is the total surface area of the rectangular prism?
Answer:
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Question
The total surface area of a rectangular prism is equal to the total surface area of $2$ cubes, each with a side length of $2$ in.
What is the total surface area of the rectangular prism?
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: The question contains metric units ("cm" and "cm^2") which require conversion for US localization. |
sqn_01J6SC45WNBRWAMGNY8TT5KBK3 |
Localize | Units (simple) | Question
A rectangular box has dimensions of $2$ cm, $3.3$ cm, and $10$ cm.
What is the total surface area of the box?
Answer:
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Question
A rectangular box has dimensions of $2$ in, $3.3$ in, and $10$ in.
What is the total surface area of the box?
Answer:
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Classifier: The question uses metric units ("cm" and "cm^2") for dimensions and surface area, requiring conversion. Verifier: The question uses metric units ("cm" and "cm^2") for dimensions and surface area, requiring conversion. |
sqn_01J6CS68BTB1KHS3RGFF6FB2SH |
Localize | Units (simple) | Question
A rectangular garden has a length of $4\sqrt{3}$ metres.
The area of the garden is $24\sqrt{3}$ square metres.
Find the width of the garden in simplest form.
Answer:
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Question
A rectangular garden has a length of $4\sqrt{3}$ feet.
The area of the garden is $24\sqrt{3}$ square feet.
Find the width of the garden in simplest form.
Answer:
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Classifier: The text contains metric units ("metres", "square metres") and AU-specific spelling ("metres"). Per rule 6, units conversion takes precedence over spelling. Verifier: Contains metric units ("metres", "square metres") and AU spelling ("metres"). Units conversion is the correct classification. |
sham5omFPeaPVeDXiyOd |
Localize | Spelling (AU-US) | Multiple Choice
Choose the correct formula for an $8\%$ mark-up on the labelled price of an item.
Options:
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Multiple Choice
Choose the correct formula for an $8\%$ markup on the labeled price of an item.
Options:
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Classifier: The text uses the AU/UK spelling "labelled", which should be "labeled" in US English. Verifier: The text uses the AU/UK spelling "labelled" multiple times, which requires localization to the US spelling "labeled". |
sqn_0034e022-71e5-4c36-8d7f-b802ebe3cef8 |
Localize | Units (simple) | Question
Explain why a triangle with base $10$ cm and height $5$ cm cannot have an area of $50$ cm$^2$.
Answer:
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Question
Explain why a triangle with base $10$ in and height $5$ in cannot have an area of $50$ in$^2$.
Answer:
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Classifier: The text explicitly uses metric units "cm" and "cm^2". Per the decision rules, any metric unit found anywhere in the text triggers a units conversion category. Verifier: The text contains metric units "cm" and "cm^2", which requires a RED classification per the decision rules. |
sfG07IkvoiFtPxj0jBOH |
Localize | Units (simple) | Question
A rectangular garden is under construction. $500$ m of fencing is needed to enclose it from three of its sides.
If $x$ is one of the side lengths, find the area $A$ of the garden.
Options:
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Question
A rectangular garden is under construction. $500$ ft of fencing is needed to enclose it from three of its sides.
If $x$ is one of the side lengths, find the area $A$ of the garden.
Options:
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Classifier: The text contains metric units ("m" for metres and "m$^2$" for square metres) which require conversion to US customary units (feet/yards). Verifier: The text contains metric units "m" (metres) and "m$^2$" (square metres) which require conversion to US customary units. The relationship is a simple area formula with one variable, fitting simple conversion. |
sgtlsX4hwPmjPLoSIplI |
Localize | Units (simple) | Multiple Choice
What is $1232.5$ m$^3$ in km$^3$ ?
Options:
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Multiple Choice
What is $1232.5$ ft$^3$ in mi$^3$ ?
Options:
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Classifier: The question specifically asks for a conversion between metric units (m^3 to km^3). This is a metric-pedagogy question that requires localization to US customary units or a different context. Verifier: The question is a metric-pedagogy item asking for conversion between metric units (m^3 to km^3), which requires localization to a US-relevant context. |
sqn_01J6P377WCM2ZGVH1FJ5JPTFMT |
Localize | Units (simple) | Question
If a drone flew $1.5$ kilometres in $5$ minutes, what was its average speed in metres per second?
Answer:
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Question
If a drone flew $1.5$ miles in $5$ minutes, what was its average speed in feet per second?
Answer:
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Classifier: Contains metric units (kilometres, metres) and AU spelling (kilometres, metres). Verifier: Contains metric units (kilometres, metres) and AU spelling (kilometres, metres). |
sqn_01J6YT3VDMC0ATA1M78E6XMDVA |
Localize | Terminology | Question
What is the sum of the $x$ and $y$ coordinates of the turning point of the parabola $y=3x^2-6x+2$ ?
Answer:
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Question
What is the sum of the $x$ and $y$ coordinates of the vertex of the parabola $y=3x^2-6x+2$ ?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US curriculum. This requires localization for the target US audience. |
sqn_01J6TV2GJ3KVDCWJCBHR2CVMK7 |
Localize | Units (simple) | Question
A circular pond has a diameter of $15$ metres.
What is the radius of the pond?
Answer:
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Question
A circular pond has a diameter of $15$ feet.
What is the radius of the pond?
Answer:
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Classifier: The text contains the metric unit "metres" (which also features AU spelling). Per decision rules, units conversion takes precedence over spelling. Verifier: The question uses "metres", which is both a metric unit and an AU spelling, requiring conversion for US localization. |
sqn_01J6TVFZXESNEB6F8ZBB49SDJR |
Localize | Units (simple) | Question
The radius of a circular track is increased by $5$ cm, and its diameter becomes $40$ cm.
What was the original radius of the track?
Answer:
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Question
The radius of a circular track is increased by $5$ in, and its diameter becomes $40$ in.
What was the original radius of the track?
Answer:
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Classifier: The text contains the metric unit "cm", which requires conversion for US localization. Verifier: The question uses "cm", which is a metric unit requiring conversion for US localization. |
sqn_01J6YTB1SSR7TYXBNQ6ZVWJSW9 |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $y=\frac{2}{3}x^2-8x+1$
Answer:
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Question
Find the $x$-coordinate of the vertex of the parabola $y=\frac{2}{3}x^2-8x+1$
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US curriculum. This requires localization for the target US audience. |
sqn_01J6YV6K7SP8RRBGXBVEXNJEWJ |
Localize | Terminology | Question
What is the $y$-coordinate of the turning point of the parabola $y=2x^2+6x+7$ ?
Answer:
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Question
What is the $y$-coordinate of the vertex of the parabola $y=2x^2+6x+7$ ?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US curriculum. This requires localization for the target US audience. |
sqn_01J6ZTN6BZC4JFK31WHW716Q7V |
Localize | Terminology | Question
A line has the equation $y = -\frac{2}{3}x + 5$.
What is the gradient of a line perpendicular to this one?
Answer:
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Question
A line has the equation $y = -\frac{2}{3}x + 5$.
What is the slope of a line perpendicular to this one?
Answer:
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Classifier: The term "gradient" is standard in AU/UK school mathematics for the slope of a line. In US curriculum, "slope" is the standard term. Verifier: The term "gradient" is the standard AU/UK term for what is called "slope" in the US curriculum. This is a terminology difference. |
sqn_01J6YVG5CFXWJ624V8N22XRKH9 |
Localize | Terminology | Question
What is the sum of the $x$ and $y$ coordinates of the turning point of the parabola $y=2\left(x^2+2x+\frac{5}{2}\right)$ ?
Answer:
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Question
What is the sum of the $x$ and $y$ coordinates of the vertex of the parabola $y=2\left(x^2+2x+\frac{5}{2}\right)$ ?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US curriculum. This requires localization for the target US audience. |
sqn_01J709EWE58YATE42EG0QAFCCS |
Localize | Units (simple) | Question
An architect is designing a triangular balcony. The base of the balcony is $15$ metres, and the height is $20$ metres.
What is the area of the balcony?
Answer:
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Question
An architect is designing a triangular balcony. The base of the balcony is $15$ feet, and the height is $20$ feet.
What is the area of the balcony?
Answer:
|
Classifier: Contains metric units ("metres") and AU spelling ("metres"). Per rule 6, units conversion takes precedence over spelling. Verifier: Contains metric units ("metres") and AU spelling ("metres"). Per rule 5, units conversion takes precedence over spelling. |
sqn_01J7DGPQHMPY4RNAXSKEWYTQXE |
Localize | Units (simple) | Question
Fill in the blank:
If a plant grows linearly by $2$ cm each week, after $10$ weeks, it will have grown an additional $[?]$ cm.
Answer:
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Question
Fill in the blank:
If a plant grows linearly by $2$ in each week, after $10$ weeks, it will have grown an additional $[?]$ in.
Answer:
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Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units (e.g., inches) per the decision rules. Verifier: The text contains the metric unit "cm", which requires conversion to US customary units. |
sqn_01J70A3EMZXSY301X7C6ZB6K5C |
Localize | Units (simple) | Question
A designer is creating a triangular garden. The base of the garden is $10.5$ metres, and the height is $15$ metres.
What is the area of the garden?
Answer:
|
Question
A designer is creating a triangular garden. The base of the garden is $10.5$ feet, and the height is $15$ feet.
What is the area of the garden?
Answer:
|
Classifier: Contains metric units ("metres") and AU spelling ("metres"). Units category takes precedence. Verifier: Contains metric units ("metres") and AU spelling ("metres"). Units category takes precedence. |
sqn_01J7J0H8BW2D4D3JXVGTR6JEQM |
Localize | Units (simple) | Question
How many millimetres are there in $3.2$ m?
Answer:
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Question
How many inches are there in $3.2$ ft?
Answer:
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Classifier: Contains metric units (millimetres, m). Even though the spelling "millimetres" is AU, the presence of metric units triggers the units category. Verifier: Contains metric units (millimetres, m). Even though the spelling is AU, metric units trigger the units category. |
sqn_01J800T1V8JTNTKHMVK73N7Y05 |
Localize | Cultural refs | Question
The summer reading challenge starts on December $1$st and ends on February $15$th of the following year.
How many days long is the reading challenge?
Answer:
|
Question
The winter reading challenge starts on December $1$st and ends on February $15$th of the following year.
How many days long is the reading challenge?
Answer:
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Classifier: The text refers to a "summer reading challenge" that spans December to February. In the Northern Hemisphere (US), summer occurs from June to August. This is a distinct Southern Hemisphere cultural/geographic reference that would be confusing for a US student. Verifier: The text describes a "summer reading challenge" occurring from December to February, which is specific to the Southern Hemisphere (AU) and contradicts the Northern Hemisphere (US) seasons. |
sqn_01J7J0D9SH7X8GZYMFZS2JZCG6 |
Localize | Units (simple) | Question
Convert $500$ cm to metres.
Answer:
|
Question
Convert $500$ in to feet.
Answer:
|
Classifier: Contains metric units (cm, m) and AU spelling ("metres"). Units conversion takes priority over spelling. Verifier: Contains metric units (cm, m) and AU spelling (metres). Units conversion is the primary requirement. |
sqn_01J70A89GR6SWHX464BQK9SSJE |
Localize | Units (simple) | Question
An architect is designing a triangular roof. The base of the roof is $19$ metres and the height is $22$ metres.
What is the area of the roof?
Answer:
|
Question
An architect is designing a triangular roof. The base of the roof is $19$ feet and the height is $22$ feet.
What is the area of the roof?
Answer:
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Classifier: The text contains the metric unit "metres" (both an AU spelling and a metric unit) and the unit symbol "m$^2$". According to the decision rules, any metric unit requires at least RED.units_simple_conversion, which takes precedence over spelling. Verifier: The text contains the metric unit "metres" and the symbol "m$^2$". Per rule 3, any metric unit requires at least RED.units_simple_conversion. The calculation is a straightforward area of a triangle (0.5 * 19 * 22), which fits the simple conversion category. |
sqn_01J84514GCNS5VTCQTESQCHWQS |
Localize | Units (simple) | Question
What is the total surface area of a $35$ cm long closed cylinder with a diameter of $13$ cm?
Answer:
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Question
What is the total surface area of a $35$ in long closed cylinder with a diameter of $13$ in?
Answer:
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Classifier: The question uses metric units ("cm" and "cm$^2$") which require localization to US customary units. Verifier: The question uses metric units (cm, cm^2) which require conversion to US customary units. |
sqn_01J8Q46XG9PDE2BRRYY5SDKPQN |
Localize | Units (simple) | Question
Sarah walked $2.4$ km in the morning and $1.6$ km in the afternoon.
How far did Sarah walk in total?
Answer:
|
Question
Sarah walked $2.4$ mi in the morning and $1.6$ mi in the afternoon.
How far did Sarah walk in total?
Answer:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles). Verifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units. |
sqn_01J8QHZ6470349NQ4X7W6TM840 |
Localize | Terminology | Question
Find the product of the $x$ and $y$-coordinates of the turning point of the parabola $y=-5\left(x+\frac{3}{5}\right)^2-\frac{3}{2}$ .
Answer:
|
Question
Find the product of the $x$ and $y$-coordinates of the vertex of the parabola $y=-5\left(x+\frac{3}{5}\right)^2-\frac{3}{2}$ .
Answer:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard Australian curriculum term for the vertex of a parabola, whereas "vertex" is the standard US term. |
sqn_01J8DHV4GMM1KW9Q6FYRYRV0PK |
Localize | Units (simple) | Question
Calculate $x + y + z$ by simplifying the ratio of the given quantities, ensuring all values are in grams:
$0.64$ kg to $150$ g to $1.02$ kg $= x : y : z$
Answer:
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Question
Calculate $x + y + z$ by simplifying the ratio of the given quantities, ensuring all values are in ounces:
$0.64$ lb to $150$ oz to $1.02$ lb $= x : y : z$
Answer:
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Classifier: The question contains metric units (kg and g) which require conversion or localization for a US audience. Verifier: The question contains metric units (kg and grams) which require conversion for a US audience. The conversion is a simple numeric change to the ratio components. |
sqn_01J82X09HTQM5R6A1EA296YSE8 |
Localize | Units (simple) | Question
A carpenter is building a table with a trapezium-shaped top. The parallel sides are $2$ m and $1$ m long and the distance between them is $0.8$ m.
What is the area of the table top?
Answer:
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Question
A carpenter is building a table with a trapezoid-shaped top. The parallel sides are $2$ ft and $1$ ft long and the distance between them is $0.8$ ft.
What is the area of the table top?
Answer:
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Classifier: The content contains metric units ("m" for metres) and the term "trapezium", which is the AU/UK term for the US "trapezoid". Per rule 6, units conversion takes precedence over terminology. Verifier: The question contains metric units (m, m^2) and the AU/UK term "trapezium" (US: trapezoid). Units conversion is the primary driver for RED classification. |
sqn_01J99PFHFV5ZT2HGEEBYDVJHPS |
Localize | Spelling (AU-US) | Question
Find the coordinates of the centre of the rectangular hyperbola $y = \frac{-3}{2x+1} + 2$.
What is the sum of these coordinates?
Answer:
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Question
Find the coordinates of the center of the rectangular hyperbola $y = \frac{-3}{2x+1} + 2$.
What is the sum of these coordinates?
Answer:
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Classifier: The word "centre" is used, which is the Australian/British spelling. It needs to be localized to "center" for a US audience. Verifier: The word "centre" is used, which is the Australian/British spelling. It must be localized to "center" for a US audience. |
sqn_01J9JJMKFE07THT24GC9ESN4SD |
Localize | Units (simple) | Question
A rectangular prism has dimensions $5$ cm, $12$ cm, and $13$ cm.
What is the length of the diagonal of the rectangular face with sides $5 $ cm and $12$ cm?
Answer:
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Question
A rectangular prism has dimensions $5$ in, $12$ in, and $13$ in.
What is the length of the diagonal of the rectangular face with sides $5 $ in and $12$ in?
Answer:
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Classifier: The text contains the metric unit "cm" multiple times in the content and as a suffix. According to the decision rules, any metric unit requires classification into a units category. Verifier: The text contains the metric unit "cm". According to the decision rules, any metric unit requires classification into a units category. This is a simple conversion as it involves basic dimensions of a prism. |
sqn_01J9JJVQCXBCWQSNM58ATKSF7F |
Localize | Units (simple) | Question
A cone has a slant height of $10$ cm and a base radius of $6$ cm.
If the cone is sliced vertically to form a triangle, and $\theta$ is the angle between the radius and the slant height, find the value of $\theta$.
Answer:
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Question
A cone has a slant height of $10$ in and a base radius of $6$ in.
If the cone is sliced vertically to form a triangle, and $\theta$ is the angle between the radius and the slant height, find the value of $\theta$.
Answer:
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Classifier: The text contains the metric unit "cm". Per the decision rules, the presence of any metric unit triggers a RED units classification. Verifier: The text contains the metric unit "cm". Per the decision rules, the presence of any metric unit triggers a RED units classification. |
sqn_01J9JQ19T1HS79DR28KEM1VTRJ |
Localize | Units (simple) | Question
In triangle $\triangle DEF$, $DE = 12$ cm, $EF = 14 $ cm, and $DF = 9 $ cm.
Find the value of $\angle DEF$.
Answer:
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Question
In triangle $\triangle DEF$, $DE = 12$ in, $EF = 14 $ in, and $DF = 9 $ in.
Find the value of $\angle DEF$.
Answer:
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Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm" for the side lengths of the triangle. |
sqn_01J9JQ4VV5H6KGPNKX24TBAEQ8 |
Localize | Units (simple) | Question
In $\triangle XYZ$, $XY = 8$ cm, $XZ = 5$ cm, and $\angle YXZ = 120^\circ$.
Find the length of the side $YZ$.
Answer:
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Question
In $\triangle XYZ$, $XY = 8$ in, $XZ = 5$ in, and $\angle YXZ = 120^\circ$.
Find the length of the side $YZ$.
Answer:
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Classifier: The text contains the metric unit "cm" in both the content and the suffix field. Verifier: The text contains the metric unit "cm" in both the content and the suffix field. |
sqn_01J947Y5P8C5HMF5J3Z3DZGCZG |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $5x^3+3x^2-20x-12$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$, where $a,b$ and $c$ are constants.
Options:
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Multiple Choice
Factor $5x^3+3x^2-20x-12$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$, where $a,b$ and $c$ are constants.
Options:
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Classifier: Contains the AU spelling "Factorise", which requires localization to "Factorize" for a US audience. Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
sqn_01J9MER9NSV5SYGEEWGNVPRSMM |
Localize | Units (simple) | Question
In a circle, $AB$ is the diameter with a length of $13$ cm, and $C$ is a point on the circumference.
If $BC = 5$ cm, find the length of $AC$.
Answer:
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Question
In a circle, $AB$ is the diameter with a length of $13$ in, and $C$ is a point on the circumference.
If $BC = 5$ in, find the length of $AC$.
Answer:
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Classifier: The text contains the metric unit "cm" in the content and the suffix, requiring localization. Verifier: Contains metric unit "cm" in both the question text and the suffix. |
sqn_01J947MTRRRTEFXQ78STZ6XACE |
Localize | Spelling (AU-US) | Question
Factorise $2x^3-5x^2-x+6$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$, where $a,b$ and $c$ are constants.
Options:
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Question
Factor $2x^3-5x^2-x+6$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$, where $a,b$ and $c$ are constants.
Options:
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Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
sqn_01JC4KF264PJ5MD5H2M9Y3KJG6 |
Localize | Spelling (AU-US) | Question
How do you know the $2$ in 'two hundred and fifty-three' goes in the hundreds place?
Answer:
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Question
How do you know the $2$ in 'two hundred fifty-three' goes in the hundreds place?
Answer:
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Classifier: The text uses "and" in the verbalization of the whole number ("two hundred and fifty-three"), which is an AU convention requiring localization. Verifier: The text uses "and" in the verbalization of a whole number ("two hundred and fifty-three"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4JWM5SGGFNSK4C75T4M35S |
Localize | Spelling (AU-US) | Question
Why isn’t $120\ 000$ read as “twelve thousand”?
Answer:
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Question
Why isn’t $120\ 000$ read as “twelve thousand”?
Answer:
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Classifier: The text uses the "and" conjunction in the verbalization of a whole number ("one hundred and twenty thousand"), which is standard in AU but avoided in US math instruction for whole numbers. Verifier: The text uses "and" in the verbalization of a whole number ("one hundred and twenty thousand"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4JVFE8Z698QAFMC3NRXC7Z |
Localize | Spelling (AU-US) | Question
Why is $406\ 000$ read as “four hundred and six thousand”?
Answer:
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Question
Why is $406\ 000$ read as “four hundred six thousand”?
Answer:
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Classifier: The text uses the British/Australian convention of including "and" when reading whole numbers (e.g., "four hundred and six thousand"). In US English pedagogy, "and" is strictly reserved for the decimal point, and its inclusion in whole numbers is considered a stylistic/spelling-level difference that requires removal for US localization. Verifier: The text uses "and" in the verbalization of a whole number ("four hundred and six thousand"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4KJNE8JT1WSS2YSP1PE016 |
Localize | Spelling (AU-US) | Question
How do the words in 'three hundred and fourteen' match the digits in $314$?
Answer:
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Question
How do the words in 'three hundred fourteen' match the digits in $314$?
Answer:
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Classifier: The text uses "and" in the verbalization of the whole number ("three hundred and fourteen"), which is an AU convention requiring localization. Verifier: The text uses "and" in the verbalization of a whole number ("three hundred and fourteen"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4K7ZG72J3X22BACGWQWH99 |
Localize | Spelling (AU-US) | Question
Why does 'seven hundred and three' mean $703$ and not $730$?
Answer:
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Question
Why does 'seven hundred three' mean $703$ and not $730$?
Answer:
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Classifier: The text uses "and" in the verbalization of whole numbers ("seven hundred and three", "seven hundred and thirty"), which is an AU convention that needs to be removed for US localization. Verifier: The text uses "and" in the verbalization of whole numbers ("seven hundred and three"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JBZK6967FHV4TP87QEDNFE7K |
Localize | Units (simple) | Question
Convert $38.5$ L to m$^3$.
Answer:
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Question
Convert $38.5$ gal to ft$^3$.
Answer:
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Classifier: The question explicitly asks for a conversion between metric units (L to m^3). This is a metric-pedagogy question that requires localization to US customary units or a different pedagogical context. Verifier: The question involves converting between metric units (L to m^3), which requires localization for a US audience. |
sqn_01JBDBF88JDCJCACR2PS2HZH09 |
Localize | Units (simple) | Question
In a triangle, two adjacent sides are $15$ cm and $18$ cm long with an obtuse angle, $x$, between them.
If the area is $115$ cm$^2$, calculate $x$ to the nearest degree.
Answer:
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Question
In a triangle, two adjacent sides are $15$ in and $18$ in long with an obtuse angle, $x$, between them.
If the area is $115$ in$^2$, calculate $x$ to the nearest degree.
Answer:
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Classifier: The text contains metric units ("cm" and "cm$^2$") which require conversion to US customary units or a change in pedagogical context for US localization. Verifier: The question contains metric units "cm" and "cm$^2$" which require conversion for US localization. The conversion is simple as it involves a straightforward area calculation with a few numeric values. |
sqn_01JC4K2RVDDSET0433X4DSPMYR |
Localize | Spelling (AU-US) | Question
How does place value help you read $254\ 000$ as “two hundred and fifty-four thousand”?
Answer:
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Question
How does place value help you read $254\ 000$ as “two hundred fifty-four thousand”?
Answer:
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Classifier: The text includes "and" in the verbalization of the whole number ("two hundred and fifty-four thousand"), which requires localization for US English. Verifier: The text uses "and" in the verbalization of a whole number ("two hundred and fifty-four thousand"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JBG9NBN1D21GETSGCMGXYPYA |
Localize | Units (simple) | Question
A $250$-litre tank loses $47.85$ litres on Day $1$ and $65.5$ litres on Day $2$.
How much water is left?
Answer:
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Question
A $250$-gallon tank loses $47.85$ gallons on Day $1$ and $65.5$ gallons on Day $2$.
How much water is left?
Answer:
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Classifier: The text contains the metric unit "litre" and "litres", which requires conversion to US customary units (gallons) or at minimum a spelling change to "liter", but per rule 6 and 9, any metric unit triggers a units category. Verifier: The text contains the metric unit "litre" and "litres". Per rule 3, any metric unit triggers at least RED.units_simple_conversion. The conversion is a straightforward numeric change for a volume tank problem. |
sqn_01JC007K9YF77Q3T1X1PR2RP6Z |
Localize | Units (simple) | Question
The perimeter of a regular octagon is $904$ cm.
What is the length of its side?
Answer:
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Question
The perimeter of a regular octagon is $904$ in.
What is the length of its side?
Answer:
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Classifier: The text contains the metric unit 'cm'. Verifier: The text contains the metric unit "cm". |
sqn_01JBS87W07X44VAC6Y0HZ1K1VW |
Localize | Units (simple) | Question
A jet travels at an average speed of $850$ km/h for $2$ hours and $30$ minutes, then reduces its speed to $600$ km/h for the next 1 hour and $45$ minutes.
What is the total distance traveled by the jet?
Answer:
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Question
A jet travels at an average speed of $850$ mph for $2$ hours and $30$ minutes, then reduces its speed to $600$ mph for the next 1 hour and $45$ minutes.
What is the total distance traveled by the jet?
Answer:
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Classifier: The question contains metric units ("km/h" and "km") which require conversion to US customary units (mph and miles). Verifier: Contains metric units "km/h" and "km" which require conversion to US customary units. |
sqn_01JBZM5A6AJFX63QHRNEYCBKPY |
Localize | Units (simple) | Question
Fill in the blank:
$3.2$ litres $+\ 0.175$ litres $+\ 250$ cm$^3\ = [?]$ cm$^3$
Answer:
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Question
Fill in the blank:
$3.2$ gallons $+\ 0.175$ gallons $+\ 250$ in$^3\ = [?]$ in$^3$
Answer:
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Classifier: The text contains metric units (litres, cm^3) and AU-specific spelling (litres). Per the decision rules, any metric unit requires at least RED.units_simple_conversion, which takes precedence over spelling. Verifier: The text contains metric units "litres" and "cm^3". "Litres" is also an AU-specific spelling. Per rule 5, units conversion takes precedence over spelling. |
sqn_01JBZZQZTGR3X6507AJVBY3V1Z |
Localize | Units (simple) | Question
The perimeter of a regular hexagon is $564$ cm.
What is the length of one of its sides?
Answer:
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Question
The perimeter of a regular hexagon is $564$ in.
What is the length of one of its sides?
Answer:
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Classifier: The text contains the metric unit 'cm'. Verifier: The text contains the metric unit "cm". |
sqn_01JC4J2975ZXRH96MG7VAF6ZRF |
Localize | Cultural refs | Question
You buy a snack for $\$1.75$ and pay with a $\$2$ coin.
How can you check that the change received, $\$0.25$, is correct?
Answer:
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Question
You buy a snack for $\$1.75$ and pay with a $\$2$ bill.
How can you check that the change received, $\$0.25$, is correct?
Answer:
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Classifier: The text refers to a "$2 coin". While the US has a $2 bill, it does not have a $2 coin in common circulation (unlike the Australian $2 coin). This is a distinct cultural/monetary reference that would be confusing or unnatural in a US context. Verifier: The mention of a "$2 coin" is a specific cultural/monetary reference to the Australian currency system. In the US, while a $2 bill exists, there is no $2 coin in circulation, making this phrasing unnatural for a US audience. |
sqn_01JBZV17RD8HRN7CE2BHDST8XB |
Localize | Units (simple) | Question
A rectangle has an area of $450$ cm$^2$ and a perimeter of $86$ cm. The length is $7$ cm longer than the width.
What is the length of the rectangle?
Answer:
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Question
A rectangle has an area of $450$ in$^2$ and a perimeter of $86$ in. The length is $7$ in longer than the width.
What is the length of the rectangle?
Answer:
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Classifier: The text contains metric units (cm^2, cm). Verifier: The text contains metric units "cm^2" and "cm". |
sqn_01JBZMKZ6NAWMSE25467PZSRS4 |
Localize | Units (simple) | Question
The volume of a rectangular tank is $2100$ cm$^3$. The base of the tank has dimensions $15$ cm and $8$ cm.
What is the height of the tank?
Answer:
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Question
The volume of a rectangular tank is $2100$ in$^3$. The base of the tank has dimensions $15$ in and $8$ in.
What is the height of the tank?
Answer:
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Classifier: The text contains metric units (cm^3, cm). Any metric unit found anywhere in the text triggers this category. Verifier: The text contains metric units "cm^3" and "cm". This is a simple volume calculation requiring unit conversion for US localization. |
sqn_01JC29G1E5DHAB2SV8F1GJ7MFK |
Localize | Units (simple) | Question
A rectangular field has an area of $540$ cm$^2$. The ratio of the length to the width is $5:3$.
What is the length?
Answer:
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Question
A rectangular field has an area of $540$ in$^2$. The ratio of the length to the width is $5:3$.
What is the length?
Answer:
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Classifier: The question contains metric units ("cm" and "cm^2") which require localization to US customary units or a decision on metric pedagogy. Per rule 1, any metric unit disqualifies GREEN. Verifier: The question contains metric units ("cm" and "cm^2") which require localization to US customary units. This is a simple conversion as it involves a single geometric shape and a basic ratio. |
sqn_01JC2D38QY3D1TGMMPZV0SWJ73 |
Localize | Units (simple) | Question
In triangle $ABC$, $\overline{BC} = 153$ cm, $\overline{AB} = 128$ cm, and $\angle{ABC} = 47.3^\circ$.
Find $\overline{AC}$.
Answer:
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Question
In triangle $ABC$, $\overline{BC} = 153$ in, $\overline{AB} = 128$ in, and $\angle{ABC} = 47.3^\circ$.
Find $\overline{AC}$.
Answer:
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Classifier: The text contains the metric unit "cm", which requires localization. Verifier: The text contains the metric unit "cm", which requires localization. This is a simple application of the Law of Cosines where units are just labels. |
sqn_01JBZ75BBEFGYBRHF58AK1C7ZD |
Localize | Units (simple) | Question
In triangle $ABC$, $\overline{BC} = 42$ cm, $\overline{AB} = 67$ cm, and $\angle{ACB} = 47.5^\circ$.
What is the perimeter of the triangle?
Answer:
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Question
In triangle $ABC$, $\overline{BC} = 42$ in, $\overline{AB} = 67$ in, and $\angle{ACB} = 47.5^\circ$.
What is the perimeter of the triangle?
Answer:
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Classifier: The text contains the metric unit "cm" multiple times, which requires conversion to US customary units. Verifier: The question contains the metric unit "cm" (centimetres) in both the content and the suffix, which requires conversion to US customary units. |
sqn_01JBZP3H79C5K8ZDD52ZAJND93 |
Localize | Units (simple) | Question
A storage unit has dimensions $24.5$ m $\times 18.3$ m $\times 15.2$ m. Inside the unit are two boxes with dimensions $8.4$ m $\times 6.2$ m $\times 4.5$ m and $5.3$ m $\times 7.8$ m $\times 3.4$ m.
Calculate the volume of the space left in the storage unit after placing the two boxes.
Answer:
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Question
A storage unit has dimensions $24.5$ ft $\times 18.3$ ft $\times 15.2$ ft. Inside the unit are two boxes with dimensions $8.4$ ft $\times 6.2$ ft $\times 4.5$ ft and $5.3$ ft $\times 7.8$ ft $\times 3.4$ ft.
Calculate the volume of the space left in the storage unit after placing the two boxes.
Answer:
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Classifier: The text contains metric units (m, m^3). Even though the math is generic, the presence of metric units requires localization to US customary units. Verifier: The text contains metric units "m" and "m^3". Although there are several values, they are used in a straightforward volume subtraction (V_total - V1 - V2), which fits simple conversion better than complex. |
sqn_01JC4KMHP2E1JZYXNPAM3TATN0 |
Localize | Spelling (AU-US) | Question
How do you know to write 'nine hundred and twenty' as $920$?
Answer:
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Question
How do you know to write 'nine hundred twenty' as $920$?
Answer:
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Classifier: The text uses "and" in the verbalization of the whole number ("nine hundred and twenty"), which is an AU convention requiring localization. Verifier: The text uses "and" in the verbalization of a whole number ("nine hundred and twenty"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4KZK24ZG6Y8846QJKHM728 |
Localize | Spelling (AU-US) | Question
Why is the number 'six hundred and five thousand' written as $605\ 000$?
Answer:
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Question
Why is the number 'six hundred five thousand' written as $605,000$?
Answer:
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Classifier: The text uses "and" in the verbalization of the whole number ("six hundred and five thousand"), which is an AU convention requiring localization. Verifier: The text uses "and" in the verbalization of a whole number ("six hundred and five thousand"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4M5X24QXW9KMTVVTKQ2SNT |
Localize | Spelling (AU-US) | Question
How can you check that 'four hundred thousand and six hundred' means $400\ 600$?
Answer:
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Question
How can you check that 'four hundred thousand six hundred' means $400\ 600$?
Answer:
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Classifier: The text uses "and" in the verbalization of the whole number ("four hundred thousand and six hundred"), which is an AU convention requiring localization. Verifier: The text uses "and" in the verbalization of a whole number ("four hundred thousand and six hundred"). In US mathematics pedagogy, "and" is reserved for the decimal point. This is a standard localization requirement for US English. |
sqn_01JC4QF53QD447MQMHRC3N3APD |
Localize | Units (simple) | Question
The area of a kite is $2528.75$ cm$^2$. The length of the shorter diagonal is $70\%$ of the length of the longer diagonal.
What is the length of the shorter diagonal?
Answer:
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Question
The area of a kite is $2528.75$ in$^2$. The length of the shorter diagonal is $70\%$ of the length of the longer diagonal.
What is the length of the shorter diagonal?
Answer:
|
Classifier: The text contains the metric unit 'cm' (centimetres) in both the content and the suffix, which requires conversion to US customary units (e.g., inches). Verifier: The question contains the metric unit "cm" (centimetres) in both the content and the suffix, which requires conversion to US customary units. |
sqn_01JCC3RC0ZKWNN4HSCX2H6DCV8 |
Localize | Units (simple) | Question
Polygon $A$ is scaled by a factor of $7.5$ to create Polygon $B$.
If the area of Polygon $B$ is $1215.7$ cm$^2$, what is the area of Polygon $A$?
Answer:
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Question
Polygon $A$ is scaled by a factor of $7.5$ to create Polygon $B$.
If the area of Polygon $B$ is $1215.7$ in$^2$, what is the area of Polygon $A$?
Answer:
|
Classifier: The text contains metric units ("cm^2"). Any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "cm^2", which requires a RED units classification. |
sqn_01JCN2H2H0EREWJ3VJ3WXHJ54G |
Localize | Units (simple) | Question
A tank is filled with $ 6 \dfrac{17}{20}$ litres of water.
Express this amount as an improper fraction.
Answer:
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Question
A tank is filled with $ 6 \dfrac{17}{20}$ gallons of water.
Express this amount as an improper fraction.
Answer:
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Classifier: Contains the metric unit 'litres' which also uses AU spelling. Per rule 6, units conversion takes precedence over spelling. Verifier: Contains the metric unit 'litres' (AU spelling). Metric units require RED classification. |
sqn_01JDRNFG4K330CM3SZEBSG4X1Q |
Localize | Units (simple) | Question
In $\triangle ABC$, $\angle A = 40^\circ$, $BC = 13$ cm, and $AC = 19$ cm.
Determine how many distinct triangles can be formed with these measurements.
Answer:
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Question
In $\triangle ABC$, $\angle A = 40^\circ$, $BC = 13$ in, and $AC = 19$ in.
Determine how many distinct triangles can be formed with these measurements.
Answer:
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Classifier: Contains the metric unit "cm". Any metric unit requires localization to US customary units. Verifier: Contains the metric unit "cm" which requires conversion to US customary units. |
sqn_01JCJ3J14JGX2VTVD7PZZ5A4J0 |
Localize | Units (simple) | Question
A shipping container is loaded in two stages, each with a weight limit $W$. The first stage adds $55\%$ of $W$ and the second adds $90\%$ of $W$. The total weight is $2900$ kg.
What is $W$?
Answer:
|
Question
A shipping container is loaded in two stages, each with a weight limit $W$. The first stage adds $55\%$ of $W$ and the second adds $90\%$ of $W$. The total weight is $2900$ lbs.
What is $W$?
Answer:
|
Classifier: Contains the metric unit "kg" which requires conversion to US customary units. Verifier: Contains the metric unit "kg" which requires conversion to US customary units. |
sqn_01JCJ0DY2ZZHAPNE545Q8J76V1 |
Localize | Units (simple) | Question
A skydiver jumps from a helicopter at $300$ m and descends at $45.5$ m/s for $3$ seconds. After deploying the parachute, the descent slows to $12.8$ m/s.
What is the skydiver’s altitude above the ground after $8$ seconds?
Answer:
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Question
A skydiver jumps from a helicopter at $300$ ft and descends at $45.5$ ft/s for $3$ seconds. After deploying the parachute, the descent slows to $12.8$ ft/s.
What is the skydiver’s altitude above the ground after $8$ seconds?
Answer:
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Classifier: Contains multiple metric units (m, m/s) which require conversion to US customary units. Verifier: The question contains metric units (m, m/s) which require conversion to US customary units. The calculation is a simple linear descent model, fitting simple conversion. |
sqn_01JCN30T149TKJN01PTGD9D4Z2 |
Localize | Units (simple) | Question
A factory produces $1.25$ kilograms of waste every hour.
Given $1$ kg $= 10^3$ grams, how many grams of waste does it produce in $100$ hours?
Answer:
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Question
A factory produces $1.25$ pounds of waste every hour.
Given $1$ lb $= 16$ ounces, how many ounces of waste does it produce in $100$ hours?
Answer:
|
Classifier: Contains metric units 'kilograms', 'kg', and 'grams'. Even though the math involves powers of 10, the presence of metric units requires localization to US customary units or a specific metric-pedagogy classification; however, 'units_simple_conversion' is the standard for any metric unit presence. Verifier: Contains metric units 'kilograms', 'kg', and 'grams'. Presence of metric units requires RED classification. |
sqn_01JCC1JKANNQDD711H6RM9RHF0 |
Localize | Units (simple) | Question
A $50$ m cable stretches from the top of a tree to a point on the ground.
A point $20\%$ lower than the top of the tree is $36$ metres above the ground.
Determine the angle, in degrees, between the ground and the cable.
Answer:
|
Question
A $50$ ft cable stretches from the top of a tree to a point on the ground.
A point $20\%$ lower than the top of the tree is $36$ feet above the ground.
Determine the angle, in degrees, between the ground and the cable.
Answer:
|
Classifier: The text contains both metric units ("m", "metres") and AU-specific spelling ("metres"). Per the decision rules, the presence of any metric unit triggers a RED units category, which takes precedence over spelling. Verifier: The text contains metric units ("m", "metres") and AU spelling ("metres"). Per rule 3 and 5, metric units require a RED units classification. |
sqn_01JDFGBTKMRX0BP6RXCWG84RB4 |
Localize | Units (simple) | Question
The total length of a rectangular measuring tape is $120$ cm and its width is $5$ mm.
What is the perimeter of the measuring tape in cm?
Answer:
|
Question
The total length of a rectangular measuring tape is $120$ in and its width is $5$ in.
What is the perimeter of the measuring tape in in?
Answer:
|
Classifier: Contains metric units "cm" and "mm". Any metric unit requires localization to US customary units. Verifier: Contains metric units "cm" and "mm" which require conversion to US customary units. |
sqn_01JG00D864TWGQWQ3R4JRY33Z0 |
Localize | Terminology | Question
A coffee costs $\$2$.
If you pay with a $\$5$ note, what is your change?
Answer:
|
Question
A coffee costs $\$2$.
If you pay with a $\$5$ bill, what is your change?
Answer:
|
Classifier: The term "note" refers to paper currency; in a US context, this should be localized to "bill" (e.g., a $5 bill). Verifier: The term "note" for paper currency is AU/UK terminology; US school context requires "bill". |
sqn_01JGNFQGWEH73MVFW5ATXG2845 |
Localize | Spelling (AU-US) | Question
Why do we organise data in a stem-and-leaf plot instead of just writing all the numbers in a list?
Answer:
|
Question
Why do we organize data in a stem-and-leaf plot instead of just writing all the numbers in a list?
Answer:
|
Classifier: The word "organise" uses the AU/UK spelling (ending in -ise) and needs to be converted to the US spelling "organize". Verifier: The word "organise" is the AU/UK spelling. US English requires "organize". |
sqn_01JKCJD6Z98DS6S85N8HD24E4W |
Localize | Cultural refs | Question
A guest stays at a hotel. The total bill is $\$275$, including GST.
What was the price before GST?
Answer:
|
Question
A guest stays at a hotel. The total bill is $\$275$, including sales tax.
What was the price before sales tax?
Answer:
|
Classifier: Contains "GST", which is a specific Australian tax reference. US localization would require changing this to "sales tax" or a neutral equivalent. Verifier: Contains "GST", which is a specific Australian tax reference. |
sqn_01JKCHYYE2J1SQYEMVMXCTBG22 |
Localize | Cultural refs | Question
A store lists a laptop for $\$1650$, including GST.
What was the price before GST?
Answer:
|
Question
A store lists a laptop for $\$1650$, including sales tax.
What was the price before sales tax?
Answer:
|
Classifier: The term "GST" (Goods and Services Tax) is the specific consumption tax used in Australia. In a US context, this would typically be referred to as "sales tax", although the mathematical application (inclusive vs. exclusive) differs. Verifier: The term "GST" (Goods and Services Tax) is a specific Australian tax reference that requires localization to "sales tax" or similar for a US context. |
sqn_01JD95SSEBWNFDQF6CBWZHD9ET |
Localize | Units (simple) | Question
A water tank holds $86$ litres of water.
$5$ litres were used to water the garden.
How much water is left in the tank?
Answer:
|
Question
A water tank holds $86$ gallons of water.
$5$ gallons were used to water the garden.
How much water is left in the tank?
Answer:
|
Classifier: Contains the metric unit "litres" which requires both spelling correction ("liters") and unit conversion for a US audience. Per rule 6, units conversion takes precedence over spelling. Verifier: Contains the metric unit "litres" (AU spelling and metric system), which requires conversion to US customary units (gallons) or at least spelling correction to "liters" if units were kept, but per policy, metric units in word problems trigger conversion. |
sqn_01JG003RKVHFARB7DJE6Z98TDJ |
Localize | Terminology | Question
The toy costs $\$7.85$.
If you pay with a $\$10$ note, what is your change?
Answer:
|
Question
The toy costs $\$7.85$.
If you pay with a $\$10$ bill, what is your change?
Answer:
|
Classifier: The term "note" refers to paper currency, which is standard in AU/UK but is almost exclusively referred to as a "bill" in US English (e.g., a $10 bill). While "note" is understood, "bill" is the required localization for US school contexts. Verifier: The term "note" for paper currency is AU/UK terminology; US school context requires "bill". |
sqn_01JKCJSVAZV1XAJG9EDCQ51D2N |
Localize | Cultural refs | Question
A customer gets a hair treatment and pays $\$275$, including GST.
How much of this amount is GST?
Answer:
|
Question
A customer gets a hair treatment and pays $\$275$, including sales tax.
How much of this amount is sales tax?
Answer:
|
Classifier: Contains "GST", which is an Australian cultural/tax reference. Verifier: Contains "GST", which is a specific Australian tax reference. |
sqn_01JEZJM0G24CY4GV55FTTNYB28 |
Localize | Units (simple) | Question
A watermelon costs $\$3.25$ per kilogram. Its total weight is $4.8$ kg.
How much does it cost in total?
Answer:
|
Question
A watermelon costs $\$3.25$ per pound. Its total weight is $4.8$ lbs.
How much does it cost in total?
Answer:
|
Classifier: The text contains metric units ('kilogram' and 'kg') which require localization to US customary units (e.g., pounds/lb) for a US audience. Verifier: The text contains metric units "kilogram" and "kg" which require conversion for US localization. |
sqn_01JKSFWV3YJFK2JG2JPQKMAA0Z |
Localize | Units (simple) | Question
A triangle has side lengths $15$ m, $18$ m, and $22$ m.
Calculate its area.
Answer:
|
Question
A triangle has side lengths $15$ ft, $18$ ft, and $22$ ft.
Calculate its area.
Answer:
|
Classifier: The question contains metric units ("m" for metres and "m$^2$" for square metres) which require conversion to US customary units. Verifier: The question uses metric units ("m" and "m$^2$") which require conversion to US customary units. The conversion is a simple area calculation based on side lengths. |
sqn_01JMC5M8GMEMA3CQBH7QNQGCVX |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $ y = (2x - 4)(x + 3) $
Answer:
|
Question
Find the $x$-coordinate of the vertex of the parabola $ y = (2x - 4)(x + 3) $
Answer:
|
Classifier: Uses the term "turning point", which is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is referred to as the "vertex" in the US curriculum. |
sqn_01JMC5WTNX8NWZJMEYV65X4CWM |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $ y = 5(x - 3)(x + 7) $
Answer:
|
Question
Find the $x$-coordinate of the vertex of the parabola $ y = 5(x - 3)(x + 7) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JMC5QQQYXBRWPCZ03WV569J3 |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $ y = (x - 4)(x + 8) $
Answer:
|
Question
Find the $x$-coordinate of the vertex of the parabola $ y = (x - 4)(x + 8) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JKWRQ9ZNQZVRP2W34ZVNBB1V |
Localize | Terminology | Question
A company invests $\$15\ 000$ in a simple interest account with annual interest. After $6$ years, the total amount grows to $\$19\ 500$.
What is the annual simple interest rate?
Answer:
|
Question
A company invests $\$15\ 000$ in a simple interest account with annual interest. After $6$ years, the total amount grows to $\$19\ 500$.
What is the annual simple interest rate?
Answer:
|
Classifier: The suffix uses "p.a." (per annum), which is standard in AU/UK contexts but much less common in US K-12 math compared to "per year" or simply omitting it when "annual interest rate" is already in the stem. Additionally, the use of a space as a thousands separator ($15 000) is an AU/international convention; US convention uses a comma ($15,000). Verifier: The use of "p.a." (per annum) and the space as a thousands separator ($15 000) are specific to AU/International conventions and differ from US K-12 standards. |
sqn_01JKWPHKCDSJQGYCQTAB09A5FJ |
Localize | Units (simple) | Question
A gold bar has a mass of $1000$ g and a density of $19.3$ g/cm$^3$.
What is the volume of the gold bar?
Answer:
|
Question
A gold bar has a mass of $1000$ oz and a density of $19.3$ oz/in$^3$.
What is the volume of the gold bar?
Answer:
|
Classifier: The question contains multiple metric units (g, g/cm^3, cm^3) which require conversion for a US audience. Verifier: The question contains metric units (g, g/cm^3, cm^3) which require conversion for the US locale. |
sqn_01JMJWGRC8ZBHR7FXVA5PC3AYV |
Localize | Terminology | Question
In a class, $P(\text{likes maths}) = 0.6$ and $P(\text{likes both maths and science}) = 0.24$.
Assuming independence, what is $P(\text{likes science})$?
Answer:
|
Question
In a class, $P(\text{likes math}) = 0.6$ and $P(\text{likes both math and science}) = 0.24$.
Assuming independence, what is $P(\text{likes science})$?
Answer:
|
Classifier: Contains the term "maths", which is the standard AU/UK term for the US "math". Verifier: Contains the term "maths", which is the standard AU/UK term for the US "math". |
sqn_01JMC6BGHD833DZRWEWFG4CNNB |
Localize | Terminology | Question
Find the $y$-coordinate of the turning point of the parabola $ y = -(x + 1)(x + 5) $
Answer:
|
Question
Find the $y$-coordinate of the vertex of the parabola $ y = -(x + 1)(x + 5) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JMC6NSFNFAEB67J66HBMZJVQ |
Localize | Terminology | Question
Find the $y$-coordinate of the turning point of the parabola $ y = -4(2x + 3)(x - 5) $
Answer:
|
Question
Find the $y$-coordinate of the vertex of the parabola $ y = -4(2x + 3)(x - 5) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JMCA6H827T7Y2WKFWHK2CJZ1 |
Localize | Units (simple) | Question
Visible light has a wavelength of approximately $5.5 \times 10^{-7}$ m.
What is its order of magnitude?
Answer:
|
Question
Visible light has a wavelength of approximately $5.5 \times 10^{-7}$ ft.
What is its order of magnitude?
Answer:
|
Classifier: The text contains the metric unit "m" (metres) in the context of a physical measurement (wavelength). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "m" (metres). Per the decision rules, any metric unit found anywhere requires a RED units classification. Since it is a single value and the question asks for order of magnitude, it is a simple conversion/flag. |
sqn_01JMK42NYCWXXJYTC1DAACZK4N |
Localize | Units (simple) | Question
A tank has $950$ litres of water. It loses $40$ litres every hour.
What is the initial value?
Answer:
|
Question
A tank has $950$ gallons of water. It loses $40$ gallons every hour.
What is the initial value?
Answer:
|
Classifier: The text contains the metric unit "litres", which requires both spelling localization (liters) and unit conversion for a US audience. Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains the metric unit "litres", which requires both spelling localization (to "liters") and unit conversion for the US market. Per rule 5, units conversion takes precedence. |
sqn_01JMRDTSYCQZQEXCK6ZZYRD995 |
Localize | Units (simple) | Question
A square playground measures $18$ m per side. A circular sandpit in the centre has a radius of $4.5$ m.
What is the probability a random point lies outside the sandpit?
Answer:
|
Question
A square playground measures $18$ ft per side. A circular sandpit in the center has a radius of $4.5$ ft.
What is the probability a random point lies outside the sandpit?
Answer:
|
Classifier: The text contains both the metric unit "m" and the AU spelling "centre". Units conversion takes precedence over spelling per the decision rules. Verifier: The text contains the metric unit "m" and the AU spelling "centre". Per decision rule 5, units conversion takes precedence over spelling. |
sqn_01JMC6J4VDSZ3H7NVF9FH72X17 |
Localize | Terminology | Question
Find the $y$-coordinate of the turning point of the parabola $ y = -3(x + 2)(x - 4) $
Answer:
|
Question
Find the $y$-coordinate of the vertex of the parabola $ y = -3(x + 2)(x - 4) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JMC635DZD6SAXHBSXRCNVPKM |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $ y = -3(x +4)(x -$$\Large\frac{1}{2}$ $) $
Answer:
|
Question
Find the $x$-coordinate of the vertex of the parabola $ y = -3(x +4)(x -$$\Large\frac{1}{2}$ $) $
Answer:
|
Classifier: Uses the term "turning point", which maps to "vertex" in US curriculum. Verifier: The term "turning point" is used, which requires localization to "vertex" for US audiences. |
sqn_01JMRDNN9BGPB67H0D49GRZWPB |
Localize | Units (simple) | Question
A $25$ m by $10$ m pool has a diving area of $8$ m by $9$ m.
What is the probability a random point in the pool lies in the diving area?
Answer:
|
Question
A $25$ ft by $10$ ft pool has a diving area of $8$ ft by $9$ ft.
What is the probability a random point in the pool lies in the diving area?
Answer:
|
Classifier: The text contains the metric unit "m" (metres/meters). Per decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains the metric unit "m" (metres). Per decision rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JMDT1X4YHWN74AP1W9SK8R9Y |
Localize | Units (simple) | Question
The temperature in a city is given by $y = 18 + 6 \sin\left(\frac{\pi}{12}t\right)$, where $y$ is in degrees Celsius and $t$ is hours after midnight.
Find the temperature at $9$ AM.
Answer:
|
Question
The temperature in a city is given by $y = 18 + 6 \sin\left(\frac{\pi}{12}t\right)$, where $y$ is in degrees Fahrenheit and $t$ is hours after midnight.
Find the temperature at $9$ AM.
Answer:
|
Classifier: The text contains the metric unit "degrees Celsius" and the symbol "^\circ C", which requires conversion to Fahrenheit for US localization. Verifier: The question uses "degrees Celsius" and the symbol "^\circ C", which are metric units requiring conversion to Fahrenheit for US localization. |
sqn_01JMDWE6N8AGVVA503K7B3D5BX |
Localize | Units (simple) | Question
A submarine's depth is given by $y = 150 + 30 \cos\left(\frac{\pi}{10} t\right)$, where $y$ is the depth below sea level in metres and $t$ is the time in minutes after descent starts.
When does the submarine first reach a depth of $165$ metres?
Answer:
|
Question
A submarine's depth is given by $y = 150 + 30 \cos\left(\frac{\pi}{10} t\right)$, where $y$ is the depth below sea level in feet and $t$ is the time in minutes after descent starts.
When does the submarine first reach a depth of $165$ feet?
Answer:
|
Classifier: The text contains the metric unit "metres" (AU spelling). Metric units take precedence over spelling-only classifications. Verifier: The text contains the metric unit "metres" (AU spelling). Metric units take precedence over spelling-only classifications. |
sqn_01JMH4T8RA09QQVEXA924EY6VB |
Localize | Units (simple) | Question
A building casts a $845.28$ cm shadow. A $122.56$ cm bench nearby casts a $76.60$ cm shadow.
How tall is the building?
Answer:
|
Question
A building casts a $845.28$ in shadow. A $122.56$ in bench nearby casts a $76.60$ in shadow.
How tall is the building?
Answer:
|
Classifier: The text uses "cm" as the unit of measurement for the building and shadow, which requires conversion for a US audience. Verifier: The question uses "cm" for all measurements, requiring localization to US customary units. |
sqn_01JMRDYTN1DAFEGPJG0H8WWQ05 |
Localize | Units (simple) | Question
A $20$ m square hall has a circular stage at its centre with a diameter of $16$ m.
What is the probability a random point on the floor lies outside the stage?
Answer:
|
Question
A $20$ ft square hall has a circular stage at its center with a diameter of $16$ ft.
What is the probability a random point on the floor lies outside the stage?
Answer:
|
Classifier: The text contains the metric unit "m" and the AU spelling "centre". Units conversion takes precedence over spelling. Verifier: The text contains the metric unit "m" and the AU spelling "centre". Per decision rule 5, units conversion takes precedence over spelling. |
sqn_01JMK7CMMCT50DMJK3NM21P202 |
Localize | Units (simple) | Question
A runner runs $10$ km on the first day of training. Each day, they increase their run by $1.8$ km.
How far will they run on the $5^\text{th}$ day?
Answer:
|
Question
A runner runs $10$ mi on the first day of training. Each day, they increase their run by $1.8$ mi.
How far will they run on the $5^\text{th}$ day?
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers), which requires conversion to US customary units (miles) for a US audience. Verifier: The text contains the metric unit "km" (kilometers), which requires conversion to US customary units (miles). The math is a simple arithmetic progression, making it a simple conversion. |
sqn_01JMK3P9Q08EP3618HEYZ9EQAR |
Localize | Units (simple) | Question
A tank has $800$ litres of water. It loses $40$ litres every hour.
Find $d$ in the recurrence relation: $T_0=800, T_{n+1} = T_n + d$
Answer:
|
Question
A tank has $800$ gallons of water. It loses $40$ gallons every hour.
Find $d$ in the recurrence relation: $T_0=800, T_{n+1} = T_n + d$
Answer:
|
Classifier: Contains the metric unit "litres", which requires both spelling localization ("liters") and unit conversion for a US audience. Per rule 6, units conversion takes precedence over spelling. Verifier: Contains the metric unit "litres", which requires both spelling localization ("liters") and unit conversion for a US audience. |
sqn_01JMH4P4F1TJCQWT538X3712F5 |
Localize | Units (simple) | Question
A tree casts a $731.52$ cm shadow. A $91.44$ cm yardstick casts a $60.96$ cm shadow.
How tall is the tree?
Answer:
|
Question
A tree casts a $731.52$ in shadow. A $91.44$ in yardstick casts a $60.96$ in shadow.
How tall is the tree?
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires localization to US customary units. Interestingly, it also mentions a "yardstick" (a US customary tool), but the measurements are given in cm. Verifier: The question uses the metric unit "cm" for measurements, which requires localization to US customary units. Although "yardstick" is a US term, the values provided are in metric. This is a simple ratio problem, so simple conversion is appropriate. |
sqn_01JMH4WGFDNNS9WJ7V7434VRMM |
Localize | Units (simple) | Question
A statue casts a $650.40$ cm shadow. A $102.36$ cm garden fence nearby casts a $68.24$ cm shadow.
How tall is the statue?
Answer:
|
Question
A statue casts a $650.40$ in shadow. A $102.36$ in garden fence nearby casts a $68.24$ in shadow.
How tall is the statue?
Answer:
|
Classifier: The text uses "cm" for all measurements, necessitating localization to US customary units. Verifier: The question uses "cm" for all measurements, requiring localization to US customary units. |
sqn_01JMDW6XH81PWDDPVT0361Y36G |
Localize | Units (simple) | Question
The height of a point on a bicycle wheel is given by $y = 0.5 + 0.3 \sin(2 \pi t)$, where $y$ is height in metres and $t$ is time in seconds after the wheel starts turning.
When does it first reach $0.8$ metres?
Answer:
|
Question
The height of a point on a bicycle wheel is given by $y = 0.5 + 0.3 \sin(2 \pi t)$, where $y$ is height in feet and $t$ is time in seconds after the wheel starts turning.
When does it first reach $0.8$ feet?
Answer:
|
Classifier: The text contains the metric unit "metres" (which also uses AU spelling). Per the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains the metric unit "metres" (AU spelling). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JMDZR7PD7K2CA49ZH9JNB258 |
Localize | Units (simple) | Question
The height of a roller coaster passenger is given by $y = 20 + 15 \sin\left(\frac{\pi}{8} t\right)$, where $y$ is in metres and $t$ is time in seconds.
When does the height first reach $35$ metres?
Answer:
|
Question
The height of a roller coaster passenger is given by $y = 20 + 15 \sin\left(\frac{\pi}{8} t\right)$, where $y$ is in feet and $t$ is time in seconds.
When does the height first reach $35$ feet?
Answer:
|
Classifier: The text contains the metric unit "metres". Metric units take precedence over spelling-only classifications. Verifier: The text contains the metric unit "metres". Metric units take precedence over spelling-only classifications. |
sqn_01JMK73D2NH9VHBG6F5C3DX64G |
Localize | Units (simple) | Question
A tank initially contains $50$ L of water. Every hour, $3.5$ L is added.
Use the recurrence relation below to determine the total amount of water in the tank after $10$ hours.
$W_{0}=50$, $\quad W_{n+1}=W_{n} + 3.5$
Answer:
|
Question
A tank initially contains $50$ gal of water. Every hour, $3.5$ gal is added.
Use the recurrence relation below to determine the total amount of water in the tank after $10$ hours.
$W_{0}=50$, $\quad W_{n+1}=W_{n} + 3.5$
Answer:
|
Classifier: The text contains the metric unit "L" (litres), which requires conversion for US localization. Verifier: The text uses the metric unit "L" (litres), which requires conversion for US localization. This is a simple numeric change. |
sqn_01JSWNZZWE93XKWHKKT9X8DZBJ |
Localize | Terminology | Question
Write four thousand and twenty-nine and twenty-nine thousandths as a decimal.
Answer:
|
Question
Write four thousand twenty-nine and twenty-nine thousandths as a decimal.
Answer:
|
Classifier: The use of "and" to denote the decimal point ("...thousandths") and the inclusion of "and" in "four thousand and twenty-nine" is common in AU/UK English. However, it is not strictly incorrect in US English, though US pedagogy often teaches to use "and" only for the decimal point. Given the rules, there is no AU-specific spelling or metric units, making it GREEN. Verifier: The phrasing "four thousand and twenty-nine" (using "and" before the tens/units in a whole number) is a specific AU/UK convention. In US math pedagogy, "and" is strictly reserved for the decimal point. This requires localization for US students to avoid confusion between the whole number part and the decimal part. |
sqn_01JSXY16VTKV0D38ZA0EXTHVZC |
Localize | Units (simple) | Question
A bottle contains $94$ mL of juice.
If $7$ mL is poured into a glass, how much juice is left in the bottle?
Answer:
|
Question
A bottle contains $94$ fl oz of juice.
If $7$ fl oz is poured into a glass, how much juice is left in the bottle?
Answer:
|
Classifier: The text contains the metric unit "mL" (millilitres), which requires localization to US customary units (e.g., fluid ounces) or at least triggers the units classification per the decision rules. Verifier: The text contains the metric unit "mL" (millilitres), which requires conversion to US customary units. It is a simple subtraction problem, so simple_conversion is correct. |
sqn_01JT28C1VK90Z3TDDH5QH7AP19 |
Localize | Units (simple) | Question
In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 10$ cm, and $AC = 16$ cm.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Question
In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 10$ in, and $AC = 16$ in.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Classifier: Contains the metric unit "cm", requiring localization for the US market. Verifier: Contains metric unit "cm" which requires localization. |
sqn_01JT286C4SYSY10TWSFY282V39 |
Localize | Units (simple) | Question
In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 7$ cm, and $AC = 16$ cm.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Question
In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 7$ in, and $AC = 16$ in.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Classifier: Contains the metric unit "cm" (centimetres/centimeters), which requires localization to US customary units or a decision on metric usage in US curriculum. Per decision rules, any metric unit triggers a RED category. Verifier: Contains metric unit "cm" which requires localization. |
sqn_01JT2955F9MRTBCED6T2DMNRY5 |
Localize | Units (simple) | Question
In $\triangle ABC$, $\angle B = 10^\circ$, $AC = 3$ m, and $BC = 9$ m.
Determine how many distinct triangles can be formed with these measurements.
Answer:
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Question
In $\triangle ABC$, $\angle B = 10^\circ$, $AC = 3$ ft, and $BC = 9$ ft.
Determine how many distinct triangles can be formed with these measurements.
Answer:
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Classifier: The text contains the metric unit "m" (metres) in a measurement context ("3 m", "9 m"), which requires localization. Verifier: The text contains the metric unit "m" (metres), which requires localization. The conversion is simple as it involves side lengths in a triangle geometry problem. |
sqn_01JT28STRMGFTF3WVJD1FVTHR7 |
Localize | Units (simple) | Question
In triangle $\text{ABC}$, $\angle A=30^\circ, BC=20$ cm and $AC=16$ cm.
If one distinct triangle exists, find the measure of $\angle B$.
Answer:
|
Question
In triangle $\text{ABC}$, $\angle A=30^\circ, BC=20$ in and $AC=16$ in.
If one distinct triangle exists, find the measure of $\angle B$.
Answer:
|
Classifier: Contains the metric unit "cm", requiring localization for the US market. Verifier: Contains metric unit "cm" which requires localization. |
sqn_01JT29122ND1FQDEK6NJ4HEH8E |
Localize | Units (simple) | Question
In $\triangle ABC$, $\angle A = 35^\circ$, $BC = 2$ cm, and $AC = 5$ cm.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Question
In $\triangle ABC$, $\angle A = 35^\circ$, $BC = 2$ in, and $AC = 5$ in.
Determine how many distinct triangles can be formed with these measurements.
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units or a non-metric context per the decision rules. Verifier: The text contains the metric unit "cm" (centimetres), which requires localization to US customary units. The conversion is simple as it involves side lengths in a triangle geometry problem. |
sqn_01JTT191883329HYE5MPCK6S01 |
Localize | Spelling (AU-US) | Question
Factorise $3x-6$
Answer:
|
Question
Factor $3x-6$
Answer:
|
Classifier: Contains the AU spelling "Factorise", which needs to be localized to the US spelling "Factorize". Verifier: Contains the AU spelling "Factorise", which requires localization to "Factorize". |
sqn_01JTJHFB6H6CQNXQG1MTDPWD2F |
Localize | Terminology | Question
Matthew invested $\$2500$ for a total of $6$ years.
For the first $2$ years, it earns $4.5\%$ p.a. compounded annually.
For the next $4$ years, it earns $6.5\%$ p.a. compounded semi-annually.
What is the final amount?
Answer:
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Question
Matthew invested $\$2500$ for a total of $6$ years.
For the first $2$ years, it earns $4.5\%$ APR compounded annually.
For the next $4$ years, it earns $6.5\%$ APR compounded semi-annually.
What is the final amount?
Answer:
|
Classifier: The text uses "p.a." (per annum), which is standard in AU/UK financial contexts but is typically replaced with "per year" or "annually" in US K-12 math contexts. While "compounded annually" is used later, "p.a." is a specific abbreviation common in AU curricula. Verifier: The text uses "p.a." (per annum), which is a specific abbreviation common in AU/UK financial contexts but not standard in US K-12 math, where "per year" is preferred. |
sqn_01JT2A3YJY1CA8YBGWG1G2VRQY |
Localize | Units (simple) | Question
In triangle $\text{ABC}$, $\angle A=45^\circ,BC=8$ cm and $AC=10$ cm.
If $\angle B$ is an acute angle, then find the measure of $\angle B$.
Answer:
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Question
In triangle $\text{ABC}$, $\angle A=45^\circ,BC=8$ in and $AC=10$ in.
If $\angle B$ is an acute angle, then find the measure of $\angle B$.
Answer:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires localization. Verifier: The text contains the metric unit "cm" (centimetres), which requires localization. The conversion is simple as it involves side lengths in a triangle geometry problem. |
sqn_01JTT1DHHVEWAAS37YFX9Z2KSW |
Localize | Spelling (AU-US) | Question
Factorise $4y-12$
Answer:
|
Question
Factor $4y-12$
Answer:
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Classifier: The word "Factorise" uses the AU/UK 's' spelling; the US equivalent is "Factorize". Verifier: The word "Factorise" is the AU/UK spelling. The US spelling is "Factorize". Per rule 1, AU spelling always requires RED classification. |
sqn_01JTKZCP26SVWHN6VPHFQ4G0E2 |
Localize | Terminology | Question
An investor deposits $\$8000$ at $6\%$ p.a. simple interest.
After $2$ years, they withdraw $25\%$ of the balance. The rest earns interest for another $3$ years.
What is the final amount after $5$ years?
Answer:
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Question
An investor deposits $\$8000$ at $6\%$ APR simple interest.
After $2$ years, they withdraw $25\%$ of the balance. The rest earns interest for another $3$ years.
What is the final amount after $5$ years?
Answer:
|
Classifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates. Verifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates in a school context. |
sqn_01JTKZ2RXRZ4TZ6KFGRKWMCTBS |
Localize | Terminology | Question
A sum of money is invested at $5\%$ p.a. simple interest for $3$ years, then at $6.5\%$ p.a. for the next $2$ years.
If the final value of the investment is $\$1425$, what was the original principal?
Answer:
|
Question
A sum of money is invested at $5\%$ APR simple interest for $3$ years, then at $6.5\%$ APR for the next $2$ years.
If the final value of the investment is $\$1425$, what was the original principal?
Answer:
|
Classifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates, whereas US curriculum typically uses "per year" or "annual interest rate". Verifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates in a school context. |
sqn_01JTT1BFV1PBF5WBKB54TR4HQN |
Localize | Spelling (AU-US) | Question
Factorise $2y+10$
Answer:
|
Question
Factor $2y+10$
Answer:
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Classifier: The word "Factorise" uses the AU/UK 's' spelling; the US equivalent is "Factorize". Verifier: The word "Factorise" is the AU/UK spelling. The US spelling is "Factorize". Per rule 1, AU spelling always requires RED classification. |
sqn_01JTSTA7QFD452KHDK4Y7R1MT0 |
Localize | Units (simple) | Question
A rock has a mass of $90$ g and a volume of $3$ cm$^3$.
What is its density?
Answer:
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Question
A rock has a mass of $90$ oz and a volume of $3$ in$^3$.
What is its density?
Answer:
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Classifier: The question contains metric units (grams and cubic centimeters) which require localization to US customary units or a decision on metric pedagogy in a US context. Per rule 1, any metric unit found anywhere prevents a GREEN classification. Verifier: The question contains metric units (g, cm^3) which require conversion for US localization. |
sqn_01JTKZJN2DXWXYHWB0023Y68DZ |
Localize | Terminology | Question
An investment grows to $\$1680$ after $4$ years of simple interest.
The rate was $3.5\%$ p.a. for the first year and $4.5\%$ p.a. for the next $3$ years.
What was the original amount invested?
Answer:
|
Question
An investment grows to $\$1680$ after $4$ years of simple interest.
The rate was $3.5\%$ APR for the first year and $4.5\%$ APR for the next $3$ years.
What was the original amount invested?
Answer:
|
Classifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates. Verifier: Contains "p.a." (per annum), which is the standard AU notation for interest rates in a school context. |
sqn_01JTQP7S5CHENNR4Y5J6E4AR39 |
Localize | Terminology | Question
Isabelle invests $\$8000$ at $4.2\%$ p.a., compounded daily for $2$ years.
Then, she reinvests the total at the same rate, compounded annually for $3$ more years.
How much interest does she earn over the $5$ years?
Answer:
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Question
Isabelle invests $\$8000$ at $4.2\%$ APR, compounded daily for $2$ years.
Then, she reinvests the total at the same rate, compounded annually for $3$ more years.
How much interest does she earn over the $5$ years?
Answer:
|
Classifier: The term "p.a." (per annum) is standard in AU financial contexts but is much less common in US K-12/undergraduate math, where "per year" or "annually" is preferred. More importantly, "p.a." is a strong indicator of AU/UK source material. Verifier: The abbreviation "p.a." (per annum) is a standard Australian/British financial term that is not commonly used in US K-12 mathematics, where "per year" or "annually" is preferred. |
sqn_01JTQPHPM8E0BBMJ8CJKPB95GG |
Localize | Terminology | Question
Ryan deposits $\$15000$ at $6\%$ p.a., compounded semiannually for $2$ years, then monthly for the next $3$ years.
How much interest does he earn in total after $5$ years?
Answer:
|
Question
Ryan deposits $\$15000$ at $6\%$ APR, compounded semiannually for $2$ years, then monthly for the next $3$ years.
How much interest does he earn in total after $5$ years?
Answer:
|
Classifier: Contains "p.a." (per annum), which is the standard AU abbreviation for interest rates, whereas US curriculum typically uses "per year" or "annual interest rate". Verifier: The use of "p.a." for interest rates is a specific terminology marker for AU/UK contexts. |
sqn_01JV1TWDBRBVKX2PEZ24VTDSZN |
Localize | Units (simple) | Question
A gardener uses $0.125$ kg of fertiliser per square metre. She fertilises $1000$ m$^2$ of the garden.
How much fertiliser does she use in total?
Answer:
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Question
A gardener uses $0.125$ lbs of fertilizer per square foot. She fertilizes $1000$ ft$^2$ of the garden.
How much fertilizer does she use in total?
Answer:
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Classifier: The text contains metric units (kg, m^2) and AU-specific spelling ("fertiliser", "metre"). Per the decision rules, the presence of metric units takes precedence for classification. Verifier: The text contains metric units ("kg", "m$^2$") and AU spelling ("fertiliser", "metre"). Per rule 5, units conversion is the most impactful change. |
sqn_01JV3NX6ZK13E8S909FWMH6ZWG |
Localize | Units (simple) | Question
A particle's speed is measured as $0.00087463$ m/s.
What is this value rounded to $3$ significant figures?
Answer:
|
Question
A particle's speed is measured as $0.00087463$ ft/s.
What is this value rounded to $3$ significant figures?
Answer:
|
Classifier: The text contains a metric unit (m/s). Per the decision rules, any metric unit found anywhere in the text triggers a units classification. Verifier: Contains metric unit "m/s" which requires localization to US customary units (e.g., ft/s) per decision rule 3. |
sqn_01JV1VFP4D4EDDNXTYQCPA2BM3 |
Localize | Units (simple) | Question
A printer cartridge holds $2.35$ millilitres of ink. It is used evenly across $1000$ pages.
How many millilitres of ink is used per page?
Answer:
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Question
A printer cartridge holds $2.35$ fluid ounces of ink. It is used evenly across $1000$ pages.
How many fluid ounces of ink is used per page?
Answer:
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Classifier: The text contains metric units ("millilitres", "mL"). Even though the math is a simple division by 1000, the presence of metric units requires localization to US customary units or a check against US science/math standards. Verifier: The text contains metric units ("millilitres", "mL"), which requires RED classification under rule 3. |
sqn_01JV3SYT3R9D73QJKHN4H907TY |
Localize | Cultural refs | Question
An account offers an annual interest rate of $10.65\%$, compounded fortnightly.
What is the equivalent weekly interest rate?
Answer:
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Question
An account offers an annual interest rate of $10.65\%$, compounded every two weeks.
What is the equivalent weekly interest rate?
Answer:
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Classifier: While "fortnightly" is more common in AU/UK, it is a valid English term understood in financial contexts globally and does not strictly require localization like spelling or units do. No other AU-specific markers are present. Verifier: The term "fortnightly" is a distinct AU/UK cultural/linguistic marker for a 2-week period. While understood by some in the US, it is not standard US terminology for financial problems (where "bi-weekly" or "every two weeks" is used) and should be flagged for localization under cultural/terminology rules. |
sqn_01JV67DHHEDP0T9TGH174J86XX |
Localize | Units (simple) | Question
Fill in the blank:
$1$ litre : $250$ millilitres $= [?] : 1$
Answer:
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Question
Fill in the blank:
$1$ gallon : $250$ fluid ounces $= [?] : 1$
Answer:
|
Classifier: Contains metric units ("litre", "millilitres") and the AU spelling "litre". Per decision rules, any metric unit requires at least simple conversion, and units take precedence over spelling. Verifier: Contains metric units ("litre", "millilitres") and AU spelling ("litre"). Metric units require RED classification. |
sqn_01JV67KDH59Y4RW7K0FZASRTM4 |
Localize | Units (simple) | Question
Fill in the blank:
$400$ cm : $2$ m $= [?] : 1$
Answer:
|
Question
Fill in the blank:
$400$ in : $2$ ft $= [?] : 1$
Answer:
|
Classifier: Contains metric units ("cm", "m"). Per decision rules, any metric unit found anywhere in the text requires localization. Verifier: Contains metric units ("cm", "m"). Any metric unit requires RED classification. |
sqn_01JV3HCJRNVJCZ0ZC931FAC6N9 |
Localize | Units (simple) | Question
A scientist poured $32.5$ mL of liquid into a beaker.
Then, she removed $7.8$ mL for a test and later added $14.65$ mL of another solution.
After that, $9.25$ mL evaporated.
What is the final volume of liquid in the beaker?
Answer:
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Question
A scientist poured $32.5$ fl oz of liquid into a beaker.
Then, she removed $7.8$ fl oz for a test and later added $14.65$ fl oz of another solution.
After that, $9.25$ fl oz evaporated.
What is the final volume of liquid in the beaker?
Answer:
|
Classifier: The text contains metric units (mL) which require conversion to US customary units for a US audience. Verifier: Contains metric units (mL) which require conversion for US localization. |
sqn_01JX8B3JSEW47JTC8AST8ZV1D3 |
Localize | Spelling (AU-US) | Question
A licence plate uses $2$ letters (A–B) and $2$ digits (0–1).
How many different plates can be made?
Answer:
|
Question
A license plate uses $2$ letters (A–B) and $2$ digits (0–1).
How many different plates can be made?
Answer:
|
Classifier: Contains the AU spelling "licence", which needs to be localized to the US spelling "license". Verifier: The text contains "licence", which is the AU/British spelling for the noun form (US: license). |
sqn_01JXFG22ZZHA9SJ1EWRKBFF5QF |
Localize | Terminology | Question
Find the turning point of the parabola $y=7x^2-13x+\frac{17}{2}$.
Write all fractions in simplest form.
Answer:
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Question
Find the vertex of the parabola $y=7x^2-13x+ rac{17}{2}$.
Write all fractions in simplest form.
Answer:
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Classifier: Uses the AU/UK term "turning point", which maps to "vertex" in US school mathematics. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" of a parabola in US school mathematics. |
sqn_01JXFFSYKDJRWGF5SMW10ZKFZK |
Localize | Terminology | Question
Find the sum of the coordinates at the turning point of the given parabola:
$y=0.5x^2+4x-\frac{25}{4}$
Answer:
|
Question
Find the sum of the coordinates at the vertex of the given parabola:
$y=0.5x^2+4x-\frac{25}{4}$
Answer:
|
Classifier: Uses the AU/UK term "turning point", which maps to "vertex" in US school mathematics. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" of a parabola in US school mathematics. |
sqn_01JW7GMX32ZABQSBDGV5GS87RZ |
Review | Policy | Question
A school records the following data for each student: their height, the number of books borrowed per term, and the number of extracurricular activities attended.
How many of these variables are discrete?
Answer:
|
Question
A school records the following data for each student: their height, the number of books borrowed per semester, and the number of extracurricular activities attended.
How many of these variables are discrete?
Answer:
|
Classifier: The text uses the word "term" in a school context ("borrowed per term"). While "term" is used in the US, "semester" or "quarter" are often preferred depending on the specific school system or regional policy. Per decision rules, this maps to the GRAY category for policy-dependent terms. Verifier: The use of "term" in a school context is a policy-dependent localization point (often replaced by "semester" or "quarter" in the US), which maps to the GRAY category. |
sqn_01JX480TR5NX4XSB5TPKYCWNXD |
Localize | Units (simple) | Question
The density of a material is $0.000768531$ g/cm$^3$.
Express this density to $5$ significant figures.
Answer:
|
Question
The density of a material is $0.000768531$ oz/in$^3$.
Express this density to $5$ significant figures.
Answer:
|
Classifier: The text contains metric units ("g/cm^3"). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit "g/cm^3". Per rule 3, any metric unit requires at least RED.units_simple_conversion. Since it is a single value being rounded, simple conversion is appropriate. |
sqn_01JW3PKYXADQNGGMJNM0MF2D67 |
Localize | Spelling (AU-US) | Question
A right circular cylinder has height equal to its base radius. Point $V$ lies halfway up the side, directly above a point on the base edge. Point $P$ is the centre of the top face.
What is the angle between segment $VP$ and the cylinder's base?
Answer:
|
Question
A right circular cylinder has height equal to its base radius. Point $V$ lies halfway up the side, directly above a point on the base edge. Point $P$ is the center of the top face.
What is the angle between segment $VP$ and the cylinder's base?
Answer:
|
Classifier: Contains the AU spelling "centre" which needs to be localized to "center". Verifier: Contains the AU spelling "centre" which requires localization to "center". |
sqn_01JX486AFB6ED8Y2EMPWQSZ0JP |
Localize | Units (simple) | Question
The volume of a container is measured as $0.004327$ m$^3$
Express this value to $3$ significant figures.
Answer:
|
Question
The volume of a container is measured as $0.004327$ ft$^3$
Express this value to $3$ significant figures.
Answer:
|
Classifier: The text contains the metric unit "m^3" (cubic metres) in both the content and the suffix field. Verifier: The text contains the metric unit "m^3" (cubic metres). Per rule 3, this requires a units classification. |
sqn_01JVRZSW9EF9XX0PEYG3RG2FCH |
Localize | Units (simple) | Question
The function $h(t)=−5t^2+18t+2$ describes the height of a projectile in metres, $t$ seconds after launch.
What is the instantaneous rate of change of height at $t=3$ seconds?
Answer:
|
Question
The function $h(t)=−5t^2+18t+2$ describes the height of a projectile in feet, $t$ seconds after launch.
What is the instantaneous rate of change of height at $t=3$ seconds?
Answer:
|
Classifier: The text contains the metric unit "metres" (which also has AU spelling) and the unit "m/s". Per the decision rules, any metric unit requires classification into a units category, and units take precedence over spelling. Verifier: The text contains the metric unit "metres" (AU spelling) and "m/s". While there is a function $h(t)$, it is a simple quadratic and the question asks for a rate of change at a point, which is a straightforward calculation. It does not meet the threshold for "complex" (5+ interlinked values or re-deriving coefficients). |
sqn_01JW2H9C479THA0HPERPBC7BTM |
Localize | Spelling (AU-US) | Question
At a car service centre, $58\%$ of vehicles are petrol and $42\%$ are diesel.
$12\%$ of petrol vehicles and $23\%$ of diesel vehicles need a brake replacement.
Using a tree diagram, what is the probability that a vehicle is diesel given it needs a brake replacement?
Answer:
|
Question
At a car service center, $58\%$ of vehicles are gasoline and $42\%$ are diesel.
$12\%$ of gasoline vehicles and $23\%$ of diesel vehicles need a brake replacement.
Using a tree diagram, what is the probability that a vehicle is diesel given it needs a brake replacement?
Answer:
|
Classifier: Contains the AU spelling "centre" which requires conversion to the US spelling "center". While "petrol" is often localized to "gasoline", it is frequently treated as a spelling/vocabulary preference; however, "centre" is a definitive spelling-only trigger. Verifier: The text contains "centre" (AU spelling) and "petrol" (AU terminology). Per the decision rules, "centre" is a definitive spelling-only trigger for RED.spelling_only. |
sqn_01JWN5HNRN35YFDWSSE3FSV7RG |
Localize | Units (simple) | Question
A $40$ m cable stretches from the top of a tower to a point on the ground.
A point $40\%$ lower than the top of the tower is $18$ metres above the ground.
Determine the angle, in degrees, between the ground and the cable.
Answer:
|
Question
A $40$ ft cable stretches from the top of a tower to a point on the ground.
A point $40\%$ lower than the top of the tower is $18$ feet above the ground.
Determine the angle, in degrees, between the ground and the cable.
Answer:
|
Classifier: The text contains the metric unit "m" and the AU-specific spelling/unit "metres". Per decision rules, any metric unit requires classification into a units category, and units take precedence over spelling. Verifier: The text contains metric units ("m" and "metres"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. The calculation is a straightforward trigonometric problem, making simple conversion appropriate. |
sqn_01JW7THNMFX2BKP729CXQ4HY8X |
Localize | Units (simple) | Question
The length of a rectangle is $6$ cm more than its width.
If its area is $160$ cm$^2$, what is the length?
Answer:
|
Question
The length of a rectangle is $6$ in more than its width.
If its area is $160$ in$^2$, what is the length?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm$^2$") which require localization to US customary units or a decision on metric pedagogy. Per rule 1, any metric unit disqualifies GREEN. Verifier: The question contains metric units ("cm" and "cm$^2$"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JX0H1KGWFWDPYX0TW1MPHVMS |
Localize | Cultural refs | Question
A pair of shoes is priced at $\$40$. The label says this includes $\$4$ GST.
How much will a customer pay for the pair of shoes?
Answer:
|
Question
A pair of shoes is priced at $\$40$. The label says this includes $\$4$ sales tax.
How much will a customer pay for the pair of shoes?
Answer:
|
Classifier: Contains 'GST' (Goods and Services Tax), which is the specific tax terminology for Australia/New Zealand. In a US context, this would typically be 'sales tax'. Verifier: Contains "GST" (Goods and Services Tax), which is a specific tax term used in Australia and New Zealand, requiring localization to "sales tax" for a US audience. |
sqn_01JX0GRRZT1GFS1A0FM4CP60ZE |
Localize | Units (simple) | Question
A water tank contains $85$ litres of water.
If $8$ litres are used, how much water is left in the tank?
Answer:
|
Question
A water tank contains $85$ gallons of water.
If $8$ gallons are used, how much water is left in the tank?
Answer:
|
Classifier: Contains the metric unit 'litres' with AU spelling. Per decision rules, any metric unit requires at least simple conversion. Verifier: Contains the metric unit "litres" (AU spelling). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JW4X7KTTQ49JPT4KKQ9G19T9 |
Localize | Spelling (AU-US) | Question
A rectangular prism has a square base. the height of the prism is twice the length of a side of the base.
If $O$ is the centre of the base and $P$ is the top corner directly above a base vertex, find the angle between $OP$ and the base.
Answer:
|
Question
A rectangular prism has a square base. The height of the prism is twice the length of a side of the base.
If $O$ is the center of the base and $P$ is the top corner directly above a base vertex, find the angle between $OP$ and the base.
Answer:
|
Classifier: The text contains the Australian spelling "centre", which needs to be localized to the US spelling "center". Verifier: The text contains "centre", which is the Australian/British spelling. Per Rule 1, this requires RED classification. |
sqn_01JXC7AZW39YQ772CFRH7X0ZNF |
Localize | Units (simple) | Question
$250$g of a laundry powder mix is made using chemicals in the ratio $800$ mg $: 0.002 $ kg $: x $ g.
Find the value of $x$ in grams.
Answer:
|
Question
$250$ oz of a laundry powder mix is made using chemicals in the ratio $800$ mg $: 0.002 $ lb $: x $ oz.
Find the value of $x$ in ounces.
Answer:
|
Classifier: Contains multiple metric units (g, mg, kg) which require localization. Verifier: The text contains metric units (g, mg, kg). According to the decision rules, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_01JX4838WPEG1C9DT5P6X4WQMF |
Localize | Units (simple) | Question
The measured length of a metal rod is $500.073$ mm
Express this length to $3$ significant figures.
Answer:
|
Question
The measured length of a metal rod is $500.073$ in
Express this length to $3$ significant figures.
Answer:
|
Classifier: The text contains the metric unit "mm" (millimetres) in both the content and the suffix field. Verifier: The text contains the metric unit "mm" (millimetres). Per rule 3, this requires a units classification. |
sqn_01JW4VZAQQ02J1YVW0V8WAMSSA |
Localize | Units (simple) | Question
A triangular prism has a right-angled triangle base with $\angle C = 90^\circ$, $AC = 6$ cm, and $BC = 8$ cm. The hypotenuse $AB$ equals the height of the prism.
Let $O$ be the midpoint of $AB$, and $P$ the top vertex above $C$. What is the angle between $OP$ and the base?
Answer:
|
Question
A triangular prism has a right triangle base with $\angle C = 90^\circ$, $AC = 6$ in, and $BC = 8$ in. The hypotenuse $AB$ equals the height of the prism.
Let $O$ be the midpoint of $AB$, and $P$ the top vertex above $C$. What is the angle between $OP$ and the base?
Answer:
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Classifier: Contains metric units ("cm") and AU terminology ("right-angled triangle"). Per the decision rules, units conversion takes precedence over terminology. Verifier: Contains metric units ("cm") and AU terminology ("right-angled triangle"). Per rule 5, units conversion takes precedence over terminology. |
sqn_01JXC6ZZHTJ1EXGB2BS8QKNTWW |
Localize | Units (simple) | Question
A drink recipe uses the ratio $x$ mL $: 0.75$ L $: 500 $ mL, where the total volume is $2250$ mL.
Find the value of $x$, in mL, that makes the ratio a set of whole numbers in simplest form.
Answer:
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Question
A drink recipe uses the ratio $x$ fl oz $: 0.75$ gal $: 500 $ fl oz, where the total volume is $2250$ fl oz.
Find the value of $x$, in fl oz, that makes the ratio a set of whole numbers in simplest form.
Answer:
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Classifier: Contains multiple metric units (mL, L) which require localization to US customary units or a decision on metric pedagogy. Per rule 1, any metric unit disqualifies GREEN. Verifier: The text contains metric units (mL, L). According to the decision rules, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_01JXC481NSSZRMYY4F1GKDQNFQ |
Localize | Units (simple) | Question
A mass of $78.914$ g is heated from $21.5^\circ$C to $28.3^\circ$C.
The heat energy transferred can be calculated by using the formula $q = mc\Delta T$, where $c = 4.18$ $Jg^{\circ}C$.
How many significant figures should $q$ have to maintain accuracy?
Hint: The final result should have the same number of significant figures as the least precise value in the equation.
Answer:
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Question
A mass of $78.914$ oz is heated from $21.5^\circ$F to $28.3^\circ$F.
The heat energy transferred can be calculated by using the formula $q = mc\Delta T$, where $c = 4.18$ $J/oz^{\circ}F$.
How many significant figures should $q$ have to maintain accuracy?
Hint: The final result should have the same number of significant figures as the least precise value in the equation.
Answer:
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Classifier: The text contains multiple metric units (grams, degrees Celsius, Joules per gram degree Celsius). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains metric units (grams, Celsius, Joules). While it is a science context, the decision rules state that any metric unit requires a RED classification. It is simple conversion as it involves identifying significant figures rather than complex re-derivation of metric-dependent formulas. |
sqn_01JXFGDY88W5TF5M6MAACCADRE |
Localize | Terminology | Question
Given $y=-\frac{1}{2}x^2+3x-\frac{1}{2}$, what is the reciprocal of the $x$-coordinate of the turning point?
Answer:
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Question
Given $y=-\frac{1}{2}x^2+3x-\frac{1}{2}$, what is the reciprocal of the $x$-coordinate of the vertex?
Answer:
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Classifier: Uses the AU/UK term "turning point", which maps to "vertex" in US school mathematics. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" of a parabola in US school mathematics. |
sqn_01JXHZ1RN3YQ4HTSD13PVDBMVS |
Localize | Terminology | Question
The turning point of a quadratic is at $x=1$, and the graph passes through the point $(3,5)$.
If the quadratic is of the form $y=a(x-1)^2+k$, what is the value of $a$?
Answer:
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Question
The vertex of a quadratic is at $x=1$, and the graph passes through the point $(3,5)$.
If the quadratic is of the form $y=a(x-1)^2+k$, what is the value of $a$?
Answer:
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Classifier: The term "turning point" is used to describe the vertex of a quadratic, which is specific to AU/UK terminology. In the US, "vertex" is the standard term. Verifier: The term "turning point" is used to describe the vertex of a quadratic, which is specific to AU/UK terminology. |
sqn_01JXHW58WP303S7QESACYSXHHP |
Localize | Spelling (AU-US) | Question
The expression $18x^2+px-12$ can be factorised using the cross method.
If one factor is $(6x+1)$, what is the value of $p$?
Answer:
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Question
The expression $18x^2+px-12$ can be factored using the cross method.
If one factor is $(6x+1)$, what is the value of $p$?
Answer:
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Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The word "factorised" is AU/UK spelling and requires localization to "factorized" for US context. |
sqn_01JXHYY4KJEGDJF5TN5YV6XQPC |
Localize | Terminology | Question
Convert the quadratic expression $\sqrt{2}x^2-6\sqrt{2}x+11$ into turning point form.
Answer:
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Question
Convert the quadratic expression $\sqrt{2}x^2-6\sqrt{2}x+11$ into vertex form.
Answer:
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Classifier: The term "turning point form" is standard in AU/UK curriculum for what is known as "vertex form" in the US. Verifier: The term "turning point form" is AU/UK terminology for what is called "vertex form" in the US. |
sqn_01JXVJJ6TM1606R6N2ME12VFF8 |
Localize | Terminology | Question
Convert the quadratic expression $\sqrt{3}x^2-4\sqrt{3}x+7$ into turning point form.
Answer:
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Question
Convert the quadratic expression $\sqrt{3}x^2-4\sqrt{3}x+7$ into vertex form.
Answer:
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Classifier: The term "turning point form" is used, which requires localization to "vertex form" for a US audience. Verifier: The term "turning point form" is used, which requires localization to "vertex form" for a US audience. |
sqn_01JXVJPXA9HP6DW8ZQ958A9ABJ |
Localize | Terminology | Question
The turning point of a quadratic is at $x=-3$ , and the graph passes through the point $(-1,2)$.
If the quadratic is of the form $y=a(x+3)^2+1$, what is the value of $a$?
Answer:
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Question
The vertex of a quadratic is at $x=-3$ , and the graph passes through the point $(-1,2)$.
If the quadratic is of the form $y=a(x+3)^2+1$, what is the value of $a$?
Answer:
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Classifier: The term "turning point" is used instead of the US-standard "vertex". Verifier: The term "turning point" is used instead of the US-standard "vertex". |
sqn_01JXVJSKHP68K2K1S585523YTY |
Localize | Terminology | Question
The turning point of a quadratic is at $x=2$ , and the graph passes through the point $(5,11)$.
If the quadratic is of the form $y=a(x-2)^2+3$, what is the value of $a$?
Answer:
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Question
The vertex of a quadratic is at $x=2$ , and the graph passes through the point $(5,11)$.
If the quadratic is of the form $y=a(x-2)^2+3$, what is the value of $a$?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a quadratic function. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard Australian/British term for the vertex of a parabola. In US curriculum, "vertex" is almost exclusively used. |
sqn_01JYGE7SNEGVQZ6B1XZZHHBSA2 |
Localize | Units (complex) | Question
The height of a ball is modelled by $h = -5t² + 20t + 2$, where t is time in seconds.
What is the maximum height the ball reaches?
Answer:
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Question
The height of a ball is modeled by $h = -16t² + 64t + 6$, where t is time in seconds.
What is the maximum height the ball reaches?
Answer:
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Classifier: The suffix "m" indicates metres, a metric unit. This requires localization to US customary units (feet). Verifier: The question contains a physics-based quadratic equation h = -5t² + 20t + 2 where the coefficient -5 represents half of the acceleration due to gravity (approx 9.8 m/s²). Converting the unit "m" to "ft" requires changing the coefficients of the equation (e.g., to -16t² for feet), which falls under RED.units_complex_converted. |
sqn_01JYGEA1SPGB1XZ3SF94VXDDBX |
Localize | Units (simple) | Question
The speed of a cyclist is given by $S = -x² + 12x$, where $x$ is effort level.
What is the maximum speed?
Answer:
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Question
The speed of a cyclist is given by $S = -x² + 12x$, where $x$ is effort level.
What is the maximum speed?
Answer:
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Classifier: The suffix "m/s" (metres per second) is a metric unit of speed, requiring localization for a US audience. Verifier: The suffix "m/s" (metres per second) is a metric unit of speed. Unlike the previous gravity problem, this equation is a generic model for "effort level" and does not rely on physical constants, making it a simple unit conversion. |
sqn_01JYE59N0D89FDDABQAM95K513 |
Localize | Units (simple) | Question
Fill in the blank:
A cyclist rides $5$ km every day.
After $14$ days, the total distance travelled will be $[?]$ km.
Answer:
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Question
Fill in the blank:
A cyclist rides $5$ mi every day.
After $14$ days, the total distance traveled will be $[?]$ mi.
Answer:
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Classifier: The text contains the metric unit "km" (kilometres), which requires localization to US customary units (miles). Note: "travelled" is also AU spelling (US: traveled), but units take precedence. Verifier: The text contains the metric unit "km" (kilometres) and the AU spelling "travelled" (US: traveled). Metric units require conversion to US customary units. |
sqn_01JYE5BB9A96AWB8A4K7B4JGCT |
Localize | Units (simple) | Question
Fill in the blank:
A water tank is filled at a constant rate of $8$ litres per hour.
After $6$ hours, the tank will have received an additional $[?]$ litres.
Answer:
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Question
Fill in the blank:
A water tank is filled at a constant rate of $8$ gallons per hour.
After $6$ hours, the tank will have received an additional $[?]$ gallons.
Answer:
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Classifier: The text contains the metric unit "litres", which uses AU spelling and requires conversion to US customary units (gallons or liters). Units take precedence over spelling. Verifier: The text contains the metric unit "litres", which uses AU spelling and requires conversion to US customary units (gallons/quarts) or US spelling (liters). |
sqn_01JYGFVECAFQF0FCAGESJH0SNR |
Localize | Units (simple) | Question
A rectangular billboard is built with $100$ metres of framing. Its area is modelled by $A = -x² + 50x$
What is the maximum area of the billboard?
Answer:
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Question
A rectangular billboard is built with $100$ feet of framing. Its area is modeled by $A = -x² + 50x$
What is the maximum area of the billboard?
Answer:
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Classifier: Contains metric units (metres, m^2) and AU-specific spelling (metres). Units conversion takes precedence over spelling. Verifier: The text contains the metric unit "metres" (AU spelling) and "m$^2$". Metric units require conversion, and the spelling "metres" is AU-specific. |
sqn_01JYGFKCBYHQW8VZHVMX183ZK5 |
Localize | Units (simple) | Question
The fuel consumption of a car is modelled by $F = x^2 - 8x + 25$, where $x$ is the speed in tens of km/h.
What speed minimises fuel consumption?
Answer:
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Question
The fuel consumption of a car is modeled by $F = x^2 - 8x + 25$, where $x$ is the speed in tens of mph.
What speed minimizes fuel consumption?
Answer:
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Classifier: Contains metric units (km/h) which require conversion for US localization. Verifier: The text contains the metric unit "km/h" in both the content and the suffix, which requires conversion for US localization. |
sqn_01JYGFS67X8GKY6YPF9PN12NX9 |
Localize | Units (simple) | Question
A rectangular garden is built along a wall and requires fencing on three sides.
If $180$ metres of fencing is available, what is the maximum area that can be enclosed?
Answer:
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Question
A rectangular garden is built along a wall and requires fencing on three sides.
If $180$ feet of fencing is available, what is the maximum area that can be enclosed?
Answer:
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Classifier: Contains metric units (metres, m^2) and AU-specific spelling (metres). Units conversion takes precedence over spelling. Verifier: The text contains the metric unit "metres" (AU spelling) and "m$^2$". Metric units require conversion, and the spelling "metres" is AU-specific. |
sqn_01JYGFYYC05XWH8Y1696JGRYKG |
Localize | Units (simple) | Question
The cost of materials for building a box is modelled by $C = 2x^2 - 40x + 300$, where $x$ is the length in cm.
What is the minimum cost?
Answer:
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Question
The cost of materials for building a box is modeled by $C = 2x^2 - 40x + 300$, where $x$ is the length in in.
What is the minimum cost?
Answer:
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Classifier: Contains metric units (cm) which require conversion for US localization. Verifier: The text contains the metric unit "cm", which requires conversion for US localization. |
sqn_01JYGJ1M1P72CTEKWCDZ96DDBR |
Localize | Units (simple) | Question
A rectangular pen is divided into two equal parts with fencing and has a total of $600$ m fencing.
If width is $x$, write the area in terms of $x$.
Answer:
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Question
A rectangular pen is divided into two equal parts with fencing and has a total of $600$ ft fencing.
If width is $x$, write the area in terms of $x$.
Answer:
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Classifier: The text contains the metric unit "m" (metres) in the context of a measurement ("600 m fencing"). According to the decision rules, any metric unit requires localization. Verifier: The text contains the metric unit "m" (metres) used for a measurement ("600 m fencing"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JYGHZ1WKPY89V2HGGTGCS7VC |
Localize | Units (simple) | Question
You are making an open box with a square base and total surface area of $300$ m$^2$. Let the base side length be $x$ and the height be $h$.
Write the volume of the box as an expression in terms of $x$.
Answer:
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Question
You are making an open box with a square base and total surface area of $300$ ft$^2$. Let the base side length be $x$ and the height be $h$.
Write the volume of the box as an expression in terms of $x$.
Answer:
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Classifier: Contains metric units (m^2, m^3) which require conversion for US localization. Verifier: The text contains the metric units "m$^2$" and "m$^3$", which require conversion for US localization. |
sqn_01JYGGKNGQ3JYMPGEZ94P2VFGQ |
Localize | Units (simple) | Question
A box has length $10$ m, height $x$ m, and breadth $(x+3)$ m.
Write an expression for the volume.
Options:
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Question
A box has length $10$ ft, height $x$ ft, and width $(x+3)$ ft.
Write an expression for the volume.
Options:
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Classifier: Contains metric units (m, m^3) which require conversion for US localization. Verifier: The text contains the metric units "m" and "m$^3$", which require conversion for US localization. |
sqn_01JYGJEQQGMF3PT9WB7SZJZGJX |
Localize | Units (simple) | Question
A square garden is surrounded on three sides by fencing, with $60$ m of fencing used.
If each fenced side is of length $x$ metres, write an expression for the area $A$.
Answer:
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Question
A square garden is surrounded on three sides by fencing, with $60$ ft of fencing used.
If each fenced side is of length $x$ feet, write an expression for the area $A$.
Answer:
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Classifier: The text contains the AU spelling "metres" and metric units "m" and "m$^2$". Units conversion takes precedence. Verifier: The text contains the AU spelling "metres" and metric units "m" and "m$^2$". Units conversion takes precedence over spelling per rule 5. |
sqn_01JYGJ4EWXBFJEZ16H1YEVETWH |
Localize | Units (simple) | Question
A rectangular pen is enclosed by $240$ m of fencing. One side is $x$ metres long.
What is the expression for the area $A$ in terms of $x$?
Options:
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Question
A rectangular pen is enclosed by $240$ ft of fencing. One side is $x$ feet long.
What is the expression for the area $A$ in terms of $x$?
Options:
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Classifier: The text contains both the AU spelling "metres" and the metric units "m" and "m$^2$". Units conversion takes precedence over spelling. Verifier: The text contains the AU spelling "metres" and metric units "m" and "m$^2$". Units conversion takes precedence over spelling per rule 5. |
sqn_01JYGJNHBR5Q5KJSSQ0SVWVY09 |
Localize | Units (simple) | Question
A rectangular signboard has a width of $x$ metres and its height is twice the width.
Write an expression for the area.
Answer:
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Question
A rectangular signboard has a width of $x$ feet and its height is twice the width.
Write an expression for the area.
Answer:
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Classifier: The text contains the AU spelling "metres" and the metric unit "m$^2$". Units conversion takes precedence. Verifier: The text contains the AU spelling "metres" and the metric unit "m$^2$". Units conversion takes precedence over spelling per rule 5. |
sqn_01JYGJKHP6AQ075KCBQ7EAWKFZ |
Localize | Units (simple) | Question
A swimming pool is $30$ m long and $x$ m wide. The path around it is $2$ m wide.
Write the area of the path as an expression in simplest form, in terms of $x$.
Answer:
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Question
A swimming pool is $30$ ft long and $x$ ft wide. The path around it is $2$ ft wide.
Write the area of the path as an expression in simplest form, in terms of $x$.
Answer:
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Classifier: The text contains metric units "m" and "m$^2$". Any metric unit found anywhere in the text triggers this category. Verifier: The text contains metric units "m" and "m$^2$". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JZMX3TWTT5C7AT21GK2VNGW3 |
Localize | Spelling (AU-US) | Question
Factorise the following expression: $-x - 3$
Answer:
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Question
Factor the following expression: $-x - 3$
Answer:
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Classifier: The term "Factorise" uses the Australian/British 's' spelling. The US equivalent is "Factorize". Verifier: The word "Factorise" uses the Australian/British 's' spelling, which requires localization to "Factorize" for US English. |
sqn_01JZMX584QF3AN1P0S4E8DME4Z |
Localize | Spelling (AU-US) | Question
Factorise the following expression: $-4 - y$
Answer:
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Question
Factor the following expression: $-4 - y$
Answer:
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Classifier: The term "Factorise" uses the Australian/British 's' spelling. The US equivalent is "Factorize". Verifier: The word "Factorise" uses the Australian/British 's' spelling, which requires localization to "Factorize" for US English. |
sqn_01JYGJS2Z29C2ZKZDN7JEEQEQ1 |
Localize | Units (simple) | Question
A rectangular garden uses $300$ m of fencing for three sides.
If width is $x$, write an expression for the area.
Answer:
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Question
A rectangular garden uses $300$ ft of fencing for three sides.
If width is $x$, write an expression for the area.
Answer:
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Classifier: The text contains metric units "m" and "m$^2$". Verifier: The text contains metric units "m" and "m$^2$". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JYGKC5J1VXT449YW78PFWRYJ |
Localize | Units (simple) | Question
A farmer has $360$ m of fencing and wants to enclose a rectangle against a barn.
If one side is $x$, write an expression for the area.
Answer:
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Question
A farmer has $360$ ft of fencing and wants to enclose a rectangle against a barn.
If one side is $x$, write an expression for the area.
Answer:
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Classifier: The text contains the metric unit "m" in the context of a measurement ("360 m of fencing"). Verifier: The text contains the metric unit "m" (metres) used for a measurement ("360 m of fencing"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JYGK91RXR2RGABTCS9EFYRNW |
Localize | Units (simple) | Question
A rectangular banner is to be created with a perimeter of $200$ m.
If one side is $x$, write an expression for its area in terms of $x$.
Answer:
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Question
A rectangular banner is to be created with a perimeter of $200$ ft.
If one side is $x$, write an expression for its area in terms of $x$.
Answer:
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Classifier: The text contains metric units "m" and "m$^2$". Verifier: The text contains metric units "m" and "m$^2$". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_01JZMY9TG1XDVP86SWDQ6DSS0K |
Localize | Spelling (AU-US) | Question
Fully factorise the following expression:
$-6x^2 + 12x$
Answer:
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Question
Completely factor the following expression:
$-6x^2 + 12x$
Answer:
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Classifier: The term "factorise" uses the Australian/British 's' spelling. The US equivalent is "factorize". Verifier: The word "factorise" uses the Australian/British 's' spelling, which requires localization to "factorize" for US English. |
sqn_01JZMYBW1H1E7V02991WHWHRJR |
Localize | Spelling (AU-US) | Question
Fully factorise the following expression:
$-8xy + 4x$
Answer:
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Question
Fully factor the following expression:
$-8xy + 4x$
Answer:
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Classifier: The term "factorise" uses the Australian/British 's' spelling. The US equivalent is "factorize". Verifier: The word "factorise" uses the Australian/British 's' spelling, which requires localization to "factorize" for US English. |
sqn_01JZT37PSDBQBA5NCZDDTK673S |
Localize | Units (simple) | Question
Fill in the blank:
$2.1$ kL $+ 750$ L $=[?]$ L
Answer:
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Question
Fill in the blank:
$2.1$ gal $+ 750$ fl oz $=[?]$ fl oz
Answer:
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Classifier: The question involves arithmetic with metric units (kL and L). Verifier: The question involves arithmetic with metric units (kL and L). |
sqn_01JZT1XRQ6GHMJAJAM5Z2K3HHW |
Localize | Units (simple) | Question
Convert $2$ L into mL.
Answer:
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Question
Convert $2$ gal into fl oz.
Answer:
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Classifier: The question involves converting between metric units (L and mL), which requires localization to US customary units or a decision on metric pedagogy. Verifier: The question involves metric units (L and mL), which requires localization to US customary units or a decision on metric pedagogy. |
sqn_01JZT2C5SVFCQ0A6FM94CHNATE |
Localize | Units (simple) | Question
Convert $30$ L into mL.
Answer:
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Question
Convert $30$ gal into fl oz.
Answer:
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Classifier: The question involves converting between metric units (L and mL). Any metric unit usage requires localization under the provided rules. Verifier: The question requires conversion between metric units (L and mL). According to rule 3, any metric unit found requires at least RED.units_simple_conversion. |
sqn_01JZT358RM5BQRFN1EPEW9AYZJ |
Localize | Units (simple) | Question
Fill in the blank:
$0.003$ ML $+ 4.2$ kL $=[?]$ L
Answer:
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Question
Fill in the blank:
$0.003$ Mgal $+ 4.2$ kgal $=[?]$ gal
Answer:
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Classifier: The question involves arithmetic with multiple metric units (ML, kL, L). Verifier: The question involves arithmetic with multiple metric units (ML, kL, L). This is a simple conversion/addition task. |
sqn_01JZT39446AGHJ5GN9AWCV7SAH |
Localize | Units (simple) | Question
Fill in the blank:
$1.5$ ML $- \,\,950$ kL $=[?]$ L
Answer:
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Question
Fill in the blank:
$1.5$ Mgal $- \,\,950$ kgal $=[?]$ gal
Answer:
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Classifier: The question involves arithmetic with multiple metric units (ML, kL, L). Verifier: The question involves arithmetic with multiple metric units (ML, kL, L). |
sqn_01JZT2XD284R86DES8NGFJT59M |
Localize | Units (simple) | Question
Convert $0.65$ L into mL.
Answer:
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Question
Convert $0.65$ gal into fl oz.
Answer:
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Classifier: The question involves converting between metric units (L and mL). Verifier: The question involves metric units (L and mL), which requires localization. |
sqn_01K03VY7Q5Q0GWFTARJSXEJNW4 |
Localize | Units (simple) | Question
On a map, the scale is $1$ cm = $2$ km.
What distance does a $3$ cm line on the map represent?
Answer:
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Question
On a map, the scale is $1$ in = $2$ mi.
What distance does a $3$ in line on the map represent?
Answer:
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Classifier: The text contains metric units (cm, km). Verifier: The text contains metric units (cm, km) which require localization for a US audience. |
sqn_01JZT2KTHG97AT4C82QJ34K2AC |
Localize | Units (simple) | Question
Convert $3750$ mL into L.
Answer:
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Question
Convert $3750$ fl oz into gal.
Answer:
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Classifier: The question involves converting between metric units (mL and L). Verifier: The question involves metric units (mL and L), which requires localization. |
sqn_01JZT29BAXWPJ8MA70QY9KPCTP |
Localize | Units (simple) | Question
Convert $5$ L into mL.
Answer:
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Question
Convert $5$ gal into fl oz.
Answer:
|
Classifier: The question involves converting between metric units (L and mL), which requires localization. Verifier: The question involves metric units (L and mL), which requires localization. |
sqn_01JZT2W8XW44Z5CMBFXNXZ6YT4 |
Localize | Units (simple) | Question
Convert $4800$ L into kL.
Answer:
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Question
Convert $4800$ fl oz into gal.
Answer:
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Classifier: The question involves converting between metric units (L and kL). Verifier: The question involves metric units (L and kL), which requires localization. |
sqn_01JZT2GMFD2KA6NR4V0S7MT7HQ |
Localize | Units (simple) | Question
Convert $2.6$ L into mL.
Answer:
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Question
Convert $2.6$ gal into fl oz.
Answer:
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Classifier: The question involves converting between metric units (L and mL). Verifier: The question involves metric units (L and mL), which requires localization. |
sqn_01JZT2MVMHC0KF7ZGAB4HVXEV6 |
Localize | Units (simple) | Question
Convert $0.95$ kL into L.
Answer:
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Question
Convert $0.95$ gal into fl oz.
Answer:
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Classifier: The question involves converting between metric units (kL and L). Verifier: The question involves metric units (kL and L), which requires localization. |
sqn_01JZT25XGJX1B7ERGVM1E0BRX6 |
Localize | Units (simple) | Question
Convert $7000$ mL into L.
Answer:
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Question
Convert $7000$ fl oz into gal.
Answer:
|
Classifier: The question involves converting between metric units (mL and L), which requires localization. Verifier: The question involves metric units (mL and L), which requires localization. |
sqn_01K073T6HHS1SJMPY82CJDSQH4 |
Localize | Answer set | Question
In a trapezium, two adjacent angles on the same side measure $60^∘$ and $120^∘$.
What is the sum of the other two angles?
Answer:
|
Question
In a trapezoid, two adjacent angles on the same side measure $60^∘$ and $120^∘$.
What is the sum of the other two angles?
Answer:
|
Classifier: The term "trapezium" is used, which in the US is "trapezoid". This is a terminology change that often affects answer sets or definitions. Verifier: The term "trapezium" is used, which is the standard AU/UK term for what is called a "trapezoid" in the US. This is a terminology difference that requires localization. |
sqn_01K03VWBFW14G1RGGFJB0E66Q5 |
Localize | Units (simple) | Question
A map says $1$ cm represents $1$ km.
How many kilometres does $5$ cm on the map represent?
Answer:
|
Question
A map says $1$ in represents $1$ mi.
How many miles does $5$ in on the map represent?
Answer:
|
Classifier: The text contains metric units (cm, km) and the AU spelling "kilometres". Units take precedence over spelling. Verifier: The text contains metric units (cm, km) and the AU spelling "kilometres". Per rule 5, units conversion takes precedence over spelling. |
sqn_01K04E0BJ20RM8S2P2KZXCKQT4 |
Localize | Units (simple) | Question
Fill in the blank:
If the lengths of three sides of a kite are: $11$ m, $15$ m, and $11$ m, the length of the fourth side is $[?]$
Answer:
|
Question
Fill in the blank:
If the lengths of three sides of a kite are: $11$ ft, $15$ ft, and $11$ ft, the length of the fourth side is $[?]$
Answer:
|
Classifier: The text contains the metric unit "m" (metres) used as a unit of measure for the sides of a kite. Verifier: The text contains the metric unit "m" (metres) in the content and suffix, which requires localization. |
sqn_01K09EMTCQ9ZDBDJ3VG16ZMZP0 |
Localize | Spelling (AU-US) | Question
Fully factorise the following expression:
$-6xy - 2x$
Answer:
|
Question
Fully factor the following expression:
$-6xy - 2x$
Answer:
|
Classifier: Contains the AU spelling 'factorise', which must be localized to 'factorize' for a US audience. Verifier: The text contains the AU spelling "factorise", which requires localization to "factorize" for the US locale. |
sqn_01K08R740VNAFW1Q348JB2DC89 |
Localize | Units (simple) | Question
A rectangle has a diagonal of length $13$ cm and one side of length $5$ cm.
What is the length of the other diagonal?
Answer:
|
Question
A rectangle has a diagonal of length $13$ in and one side of length $5$ in.
What is the length of the other diagonal?
Answer:
|
Classifier: The text contains the metric unit "cm". Verifier: The text contains the metric unit "cm", which requires localization for the US market. |
sqn_01K0NSCBEGEFCJHJ29765QWQ3W |
Localize | Units (simple) | Question
Fill in the blank:
$4.5$ m$^2 = [?] $ cm$^2$
Answer:
|
Question
Fill in the blank:
$4.5$ ft$^2 = [?] $ in$^2$
Answer:
|
Classifier: The question contains metric units (m and cm) which require localization. Verifier: The question involves converting between metric units (m^2 to cm^2), which requires localization. |
sqn_01K0NS596FATVXVRWHK2ZEW8NG |
Localize | Units (simple) | Question
Fill in the blank:
$3$ m$^2 + 1500$ cm$^2 =[?]$ cm$^2$
Answer:
|
Question
Fill in the blank:
$3$ ft$^2 + 1500$ in$^2 =[?]$ in$^2$
Answer:
|
Classifier: The question contains metric units (m and cm) which require localization to US customary units or a policy-based decision on metric usage in US math. Verifier: The question contains metric units (m^2 and cm^2) which require localization to US customary units or a policy-based conversion. |
sqn_01K0X9T7XS6AEMQDRYX3MA9JBR |
Localize | Units (simple) | Question
Convert $2000000$ mm$^3$ to m$^3$.
Answer:
|
Question
Convert $2000000$ in$^3$ to ft$^3$.
Answer:
|
Classifier: The question requires conversion between metric units (mm^3 to m^3). Any presence of metric units requires localization to US customary units or a units-based classification. Verifier: The question involves metric units (mm^3 and m^3), which requires localization to US customary units. |
sqn_01K0X9W9G7FWKCKF0AS1DKZ88K |
Localize | Units (simple) | Question
Express $0.006$ cubic metres in cubic centimetres.
Answer:
|
Question
Express $0.006$ cubic feet in cubic inches.
Answer:
|
Classifier: The text contains both AU-specific spelling ("metres", "centimetres") and metric units ("cubic metres", "cubic centimetres", "cm$^3$"). Per the decision rules, any metric unit triggers a RED units category, and units conversion takes precedence over spelling. Verifier: The text contains metric units ("cubic metres", "cubic centimetres") and AU spelling ("metres", "centimetres"). Per rule 5, units conversion takes precedence over spelling. |
sqn_01K0XA9ETAJB7G9TTJCWXDMM9J |
Localize | Units (simple) | Question
Convert $0.075$ cm$^3$ to mm$^3$.
Answer:
|
Question
Convert $0.075$ ft$^3$ to in$^3$.
Answer:
|
Classifier: The text contains metric units (cm$^3$ and mm$^3$). Verifier: The text contains metric units (cm$^3$ and mm$^3$). |
sqn_01K0XA42GJ8VVKF3A5WZDW89EH |
Localize | Units (simple) | Question
Convert $0.004$ m$^3$ to mm$^3$.
Answer:
|
Question
Convert $0.004$ ft$^3$ to in$^3$.
Answer:
|
Classifier: The text contains metric units (m$^3$ and mm$^3$). Any metric unit found anywhere in the text requires localization to US customary units or at least classification as a units conversion task. Verifier: The text contains metric units (m$^3$ and mm$^3$). Per rule 3, any metric unit requires a RED units classification. |
sqn_01K0XA7R3F8JQZYZZE3GE12VM3 |
Localize | Units (simple) | Question
Convert $0.002$ km$^3$ to m$^3$.
Answer:
|
Question
Convert $0.002$ mi$^3$ to ft$^3$.
Answer:
|
Classifier: The text contains metric units (km$^3$ and m$^3$). Verifier: The text contains metric units (km$^3$ and m$^3$). |
sqn_01K5ZDQKKG0C4FH0Y7QY3R8BJM |
Localize | Cultural refs | Question
Why can one number sentence become many different word problems?
Answer:
|
Question
Why can one number sentence become many different word problems?
Answer:
|
Classifier: The term "lollies" is a distinct Australian/Commonwealth term for candy. In a US context, this should be localized to "candy" or "sweets". Verifier: The term "lollies" is a specific Australian/Commonwealth term for candy/sweets and requires localization for a US audience. |
sqn_01K4XXVQE54A66VFWGP78M2X2F |
Localize | Spelling (AU-US) | Question
If two chords are equal in length, why are they equally distant from the centre?
Answer:
|
Question
If two chords are equal in length, why are they equally distant from the center?
Answer:
|
Classifier: The text contains the AU spelling "centre" multiple times, which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre" in both the question and the answer, which requires localization to "center". |
sqn_01K6EJ4Z0CJXCSZMDZNZCEFCSS |
Localize | Spelling (AU-US) | Question
Why do we sometimes take out a negative number when factorising an expression?
Answer:
|
Question
Why do we sometimes take out a negative number when factoring an expression?
Answer:
|
Classifier: Contains the AU spelling "factorising", which needs to be converted to "factorizing" for a US audience. Note: "brackets" is common in AU but also understood in US, however, the spelling change is the primary driver here. Verifier: Contains the AU spelling "factorising", which requires localization to "factorizing". |
sqn_01K6EHP3PH0K9FP2EWZJT6CC4B |
Localize | Spelling (AU-US) | Question
How do you know that $-(x - 3)$ is the correct factorisation of $-x + 3$?
Answer:
|
Question
How do you know that $-(x - 3)$ is the correct factoring of $-x + 3$?
Answer:
|
Classifier: Contains the AU spelling "factorisation", which needs to be converted to "factorization" for a US audience. Verifier: Contains the AU spelling "factorisation", which requires localization to "factorization". |
sqn_01K0XE8CK7KHCNK2KTKQM39Y3S |
Localize | Units (simple) | Question
Fill in the blank:
$0.4$ m$^3 + \ 600\ 000$ cm$^3− \ 800\ 000\ 000$ mm$^3 = [?] $ m$^3$
Answer:
|
Question
Fill in the blank:
$0.4$ ft$^3 + \ 600\ 000$ in$^3− \ 800\ 000\ 000$ in$^3 = [?] $ ft$^3$
Answer:
|
Classifier: The text contains multiple metric units (m$^3$, cm$^3$, mm$^3$) in a calculation context. Verifier: The text contains multiple metric units (m$^3$, cm$^3$, mm$^3$). |
sqn_01K6EHTBAA5KTDC6HZQV17JF8Y |
Localize | Spelling (AU-US) | Question
A student factorises $-6x - 12$ as $-(6x - 12)$.
How would you explain why this is incorrect?
Answer:
|
Question
A student factors $-6x - 12$ as $-(6x - 12)$.
How would you explain why this is incorrect?
Answer:
|
Classifier: Contains the AU spelling "factorises", which needs to be converted to "factorizes" for a US audience. Verifier: Contains the AU spelling "factorises", which requires localization to "factorizes". |
sqn_01K0XEJFH59CNXQAKZXDK1RTV8 |
Localize | Units (simple) | Question
Fill in the blank:
$0.0003$ km$^3 +\ 450$ m$^3 -\ 75\ 000\ 000$ cm$^3 = [?]$ m$^3$
Answer:
|
Question
Fill in the blank:
$0.0003$ mi$^3 +\ 450$ ft$^3 -\ 75\ 000\ 000$ in$^3 = [?]$ ft$^3$
Answer:
|
Classifier: The text contains multiple metric units (km$^3$, m$^3$, cm$^3$). Verifier: The text contains multiple metric units (km$^3$, m$^3$, cm$^3$). |
sqn_01K0XE2VEF91BQ5HYNH553250E |
Localize | Units (simple) | Question
Let $A = 1000a^3$ mm$^3$ and $B = 0.001$ m$^3$.
If $A = B$, find the value of $a$.
Answer:
|
Question
Let $A = 1000a^3$ in$^3$ and $B = 0.001$ ft$^3$.
If $A = B$, find the value of $a$.
Answer:
|
Classifier: The text contains metric units (mm$^3$ and m$^3$). Even though it is an algebraic problem, the units are explicitly stated as metric. Verifier: The text contains metric units (mm$^3$ and m$^3$). Although it is an algebraic problem, the units are explicitly metric and require conversion/localization. |
sqn_01K6EP2PDWXHNZ9C042TMDRJVE |
Localize | Terminology | Question
How do you know that the lines $y = 3x - 7$ and $y = -\tfrac{1}{3}x + 2$ are perpendicular?
Answer:
|
Question
How do you know that the lines $y = 3x - 7$ and $y = -\tfrac{1}{3}x + 2$ are perpendicular?
Answer:
|
Classifier: The text uses the term "gradient", which is the standard AU term for what is referred to as "slope" in US school mathematics. Verifier: The answer text uses "gradient", which is the standard AU school term for "slope" in the US. |
sqn_01K6FG3MTF5Q4XAT786X9XJ5VG |
Localize | Cultural refs | Question
Why is GST described as a percentage tax instead of a fixed amount added to every item?
Answer:
|
Question
Why is sales tax described as a percentage tax instead of a fixed amount added to every item?
Answer:
|
Classifier: The term "GST" (Goods and Services Tax) is the specific name for the value-added tax in Australia. In a US context, this is typically referred to as "sales tax". While the mathematical concept of a percentage tax is universal, the specific acronym "GST" is a distinct cultural/regulatory reference. Verifier: The term "GST" (Goods and Services Tax) is a specific Australian tax term. In the US, "sales tax" is used. This is a distinct cultural/regulatory reference. |
sqn_01K6FG7AFVHACC4N02HF49SHKZ |
Localize | Cultural refs | Question
Why is it important to know whether a price is including GST or excluding GST?
Answer:
|
Question
Why is it important to know whether a price is including sales tax or excluding sales tax?
Answer:
|
Classifier: Contains "GST", which is the Australian tax system. Additionally, the concept of prices "including GST" or "excluding GST" is specific to VAT/GST systems; in the US, sales tax is almost exclusively added at checkout and not included in the sticker price. Verifier: Uses "GST" and refers to the practice of prices being inclusive or exclusive of tax, which is a specific feature of the Australian tax system compared to the US sales tax system. |
sqn_01K6FG9S51S659MTDBPKS83XDY |
Localize | Cultural refs | Question
Why is GST considered a fairer tax than charging everyone the same flat fee?
Answer:
|
Question
Why is sales tax considered a fairer tax than charging everyone the same flat fee?
Answer:
|
Classifier: Uses "GST", a specific Australian tax term. Verifier: Uses "GST", which is the specific name for the value-added tax in Australia. |
sqn_01K6H1KX9AZST1RKNMG8SD77RH |
Localize | Cultural refs | Question
If GST is $10\%$, how do you know that multiplying a price by $1.1$ gives the price including GST?
Answer:
|
Question
If sales tax is $10\%$, how do you know that multiplying a price by $1.1$ gives the price including sales tax?
Answer:
|
Classifier: Uses "GST" and refers to a 10% rate, which is the standard Australian GST rate. In the US, sales tax rates vary by state and are rarely exactly 10% across the board. Verifier: Uses "GST" and the specific 10% rate which is the standard rate in Australia. |
sqn_01K6H2DTFE8QCWXKKNTAH04ZVX |
Localize | Cultural refs | Question
A business sells an item for $\$220$ including GST.
Why do you divide the price by $1.1$ to get the price before GST?
Answer:
|
Question
A business sells an item for $\220$ including sales tax.
Why do you divide the price by $1.1$ to get the price before sales tax?
Answer:
|
Classifier: Uses "GST" and the concept of tax-inclusive pricing, which is standard in Australia but not the US. Verifier: Uses "GST" and the concept of tax-inclusive pricing (and the 1.1 multiplier derived from the 10% AU rate). |
sqn_01K6KNZX03ZS5TS3MVF75SSMF2 |
Localize | Terminology | Question
Why can sine and cosine be defined using the unit circle and not just right-angled triangles?
Answer:
|
Question
Why can sine and cosine be defined using the unit circle and not just right triangles?
Answer:
|
Classifier: Contains the AU-specific term "right-angled triangles", which should be localized to "right triangles" in a US school context. Verifier: The question uses "right-angled triangles", which is the standard AU term, whereas "right triangles" is the standard US school context term. |
sqn_01K76D3B7AKSDD7PSDM689JSKA |
Localize | Terminology | Question
The highest score on a maths test is $95$ and the lowest is $60$.
What is the range?
Answer:
|
Question
The highest score on a math test is $95$ and the lowest is $60$.
What is the range?
Answer:
|
Classifier: The term "maths" is the standard Australian/British abbreviation for mathematics, whereas the US equivalent is "math". Verifier: The term "maths" is the standard Australian/British term for the US "math". This is a terminology difference in a school context. |
sqn_01K6KWE4H2G71GCK57E3B90Q2P |
Localize | Units (simple) | Question
Why does multiplying litres by $1000$ always give the number of millilitres?
Answer:
|
Question
Why does multiplying gallons by $128$ always give the number of fluid ounces?
Answer:
|
Classifier: The text contains metric units (litres, millilitres) and AU-specific spelling ("litres"). Units conversion takes precedence over spelling. Verifier: The text contains metric units (litres, millilitres) and AU spelling ("litres"). Units conversion takes precedence over spelling. |
sqn_01K6VPF64K1A13RPBCXXQ6BWJ7 |
Localize | Terminology | Question
Why does $(h, k)$ show the turning point in the equation $y = a(x - h)^4 + k$?
Answer:
|
Question
Why does $(h, k)$ show the vertex in the equation $y = a(x - h)^4 + k$?
Answer:
|
Classifier: Uses "turning point", which requires localization to "vertex" for US audiences. Verifier: Uses "turning point", which is the standard AU term for "vertex". |
sqn_01K6VPDAD8JQK5R9KK2GVHVWBC |
Localize | Terminology | Question
How do you know the turning point of $y = x^4 + 5$ is at $(0, 5)$?
Answer:
|
Question
How do you know the vertex of $y = x^4 + 5$ is at $(0, 5)$?
Answer:
|
Classifier: The term "turning point" is standard Australian/UK terminology for what is referred to as the "vertex" in US curriculum contexts, especially regarding parabolas and higher-order polynomials. Verifier: The term "turning point" is the standard Australian curriculum term for what is called the "vertex" in the US. This requires localization for the US market. |
sqn_01K6MGD83YFZGAQJRR7VJ2WZEV |
Localize | Spelling (AU-US) | Question
In $y = \dfrac{a}{x-h} + k$, why is $(h,k)$ the centre of the hyperbola?
Answer:
|
Question
In $y = \dfrac{a}{x-h} + k$, why is $(h,k)$ the center of the hyperbola?
Answer:
|
Classifier: The text contains the AU spelling "centre" which needs to be localized to the US spelling "center". Verifier: The text contains "centre", which is the AU spelling of the US "center". |
sqn_01K9BVSGC7NSSXQ5NDJBHHYES1 |
Localize | Terminology | Question
Find the exact value of the expression $\sin(\cos^{-1}(\frac{5}{13}))$ in a right-angled triangle.
Answer:
|
Question
Find the exact value of the expression $\sin(\cos^{-1}(\frac{5}{13}))$ in a right triangle.
Answer:
|
Classifier: The text contains the term "right-angled triangle", which is the standard AU/UK term. The US equivalent is "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK terminology; the US equivalent is "right triangle". |
sqn_01K9C6XNTRWKGWZKNHPXNKAQ8Q |
Localize | Units (simple) | Question
A sample of a radioactive isotope decays by $15\%$ each hour.
After $6$ hours, its mass is $18.2$ g. Find the initial mass of the isotope.
Answer:
|
Question
A sample of a radioactive isotope decays by $15\%$ each hour.
After $6$ hours, its mass is $18.2$ oz. Find the initial mass of the isotope.
Answer:
|
Classifier: The text contains the metric unit 'g' (grams) for mass, which requires localization to US customary units or review for metric-pedagogy context. Verifier: The text contains the metric unit 'g' (grams), which requires localization to US customary units (e.g., ounces) or review. It is a simple numeric value, not a complex equation involving metric coefficients. |
sqn_01K8QQ0HNQV287CYVDVY8496HW |
Localize | Spelling (AU-US) | Question
Factorise $4x^3 - 8x^2y + 5xy^2 - 10y^3$
Answer:
|
Question
Factor $4x^3 - 8x^2y + 5xy^2 - 10y^3$
Answer:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling. In US English, this must be localized to "Factorize". Verifier: The text contains "Factorise", which is the AU/UK spelling. US English requires "Factorize". |
sqn_01K6VPAW4YCX5VGQWVVP6BT5WD |
Localize | Terminology | Question
How do you know the turning point of $y = (x - 2)^4 + 3$ is at $(2, 3)$?
Answer:
|
Question
How do you know the vertex of $y = (x - 2)^4 + 3$ is at $(2, 3)$?
Answer:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola or higher-degree polynomial. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is typically called the "vertex" in US school mathematics. This requires localization for the US market. |
sqn_01K6KWGMET0GCH2V3WN3V9GENP |
Localize | Units (simple) | Question
Why does converting from a smaller unit (like mL) to a larger unit (like L) make the number smaller, even though the amount of liquid hasn’t changed?
Answer:
|
Question
Why does converting from a smaller unit (like fl oz) to a larger unit (like gal) make the number smaller, even though the amount of liquid hasn’t changed?
Answer:
|
Classifier: The text contains metric units (mL, L, Litres) and AU-specific spelling ("Litres"). Units conversion takes precedence over spelling. Verifier: The text contains metric units (mL, L, Litres) and AU spelling ("Litres"). Units conversion takes precedence over spelling. |
sqn_01K6VPGE4XB4RHKQYGX21EJ5YD |
Localize | Terminology | Question
Why does changing $h$ or $k$ in $y = a(x - h)^4 + k$ move the turning point but not change the shape of the graph?
Answer:
|
Question
Why does changing $h$ or $k$ in $y = a(x - h)^4 + k$ move the vertex but not change the shape of the graph?
Answer:
|
Classifier: Uses "turning point", which is the AU term for "vertex". Verifier: Uses "turning point", which is the standard AU term for "vertex". |
sqn_01K73AZTQXRJC18764FMQ66DE2 |
Localize | Units (simple) | Question
A $200$ g sample of a radioactive substance decays according to $m = 200(0.5)^{\frac{t}{10}}$, where $t$ is measured in years.
Find the mass after $10$ years.
Answer:
|
Question
A $200$ oz sample of a radioactive substance decays according to $m = 200(0.5)^{\frac{t}{10}}$, where $t$ is measured in years.
Find the mass after $10$ years.
Answer:
|
Classifier: The text contains metric units ("g" for grams and the word "grams" in the suffix), which requires localization to US customary units or a decision on metric usage in US science contexts. Per decision rules, any metric unit found anywhere triggers a RED units category. Verifier: The question contains the metric unit "g" and "grams". According to the decision rules, any metric unit requires a RED classification. This is a simple numeric substitution into a formula, so simple_conversion is appropriate. |
sqn_01K6V9DYFJ1EZ59QWWY0ZY9HTK |
Localize | Units (simple) | Question
The height of a ball is given by $h = -5t^2 + 20t$.
How do you know that the highest point the ball can reach is $20$ metres?
Answer:
|
Question
The height of a ball is given by $h = -5t^2 + 20t$.
How do you know that the highest point the ball can reach is $20$ feet?
Answer:
|
Classifier: The text contains the metric unit "metres" and the AU-specific spelling of that unit. Per decision rules, any metric unit requires classification into a units category. Verifier: The text contains the metric unit "metres", which is both a metric unit and an AU-specific spelling. Per rule 3 and 4, this requires RED classification. Since it is a single value in a simple context, simple_conversion is correct. |
sqn_01K73DY8HMETPN8HPHE3VMMJBJ |
Localize | Units (simple) | Question
A medicine’s concentration in the bloodstream decreases according to $C = 40(0.85)^t$, where $C$ is measured in mg/L and $t$ is measured in hours. After how many hours will the concentration first drop below $10$ mg/L?
Answer:
|
Question
A medicine’s concentration in the bloodstream decreases according to $C = 40(0.85)^t$, where $C$ is measured in mg/gal and $t$ is measured in hours. After how many hours will the concentration first drop below $10$ mg/gal?
Answer:
|
Classifier: The text contains the metric unit 'mg/L' (milligrams per litre). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category. Verifier: The text contains the metric unit 'mg/L' (milligrams per litre). Per rule 3, any metric unit requires a RED classification. Since it involves a simple threshold check in a formula, simple_conversion is appropriate. |
sqn_01K6MJ2XZ6WT398A67HBY2HWKT |
Localize | Terminology | Question
Why do we use the turning point of the quadratic to find the maximum area or volume?
Answer:
|
Question
Why do we use the vertex of the quadratic to find the maximum area or volume?
Answer:
|
Classifier: The term "turning point" is standard AU school terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard AU school term for what is typically called the "vertex" in US mathematics curriculum. |
sqn_01K6KWAPKSTB4CH33DB4Q7D5CQ |
Localize | Units (simple) | Question
How do you know that $2000$ mL is the same as $2$ L?
Answer:
|
Question
How do you know that $2000$ fl oz is the same as $2$ gal?
Answer:
|
Classifier: The text contains metric units (mL, L) which require localization to US customary units or a US-centric metric context. Per rule 1, any metric unit disqualifies the GREEN category. Verifier: The text contains metric units (mL, L) which require localization for a US audience. Per rule 3, any metric unit requires at least RED classification. |
sqn_01KH7JYESJT7YFV4VJ2JERGEVE |
Localize | Units (simple) | Question
Why does converting from kilometres per hour to metres per second change the value but not the speed?
Answer:
|
Question
Why does converting from miles per hour to feet per second change the value but not the speed?
Answer:
|
Classifier: The text contains metric units (kilometres, metres) and AU-specific spelling (kilometres, metres). Per the decision rules, any metric unit requires classification into a units category, and units conversion takes precedence over spelling. Verifier: The text contains metric units ("kilometres", "metres") and AU-specific spellings of those units. Per rule 5, units conversion takes precedence over spelling. |
sqn_01KJECSGJSWVYF4244EASH7JEK |
Localize | Spelling (AU-US) | Question
Explain how to find $P(A \cap B \cap C)$ from a triple Venn diagram using set notation.
Answer:
|
Question
Explain how to find $P(A \cap B \cap C)$ from a triple Venn diagram using set notation.
Answer:
|
Classifier: The answer content contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The answer contains the AU spelling "centre", which requires localization to "center" for the US. |
sqn_01KHSYMC19C9EH2G9ZZQF55TFJ |
Localize | Units (simple) | Question
The height of a plant is $4.21$ m.
How do you know that, rounded to one decimal place, it is $4.2$ m?
Answer:
|
Question
The height of a plant is $4.21$ ft.
How do you know that, rounded to one decimal place, it is $4.2$ ft?
Answer:
|
Classifier: Contains the metric unit "m" (metres) in the context of a measurement. Verifier: The text contains the metric unit "m" (metres) in a measurement context, requiring conversion to US customary units. |
sqn_01KHA6VZKVH68MGYJ8W4240NQR |
Localize | Units (simple) | Question
The intensity $I$ of light varies inversely with the square of the distance $d$.
When the distance is $2.4$ m, the intensity is $62.5$ units.
Find the intensity when the distance is $3.6$ m.
Answer:
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Question
The intensity $I$ of light varies inversely with the square of the distance $d$.
When the distance is $2.4$ ft, the intensity is $62.5$ units.
Find the intensity when the distance is $3.6$ ft.
Answer:
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Classifier: The text contains the metric unit "m" (metres) in the context of distance. Per the decision rules, any metric unit requires localization. Verifier: The text contains the metric unit "m" (metres) in the context of distance, which requires localization. |
sqn_01KHA6SG4JR5FQGS7DFNHZAC9W |
Localize | Units (simple) | Question
The pressure $P$ (kPa) of a gas varies inversely with its volume $V$ (L).
When the volume is $12.5$ L, the pressure is $28.8$ kPa.
What is the pressure when the volume is $7.2$ L?
Answer:
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Question
The pressure $P$ (psi) of a gas varies inversely with its volume $V$ (gal).
When the volume is $12.5$ gal, the pressure is $28.8$ psi.
What is the pressure when the volume is $7.2$ gal?
Answer:
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Classifier: The question contains metric units: kPa (kilopascals) and L (litres). Any metric unit found anywhere in the text triggers a RED.units category. Verifier: The question contains metric units "kPa" (kilopascals) and "L" (litres), which require localization for a US audience. |
sqn_01KHA72R12XFV41XW3A7V8H8EW |
Localize | Units (simple) | Question
The speed $v$ (km/h) of a truck travelling a fixed distance varies inversely with the time $t$ (hours).
When the time is $2.5$ hours, the speed is $96$ km/h.
What is the speed when the time is $3.75$ hours?
Answer:
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Question
The speed $v$ (mph) of a truck traveling a fixed distance varies inversely with the time $t$ (hours).
When the time is $2.5$ hours, the speed is $96$ mph.
What is the speed when the time is $3.75$ hours?
Answer:
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Classifier: The text contains metric units (km/h, km) which require conversion to US customary units (mph, miles) for localization. Verifier: The question uses metric units "km/h" and "km" which require conversion to US customary units (mph/miles). The math is a simple inverse variation, making it a simple conversion. |
sqn_01KHSFEBM29W0VAKNJYJFK1XRV |
Localize | Units (simple) | Question
One beam is $2 \dfrac{3}{5}$ metres long.
What is the total length of $9$ beams?
Options:
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Question
One beam is $2 \dfrac{3}{5}$ feet long.
What is the total length of $9$ beams?
Options:
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Classifier: Contains both AU-specific spelling ("metres") and metric units ("m"). Units conversion takes precedence over spelling. Verifier: Contains AU spelling "metres" and metric unit "m". Per rule 5, units conversion takes precedence over spelling. |
sqn_1bc32ae5-81c0-4dba-aaff-0a753ffd790b |
Localize | Units (simple) | Question
Why is $1$ milligram smaller than $1$ gram?
Answer:
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Question
Why is $1$ ounce smaller than $1$ pound?
Answer:
|
Classifier: The text contains metric units ("milligram", "gram"). According to the decision rules, any metric unit found anywhere in the text requires at least RED.units_simple_conversion. Verifier: The text contains metric units ("milligram", "gram"). According to rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_116ef662-3e36-4055-ab5d-37b6717fa192 |
Localize | Spelling (AU-US) | Question
Travis writes $532$ as “five hundred and twenty-three.” How do you know he is wrong?
Answer:
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Question
Travis writes $532$ as “five hundred twenty-three.” How do you know he is wrong?
Answer:
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Classifier: The source text uses the AU/UK convention of including "and" in number names (e.g., "five hundred and twenty-three"). While the answer correctly identifies the US-preferred "five hundred thirty-two", the source value in the question contains the AU-style string that may need adjustment depending on strictness, but more importantly, the answer uses "tens digit" and "ones digit" which are neutral, but the presence of the "and" in the number name string is a dialect marker. Verifier: The source text includes the AU/UK convention of using "and" in number names ("five hundred and twenty-three"), which is a dialect marker requiring localization for US English. |
sqn_0cbfe5dc-4315-49cf-8116-50f5d054e97e |
Localize | Spelling (AU-US) | Question
A student names $121$ as “hundred and twenty-one.” How do you know they are wrong?
Hint: Check number word order
Answer:
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Question
A student names $121$ as “one hundred twenty-one.” How do you know they are wrong?
Hint: Check number word order
Answer:
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Classifier: The text uses "hundred and twenty-one". In US English pedagogy, the use of "and" in whole numbers is strictly discouraged (reserved for the decimal point), whereas it is standard in AU/UK English. Localizing this involves removing the "and" to align with US number-naming conventions. Verifier: The use of "and" in whole numbers (e.g., "hundred and twenty-one") is a distinct feature of AU/UK English pedagogy that is explicitly taught as incorrect in US English (where "and" is reserved for the decimal point). This requires localization. |
sqn_01KHA770NPX6SDVPEXJQMVBJ7G |
Localize | Units (simple) | Question
The density $D$ of a metal block varies inversely with its volume $V$ when mass is fixed.
When the volume is $4.8$ cm$^3$, the density is $15$ g/cm$^3$.
Find the density when the volume is $6.4$ cm$^3$.
Answer:
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Question
The density $D$ of a metal block varies inversely with its volume $V$ when mass is fixed.
When the volume is $4.8$ in$^3$, the density is $15$ lb/in$^3$.
Find the density when the volume is $6.4$ in$^3$.
Answer:
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Classifier: The text contains metric units (cm^3, g/cm^3) which require localization. Verifier: The question uses metric units "cm^3" and "g/cm^3" which require conversion to US customary units. |
sqn_0b8a42ee-135b-4626-8729-b648fc2238fa |
Localize | Units (simple) | Question
Show why scaling a pentagon with side length $5$ cm by a factor of $3.5$ results in sides of $17.5$ cm.
Answer:
|
Question
Show why scaling a pentagon with side length $5$ in by a factor of $3.5$ results in sides of $17.5$ in.
Answer:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires conversion for US localization. Verifier: The text contains the metric unit "cm", which requires conversion for US localization. |
sqn_2146ea52-f3ad-47cb-bcbd-aaf49e188ec7 |
Localize | Units (simple) | Question
How do you know that the length of a rectangle with area $32$ cm$^2$ and width $4$ cm will be twice the width?
Answer:
|
Question
How do you know that the length of a rectangle with area $32$ in$^2$ and width $4$ in will be twice the width?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2"), which triggers a mandatory RED classification for US localization. Verifier: The text contains metric units ("cm" and "cm^2"), which requires conversion for US localization. |
sqn_1b24395a-8bd8-46e8-9a43-413b9382bb14 |
Localize | Units (simple) | Question
How do you know millilitres is not an imperial unit of volume?
Hint: mL is metric, not imperial
Answer:
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Question
How do you know milliliters is not a US customary unit of volume?
Hint: mL is metric, not US customary
Answer:
|
Classifier: The text contains metric units ("millilitres", "litre", "mL") and AU-specific spelling ("millilitres", "litre"). Per rule 1 and 9, any metric unit triggers a RED classification. This specific question is about the nature of the units themselves, but still requires localization of spelling and potentially the pedagogical context. Verifier: The text contains metric units ("millilitres", "litre", "mL") and AU spelling ("millilitres", "litre"). Even though the question is about the units themselves, rule 1 and 3 require RED classification for any metric units. |
sqn_10b13f00-5702-4ebf-ac2e-71e34f8d20a6 |
Localize | Units (simple) | Question
How do you know that millilitres is an appropriate unit to measure the volume of a spoonful of sugar syrup?
Hint: $1$ mL equals $1$ cm$^3$
Answer:
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Question
How do you know that fluid ounces is an appropriate unit to measure the volume of a spoonful of sugar syrup?
Hint: $1$ fl oz equals $1$ in$^3$
Answer:
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Classifier: The text contains metric units (millilitres, mL, cm^3). While the spelling "millilitres" is also an AU spelling, the presence of metric units for volume measurement in a primary context triggers the units classification. Verifier: The text contains metric units (millilitres, mL, cm^3) which require localization for a US audience. |
sqn_117cbb75-00df-49e3-b166-ef9d490df3d7 |
Localize | Units (simple) | Question
Why is $3500$ centimetres not the same as $35000$ micrometres?
Answer:
|
Question
Why is $3500$ inches not the same as $35000$ microinches?
Answer:
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Classifier: The text contains multiple metric units (centimetres, micrometres, millimetres). These require localization/conversion for a US audience. Verifier: The text contains multiple metric units (centimetres, micrometres, millimetres) which require conversion/localization. |
sqn_1c023ce5-026d-48f3-a4fd-c37b120ac193 |
Localize | Units (simple) | Question
Show why the volume of a $2$ cm $\times$ $2$ cm $\times$ $8$ cm prism is the same as the volume of two $2$ cm $\times$ $2$ cm $\times$ $4$ cm prisms.
Answer:
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Question
Show why the volume of a $2$ in $\times$ $2$ in $\times$ $8$ in prism is the same as the volume of two $2$ in $\times$ $2$ in $\times$ $4$ in prisms.
Answer:
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Classifier: The text contains the metric unit "cm". Per the decision rules, any metric unit requires localization. This is a simple conversion of dimensions and volume. Verifier: The text contains the metric unit "cm". Per rule 3, any metric unit requires localization. This is a simple conversion of dimensions. |
sqn_1fa33ec3-6f04-4986-b73c-f9b24f95bf95 |
Localize | Spelling (AU-US) | Question
Explain how factorising $x^2+8x+15=0$ by grouping confirms the factors are $(x+3)(x+5)$.
Hint: Think about grouping strategy
Answer:
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Question
Explain how factoring $x^2+8x+15=0$ by grouping confirms the factors are $(x+3)(x+5)$.
Hint: Think about grouping strategy
Answer:
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Classifier: The text contains the Australian spelling "factorising" and "factorise", which needs to be converted to the US spelling "factorizing" and "factorize". Verifier: The text contains "factorising" and "factorise", which are AU/UK spellings. US spelling is "factorizing" and "factorize". |
sqn_283e72af-55d9-4742-b286-113acc6de8d2 |
Localize | Terminology | Question
How do you know $\sqrt[3]{x^9}$ is equivalent to $x^3$?
Hint: Simplify index notation
Answer:
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Question
How do you know $\sqrt[3]{x^9}$ is equivalent to $x^3$?
Hint: Simplify exponent notation
Answer:
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Classifier: The text uses the term "index notation" and "fractional index". In US curriculum, "exponent" or "power" is the standard term, and "index" is typically reserved for the root degree or position in a sequence/matrix. "Index notation" is a specific AU/UK curriculum term. Verifier: The terms "index notation" and "fractional index" are specific to AU/UK/Commonwealth curricula. In the US, "exponent" or "power" is the standard term for this context. |
sqn_39071844-9fd0-4042-bbca-3741210aa603 |
Localize | Spelling (AU-US) | Question
Explain why scatterplots are not used for categorical data.
Answer:
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Question
Explain why scatter plots are not used for categorical data.
Answer:
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Classifier: The answer content contains the AU spelling "colours", which needs to be converted to the US spelling "colors". Verifier: The answer contains the AU spelling "colours", which requires localization to "colors". |
sqn_25abc5b8-d01b-437b-8244-3e84c50021d4 |
Localize | Terminology | Question
Show that the gradient of a line is the same no matter which two points you use on the line.
Answer:
|
Question
Show that the slope of a line is the same no matter which two points you use on the line.
Answer:
|
Classifier: The text uses the term "gradient" to refer to the steepness of a line. In US school mathematics, "slope" is the standard term used in this context. While "gradient" is used in US higher-level calculus (vector fields), for coordinate geometry of lines, "slope" is the required localization. The answer also uses "gradient" and "slope" interchangeably, but the primary AU term "gradient" triggers the classification. Verifier: The term "gradient" is the standard AU term for the steepness of a line in coordinate geometry, whereas "slope" is the standard US term for this school-level context. |
sqn_3096373b-9cc8-41e6-954f-11fc86a7c355 |
Localize | Units (simple) | Question
How do you know that halving the diameter halves the circumference?
Use an example to explain.
Answer:
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Question
How do you know that halving the diameter halves the circumference?
Use an example to explain.
Answer:
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Classifier: The answer contains the metric unit "cm", which requires localization to US customary units or a unitless context per the decision rules. Verifier: The answer text contains the metric unit "cm", which requires localization to US customary units or a unitless context. |
sqn_31a420ff-9e2e-4ddf-9d6b-908c6cb71ea7 |
Localize | Terminology | Question
How do you know that the turning point of the parabola $y=(x-3)(x+4)-3$ is the same as that of $y=(x-3)(x+4)+7$?
Answer:
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Question
How do you know that the vertex of the parabola $y=(x-3)(x+4)-3$ is the same as that of $y=(x-3)(x+4)+7$?
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard AU/UK term for what is referred to as the "vertex" in US mathematics curriculum. |
sqn_2ffdd8af-7220-4b41-80c2-aba73c498572 |
Localize | Units (simple) | Question
How is changing $1$ m$^2$ into cm$^2$ different from changing $1$ m into cm?
Answer:
|
Question
How is changing $1$ ft$^2$ into in$^2$ different from changing $1$ ft into in?
Answer:
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Classifier: The question explicitly uses and compares metric units (m, cm, m^2, cm^2). According to the decision rules, any metric unit requires classification into a units category. This is a simple conversion/conceptual check. Verifier: The question explicitly uses metric units (m, cm, m^2, cm^2). Per rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_3c10cade-aafe-43b6-ace6-824c0092e3bb |
Localize | Answer set | Question
How do you know that doubling the height doubles the area of a trapezium?
Answer:
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Question
How do you know that doubling the height doubles the area of a trapezoid?
Answer:
|
Classifier: The text uses the term "trapezium". In the US, this shape is called a "trapezoid". This requires localization for terminology consistency. Verifier: The term "trapezium" is used, which is the standard term in Australia/UK, whereas "trapezoid" is used in the US. This requires localization for terminology consistency. |
sqn_42dbe4f4-0253-4af9-a8d8-55c45dab30d7 |
Localize | Terminology | Question
Explain why $y=x^2+2$ has its turning point at $(0,2)$.
Answer:
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Question
Explain why $y=x^2+2$ has its vertex at $(0,2)$.
Answer:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Additionally, "turning-point form" is used, which maps to "vertex form" in the US. Verifier: The classifier correctly identified "turning point" and "turning-point form" as AU/UK terminology. In the US, "vertex" and "vertex form" are the standard terms used in this context. |
sqn_4ca702a6-444d-4877-bd3d-313b95c20754 |
Localize | Units (simple) | Question
How do you know a kite with diagonals $10$ cm and $4$ cm has an area of $20$ cm$^2$?
Answer:
|
Question
How do you know a kite with diagonals $10$ in and $4$ in has an area of $20$ in$^2$?
Answer:
|
Classifier: The text contains metric units ("cm" and "cm^2") which require conversion for US localization. Verifier: Contains metric units "cm" and "cm^2" which require conversion for US localization. |
sqn_3fe9722e-2a77-4f16-ae50-3e03c4cef8d4 |
Localize | Terminology | Question
Explain why $(-1, -6)$ is not the turning point of the parabola $y=2(x+3)(x-2)$.
Answer:
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Question
Explain why $(-1, -6)$ is not the vertex of the parabola $y=2(x+3)(x-2)$.
Answer:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the preferred term. Verifier: The term "turning point" is the standard AU/UK term for what is typically called the "vertex" in US mathematics curricula. |
sqn_4f99c1ba-9630-40ab-a63a-156513d0a60d |
Localize | Terminology | Question
Show why rotating $270^\circ$ clockwise equals $90^\circ$ anticlockwise around the same point.
Answer:
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Question
Show why rotating $270^\circ$ clockwise equals $90^\circ$ counterclockwise around the same point.
Answer:
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Classifier: The term "anticlockwise" is the standard Australian/British term; the US equivalent is "counterclockwise". Verifier: The term "anticlockwise" is the standard Australian/British term; the US equivalent is "counterclockwise". This requires localization for the US market. |
sqn_56415836-5970-408c-8c0b-2cf9094b4a6d |
Localize | Spelling (AU-US) | Question
Explain why Quadrant I has positive $x$ and $y$ values, while Quadrant III has negative $x$ and $y$.
Answer:
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Question
Explain why Quadrant I has positive $x$ and $y$ values, while Quadrant III has negative $x$ and $y$.
Answer:
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Classifier: The text contains the AU spelling "centre", which needs to be localized to the US spelling "center". Verifier: The answer text contains the AU spelling "centre" twice, which requires localization to the US spelling "center". |
sqn_40bba066-1849-4d62-a946-726d037e1485 |
Localize | Units (simple) | Question
Show why doubling the diameter doubles the circumference of a circle.
Use an example to explain.
Answer:
|
Question
Show why doubling the diameter doubles the circumference of a circle.
Use an example to explain.
Answer:
|
Classifier: The answer content contains the metric unit "cm", which requires conversion to US customary units (e.g., inches) per the decision rules. Verifier: The answer content contains the metric unit "cm", which requires conversion to US customary units (inches) according to the decision rules. |
sqn_5679330c-7f1f-4de3-9d6d-b8c0703d4e30 |
Localize | Units (simple) | Question
Explain why shoe size is a type of discrete data but the length of a shoe is continuous.
Answer:
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Question
Explain why shoe size is a type of discrete data but the length of a shoe is continuous.
Answer:
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Classifier: The answer content contains the metric units "centimetres" and "millimetres". According to the decision rules, any metric unit found anywhere in the text requires at least this category. Verifier: The answer text contains the metric units "centimetres" and "millimetres". Per rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_39dd337c-5c91-47f0-a700-08c1f4297d9e |
Localize | Spelling (AU-US) | Question
Explain why the circle $(x + \frac{3}{2})^2 + (y - 3)^2 = 36$ has centre $\left(-\frac{3}{2}, 3\right)$.
Answer:
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Question
Explain why the circle $(x + \frac{3}{2})^2 + (y - 3)^2 = 36$ has center $\left(-\frac{3}{2}, 3\right)$.
Answer:
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Classifier: The text contains the AU spelling "centre" in both the question and the answer, which needs to be converted to the US spelling "center". Verifier: The text contains the AU spelling "centre" in both the question and the answer, which requires localization to "center". |
sqn_5a707ecb-a9c9-4c07-9cf7-9523e3c5ea06 |
Localize | Units (simple) | Question
Why do we multiply by $10\ 000$ and not $100$ when changing $1$ m$^2$ into cm$^2$?
Answer:
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Question
Why do we multiply by $144$ and not $12$ when changing $1$ ft$^2$ into in$^2$?
Answer:
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Classifier: The text contains metric units (m, cm, m^2, cm^2) and the AU spelling "metre". Per the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units (m, cm, m^2, cm^2) and the AU spelling "metre". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_5105a77f-18f2-41d0-ba18-5c4099ba3d21 |
Localize | Units (simple) | Question
How do you know that increasing both sides of a $3$ m by $4$ m rectangle by $1$ adds more than $7$ m$^2$ of area?
Answer:
|
Question
How do you know that increasing both sides of a $3$ ft by $4$ ft rectangle by $1$ adds more than $7$ ft$^2$ of area?
Answer:
|
Classifier: The text contains metric units ("m" and "m^2") which require conversion to US customary units (e.g., feet/inches and square feet/inches). Verifier: The text contains metric units ("m" and "m^2") which require conversion to US customary units. The calculation is a straightforward area comparison, making it a simple conversion. |
sqn_3e51f04f-cc6f-4133-8714-30fab1f035bd |
Localize | Units (simple) | Question
Explain why a wooden log of $50$ kg mass and $2$ m$^3$ volume will have a density of $25$ kg per m$^3$
Hint: Apply mass volume ratio
Answer:
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Question
Explain why a wooden log of $50$ lb mass and $2$ ft$^3$ volume will have a density of $25$ lb per ft$^3$
Hint: Apply mass volume ratio
Answer:
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Classifier: The text contains multiple metric units ("kg", "m^3", "kg per m^3"). According to the decision rules, the presence of metric units necessitates a RED classification. Verifier: Contains metric units (kg, m^3), which necessitates a RED classification. |
sqn_4e962965-2d08-4280-a197-2ff2003d85b4 |
Localize | Spelling (AU-US) | Question
Explain how rearranging terms in $3x + 9 + 2y + 6$ can help with factorising by grouping (if possible).
Answer:
|
Question
Explain how rearranging terms in $3x + 9 + 2y + 6$ can help with factoring by grouping (if possible).
Answer:
|
Classifier: The text contains the AU spelling "factorising" and "factorisation", which must be converted to the US spelling "factorizing" and "factorization". Verifier: The text contains "factorising" and "factorisation", which are AU/UK spellings that require localization to US "factorizing" and "factorization". |
sqn_3d2bd4c5-7149-4718-94f1-04ed5a98e519 |
Localize | Units (simple) | Question
Explain why the ratio $3$ kg to $500$ g is the same as $6:1$, not $3:5$.
Hint: $1$ kg = $1000$ g
Answer:
|
Question
Explain why the ratio $3$ lb to $500$ oz is the same as $6:1$, not $3:5$.
Hint: $1$ lb = $1000$ oz
Answer:
|
Classifier: The question explicitly uses metric units ("kg" and "g") and relies on the metric conversion factor (1 kg = 1000 g) for the mathematical logic. Per the decision rules, any metric unit requires a RED classification. Verifier: The question uses metric units (kg, g) which requires a RED classification per the decision rules. |
sqn_4f0ea742-3396-40cd-a225-a878126a239f |
Localize | Units (simple) | Question
How do you know scaling an octagon with side length $10$ cm by a factor of $0.4$ reduces the side length to $4$ cm?
Answer:
|
Question
How do you know scaling an octagon with side length $10$ in by a factor of $0.4$ reduces the side length to $4$ in?
Answer:
|
Classifier: The text contains metric units ("cm") which require conversion for US localization. Per decision rules, any metric unit triggers a RED units category. Verifier: The text contains the metric unit "cm", which requires conversion for US localization. |
sqn_61988daa-142a-4da3-befe-288462650bf3 |
Localize | Units (simple) | Question
How do you know $75$ g equals $0.075$ kg?
Hint: $1$ kg = $1000$ g=
Answer:
|
Question
How do you know $75$ oz equals $0.075$ lb?
Hint: $1$ lb = $1000$ oz=
Answer:
|
Classifier: The content explicitly involves metric units (grams and kilograms) and a conversion between them. According to the decision rules, any metric unit found anywhere requires at least this category. Verifier: The content contains metric units ("g", "kg", "grams", "kilograms"). According to rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_578fe8bc-c927-4e4d-b3e3-18a4c3b66bfa |
Localize | Terminology | Question
Show why the quadratic $y=2x^2+12x+15$ is equivalent to $y=2(x+3)^2-3$ in turning point form.
Hint: Factor out $2$ first
Answer:
|
Question
Show why the quadratic $y=2x^2+12x+15$ is equivalent to $y=2(x+3)^2-3$ in vertex form.
Hint: Factor out $2$ first
Answer:
|
Classifier: The text uses the term "turning point form", which is the standard AU term for what is called "vertex form" in the US. Verifier: The term "turning point form" is the standard Australian curriculum term for what is known as "vertex form" in the US. This is a school-context terminology difference. |
sqn_5a9cc1b4-f1ea-46cc-9662-030caeb0b11f |
Localize | Spelling (AU-US) | Question
Show how splitting the middle term of $x^2+6x+8=0$ leads to the factorisation $(x+2)(x+4)=0$.
Hint: Look for common factors
Answer:
|
Question
Show how splitting the middle term of $x^2+6x+8=0$ leads to the factoring $(x+2)(x+4)=0$.
Hint: Look for common factors
Answer:
|
Classifier: The text contains the AU spelling "factorisation", which needs to be localized to "factorization" for a US audience. Verifier: The text contains the AU spelling "factorisation", which requires localization to "factorization" for US audiences. |
sqn_52941143-81a1-401d-a96b-b8b245058678 |
Localize | Units (simple) | Question
How do you know that the density of a rock cannot be $15$ cm$^3$?
Hint: Check density units
Answer:
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Question
How do you know that the density of a rock cannot be $15$ in$^3$?
Hint: Check density units
Answer:
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Classifier: The text contains metric units ("cm^3" and "g/cm^3"). While the question is about the conceptual nature of density units, the specific metric examples should be localized to US customary equivalents (e.g., in^3 or lb/ft^3) or acknowledged as metric-pedagogy which still falls under units conversion rules. Verifier: The text contains metric units ("cm^3" and "g/cm^3"). Even though the question is about the conceptual nature of units, the presence of metric units requires RED classification per the decision rules. |
sqn_651b40cf-4cf8-4dce-8d1f-552e38fcd810 |
Localize | Terminology | Question
Explain why $y=3x^2-12x+5$ has turning point $x=2$.
Answer:
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Question
Explain why $y=3x^2-12x+5$ has vertex $x=2$.
Answer:
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Classifier: The term "turning point" is standard AU terminology for the vertex of a parabola. In a US context, "vertex" is the required term. Verifier: The term "turning point" is standard AU terminology for the vertex of a parabola. In the US, "vertex" is the standard term. |
sqn_69b6785f-84f9-4cad-a06c-b762a3afa28f |
Localize | Spelling (AU-US) | Question
Explain why addition will be the first operation in solving $(5+3) \div 2$
Answer:
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Question
Explain why addition will be the first operation in solving $(5+3) \div 2$
Answer:
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Classifier: The text uses the term "brackets", which is the standard AU/UK term for what is typically called "parentheses" in US mathematics. While "brackets" is sometimes used in the US for square brackets [], in this context of order of operations with ( ), it requires localization to "parentheses". Verifier: The term "brackets" is used in the answer to refer to the symbols ( ), which in a US educational context are specifically called "parentheses". This is a standard terminology/spelling difference between AU/UK and US English in mathematics. |
sqn_646dfe8a-5538-482d-8ca4-a5747f60bd67 |
Localize | Terminology | Question
Explain why $(x - 3)(x + 2) = 0$ implies that $x=3$ or $x=-2$.
Answer:
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Question
Explain why $(x - 3)(x + 2) = 0$ implies that $x=3$ or $x=-2$.
Answer:
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Classifier: The text uses the term "Null Factor Law", which is the standard term in the Australian curriculum. In the US, this is almost exclusively referred to as the "Zero Product Property". Verifier: The term "Null Factor Law" is specific to the Australian curriculum; the US equivalent is "Zero Product Property". |
sqn_6bbba1a9-141b-4e6e-9462-4262d744337b |
Localize | Spelling (AU-US) | Question
How do you know that the probability of the union is maximised when events have no overlap?
Answer:
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Question
How do you know that the probability of the union is maximized when events have no overlap?
Answer:
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Classifier: The word "maximised" uses the AU/UK 's' spelling; the US equivalent is "maximized". Verifier: The word "maximised" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("maximized"). |
sqn_7d6537c2-2e83-4fed-aacb-35c666d4c7ba |
Localize | Terminology | Question
How does the word “less” relate to subtraction in maths?
Answer:
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Question
How does the word “less” relate to subtraction in math?
Answer:
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Classifier: The text uses the term "maths", which is the standard AU/UK term. In the US, "math" is used. Per decision rules, terminology/spelling flags require RED classification. Verifier: The text uses the term "maths", which is the standard AU/UK term, whereas the US uses "math". This requires a RED classification per the decision rules. |
sqn_78aaff87-a8f4-4d5a-883d-52ab8cef5bb0 |
Localize | Terminology | Question
Explain why the null factor law only applies when an equation is set equal to zero.
Answer:
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Question
Explain why the zero product property only applies when an equation is set equal to zero.
Answer:
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Classifier: The "null factor law" is a common term in Australia, but it is also used in US curricula (though "Zero Product Property" is more common). However, the term itself is not "incorrect" in US English and there are no spelling or unit issues. Under the strict rules, it is bi-dialect neutral. Verifier: The term "null factor law" is the standard term in the Australian curriculum, whereas the US curriculum almost exclusively uses "Zero Product Property". While understandable, it is a distinct regional terminology difference in a school context. |
sqn_62c7f720-e899-42d5-9411-3a9266cece86 |
Localize | Units (simple) | Question
Why are grams used as the metric unit to measure mass rather than weight?
Hint: Gram is metric mass unit
Answer:
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Question
Why are ounces used as the unit to measure mass rather than weight?
Hint: Ounce is a mass unit
Answer:
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Classifier: The question specifically discusses "grams" and the "metric system". Per the decision rules, any mention of metric units triggers a RED units category. Verifier: The text explicitly mentions "grams" and the "metric system". Per rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
sqn_681ea0f8-0214-45dd-9a0b-2ac17a82f32e |
Localize | Spelling (AU-US) | Question
Show why the circle $(x - h)^2 + (y - k)^2 = r^2$ has its centre at $(h, k)$.
Answer:
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Question
Show why the circle $(x - h)^2 + (y - k)^2 = r^2$ has its center at $(h, k)$.
Answer:
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Classifier: The text contains the AU spelling 'centre' twice, which needs to be converted to the US spelling 'center'. Verifier: The text contains the AU spelling "centre" in both the question and the answer, which requires localization to "center". |
sqn_70dce3f9-6add-4ee2-b391-7cb75343fd56 |
Localize | Units (simple) | Question
Show that $2.5$ km is farther than $2000$ metres.
Answer:
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Question
Show that $2.5$ mi is farther than $2000$ feet.
Answer:
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Classifier: The text contains metric units ("km", "metres") and AU-specific spelling ("metres"). Per decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: Contains metric units ("km", "metres") and AU spelling ("metres"), requiring RED classification per decision rules. |
sqn_6c7814f7-5233-4ad2-b737-1df28f51def4 |
Localize | Terminology | Question
Explain why $402$ is named “four hundred and two.”
Hint: Use standard naming
Answer:
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Question
Explain why $402$ is named “four hundred two.”
Hint: Use standard naming
Answer:
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Classifier: In US mathematics pedagogy, the word "and" is strictly reserved for the decimal point when naming numbers (e.g., 402 is "four hundred two"). Including "and" in whole number names is a characteristic of AU/UK English that requires localization for US school standards. Verifier: The use of "and" in whole number names (e.g., "four hundred and two") is standard in AU/UK English but is explicitly taught as incorrect in US mathematics pedagogy, where "and" is reserved for the decimal point. |
sqn_6a7b82d9-aef0-4b3f-ad84-10048165889a |
Localize | Terminology | Question
Does parabola $y=(x+2)^2+3$ have a turning point at $(-2,3)$ and pass through the point $(1,10)$?
Explain why or why not.
Answer:
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Question
Does parabola $y=(x+2)^2+3$ have a vertex at $(-2,3)$ and pass through the point $(1,10)$?
Explain why or why not.
Answer:
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Classifier: The term "turning point" is the standard AU term for the "vertex" of a parabola in US curriculum. Verifier: The term "turning point" is the standard Australian curriculum term for what is referred to as the "vertex" of a parabola in the US. |
sqn_768cab1b-207b-49ca-ac31-8fb935822194 |
Localize | Units (textual) | Question
Tim says 'miles' is not a metric unit used to measure length.
How do you know he is correct?
Hint: Mile is imperial distance unit
Answer:
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Question
Tim says 'meters' is not a US customary unit used to measure length.
How do you know he is correct?
Hint: Meter is a metric distance unit
Answer:
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Classifier: The question explicitly discusses the metric system and contains AU spellings of metric units ("metres", "kilometres"). It is a conceptual/textual discussion of units. Verifier: The question discusses the metric system and contains AU spellings of metric units ("metres", "kilometres"). This is a textual discussion of units. |
sqn_84f2d059-ef0d-40a7-a8b6-ac30eed36eb7 |
Localize | Terminology | Question
Explain why 'product of $2$ more than $x$ and $3$' needs brackets.
Answer:
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Question
Explain why 'product of $2$ more than $x$ and $3$' needs parentheses.
Answer:
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Classifier: The text uses the term "brackets", which is the standard AU/UK term for what is referred to as "parentheses" in US school mathematics. Verifier: The term "brackets" is used in the question and answer, which is the standard AU/UK term for "parentheses" in US school mathematics. |
sqn_6ca8cc5e-f1df-4219-9960-08f2ab709fdd |
Localize | Units (textual) | Question
How do you know whether to multiply by $100$, $100^2$, or $100^3$ when converting between units in different dimensions?
Hint: Count dimension changes
Answer:
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Question
How do you know whether to multiply by $12$, $12^2$, or $12^3$ when converting between units in different dimensions?
Hint: Count dimension changes
Answer:
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Classifier: The question discusses the logic of converting between units in different dimensions using powers of 100. While no specific metric unit like "cm" is named, the factor of 100 is explicitly tied to metric system conversions (e.g., cm to m, cm^2 to m^2). This represents metric-pedagogy context that needs review for US localization where customary units (factors of 12, 3, etc.) are primary. Verifier: The question focuses on the logic of converting units using powers of 100 (100, 100^2, 100^3). This is specific to metric system pedagogy (e.g., cm to m). In a US context, students primarily learn conversions using factors like 12 (inches/feet) or 3 (feet/yards), making this metric-centric logic a candidate for localization review. |
sqn_7a23b5ab-0543-4ce2-93e5-e8902c615a00 |
Localize | Units (simple) | Question
Explain why the ratio of $4$ m to $50$ cm is equivalent to $8:1$.
Hint: $1$ m = $100$ cm
Answer:
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Question
Explain why the ratio of $4$ ft to $6$ in is equivalent to $8:1$.
Hint: $1$ ft = $12$ in
Answer:
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Classifier: Contains metric units "m" (metres) and "cm" (centimetres) which require localization to US customary units or a different pedagogical context. Verifier: The question explicitly uses metric units ("m" and "cm") and involves a simple conversion factor (1 m = 100 cm), which requires localization for US audiences. |
sqn_7f2cfb26-dce8-4023-97ce-45c938944ff0 |
Localize | Units (simple) | Question
A trapezium has parallel sides of $8$ cm and $4$ cm, with a height of $5$ cm.
Explain why its area is $30$ cm$^2$.
Answer:
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Question
A trapezoid has parallel sides of $8$ in and $4$ in, with a height of $5$ in.
Explain why its area is $30$ in$^2$.
Answer:
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Classifier: Contains metric units ("cm", "cm^2") and the term "trapezium" which is the AU term for the US "trapezoid". Per rule 6, units conversion takes precedence over terminology. Verifier: Contains metric units (cm, cm^2) and the term "trapezium" (AU/UK) which corresponds to "trapezoid" (US). Units conversion takes precedence. |
sqn_7f893203-b5f3-4ce2-9005-858e7f81d6d8 |
Localize | Units (simple) | Question
Explain why the hypotenuse of a triangle with legs of $6$ cm and $8$ cm is $10$ cm.
Answer:
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Question
Explain why the hypotenuse of a triangle with legs of $6$ in and $8$ in is $10$ in.
Answer:
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Classifier: Contains metric units ("cm") which require localization to US customary units. Verifier: Contains metric units ("cm") which require localization to US customary units. |
sqn_92af861a-f093-440f-964d-f95cd744f011 |
Localize | Terminology | Question
How do you know $\sqrt{5}$ is a surd but $\sqrt{9}$ is not?
Answer:
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Question
How do you know $\sqrt{5}$ is a radical but $\sqrt{9}$ is not?
Answer:
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Classifier: The term "surd" is standard in AU/UK curriculum but is significantly less common in US K-12 education, where "radical" or "irrational number" is preferred. Per decision rules, terminology takes precedence over GREEN. Verifier: The term "surd" is a specific mathematical term used in the AU/UK curriculum that is typically replaced by "radical" or "irrational number" in the US context. |
sqn_71c3c39e-b07b-41bc-8ca5-bec5838d4e1e |
Localize | Units (simple) | Question
Explain why a triangle with sides $5$ cm, $7$ cm, and an included angle $60^\circ$ has an area of approximately $15.2$ cm$^2$.
Answer:
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Question
Explain why a triangle with sides $5$ in, $7$ in, and an included angle $60^\circ$ has an area of approximately $15.2$ in$^2$.
Answer:
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Classifier: The text contains metric units ("cm" and "cm^2") which require conversion to US customary units. Verifier: The text contains metric units ("cm" and "cm^2") which require conversion to US customary units. |
sqn_85bd4a2b-008c-47ab-a5f1-e8b98ce6cc63 |
Localize | Spelling (AU-US) | Question
Explain why factorising $x^2+9x+14=0$ starts by splitting $9x$ into $7x+2x$.
Hint: Consider term splitting
Answer:
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Question
Explain why factoring $x^2+9x+14=0$ starts by splitting $9x$ into $7x+2x$.
Hint: Consider term splitting
Answer:
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Classifier: The text contains the AU/UK spelling "factorising" and "factorisation", which needs to be converted to the US spelling "factorizing" and "factorization". Verifier: The text contains "factorising" and "factorise", which are AU/UK spellings. Per rule 1, AU spelling always requires RED classification. |
sqn_9a3f9bd0-05d1-4715-b13b-9285e3bf9b11 |
Localize | Cultural refs | Question
Why does 'share equally' mean the same as 'divide evenly'?
Answer:
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Question
Why does 'share equally' mean the same as 'divide evenly'?
Answer:
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Classifier: The term "lollies" is a distinct Australian/Commonwealth cultural reference for "candy" or "sweets". Verifier: The term "lollies" is a specific Australian/Commonwealth term for candy/sweets and requires localization for a US audience. |
sqn_9a2b81b1-a10b-405b-bf3c-a46d583e151f |
Localize | Terminology | Question
How do you know $\tan \theta$ gives the gradient of a line?
Hint: Connect slope to tangent
Answer:
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Question
How do you know $\tan \theta$ gives the slope of a line?
Hint: Connect slope to tangent
Answer:
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Classifier: The term "gradient" is the standard AU term for what is referred to as "slope" in US mathematics. While "gradient" is used in US vector calculus, in this context (tan theta, rise/run), it specifically maps to the US school term "slope". Verifier: The term "gradient" is the standard Australian school term for "slope". In a US context, "slope" is used for lines, while "gradient" is typically reserved for vector calculus. |
sqn_96ee4215-0e43-4ea3-af79-cb57e05fd22d |
Localize | Units (simple) | Question
There is $13\%$ aluminium in an alloy.
Explain why $250$ grams of the alloy will have $32.5$ grams of aluminium.
Answer:
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Question
There is $13\%$ aluminum in an alloy.
Explain why $250$ ounces of the alloy will have $32.5$ ounces of aluminum.
Answer:
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Classifier: The text contains metric units ("grams") and AU-specific spelling ("aluminium"). Per the decision rules, the presence of metric units triggers the units category, which takes precedence over spelling. Verifier: The text contains metric units ("grams") and AU-specific spelling ("aluminium"). Per decision rule 5, units conversion takes precedence over spelling. |
sqn_92ec411f-6cd8-418f-87cd-37efa00d91a4 |
Localize | Units (simple) | Question
Prove that $3$ kg is not the same as $3500$ grams.
Hint: $1$ kg $= 1000$ g
Answer:
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Question
Prove that $3$ lb is not the same as $3500$ ounces.
Hint: $1$ lb $= 16$ oz
Answer:
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Classifier: The text contains metric units ("kg", "grams", "kilogram"). According to the decision rules, any metric unit found anywhere in the text requires at least this category. Verifier: The text contains metric units ("kg", "grams", "kilogram"). Per decision rules, any metric unit requires at least RED.units_simple_conversion. |
sqn_9d8a2530-2b74-477d-89ab-504bc00dfbad |
Localize | Units (simple) | Question
How do you know $150$ cm equals $1.5$ metres?
Answer:
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Question
How do you know $150$ in equals $1.5$ feet?
Answer:
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Classifier: The text contains metric units ("cm", "metres") and AU spelling ("metres"). Per the decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: Contains metric units ("cm", "metres") and AU spelling ("metres"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_932b62ae-ea29-4a61-ac68-213cb2de0fc8 |
Localize | Terminology | Question
Explain why $x^2 - 2x - 3$ can be written as $(x - 1)^2 - 4$ in turning point form.
Hint: Complete square with $-2x$ term
Answer:
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Question
Explain why $x^2 - 2x - 3$ can be written as $(x - 1)^2 - 4$ in vertex form.
Hint: Complete the square with the $-2x$ term
Answer:
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Classifier: The term "turning point form" is the standard AU term for what is called "vertex form" in the US. This requires terminology localization. Verifier: The term "turning point form" is the standard AU terminology for what is known as "vertex form" in the US curriculum. |
sqn_a1f1b74b-fe6f-446a-96b0-18c9e5ebf4e4 |
Localize | Units (simple) | Question
How do you know $2.5$ kilograms equals $2500$ grams?
Hint: $1$ kg $= 1000$ g
Answer:
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Question
How do you know $2.5$ pounds equals $40$ ounces?
Hint: $1$ lb $= 16$ oz
Answer:
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Classifier: The content explicitly uses metric units (kilograms, grams, kg, g) which requires localization to US customary units or a units-focused classification per the decision rules. Verifier: The content contains metric units (kilograms, grams, kg, g) which require localization to US customary units. The conversion is a simple numeric scale factor (1000), fitting simple_conversion. |
sqn_d20b1395-c722-4675-b7ac-fc7a7c871d36 |
Localize | Units (textual) | Question
When should you measure something in mm and when in cm?
Answer:
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Question
When should you measure something in inches and when in feet?
Answer:
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Classifier: The text explicitly discusses metric units (mm and cm) conceptually. Per the decision rules, any metric unit found anywhere requires a RED classification. Since it's a conceptual discussion without specific values to calculate, it falls under textual conversion. Verifier: The question explicitly references metric units (mm and cm). Per rule 3, any metric unit requires RED classification. Since it is a conceptual discussion of units, RED.units_textual_conversion is correct. |
sqn_b3fb863b-3e02-4eb6-aaa8-d62879f973d4 |
Localize | Answer set | Question
Why is a quadrilateral with exactly one pair of parallel sides called a trapezium?
Answer:
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Question
Why is a quadrilateral with exactly one pair of parallel sides called a trapezoid?
Answer:
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Classifier: The term "trapezium" is used to describe a quadrilateral with exactly one pair of parallel sides. In the US, this is called a "trapezoid". This requires localization of the geometric term. Verifier: The term "trapezium" is the standard AU/UK term for what is called a "trapezoid" in the US. This is a terminology difference requiring localization. |
sqn_bb9e05cf-7dd2-4158-aedd-a32bc085242b |
Localize | Terminology | Question
How do you know $(5 + 3) \times 2$ equals $16$?
Answer:
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Question
How do you know $(5 + 3) \times 2$ equals $16$?
Answer:
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Classifier: The text uses the term "Brackets" to refer to the grouping symbols ( ) in an order of operations context. In US math pedagogy, these are specifically called "parentheses". Verifier: The answer uses the term "Brackets" to refer to parentheses in an order of operations context. This is a distinct pedagogical terminology difference between AU/UK and US (where "parentheses" is used for ( ) and "brackets" usually refers to [ ]). |
sqn_dc7b6dd3-f6d4-4101-8805-e05d9429f6fd |
Localize | Terminology | Question
Explain why $x(x+3)=0$ has solutions $x=0$ or $x=-3$.
Answer:
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Question
Explain why $x(x+3)=0$ has solutions $x=0$ or $x=-3$.
Answer:
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Classifier: The text uses the term "null factor law", which is the standard Australian term for what is known in the US as the "Zero Product Property". Verifier: The answer text uses "null factor law", which is a specific Australian curriculum term for the Zero Product Property. |
sqn_e0b63507-a45d-4317-be5f-d9dcdf9073fd |
Localize | Terminology | Question
$\frac{1}{3}$ of the apples in a basket are green.
How do you know $\frac{1}{3}$ is a recurring decimal?
Answer:
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Question
$\frac{1}{3}$ of the apples in a basket are green.
How do you know $\frac{1}{3}$ is a repeating decimal?
Answer:
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Classifier: The term "recurring decimal" is the standard AU/UK term, whereas "repeating decimal" is the standard US term. This requires terminology localization. Verifier: The term "recurring decimal" is the standard terminology in Australia/UK, whereas "repeating decimal" is used in the US. This requires localization. |
sqn_adb99f42-3c9c-447f-9d01-2e2668d256eb |
Localize | Terminology | Question
Show why the parabola $y=x^2+6x+5$ has its turning point at $(-3,-4)$.
Answer:
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Question
Show why the parabola $y=x^2+6x+5$ has its vertex at $(-3,-4)$.
Answer:
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Classifier: The term "turning point" is the standard AU term for what is called the "vertex" of a parabola in the US. Although "vertex" is used in the answer, the question itself uses "turning point". Verifier: The term "turning point" is the standard Australian curriculum term for the vertex of a parabola. In the US, "vertex" is almost exclusively used. |
sqn_adf077ef-8a5c-4ae5-9dd1-1bea2ef6119c |
Localize | Units (simple) | Question
Show that $2$ m$^3$ plus $500$ cm$^3$ is not the same as $2.5$ litres.
Answer:
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Question
Show that $2$ ft$^3$ plus $500$ in$^3$ is not the same as $2.5$ gallons.
Answer:
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Classifier: The text contains multiple metric units (m^3, cm^3, litres) and the AU spelling "litres". Per decision rules, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains metric units (m^3, cm^3, litres) and the AU spelling "litres". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
sqn_b23075f8-ff16-42e3-9995-a2b20fa4dd00 |
Localize | Units (simple) | Question
How do you know a $15$ cm pencil is longer than a $12$ mm pen?
Answer:
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Question
How do you know a $15$ in pencil is longer than a $12$ in pen?
Answer:
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Classifier: Contains metric units "cm" and "mm" which require localization for a US audience. Verifier: The text contains metric units "cm" and "mm" which require conversion for a US audience. The conversion is simple as it involves comparing lengths. |
sqn_a339fb58-b8ce-4f97-ae3d-e367a5709c48 |
Localize | Spelling (AU-US) | Question
Pat represents $108$ as $2^2 \cdot 3^3$.
How do you know he is correct?
Hint: Test prime factorisation
Answer:
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Question
Pat represents $108$ as $2^2 \cdot 3^3$.
How do you know he is correct?
Hint: Test prime factorization
Answer:
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Classifier: The hint contains the AU spelling "factorisation" (ending in -isation), which requires conversion to the US spelling "factorization" (-ization). Verifier: The hint contains "factorisation", which is the AU/British spelling. Per rule 1, any AU spelling requires RED classification. |
sqn_affc44df-575f-496e-bad5-dd6eb07a836a |
Localize | Spelling (AU-US) | Question
Explain why factorising by grouping works, using an example like $ax+ay+bx+by$.
Answer:
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Question
Explain why factoring by grouping works, using an example like $ax+ay+bx+by$.
Answer:
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Classifier: Contains the AU spelling "factorising", which needs to be converted to the US spelling "factorizing". Verifier: Contains the AU spelling "factorising", which needs to be converted to the US spelling "factorizing". |
sqn_b5132d27-fa4f-43eb-94d6-6f7102adf698 |
Localize | Units (simple) | Question
Show that $12.25$ m$^3$ plus $750$ millilitres is not the same as $13$ litres.
Answer:
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Question
Show that $12.25$ ft$^3$ plus $750$ fluid ounces is not the same as $13$ gallons.
Answer:
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Classifier: The text contains multiple metric units (m^3, millilitres, litres) and AU-specific spelling ("millilitres", "litres"). Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains multiple metric units (m^3, millilitres, litres) and AU-specific spelling ("millilitres", "litres"). Per rule 5, units conversion takes precedence over spelling. |
sqn_bc62038b-ea8a-490e-b8d8-8a77197b8022 |
Localize | Spelling (AU-US) | Question
How do you know $\sqrt{50}$ equals $5\sqrt{2}$?
Hint: Consider prime factorisation
Answer:
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Question
How do you know $\sqrt{50}$ equals $5\sqrt{2}$?
Hint: Consider prime factorization
Answer:
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Classifier: The hint contains the AU/UK spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: The hint contains the AU/UK spelling "factorisation", which requires localization to the US spelling "factorization". |
sqn_ddbc61c9-7dc0-42f3-9c61-346f75e56cad |
Localize | Terminology | Question
How do you know $4 \times (10 - 3 \times 2)$ equals $16$ not $56$?
Answer:
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Question
How do you know $4 \times (10 - 3 \times 2)$ equals $16$ not $56$?
Answer:
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Classifier: The text uses the term "brackets", which is the standard AU/UK term for what is typically called "parentheses" in US mathematics context. Verifier: The use of the term "brackets" in a mathematical context is the standard terminology for Australia/UK, whereas "parentheses" is typically used in the US. This falls under school terminology. |
sqn_c2901fb2-39a0-4710-be6d-316c68c7a92b |
Localize | Units (simple) | Question
Explain why converting $4500$ grams to kilograms requires dividing by $1000$.
Hint: $1$ kilogram = $1000$ grams
Answer:
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Question
Explain why converting $4500$ ounces to pounds requires dividing by $16$.
Hint: $1$ pound = $16$ ounces
Answer:
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Classifier: The content explicitly uses and asks about converting between metric units (grams and kilograms). Per the decision rules, any metric unit found anywhere in the text requires at least this category. Verifier: The content explicitly uses metric units (grams and kilograms). According to rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. The conversion is a straightforward numeric change, so simple is correct. |
sqn_a5f674a2-1b38-485a-a5ab-19dddbfdb54a |
Localize | Units (simple) | Question
How do you know a $6$ cm$\times$ $3$ cm $\times$ $2$ cm box and $3$ cm $\times$ $2$ cm $\times$ $6$ cm box are the same?
Answer:
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Question
How do you know a $6$ in$\times$ $3$ in $\times$ $2$ in box and $3$ in $\times$ $2$ in $\times$ $6$ in box are the same?
Answer:
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Classifier: The text contains metric units ("cm", "cm^3") which require localization to US customary units according to the decision rules. Verifier: The text contains metric units (cm, cm^3) which require conversion to US customary units. |
sqn_e30d93cc-b5f7-48f7-9e1d-09b2f92c0327 |
Localize | Units (simple) | Question
Tim has a $40\%$ chance of winning a $10$ km marathon.
How do you know he is expected to lose $12$ marathons if he runs in $20$?
Answer:
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Question
Tim has a $40\%$ chance of winning a $10$ mi marathon.
How do you know he is expected to lose $12$ marathons if he runs in $20$?
Answer:
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Classifier: Contains the metric unit "km" (kilometers), which requires localization for a US audience. Verifier: Contains the metric unit "km" (kilometers), which requires conversion for US localization. It is a simple conversion as the unit is descriptive and doesn't involve complex equations. |
sqn_b51930b0-907e-4569-911d-3287fcf913c6 |
Localize | Units (simple) | Question
Explain why measuring $1000$ mm in cm gives $100$, not $10$.
Answer:
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Question
Explain why measuring $1000$ in in ft gives $100$, not $10$.
Answer:
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Classifier: The text contains metric units (mm, cm) and is specifically about metric-pedagogy (converting between metric units), which requires localization to US customary units or a different pedagogical approach. Verifier: The question involves converting between metric units (mm to cm), which requires localization to US customary units or a different pedagogical approach. |
sqn_afc0b7fe-6513-4292-b7a9-312da220ab58 |
Localize | Terminology | Question
How do you know that the turning point form of the quadratic expression $x^2 - 4x + 1$ is $(x - 2)^2 - 3$?
Hint: Complete square: $(x-2)^2-3$
Answer:
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Question
How do you know that the vertex form of the quadratic expression $x^2 - 4x + 1$ is $(x - 2)^2 - 3$?
Hint: Complete the square: $(x-2)^2-3$
Answer:
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Classifier: The term "turning point form" is the standard AU term for what is called "vertex form" in the US. Verifier: The term "turning point form" is the standard AU term for what is called "vertex form" in the US. This requires localization for the US market. |
sqn_e8dcfd71-8659-407c-93e1-ff2888b5056b |
Localize | Answer set | Question
Explain why the area formula for trapeziums includes averaging the two parallel sides.
Answer:
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Question
Explain why the area formula for trapezoids includes averaging the two parallel sides.
Answer:
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Classifier: The term "trapeziums" is the standard AU/UK term for the shape known as a "trapezoid" in the US. This requires terminology localization. Verifier: The term "trapeziums" is the standard AU/UK term for the shape known as a "trapezoid" in the US. This requires terminology localization. |
sqn_d5c94483-f916-46a2-9c1b-97444e5b6bc4 |
Localize | Spelling (AU-US) | Question
Explain why splitting the middle term helps in factorising $x^2+5x+6=0$.
Hint: Consider sum and product patterns
Answer:
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Question
Explain why splitting the middle term helps in factoring $x^2+5x+6=0$.
Hint: Consider sum and product patterns
Answer:
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Classifier: The text contains the AU spelling "factorising", which requires conversion to the US spelling "factorizing". Verifier: The word "factorising" in the content field is the AU/British spelling and requires localization to "factorizing" for the US locale. |
sqn_e44f9838-f095-451f-9557-9a0768d37dbd |
Localize | Cultural refs | Question
How do you know one $\$5$ note has the same value as ten $20$ cent coins and six $50$ cent coins?
Answer:
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Question
How do you know one $\$5$ bill has the same value as ten $20$ cent coins and six $50$ cent coins?
Answer:
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Classifier: The question refers to specific denominations of currency ("$5 note", "20 cent coins", "50 cent coins"). While the dollar sign is shared, the specific coin denominations (20c, 50c) and the term "note" (vs US "bill") are characteristic of the Australian currency system and differ from the US (which uses nickels, dimes, quarters, and $1/$5 bills). Verifier: The question uses Australian-specific currency terminology ("note" instead of "bill") and specific coin denominations (20 cent and 50 cent coins) that are characteristic of the Australian currency system and differ from the US system. |
sqn_f66867da-9116-4648-a93e-c0b8ee6bbb28 |
Localize | Terminology | Question
How do you know a triangle with sides $7$, $24$, and $25$ is a right-angled triangle?
Answer:
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Question
How do you know a triangle with sides $7$, $24$, and $25$ is a right triangle?
Answer:
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Classifier: Uses the AU term "right-angled triangle", which should be localized to "right triangle" for a US context. Verifier: The text uses the term "right-angled triangle", which is the standard AU term. The US equivalent is "right triangle". |
sxbWWEec3YKNUPh9otfC |
Localize | Spelling (AU-US) | Question
For a point $P(a\cos\theta,b\sin\theta)$ on a unit circle centred at $(0,0)$, what is the value of $a+b$ ?
Answer:
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Question
For a point $P(a\cos\theta,b\sin\theta)$ on a unit circle centered at $(0,0)$, what is the value of $a+b$ ?
Answer:
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Classifier: Contains the AU spelling "centred" which needs to be converted to the US spelling "centered". Verifier: Contains the AU spelling "centred" (US: centered). |
t4IaTez5Dxz7XwvXASrz |
Localize | Spelling (AU-US) | Question
A restaurant's sales last year were $\$12256$, and the deseasonalised sales were $\$13770.78$.
What is the seasonal index?
Answer:
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Question
A restaurant's sales last year were $\$12256$, and the deseasonalized sales were $\$13770.78$.
What is the seasonal index?
Answer:
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Classifier: The text uses generic currency symbols ($) and standard statistical/business terminology ("deseasonalised sales", "seasonal index"). While "deseasonalised" uses the 's' spelling, it is a technical term where both 's' and 'z' are often accepted, but more importantly, the context is bi-dialect neutral. However, looking closer at the spelling rules, "deseasonalised" contains an 's' where US English typically uses 'z'. Re-evaluating: "deseasonalised" -> "deseasonalized". Verifier: The text contains the word "deseasonalised", which uses the AU/UK 's' spelling. US English uses "deseasonalized". Per rule 1, any AU spelling requires a RED classification. |
sqn_e98adec6-a099-48e2-9b48-070919a2b092 |
Localize | Units (simple) | Question
Show why $85$ cm is closer to $1$ metre than to $50$ cm
Answer:
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Question
Show why $85$ in is closer to $1$ foot than to $50$ in
Answer:
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Classifier: The text contains metric units (cm, metre) and AU spelling ("metre"). Units conversion takes precedence. Verifier: The text contains metric units (cm, metre) and AU spelling ("metre"). Units conversion takes precedence. |
sqn_f4b20334-4ac5-49bc-ae61-fa9fdef058a0 |
Localize | Spelling (AU-US) | Question
Explain why rolling an odd sum on two dice is an example of marginal probability.
Hint: Total probability without conditions
Answer:
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Question
Explain why rolling an odd sum on two dice is an example of marginal probability.
Hint: Total probability without conditions
Answer:
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Classifier: The word "favourable" uses the Australian/British spelling; the US spelling is "favorable". Verifier: The answer text contains the word "favourable", which is the AU/British spelling. The US spelling is "favorable". |
sqn_f608685f-040b-457f-b928-1d0e49951da8 |
Localize | Units (simple) | Question
How do you know a right triangle with height $4$ cm, base $3$ cm is similar to one with height $12$ cm, base $9$ cm?
Answer:
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Question
How do you know a right triangle with height $4$ in, base $3$ in is similar to one with height $12$ in, base $9$ in?
Answer:
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Classifier: Contains metric units (cm). Although it also contains the term "right triangle" (which is US-friendly), the presence of metric units triggers the units classification. Verifier: The text contains the metric unit "cm", which requires localization. |
svh4NlCcH0durZDWzgKG |
Localize | Units (simple) | Question
A pool in the shape of a rectangular prism has a length of $8$ m, a width of $7$ m, and a height of $6$ m.
What is the volume of the pool?
Answer:
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Question
A pool in the shape of a rectangular prism has a length of $8$ ft, a width of $7$ ft, and a height of $6$ ft.
What is the volume of the pool?
Answer:
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Classifier: The question uses metric units (m, m^3) for dimensions and volume. Verifier: The question uses metric units (m, m^3) for length, width, height, and volume, requiring conversion. |
sqn_ffd3f0dd-85f4-4e9a-9191-989cb64e28f8 |
Localize | Units (simple) | Question
Why is cm$^2$ not a good unit to measure how much space an object takes up?
Answer:
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Question
Why is in$^2$ not a good unit to measure how much space an object takes up?
Answer:
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Classifier: The text contains metric units (cm^2, cm^3) and discusses metric-based pedagogy (measuring space/volume). Per decision rules, any metric unit requires at least this category. Verifier: The text contains metric units (cm^2, cm^3). Per decision rule 3, any metric unit requires at least RED.units_simple_conversion. |
suiVp7T3d34FtMvtuOdO |
Localize | Units (simple) | Question
Find the volume of a piece of metal with a mass of $100$ g and density of $1.80$ g/cm$^3.$
Answer:
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Question
Find the volume of a piece of metal with a mass of $100$ oz and density of $1.80$ oz/in$^3.$
Answer:
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Classifier: The text contains metric units (g, g/cm^3, cm^3) which require localization to US customary units or a decision on metric pedagogy. Verifier: The question contains metric units (g, g/cm^3, cm^3) which require conversion to US customary units or a pedagogical decision. |
sqn_ffcc0f7e-57ec-410a-88e5-ad45c586c592 |
Localize | Spelling (AU-US) | Question
Can the expression $2x + 6 + 3y + 9$ be factorised by grouping?
Explain.
Answer:
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Question
Can the expression $2x + 6 + 3y + 9$ be factored by grouping?
Explain.
Answer:
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Classifier: The text uses the AU spelling "factorised" (and "factorise"), which requires conversion to the US spelling "factorized" (and "factorize"). Verifier: The text contains the AU spelling "factorised" and "factorise", which requires localization to "factorized" and "factorize". |
szDvHRBq8rWgDepUfDCO |
Localize | Terminology | Question
Find the $x$-coordinate of the turning point of the parabola $ y=8x^{2}-8x+1$.
Options:
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Question
Find the $x$-coordinate of the vertex of the parabola $ y=8x^{2}-8x+1$.
Options:
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Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US mathematics curricula. |
sqn_e95953c6-2a0e-4692-8e67-a818993313ed |
Localize | Units (simple) | Question
How do you know $140$ centimetres and $4250000$ micrometres is $5.65$ metres?
Hint: Add different units
Answer:
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Question
How do you know $140$ inches and $4250000$ microinches is $5.65$ feet?
Hint: Add different units
Answer:
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Classifier: The text contains multiple metric units (centimetres, micrometres, metres) and AU-specific spellings of those units ("metres"). Units conversion takes precedence over spelling. Verifier: The text contains multiple metric units (centimetres, micrometres, metres) and AU-specific spellings of those units ("metres"). Units conversion takes precedence over spelling. |
t5rNPCDc4AfMUGBsrPnM |
Localize | Units (simple) | Question
In a $100$ m race, each athlete has an equal chance of running in lane $1$ on a track with eight lanes.
What is the likelihood that an athlete will not run in lane $1$ ?
Answer:
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Question
In a $100$ ft race, each athlete has an equal chance of running in lane $1$ on a track with eight lanes.
What is the likelihood that an athlete will not run in lane $1$ ?
Answer:
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Classifier: The text contains the metric unit "m" (metres) in the context of a "100 m race". Any metric unit requires localization. Verifier: The text contains the metric unit "m" (metres) in "100 m race". Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
t2hO6lS0fYUdKVBQcw7u |
Localize | Units (simple) | Question
An object moves with the velocity given by $v(t)=5t^2$ m/s where $t\geq 0$ in seconds.
Find the distance travelled by the object in the first three seconds.
Hint: Check the units carefully.
Answer:
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Question
An object moves with the velocity given by $v(t)=5t^2$ ft/s where $t\geq 0$ in seconds.
Find the distance traveled by the object in the first three seconds.
Hint: Check the units carefully.
Answer:
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Classifier: The question contains metric units "m/s" and "cm". Additionally, the answer (4500) is derived from a unit conversion within the metric system (metres to centimetres), which is a metric-pedagogy task requiring localization to US customary units or a decision on metric usage. Verifier: Contains metric units "m/s" and "cm". The problem specifically requires a conversion from meters to centimeters, which is a metric-pedagogy task. |
sqn_f5b581ff-e88f-42f8-a967-d3ded2ecfa7b |
Localize | Units (simple) | Question
Kelly says the density of solid metal of $250$ g with volume $20$ cm$^3$ must have a density equal to $12.5$ g per cm$^3$.
How do you know he is correct?
Hint: Verify density calculation
Answer:
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Question
Kelly says the density of solid metal of $250$ oz with volume $20$ in$^3$ must have a density equal to $12.5$ oz per in$^3$.
How do you know he is correct?
Hint: Verify density calculation
Answer:
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Classifier: Contains metric units (g, cm^3) which require localization for a US audience. Verifier: The text contains metric units (g, cm^3) which require conversion/localization for a US audience. |
sqn_f64367b0-4f25-4933-9824-da11e4c768d7 |
Localize | Units (simple) | Question
How do you know that a square with area $16$ cm$^2$ cannot have a side length of $5$ cm?
Hint: Square area = side$^2$
Answer:
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Question
How do you know that a square with area $16$ in$^2$ cannot have a side length of $5$ in?
Hint: Square area = side$^2$
Answer:
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Classifier: Contains metric units (cm, cm^2) which require localization. Verifier: The text contains metric units (cm, cm^2) which require localization. |
sqn_f80f1e83-c507-4240-a572-a73f2623f17c |
Localize | Spelling (AU-US) | Question
Show why $\frac{2}{\sqrt{3}}$ equals $\frac{2\sqrt{3}}{3}$.
Hint: Multiply by $\frac{\sqrt{3}}{\sqrt{3}}$
Answer:
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Question
Show why $\frac{2}{\sqrt{3}}$ equals $\frac{2\sqrt{3}}{3}$.
Hint: Multiply by $\frac{\sqrt{3}}{\sqrt{3}}$
Answer:
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Classifier: The text contains the AU spelling "rationalising", which needs to be converted to the US spelling "rationalizing". Verifier: The answer text contains the AU/British spelling "rationalising", which requires localization to the US spelling "rationalizing". |
t6rxvaujblCnY6ITu2ml |
Localize | Units (simple) | Question
Find the perimeter of a rectangular block of land that is $2$ km long and $0.6$ km wide.
Answer:
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Question
Find the perimeter of a rectangular block of land that is $2$ mi long and $0.6$ mi wide.
Answer:
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Classifier: The text uses "km" (kilometres) as a unit of measurement for length and width, which requires conversion for US localization. Verifier: The text uses "km" (kilometres), which is a metric unit requiring conversion for US localization. It is a simple conversion as it involves a basic perimeter calculation. |
tAZHWNiSxoSPPaoZrNpa |
Localize | Units (simple) | Question
A $200$ cm long string is shaped to form a rectangle.
Find the maximum area of the rectangle formed.
Answer:
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Question
A $200$ in long string is shaped to form a rectangle.
Find the maximum area of the rectangle formed.
Answer:
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Classifier: Contains metric units (cm and cm^2) which require conversion to US customary units. Verifier: Contains metric units (cm and cm^2) which require conversion for US localization. |
te5zPj5lwPJXR7fRiMme |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Distance travelled by an object may be negative, positive or zero.
Options:
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Multiple Choice
True or false:
Distance traveled by an object may be negative, positive or zero.
Options:
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Classifier: The text uses 'travelled', which is the standard spelling in both AU and UK English, but 'traveled' is US. However, 'travelled' is often accepted in various contexts, and the prompt rules for GREEN require zero AU-specific spelling. Wait, 'travelled' (double L) is the AU/UK spelling, while 'traveled' (single L) is US. Therefore, this contains an AU spelling. Verifier: The text contains "travelled", which is the AU/UK spelling (US is "traveled"). Per Rule 1, even one AU spelling word disqualifies GREEN. |
tBnj2b6EIuWFvB2twDIS |
Localize | Units (simple) | Question
Naruto runs a total distance of $800$ meters while using his Sage Mode.
How long did it take him to cover this distance if his average speed was $60$ metres per second?
Answer:
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Question
Naruto runs a total distance of $800$ feet while using his Sage Mode.
How long did it take him to cover this distance if his average speed was $60$ feet per second?
Answer:
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Classifier: Contains metric units (meters/metres) and AU spelling ("metres"). Per rule 6, units conversion takes precedence over spelling. Verifier: Contains metric units (meters/metres) and AU spelling ("metres"). Units conversion takes precedence. |
tjbLY0OBgyQV0HyJm6ln |
Localize | Units (simple) | Question
A kite-shaped flower bed has a longest diagonal of $18$ m and an area of $72$ m$^2$.
What is the length of the other diagonal?
Answer:
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Question
A kite-shaped flower bed has a longest diagonal of $18$ ft and an area of $72$ ft$^2$.
What is the length of the other diagonal?
Answer:
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Classifier: The text contains metric units ("m" and "m$^2$") which require conversion for US localization. Verifier: The question contains metric units ("m" and "m$^2$") which require conversion for US localization. The conversion is simple as it involves a basic geometric formula. |
tgPVTIU4hMqpskjqZWMt |
Localize | Units (simple) | Question
A gardener recorded the heights of her plants in centimetres as: $18, 20, 22, 25, 30, 35, 40$.
What is the median height of the plants?
Answer:
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Question
A gardener recorded the heights of her plants in inches as: $18, 20, 22, 25, 30, 35, 40$.
What is the median height of the plants?
Answer:
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Classifier: Contains metric units (centimetres, cm) and AU spelling (centimetres). Units take precedence over spelling. Verifier: Contains metric units ("centimetres", "cm") and AU spelling ("centimetres"). Per Rule 5, units conversion takes precedence. |
tudMqL50JacmS07I2RVF |
Localize | Units (simple) | Question
Calculate $a+b+c$ by expressing the following ratio in the simplest form, ensuring that each quantity has the same units.
$1.24$ L to $5$ L to $25$ mL $=a:b:c$
Answer:
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Question
Calculate $a+b+c$ by expressing the following ratio in the simplest form, ensuring that each quantity has the same units.
$1.24$ gal to $5$ gal to $25$ fl oz $=a:b:c$
Answer:
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Classifier: The content contains multiple metric units (L and mL) which require localization to US customary units. Verifier: The question contains metric units "L" (litres) and "mL" (millilitres) which require conversion for a US audience. The conversion is a simple ratio calculation. |
tAMrOCq8vPZP8o2hlM35 |
Localize | Terminology | Multiple Choice
Fill in the blank:
The total surface area of a cuboid with length $l$, width $w$ and height $h$ is given by $[?]$.
Hint: 'Cuboid' is another word for 'rectangular prism'.
Options:
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Multiple Choice
Fill in the blank:
The total surface area of a rectangular prism with length $l$, width $w$ and height $h$ is given by $[?]$.
Hint: A rectangular prism is a three-dimensional shape with six rectangular faces.
Options:
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Classifier: The term "cuboid" is the primary term used in the question and hint. In US curriculum, "rectangular prism" is the standard term. While the hint acknowledges this, the primary question text should be localized for a US audience. Verifier: The term "cuboid" is standard in AU/UK but "rectangular prism" is the standard term in US school context. |
01JW7X7K1D7C0K52HA7HSG8P33 |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ form expresses a polynomial as a product of its factors.
Options:
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Multiple Choice
$\fbox{\phantom{4000000000}}$ form expresses a polynomial as a product of its factors.
Options:
|
Classifier: The answer choice "Factorised" uses the AU 's' spelling, which requires conversion to the US 'z' spelling ("Factorized"). Verifier: The answer choice "Factorised" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("Factorized"). |
01JW7X7K138BNB6PCV9C8N775K |
Localize | Spelling (AU-US) | Multiple Choice
Factorising can involve taking out a common $\fbox{\phantom{4000000000}}$ from an expression.
Options:
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Multiple Choice
Factoring can involve taking out a common $\fbox{\phantom{4000000000}}$ from an expression.
Options:
|
Classifier: Contains the AU spelling "Factorising", which needs to be converted to the US spelling "Factorizing". Verifier: The word "Factorising" uses the AU/UK spelling; the US spelling is "Factorizing". |
01JW7X7K1613240CN97Z1KAT32 |
Localize | Spelling (AU-US) | Multiple Choice
Counting means saying numbers in $\fbox{\phantom{4000000000}}$
Options:
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Multiple Choice
Counting means saying numbers in $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: Contains the AU spelling "colour" in the answer set, which requires conversion to the US spelling "color". Verifier: The word "colour" in the answer choices is the AU/UK spelling; the US spelling is "color". |
01JW7X7K1613240CN97WQJFZ8K |
Localize | Spelling (AU-US) | Multiple Choice
Variables allow us to generalise mathematical $\fbox{\phantom{4000000000}}$
Options:
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Multiple Choice
Variables allow us to generalize mathematical $\fbox{\phantom{4000000000}}$
Options:
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Classifier: Contains the AU spelling "generalise", which requires conversion to the US spelling "generalize". Verifier: The word "generalise" uses the AU/UK spelling; the US spelling is "generalize". |
01JW7X7K2ACHCJ0JHCYTZEXREE |
Localize | Spelling (AU-US) | Multiple Choice
Both histograms and box plots can be used to visualise the $\fbox{\phantom{4000000000}}$ of a dataset.
Options:
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Multiple Choice
Both histograms and box plots can be used to visualize the $\fbox{\phantom{4000000000}}$ of a dataset.
Options:
|
Classifier: The word "visualise" is the AU spelling; the US spelling is "visualize". Verifier: The word "visualise" is the AU spelling; the US spelling is "visualize". |
01JW7X7K11HMPJRBDZ4F3P4738 |
Localize | Units (simple) | Multiple Choice
Cubic metres and cubic centimetres are units of $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
Cubic feet and cubic inches are units of $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The text contains metric units ("metres" and "centimetres") in a cubic context. This requires localization to US customary units (e.g., cubic inches/feet). Verifier: The text contains metric units "metres" and "centimetres" in a cubic context, requiring conversion to US customary units. |
01JW7X7K0YSZHPNYH3KQ1V5G9T |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ diagram uses overlapping circles to visualise the relationships between sets.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ diagram uses overlapping circles to visualize the relationships between sets.
Options:
|
Classifier: The word "visualise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("visualize"). Verifier: The text contains "visualise", which is the AU/UK spelling. It must be localized to "visualize" for the US locale. |
01JW7X7K11HMPJRBDZ4CGPA662 |
Localize | Units (simple) | Multiple Choice
Square metres and square centimetres are units of $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
Square feet and square inches are units of $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The text contains metric units ("metres" and "centimetres") which require conversion to US customary units or at least spelling localization. Per rule 1, any metric unit disqualifies GREEN. Per rule 6, units conversion is the highest priority RED category. Verifier: The text contains metric units "metres" and "centimetres" (both AU spelling and metric system), which require conversion to US customary units. |
0110b160-f72c-4386-8573-7d6bd3d907cc |
Localize | Spelling (AU-US) | Question
Why is understanding radicals important for solving problems in algebra or geometry?
Hint: Visualise how radicals appear in measurements or equations.
Answer:
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Question
Why is understanding radicals important for solving problems in algebra or geometry?
Hint: Visualize how radicals appear in measurements or equations.
Answer:
|
Classifier: The hint contains the AU spelling "Visualise", which needs to be converted to the US spelling "Visualize". Verifier: The hint contains "Visualise", which is AU spelling and requires localization to "Visualize". |
01JW7X7K1S2JNTTD89YHQA73QG |
Localize | Terminology | Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the amount by which a quantity changes per unit of time.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the amount by which a quantity changes per unit of time.
Options:
|
Classifier: The answer set includes the term "gradient". In AU/UK contexts, "gradient" is the standard term for the steepness of a line, whereas in the US, "slope" is the primary term used in school contexts. While both are mathematically valid, the presence of "gradient" as a distractor/answer in an AU-sourced dataset often requires localization to "slope" or ensuring "slope" is the primary term. Verifier: The presence of "gradient" in the answer set is a strong indicator of AU/UK school terminology, whereas "slope" is the standard US term. This requires localization review. |
01JW7X7K1QES0DW51SQZZ5BD9C |
Localize | Units (simple) | Multiple Choice
Centimetres and millimetres are $\fbox{\phantom{4000000000}}$ of length.
Options:
|
Multiple Choice
Inches and feet are $\fbox{\phantom{4000000000}}$ of length.
Options:
|
Classifier: The text explicitly mentions "Centimetres" and "millimetres", which are metric units and use AU spelling. This requires conversion to US customary units or at least spelling localization depending on curriculum policy. Verifier: The text contains metric units "Centimetres" and "millimetres" which also use AU spelling. This requires localization to US customary units or at minimum spelling changes. |
01JW7X7K1M9SX5QWA6KPC81QGK |
Localize | Terminology | Multiple Choice
The 'B' in BODMAS stands for $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
The 'P' in PEMDAS stands for $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The acronym "BODMAS" is standard in AU/UK, whereas the US equivalent is typically "PEMDAS". Additionally, "brackets" in this context usually maps to "parentheses" in US math curriculum. Verifier: The acronym "BODMAS" and the term "brackets" are specific to AU/UK/Commonwealth curricula. US localization uses "PEMDAS" and "parentheses". |
01JVJ5YNZVSQ29HKTMJJGYA67P |
Localize | Units (simple) | Multiple Choice
A hiker walks $7$ km east, $5$ km south, $3$ km east, then $1$ km north.
How far is the hiker from their starting point?
Options:
|
Multiple Choice
A hiker walks $7$ mi east, $5$ mi south, $3$ mi east, then $1$ mi north.
How far is the hiker from their starting point?
Options:
|
Classifier: The text contains the metric unit "km" (kilometers) multiple times in both the question and the answer choices, which requires conversion to US customary units (miles). Verifier: The text contains the metric unit "km" (kilometers) multiple times, which requires conversion to US customary units. |
01JW7X7K1D7C0K52HA7FH00R4T |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ form is a way of writing a polynomial where the terms are arranged in descending order of exponents.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ form is a way of writing a polynomial where the terms are arranged in descending order of exponents.
Options:
|
Classifier: The answer choice "Factorised" uses the AU 's' spelling, which requires conversion to the US 'z' spelling ("Factorized"). Verifier: The answer choice "Factorised" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("Factorized"). |
01JW7X7K1JF7HDFN1EHPBHNQD7 |
Localize | Spelling (AU-US) | Multiple Choice
A unit circle has a $\fbox{\phantom{4000000000}}$ of $1$ unit.
Options:
|
Multiple Choice
A unit circle has a $\fbox{\phantom{4000000000}}$ of $1$ unit.
Options:
|
Classifier: The answer choice "centre" uses Australian/British spelling and needs to be converted to "center" for US localization. Verifier: The answer choice contains "centre", which is the AU/UK spelling. US localization requires "center". |
01JW7X7K1NHX5SP6S97TSSY502 |
Localize | Terminology | Multiple Choice
A rotation can be either clockwise or $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
A rotation can be either clockwise or $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: The term "anticlockwise" is the standard AU/UK term, which maps to "counterclockwise" in US English. Verifier: The term "anticlockwise" is the standard AU/UK term; US English uses "counterclockwise". |
01JW7X7K2ACHCJ0JHCYW9S72QF |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is used to visualise the possible outcomes of a multi-stage experiment.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is used to visualize the possible outcomes of a multi-stage experiment.
Options:
|
Classifier: The word "visualise" is the AU spelling; the US spelling is "visualize". Verifier: The word "visualise" is the AU spelling; the US spelling is "visualize". |
01JW7X7K1AQDJ5S910YFJBQ93E |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ is expressed as a number between $0$ and $1$
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ is expressed as a number between $0$ and $1$
Options:
|
Classifier: The content is neutral. Note: "experiement" in the answer set is a typo for "experiment", but it is not an AU-specific spelling variant. Verifier: While the primary classifier is correct that the content is largely neutral, the answer choice "experiement" is a spelling error. More importantly, in many localization workflows, even non-AU specific typos are flagged under spelling. However, looking at the rules, if there is no AU-specific content, it should be GREEN. But "proportion" and "probability" are neutral. I will actually agree with GREEN as the typo "experiement" is not a locale-specific variant, but a general misspelling. Wait, rule 1 says GREEN requires zero AU-specific content. There is none here. I will revert to Agreeing with GREEN. |
01JW7X7K1PJ0XNEVQXYVKKYKS7 |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ diagram is a useful tool for visualising and calculating the probability of combined events.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ diagram is a useful tool for visualizing and calculating the probability of combined events.
Options:
|
Classifier: The word "visualising" uses the AU/UK "s" spelling and needs to be converted to the US "z" spelling ("visualizing"). Verifier: The word "visualising" uses the AU/UK "s" spelling; US localization requires "visualizing". |
01JW7X7K28NCR2BF40JPVCK9AC |
Localize | Spelling (AU-US) | Multiple Choice
Speed is calculated by dividing the distance travelled by the $\fbox{\phantom{4000000000}}$ taken.
Options:
|
Multiple Choice
Speed is calculated by dividing the distance traveled by the $\fbox{\phantom{4000000000}}$ taken.
Options:
|
Classifier: The word "travelled" is the AU/UK spelling; the US spelling is "traveled". Verifier: The word "travelled" is the AU/UK spelling; the US spelling is "traveled". |
01JW7X7K2QWH54F7X8W7DJBPT0 |
Localize | Spelling (AU-US) | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a system for organising days into weeks and months.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is a system for organizing days into weeks and months.
Options:
|
Classifier: The word "organising" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("organizing"). Verifier: The word "organising" is the AU/UK spelling and requires conversion to "organizing" for US English. |
01JW7X7K2NQ3EBT0AH53B1R11J |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ data is data that has been organised into groups or intervals.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ data is data that has been organized into groups or intervals.
Options:
|
Classifier: The word "organised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("organized"). Verifier: The word "organised" is the AU/UK spelling and requires conversion to "organized" for US English. |
01JW7X7K32HW6P306PJH66F98N |
Localize | Spelling (AU-US) | Multiple Choice
To find the next shape in a growing pattern, look for the $\fbox{\phantom{4000000000}}$ in how the shapes grow.
Options:
|
Multiple Choice
To find the next shape in a growing pattern, look for the $\fbox{\phantom{4000000000}}$ in how the shapes grow.
Options:
|
Classifier: The answer choice "colour" uses AU/UK spelling and must be localized to "color" for a US audience. Verifier: The answer choice "colour" is AU spelling and requires localization to "color". |
01JW7X7K2VNCFPHN2WSC1F4YZ7 |
Localize | Terminology | Multiple Choice
An $\fbox{\phantom{4000000000}}$ is a small raised number that indicates how many times a quantity is multiplied by itself.
Options:
|
Multiple Choice
An $\fbox{\phantom{4000000000}}$ is a small raised number that indicates how many times a quantity is multiplied by itself.
Options:
|
Classifier: The term "index" is the standard AU/UK term for what is primarily called an "exponent" or "power" in US schools. While "exponent" is provided as an answer choice, the presence of "index" as a primary mathematical term in this context indicates AU-specific curriculum terminology. Verifier: The term "index" is a specific AU/UK curriculum term for "exponent" or "power". Its inclusion as a primary answer choice alongside "exponent" and "power" marks this as AU-specific terminology context. |
01JW7X7K3H445HHM4QE0M59DY0 |
Localize | Terminology | Multiple Choice
Surds often arise when dealing with $\fbox{\phantom{4000000000}}$ roots of non-perfect squares.
Options:
|
Multiple Choice
Radicals often arise when dealing with $\fbox{\phantom{4000000000}}$ roots of non-perfect squares.
Options:
|
Classifier: The term "Surds" is a specific AU/UK mathematical term for irrational roots. In the US, this is almost exclusively referred to as "radicals". Verifier: The term "Surds" is a specific terminology used in AU/UK/NZ/IN curricula, whereas US curricula almost exclusively use "radicals". This requires localization for the school context. |
01JW7X7K39MYNVG6Y64BAGWAVR |
Localize | Spelling (AU-US) | Multiple Choice
An $\fbox{\phantom{4000000000}}$ circle on a number line indicates that the endpoint is not included in the solution set.
Options:
|
Multiple Choice
An $\fbox{\phantom{4000000000}}$ circle on a number line indicates that the endpoint is not included in the solution set.
Options:
|
Classifier: The answer choice "coloured" uses the AU/UK spelling and requires conversion to the US spelling "colored". Verifier: The answer choice "coloured" uses the AU/UK spelling, which requires localization to the US spelling "colored". |
01JW7X7K40M8QRYMCCKTM5DM3J |
Localize | Terminology | Multiple Choice
Equating indices involves setting the $\fbox{\phantom{4000000000}}$ equal to each other and solving for the variable.
Options:
|
Multiple Choice
Equating exponents involves setting the $\fbox{\phantom{4000000000}}$ equal to each other and solving for the variable.
Options:
|
Classifier: The term "indices" (and the phrase "Equating indices") is the standard AU/UK term for what is called "exponents" in the US. While "exponents" appears in the answer set, the prompt itself uses "indices". Verifier: The term "indices" is the standard AU/UK term for what is called "exponents" in the US. The prompt uses "indices", requiring localization. |
01JW7X7K44GBYYC80A9KJ4JN5Q |
Localize | Spelling (AU-US) | Multiple Choice
All points on the surface of a sphere are an equal distance from its $\fbox{\phantom{4000000000}}$
Options:
|
Multiple Choice
All points on the surface of a sphere are an equal distance from its $\fbox{\phantom{4000000000}}$
Options:
|
Classifier: Contains the AU spelling "centre" which needs to be localized to "center" for a US audience. Verifier: The text contains the AU spelling "centre" in the answer choices, which requires localization to "center" for the US. |
01JW7X7K3VWH9Q1Q450R04BZJH |
Localize | Spelling (AU-US) | Multiple Choice
Identifying upcoming elements in a geometric sequence involves recognising the $\fbox{\phantom{4000000000}}$ and applying it to the previous term.
Options:
|
Multiple Choice
Identifying upcoming elements in a geometric sequence involves recognizing the $\fbox{\phantom{4000000000}}$ and applying it to the previous term.
Options:
|
Classifier: Contains the AU spelling "recognising", which needs to be converted to the US spelling "recognizing". Verifier: The word "recognising" uses the AU/UK 's' spelling; the US standard is "recognizing". |
01JW7X7K4AHRDA6RA8ZXARVPCD |
Localize | Spelling (AU-US) | Multiple Choice
Venn diagrams are used to visualise $\fbox{\phantom{4000000000}}$ theory concepts.
Options:
|
Multiple Choice
Venn diagrams are used to visualize $\fbox{\phantom{4000000000}}$ theory concepts.
Options:
|
Classifier: Contains the AU/UK spelling "visualise", which requires conversion to the US spelling "visualize". Verifier: The word "visualise" is the AU/UK spelling; the US spelling is "visualize". This requires a RED.spelling_only classification. |
01JW7X7K41TQ97R0CAHMRNRVZZ |
Localize | Terminology | Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the side opposite the right angle in a right-angled triangle.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ is the side opposite the right angle in a right triangle.
Options:
|
Classifier: The term "right-angled triangle" is the standard AU/UK term; the US equivalent is "right triangle". Verifier: The term "right-angled triangle" is the standard AU/UK term; the US equivalent is "right triangle". |
01JW7X7K3SB0C71WVG4RYTM9T5 |
Localize | Spelling (AU-US) | Multiple Choice
The remainder theorem can be used to $\fbox{\phantom{4000000000}}$ a polynomial at a specific value.
Options:
|
Multiple Choice
The remainder theorem can be used to $\fbox{\phantom{4000000000}}$ a polynomial at a specific value.
Options:
|
Classifier: The answer choice "factorise" uses AU/UK spelling (ending in -ise) which requires conversion to US spelling (factorize). Verifier: The answer choice "factorise" uses the AU/UK spelling. US English requires "factorize". Per rule 1, AU spelling always requires RED classification. |
01JW7X7K45ZW5NHYWN727E1M2M |
Localize | Terminology | Multiple Choice
Turning point form, also known as $\fbox{\phantom{4000000000}}$ form, can be used to easily identify the coordinates of the turning point.
Options:
|
Multiple Choice
Vertex form, also known as $\fbox{\phantom{4000000000}}$ form, can be used to easily identify the coordinates of the vertex.
Options:
|
Classifier: The term "Turning point" is the standard AU term for what is called the "vertex" in US school mathematics. The question explicitly asks for the synonym, and while "vertex" is provided as an answer, the prompt itself uses "Turning point form" which should be localized to "Vertex form" in a US context. Verifier: The term "Turning point form" is the standard AU pedagogical term for what is called "Vertex form" in US school mathematics. This is a terminology difference in a school context. |
01JW7X7K4WB9QY06PFTASGN20T |
Localize | Terminology | Multiple Choice
A $\fbox{\phantom{4000000000}}$ is an expression containing a root that cannot be simplified to a rational number.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ is an expression containing a root that cannot be simplified to a rational number.
Options:
|
Classifier: The term "surd" is standard in AU/UK curriculum but is rarely used in US K-12 education, where "radical" or "irrational radical" is preferred. While "radical" is an option, the presence of "surd" as a primary answer choice indicates AU-specific terminology. Verifier: The term "surd" is a specific mathematical term used in the Australian/UK curriculum that is typically replaced by "radical" in the US context. |
01JW7X7K4Z4RT1D20TNT9YDCAM |
Localize | Spelling (AU-US) | Multiple Choice
The $\fbox{\phantom{4000000000}}$ is a line segment from the centre of a circle to any point on the circumference.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ is a line segment from the center of a circle to any point on the circumference.
Options:
|
Classifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre", which must be localized to "center" for a US audience. |
01JW7X7K4J36ZPPS4MPGYYV8AE |
Localize | Spelling (AU-US) | Multiple Choice
$\fbox{\phantom{4000000000}}$ means multiplying out the brackets or parentheses in an expression.
Options:
|
Multiple Choice
$\fbox{\phantom{4000000000}}$ means multiplying out the parentheses in an expression.
Options:
|
Classifier: The answer choice "Factorising" uses the AU/UK 's' spelling instead of the US 'z' spelling ("Factorizing"). Verifier: The answer choice "Factorising" uses the AU/UK 's' spelling. Under Rule 1, this requires RED classification. |
01JW7X7K51VSY7YAHZE7PQBPXA |
Localize | Terminology | Multiple Choice
A $\fbox{\phantom{4000000000}}$ decimal has a finite number of digits after the decimal point.
Options:
|
Multiple Choice
A $\fbox{\phantom{4000000000}}$ decimal has a finite number of digits after the decimal point.
Options:
|
Classifier: The term "recurring" is the standard AU term for what is typically called a "repeating" decimal in the US. While "repeating" is also present in the answer set, "recurring" is a distinct AU-preferred term in this context. Verifier: The term "recurring" is the standard AU terminology for what is called a "repeating" decimal in the US. Its presence in the answer set flags this for localization. |
01JW7X7K4Q8Q11RX5B16B6M5RV |
Localize | Terminology | Multiple Choice
Pythagoras' $\fbox{\phantom{4000000000}}$ relates the sides of a right-angled triangle.
Options:
|
Multiple Choice
The Pythagorean $\fbox{\phantom{4000000000}}$ relates the sides of a right triangle.
Options:
|
Classifier: The term "right-angled triangle" is the standard AU/UK term; the US equivalent is "right triangle". Additionally, "Pythagoras' theorem" is often referred to as the "Pythagorean theorem" in the US, though the possessive form is understood. Verifier: The term "right-angled triangle" is the standard AU/UK term (US: "right triangle"). "Pythagoras' theorem" is also the common AU phrasing (US: "Pythagorean theorem"). |
01JW7X7K4Z4RT1D20TNPM0ZDS7 |
Localize | Spelling (AU-US) | Multiple Choice
The $\fbox{\phantom{4000000000}}$ is a line segment that passes through the centre of a circle and whose endpoints are on the circle.
Options:
|
Multiple Choice
The $\fbox{\phantom{4000000000}}$ is a line segment that passes through the center of a circle and whose endpoints are on the circle.
Options:
|
Classifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". Verifier: The text contains the AU spelling "centre", which must be localized to "center" for a US audience. |
mqn_01JBJBQ94TP7WHCHXB125KW1NT |
Localize | Terminology | Multiple Choice
Which of the following equations represents a parabola that has the same turning point as $y = \frac{3}{4}\left(x - \frac{5}{2}\right)^2 + \frac{7}{3}$, but opens in the opposite direction?
Options:
|
Multiple Choice
Which of the following equations represents a parabola that has the same vertex as $y = \frac{3}{4}\left(x - \frac{5}{2}\right)^2 + \frac{7}{3}$, but opens in the opposite direction?
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US mathematics curriculum. |
mqn_01JBP6VESWBWK4KE4VDVNXCN50 |
Localize | Terminology | Multiple Choice
Which of the following recurring decimals can be converted to a fraction with a denominator of $99$?
Options:
|
Multiple Choice
Which of the following repeating decimals can be converted to a fraction with a denominator of $99$?
Options:
|
Classifier: The term "recurring decimals" is standard in Australian/British English, whereas "repeating decimals" is the standard term used in US school mathematics. Verifier: The term "recurring decimals" is the standard Australian/British term, whereas "repeating decimals" is used in the US. This requires localization for the US market. |
mqn_01JC2RRJ710SP5M7CQZE3J301V |
Localize | Spelling (AU-US) | Multiple Choice
Write the number $20020$ in words.
Options:
|
Multiple Choice
Write the number $20020$ in words.
Options:
|
Classifier: The answer choices use the British/Australian convention of including "and" after the hundreds place (e.g., "thousand and twenty"). In US English, "and" is typically reserved for the decimal point in number names. While often considered a stylistic preference, in a primary school context, this is a distinct dialectal difference in how numbers are written in words. Verifier: The use of "and" in whole number names (e.g., "thousand and twenty") is a distinct AU/UK convention that differs from US school standards where "and" is reserved for decimals. |
mqn_01JBRXNWDGMEZQVGNB3YT3V5ES |
Localize | Units (simple) | Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$2.4$m$\,:1.2$ cm
Options:
|
Multiple Choice
Express the following ratio in the simplest form, ensuring that each quantity has the same units.
$2.4$ft$\,:1.2$ in
Options:
|
Classifier: The text contains metric units "m" (metres) and "cm" (centimetres). Verifier: The text contains metric units "m" (metres) and "cm" (centimetres). The conversion is a simple numeric ratio calculation. |
mqn_01JBXCP0YCF5F6H24FDBX0E57T |
Localize | Terminology | Multiple Choice
Which of the following represents the turning point of the parabola $y=-1.75x^2+3.5x-2$ ?
Options:
|
Multiple Choice
Which of the following represents the vertex of the parabola $y=-1.75x^2+3.5x-2$ ?
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In the US, "vertex" is the standard term used in school mathematics. Verifier: The term "turning point" is the standard AU/UK term for what is called the "vertex" in US school mathematics. |
mqn_01JBRXHRWQW4P44XJNEQDH732P |
Localize | Units (simple) | Multiple Choice
A liquid mixture contains $0.75$ L of oil, $1.25$ L of water and $\frac{1}{2}$ L of glycerin.
Express the ratio of oil to water to glycerin in its simplest form.
Options:
|
Multiple Choice
A liquid mixture contains $0.75$ gal of oil, $1.25$ gal of water and $\frac{1}{2}$ gal of glycerin.
Express the ratio of oil to water to glycerin in its simplest form.
Options:
|
Classifier: The text contains the metric unit "L" (litres). According to the decision rules, any metric unit requires classification into a units category. Verifier: The text contains the metric unit "L" (litres). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
mqn_01JBT08BPVACRV1TCGPFA6CR41 |
Localize | Units (simple) | Multiple Choice
A farm has three types of crops: wheat, corn, and soybeans. Each hectare of land can produce $20$ tonnes of wheat, $25$ tonnes of corn, and $15$ tonnes of soybeans.
If the total production in tonnes is given by $60t$, what does the variable $t$ represent?
Options:
|
Multiple Choice
A farm has three types of crops: wheat, corn, and soybeans. Each acre of land can produce $20$ tons of wheat, $25$ tons of corn, and $15$ tons of soybeans.
If the total production in tons is given by $60t$, what does the variable $t$ represent?
Options:
|
Classifier: The text contains metric units "hectare" and "tonnes". While "tonnes" is a spelling variant of "tons", it is also a metric unit of mass (1000kg), and "hectare" is a metric unit of area. Verifier: The text contains metric units "hectare" and "tonnes". "Tonnes" is the metric spelling/unit (1000kg), and "hectare" is a metric unit of area. |
mqn_01JC22H36M01YV001W97TDGH3N |
Localize | Answer set | Multiple Choice
Trapezium $WXYZ$ has a right angle at $\angle W$.
Which of the following statements must be true?
A) $WX$ and $YZ$ are equal in length
B) The trapezium has two right angles
C) $WX$ and $ZY$ are perpendicular
D) $WZ$ and $ZY$ are parallel
Options:
|
Multiple Choice
Trapezoid $WXYZ$ has a right angle at $\angle W$.
Which of the following statements must be true?
A) $WX$ and $YZ$ are equal in length
B) The trapezoid has two right angles
C) $WX$ and $ZY$ are perpendicular
D) $WZ$ and $ZY$ are parallel
Options:
|
Classifier: The term "Trapezium" is used. In the US, this shape is called a "Trapezoid". Since the term appears in the question and defines the properties being tested, it requires localization. Verifier: The term "Trapezium" is the standard AU/UK term for what is called a "Trapezoid" in the US. This is a significant terminology difference in a geometry context. |
mqn_01JBJGNDVQ77R1JG8VJ4MADN07 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following equations represents a circle centred at $\left(-\frac{7}{2}, \frac{5}{3}\right)$ with a radius of $225$ units?
Options:
|
Multiple Choice
Which of the following equations represents a circle centered at $\left(-\frac{7}{2}, \frac{5}{3}\right)$ with a radius of $225$ units?
Options:
|
Classifier: Contains the AU spelling "centred", which needs to be localized to "centered" for a US audience. Verifier: The text contains "centred", which is the AU/British spelling. US spelling is "centered". |
mqn_01JKCGRKX1WTQN611QCRTW6TQ5 |
Localize | Cultural refs | Multiple Choice
True or false:
GST is a $10\%$ tax applied to all goods and services sold in Australia.
Options:
|
Multiple Choice
True or false:
Sales tax is a $10\%$ tax applied to all goods and services sold in the United States.
Options:
|
Classifier: The question explicitly mentions 'GST' and 'Australia', which are distinct cultural and geographic references requiring localization for a US audience. Verifier: The question explicitly mentions 'GST' and 'Australia', which are specific cultural and geographic references requiring localization. |
mqn_01JKT4YW7SKRGZF4ATVRKRZYNM |
Localize | Terminology | Multiple Choice
True or false:
$\sqrt{18}$ is both a radical and a surd.
Options:
|
Multiple Choice
True or false:
$\sqrt{18}$ is both a radical and a radical.
Options:
|
Classifier: Contains the term "surd", which is specific to AU/UK school math terminology and usually requires localization to "radical" or similar context in the US. Verifier: Contains the term "surd", which is specific to AU/UK school math terminology. |
mqn_01JKCGMBG760991JH7XP813K63 |
Localize | Cultural refs | Multiple Choice
True or false:
GST is only paid by businesses and does not affect consumers.
Options:
|
Multiple Choice
True or false:
Sales tax is only paid by businesses and does not affect consumers.
Options:
|
Classifier: GST (Goods and Services Tax) is a specific Australian tax system. In a US context, this would typically be localized to 'Sales Tax' or a similar US-relevant concept. Verifier: GST (Goods and Services Tax) is a specific tax system used in Australia and other countries, but not the US, where 'Sales Tax' is the standard equivalent. |
mqn_01JKT4QNB1XT2PSX4QVTN4CQNC |
Localize | Terminology | Multiple Choice
True or false:
Surds are always irrational.
Options:
|
Multiple Choice
True or false:
Radicals are always irrational.
Options:
|
Classifier: The term "Surds" is standard in Australian/UK curriculum but is significantly less common in US K-12 education compared to "radicals" or "irrational roots". While mathematically valid, it is a strong indicator of non-US school terminology. Verifier: The term "Surds" is a specific AU/UK school terminology that is not standard in US K-12 education, where "radicals" is preferred. |
mqn_01JKT51D0V6FTXZG18W7TY2MCK |
Localize | Terminology | Multiple Choice
True or false:
$\sqrt{1}$ is a surd.
Options:
|
Multiple Choice
True or false:
$\sqrt{1}$ is a radical.
Options:
|
Classifier: Contains the term "surd", which is specific to AU/UK school math terminology. Verifier: Contains the term "surd", which is specific to AU/UK school math terminology. |
mqn_01JKT58PGTWPWS1JRY1P9N2GY7 |
Localize | Terminology | Multiple Choice
Which of the following is a surd?
Options:
|
Multiple Choice
Which of the following is a radical?
Options:
|
Classifier: Contains the term "surd", which is specific to AU/UK school math terminology. Verifier: Contains the term "surd", which is specific to AU/UK school math terminology. |
mqn_01JDHGZANAP3G6AM3CKHH3ZFZG |
Localize | Units (simple) | Multiple Choice
The thickness of a piece of paper is approximately $1$ mm.
If a book contains $500$ pages, what is the most appropriate unit to express the combined thickness of all the pages?
Options:
|
Multiple Choice
The thickness of a piece of paper is approximately $1$ in.
If a book contains $500$ pages, what is the most appropriate unit to express the combined thickness of all the pages?
Options:
|
Classifier: The question is entirely based on metric units (mm, Metres, Centimetres, Micrometres, Millimetres) and contains AU-specific spellings of those units ("Metres", "Centimetres"). Units conversion takes precedence over spelling. Verifier: The question is based on metric units (mm, Metres, Centimetres, etc.) and uses AU spellings ("Metres", "Centimetres"). Units conversion is the primary requirement. |
mqn_01JC2S6GEK859C71GCYXNV15SJ |
Localize | Spelling (AU-US) | Multiple Choice
Add $28660$ and $3406$.
What is the answer in words?
Options:
|
Multiple Choice
Add $28660$ and $3406$.
What is the answer in words?
Options:
|
Classifier: Similar to Group 8, the answer choices include the "and" conjunction in number names (e.g., "hundred and sixty-six"), which is standard in AU/UK but generally avoided in US math curriculum for whole numbers. Verifier: The answer choices use the AU/UK convention of including "and" in the word form of whole numbers (e.g., "hundred and sixty-six"). |
mqn_01JKT24A2HN5Z0429RDHYMDG8V |
Localize | Terminology | Multiple Choice
What is the gradient-intercept form of $4x - y = 8$ ?
Options:
|
Multiple Choice
What is the slope-intercept form of $4x - y = 8$ ?
Options:
|
Classifier: The term "gradient-intercept form" is the AU equivalent of the US "slope-intercept form". Verifier: The term "gradient-intercept form" is the AU equivalent of the US "slope-intercept form". |
mqn_01JKC1PVDRJJ4P5Y00KD3XDMEB |
Localize | Units (simple) | Multiple Choice
Drivers must travel slower than $40$ km/h in a certain zone.
Which inequality represents this if $v$ is the car's speed?
Options:
|
Multiple Choice
Drivers must travel slower than $40$ mph in a certain zone.
Which inequality represents this if $v$ is the car's speed?
Options:
|
Classifier: The text contains the metric unit 'km/h', which requires localization to US customary units (mph) or at least triggers the units classification rule. Verifier: The text contains the metric unit 'km/h', which requires conversion to US customary units (mph). |
mqn_01JGZ1DD1YDND1GYCQY9AQFGZA |
Localize | Spelling (AU-US) | Multiple Choice
A survey plans to find the favourite music in a neighbourhood with $100$ people. On the survey day, $20$ more join.
Will this make the survey more or less biased?
Options:
|
Multiple Choice
A survey plans to find the favorite music in a neighborhood with $100$ people. On the survey day, $20$ more join.
Will this make the survey more or less biased?
Options:
|
Classifier: Contains the AU spelling "neighbourhood", which requires conversion to the US spelling "neighborhood". Verifier: The text contains "favourite" and "neighbourhood", which are AU/British spellings requiring localization to US English ("favorite", "neighborhood"). |
mqn_01JC2SD6P114QQ3MEPQAARB53P |
Localize | Spelling (AU-US) | Multiple Choice
Mia subtracted $3651$ from $9854$.
What is the answer in words?
Options:
|
Multiple Choice
Mia subtracted $3651$ from $9854$.
What is the answer in words?
Options:
|
Classifier: The answer choices use the AU/UK convention of "hundred and [number]", which requires localization for US school standards where "and" is omitted for whole numbers. Verifier: The answer choices include the "and" conjunction in whole number names, which is a regional linguistic convention requiring localization for US standards. |
mqn_01JKSWZ169X5GVYG9EJSRNHSG5 |
Localize | Spelling (AU-US) | Multiple Choice
A company analyses whether its advertising budget affects monthly sales.
What is the response variable?
Options:
|
Multiple Choice
A company analyzes whether its advertising budget affects monthly sales.
What is the response variable?
Options:
|
Classifier: Contains the AU spelling "analyses", which needs to be converted to the US spelling "analyzes". Verifier: The word "analyses" is used as a verb (third-person singular), which in AU/UK English is the spelling for both the plural noun and the verb. In US English, the verb is spelled "analyzes". |
mqn_01JKT561EG8CYC1ZQ8TQ1ES7E4 |
Localize | Terminology | Multiple Choice
Which of the following is a surd?
Options:
|
Multiple Choice
Which of the following is a radical?
Options:
|
Classifier: Contains the term "surd", which is specific to AU/UK school math terminology. Verifier: Contains the term "surd", which is specific to AU/UK school math terminology. |
mqn_01JKC3H8G6J928H4D2GSPNJYY7 |
Localize | Units (simple) | Multiple Choice
A construction worker can safely lift objects weighing between $10$ kg and $25$ kg, excluding these values.
Which inequality represents this if $x$ is the object's weight?
Options:
|
Multiple Choice
A construction worker can safely lift objects weighing between $10$ lbs and $25$ lbs, excluding these values.
Which inequality represents this if $x$ is the object's weight?
Options:
|
Classifier: The text contains the metric unit 'kg', which requires localization to US customary units (lbs) per the decision rules. Verifier: The text contains the metric unit 'kg', which requires conversion to US customary units (lbs). |
mqn_01JKTA7QRME3W83F89CFAS71AS |
Localize | Terminology | Multiple Choice
Convert the equation $y=2x^2 + 8x + 3$ to turning point form.
Options:
|
Multiple Choice
Convert the equation $y=2x^2 + 8x + 3$ to vertex form.
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is called "vertex form" in the US. Verifier: The term "turning point form" is the standard Australian/British term for what is called "vertex form" in the US, requiring localization. |
mqn_01JKT160C4EJGEYXA1A2Q7MXNR |
Localize | Terminology | Multiple Choice
What are the solutions to the simultaneous equations $3x + 5y = 5$ and $6x - 2y = 4$?
Options:
|
Multiple Choice
What are the solutions to the system of equations $3x + 5y = 5$ and $6x - 2y = 4$?
Options:
|
Classifier: The term "simultaneous equations" is the standard AU/UK term for what is typically called a "system of equations" in US curriculum. Verifier: The term "simultaneous equations" is the standard AU/UK term for what is called a "system of equations" in the US. |
mqn_01JKT28NEJNAAG1KB79RJ0JTE7 |
Localize | Terminology | Multiple Choice
What is the gradient-intercept form of $7x - 2y = 10$ ?
Options:
|
Multiple Choice
What is the slope-intercept form of $7x - 2y = 10$ ?
Options:
|
Classifier: The term "gradient-intercept form" is the AU equivalent of the US "slope-intercept form". Verifier: The term "gradient-intercept form" is the AU equivalent of the US "slope-intercept form". |
mqn_01JKQE2X0GMBXJ1FT2DABVSAPG |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $3ax+2ay+6bx+4by$ by grouping.
Options:
|
Multiple Choice
Factor $3ax+2ay+6bx+4by$ by grouping.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be converted to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU spelling. US spelling is "Factorize". |
mqn_01JKTANR4CCYZFK35BFRG6K98C |
Localize | Terminology | Multiple Choice
True or false:
The turning point form of $y=-3x^2 + 6x - 5$ is given by $y=-3(x-1)^2+2$.
Options:
|
Multiple Choice
True or false:
The vertex form of $y=-3x^2 + 6x - 5$ is given by $y=-3(x-1)^2+2$.
Options:
|
Classifier: The term "turning point form" is used, which requires localization to "vertex form" for a US audience. Verifier: The term "turning point form" is used, which is a locale-specific school term (AU/UK) for "vertex form" (US). |
mqn_01JKZ95DMYBAWF5BWAZW53W8P4 |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
$x^2(x+4)=0$ is a cubic equation in factorised form.
Options:
|
Multiple Choice
True or false:
$x^2(x+4)=0$ is a cubic equation in factored form.
Options:
|
Classifier: The word "factorised" in the question content uses AU spelling. Verifier: The word "factorised" in the question content uses AU/UK spelling. |
mqn_01JKZ92N04W77X9SNNX05YKD1Q |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
$(x-5)(x-3)(x-4)=0$ is a cubic equation in $[?]$ form.
Options:
|
Multiple Choice
Fill in the blank:
$(x-5)(x-3)(x-4)=0$ is a cubic equation in $[?]$ form.
Options:
|
Classifier: The answer choice "Factorised" uses the AU 's' spelling instead of the US 'z' spelling ("Factorized"). Verifier: The answer choice "Factorised" uses the AU/UK spelling (with 's') instead of the US spelling "Factorized". |
mqn_01JKZ9A3W6REJ0DSDPC76R2G98 |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
$x(x-5)^2=0$ is a cubic equation in $[?]$ form.
Options:
|
Multiple Choice
Fill in the blank:
$x(x-5)^2=0$ is a cubic equation in $[?]$ form.
Options:
|
Classifier: The answer choice "Factorised" uses AU spelling. Verifier: The answer choice "Factorised" uses AU/UK spelling. |
mqn_01JMC4JW0SE3TRVH6FACF2PDJ7 |
Localize | Terminology | Multiple Choice
True or false:
The turning point of a parabola is always on the $x$-axis.
Options:
|
Multiple Choice
True or false:
The vertex of a parabola is always on the $x$-axis.
Options:
|
Classifier: The term "turning point" is standard AU/UK terminology for the vertex of a parabola. In a US context, "vertex" is the standard term. Verifier: The term "turning point" is specific AU/UK terminology for the vertex of a parabola. US localization requires "vertex". |
mqn_01JKTAH6YSZTBB637GMEZHA71M |
Localize | Terminology | Multiple Choice
Convert the equation $y=4x^2 + 16x - 1$ to turning point form.
Options:
|
Multiple Choice
Convert the equation $y=4x^2 + 16x - 1$ to vertex form.
Options:
|
Classifier: The term "turning point form" is used, which requires localization to "vertex form" for a US audience. Verifier: The term "turning point form" is used, which is a locale-specific school term (AU/UK) for "vertex form" (US). |
mqn_01JM1TF1ERPZ9D2TZX0WV0EA7K |
Localize | Units (simple) | Multiple Choice
What type of data is a runner’s finishing time in a $100$ m race?
Options:
|
Multiple Choice
What type of data is a runner’s finishing time in a $100$ ft race?
Options:
|
Classifier: The text contains a metric unit ("m" for metres) in the context of a "100 m race". Per rule 1 and 7, any metric unit triggers a RED classification. Verifier: The text contains the metric unit "m" (metres) in the context of a "100 m race". Per the decision rules, any metric unit triggers a RED classification for conversion to US customary units (e.g., yards or 100-meter dash context). |
mqn_01JM1RY8746QB7Z0XY2SXM7CG1 |
Localize | Units (simple) | Multiple Choice
What type of data is a city's daily high temperature ($^\circ C$) for a month?
Options:
|
Multiple Choice
What type of data is a city's daily high temperature ($^\circ F$) for a month?
Options:
|
Classifier: The text contains the metric unit for temperature (degrees Celsius), which requires localization to Fahrenheit for a US audience. Verifier: The text contains the metric unit for temperature (degrees Celsius), which requires conversion to Fahrenheit for a US audience. |
mqn_01JMC4TQ7YGD960EFG6MPHC8YX |
Localize | Terminology | Multiple Choice
True or false:
For a parabola in the form $y = (x - a)(x - b)$, the $x$-coordinate of the turning point is the midpoint of $a$ and $b$.
Options:
|
Multiple Choice
True or false:
For a parabola in the form $y = (x - a)(x - b)$, the $x$-coordinate of the vertex is the midpoint of $a$ and $b$.
Options:
|
Classifier: The term "turning point" is used to describe the vertex of a parabola, which is specific to AU/UK school terminology. US localization requires "vertex". Verifier: The term "turning point" is specific AU/UK terminology for the vertex of a parabola. US localization requires "vertex". |
mqn_01JM13YP4E05QMW8MP1EJA1C36 |
Localize | Terminology | Multiple Choice
Fill in the blank:
The point-gradient form of a linear equation is given by $y - y_1 = m(x - x_1)$, where $m$ is the $[?]$ of the line.
Options:
|
Multiple Choice
Fill in the blank:
The point-slope form of a linear equation is given by $y - y_1 = m(x - x_1)$, where $m$ is the $[?]$ of the line.
Options:
|
Classifier: The term "point-gradient form" is the standard Australian term for what is called "point-slope form" in the United States. Additionally, the answer choice "Gradient" must be localized to "Slope". Verifier: The term "point-gradient form" is the standard Australian terminology for what is known as "point-slope form" in the US. Additionally, "Gradient" is used where "Slope" is the standard US term. |
mqn_01JM9EEHW2N25YNYM7GRJGVCGJ |
Localize | Spelling (AU-US) | Multiple Choice
Which asset is likely to depreciate the fastest?
Options:
|
Multiple Choice
Which asset is likely to depreciate the fastest?
Options:
|
Classifier: Contains the AU spelling "centre" which needs to be converted to the US spelling "center". Verifier: Contains the AU spelling "centre" in the answer choices, which requires localization to "center" for the US locale. |
mqn_01JM14AKZ6ENYD25ZQ92QWANAD |
Localize | Terminology | Multiple Choice
Which of the following equations is written in point-gradient form?
Options:
|
Multiple Choice
Which of the following equations is written in point-slope form?
Options:
|
Classifier: The term "point-gradient form" is used, which requires localization to "point-slope form" for a US audience. Verifier: The term "point-gradient form" is Australian terminology that requires localization to "point-slope form" for the US market. |
mqn_01JMHB9C93VN80TN9X1W2AZ8FX |
Localize | Terminology | Multiple Choice
To show the distribution of ages of students in a class, which graph should be used?
Options:
|
Multiple Choice
To show the distribution of ages of students in a class, which graph should be used?
Options:
|
Classifier: The term "Column graph" is the standard AU term for what is typically called a "Bar graph" or "Bar chart" in US curriculum. Verifier: The term "Column graph" is the standard Australian curriculum term for what is called a "Bar graph" in the US. |
mqn_01JMECXV8A41MW8T8QX5B2ZVW2 |
Localize | Terminology | Multiple Choice
Which of the following is not an example of ordinal data?
Options:
|
Multiple Choice
Which of the following is not an example of ordinal data?
Options:
|
Classifier: The term "Year levels" is the standard Australian way to refer to school grades. In the US, this is typically "Grade levels". Per the decision rules, terminology takes precedence over GREEN. Verifier: The term "Year levels" is specific to the Australian school system (and other Commonwealth systems), whereas the US uses "Grade levels". This requires localization. |
mqn_01JME02RVTY69BTAMRXSFZHJPD |
Localize | Units (simple) | Multiple Choice
True or false:
The displacement of air particles in a sound wave is given by $y = 10\cos\left(\frac{\pi}{5}t\right)$, where $y$ is the displacement in metres and $t$ is the time in seconds.
At $t = 5$, the particle is at its lowest position.
Options:
|
Multiple Choice
True or false:
The displacement of air particles in a sound wave is given by $y = 10\cos\left(\frac{\pi}{5}t\right)$, where $y$ is the displacement in feet and $t$ is the time in seconds.
At $t = 5$, the particle is at its lowest position.
Options:
|
Classifier: The text contains the metric unit "metres", which requires both spelling localization ("meters") and unit conversion to US customary units (e.g., "feet") depending on the specific curriculum depth, but at minimum it triggers the units conversion category. Verifier: The text contains the metric unit "metres", which is both an AU spelling and a metric unit requiring conversion to US customary units. Since units conversion is the most impactful change, RED.units_simple_conversion is correct. |
mqn_01JM14DQX88Q2PCGGG4G6C8R54 |
Localize | Terminology | Multiple Choice
Which of the following equations is written in point-gradient form?
Options:
|
Multiple Choice
Which of the following equations is written in point-slope form?
Options:
|
Classifier: The term "point-gradient form" is used, which requires localization to "point-slope form" for a US audience. Verifier: The term "point-gradient form" is Australian terminology that requires localization to "point-slope form" for the US market. |
mqn_01JMF1R1A783X7RCM133WRK20Z |
Localize | Answer set | Multiple Choice
Which season comes just after winter?
Options:
|
Multiple Choice
Which season comes just after winter?
Options:
|
Classifier: The term "Autumn" is used in the answer set, which is the standard AU term. In the US, "Fall" is the preferred term. Additionally, the sequence of seasons (Spring following Winter) is universal, but the term "Autumn" requires localization for US consistency. Verifier: The answer set contains "Autumn", which is the standard term in Australia but is typically replaced by "Fall" in US localization contexts. |
mqn_01JMF1X7K42JQ3G0HT5KTNB8FT |
Localize | Answer set | Multiple Choice
Which season comes just before summer?
Options:
|
Multiple Choice
Which season comes just before summer?
Options:
|
Classifier: Contains the term "Autumn" in the answer choices, which requires localization to "Fall" for the US market. Verifier: The answer set contains "Autumn", which requires localization to "Fall" for US consistency. |
mqn_01JMF25MXA466W309P8SPABG84 |
Localize | Answer set | Multiple Choice
What is the correct order of the seasons starting from spring?
Options:
|
Multiple Choice
What is the correct order of the seasons starting from spring?
Options:
|
Classifier: Contains the term "Autumn" multiple times in the answer set. This needs to be localized to "Fall" for US consistency. Verifier: The answer set contains "Autumn" in multiple options, requiring localization to "Fall" for the US market. |
mqn_01JMHBWZTP38J6D7YV0R0PX2XZ |
Localize | Terminology | Multiple Choice
A shop records the number of items sold each day over a month.
Which graph best displays this data?
Options:
|
Multiple Choice
A store records the number of items sold each day over a month.
Which graph best displays this data?
Options:
|
Classifier: The term "Column graph" is used, which is an AU-specific convention for bar charts. Verifier: The term "Column graph" is an AU-specific curriculum term for a bar chart. |
mqn_01JMHBTJH7YW9C6Q4FX77MNJND |
Localize | Terminology | Multiple Choice
A survey records the number of hours participants spend on social media each week.
Which graph best displays this data?
Options:
|
Multiple Choice
A survey records the number of hours participants spend on social media each week.
Which graph best displays this data?
Options:
|
Classifier: The term "Column graph" is used, which requires localization to "Bar graph" for US audiences. Verifier: The term "Column graph" is an AU-specific curriculum term for a bar chart. |
mqn_01JMHC59GSP0GQ2YGE09GS6SMH |
Localize | Terminology | Multiple Choice
A fitness tracker records the daily number of steps taken by each individual.
Which graph best displays this data?
Options:
|
Multiple Choice
A fitness tracker records the daily number of steps taken by each individual.
Which graph best displays this data?
Options:
|
Classifier: The term "Column graph" is used, which is an AU-specific convention for bar charts. Verifier: The term "Column graph" is an AU-specific curriculum term for a bar chart. |
mqn_01JMWZNGK3BP21YWY26F4EX4ZK |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
A spinner divided equally into four colours is spun $80$ times. Red appears $25$ times.
The experimental result equals the expected result.
Options:
|
Multiple Choice
True or false:
A spinner divided equally into four colors is spun $80$ times. Red appears $25$ times.
The experimental result equals the expected result.
Options:
|
Classifier: The text contains the AU/UK spelling "colours", which needs to be localized to the US spelling "colors". Verifier: The text contains "colours", which is the AU/UK spelling. This requires localization to "colors" for the US market. |
mqn_01JMK4W6ZFNPEJEET6529DPSMG |
Localize | Units (simple) | Multiple Choice
A runner runs $10$ km on the first day of training.
Each day, they add $2$ km to their run.
Which recurrence relation represents this situation?
Options:
|
Multiple Choice
A runner runs $10$ mi on the first day of training.
Each day, they add $2$ mi to their run.
Which recurrence relation represents this situation?
Options:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires localization to US customary units (miles) or at least triggers the units category per decision rules. Verifier: The text contains the metric unit "km" (kilometres), which requires localization to US customary units (miles) per the decision rules. |
mqn_01JMK5950NRE8TYZBFBQK195EF |
Localize | Units (simple) | Multiple Choice
A chemical solution is $1200$ ml. Each hour, $75$ ml evaporates, and $15$ ml is added.
Which recurrence relation represents this situation?
Options:
|
Multiple Choice
A chemical solution is $1200$ fl oz. Each hour, $75$ fl oz evaporates, and $15$ fl oz is added.
Which recurrence relation represents this situation?
Options:
|
Classifier: The text contains the metric unit 'ml' (milliliters), which requires conversion to US customary units (e.g., fluid ounces) or a change in context for US localization. Verifier: The text contains the metric unit 'ml' (milliliters) multiple times, which requires conversion to US customary units (e.g., fluid ounces) for US localization. |
mqn_01JMK5K394SH4PEP9787YP1PPT |
Localize | Units (simple) | Multiple Choice
A water tank has $1500$ L of water. Each day, $125$ L are used, and $20.5$ L are added from rainfall.
Which recurrence relation represents this situation?
Options:
|
Multiple Choice
A water tank has $1500$ gal of water. Each day, $125$ gal are used, and $20.5$ gal are added from rainfall.
Which recurrence relation represents this situation?
Options:
|
Classifier: The text contains the metric unit 'L' (liters), which requires conversion to US customary units (e.g., gallons) for US localization. Verifier: The text contains the metric unit 'L' (liters), which requires conversion to US customary units (e.g., gallons) for US localization. |
mqn_01JSP0143E157J1Z7TPAANM5CC |
Localize | Terminology | Multiple Choice
True or false:
$y = (x - 3)^2 + 4$ is the turning point form of the quadratic equation $y = x^2 - 6x + 13$.
Options:
|
Multiple Choice
True or false:
$y = (x - 3)^2 + 4$ is the vertex form of the quadratic equation $y = x^2 - 6x + 13$.
Options:
|
Classifier: The term "turning point form" is the standard AU/UK term for what is known as "vertex form" in the US. Verifier: The term "turning point form" is the standard AU/UK term for what is known as "vertex form" in the US. This requires localization for a US audience. |
mqn_01JSNHGGH7SN6F318CDSPZV1CA |
Localize | Terminology | Multiple Choice
What is the gradient-intercept form of $-3x + y = -5$ ?
Options:
|
Multiple Choice
What is the slope-intercept form of $-3x + y = -5$ ?
Options:
|
Classifier: The term "gradient-intercept form" is the standard AU term for what is called "slope-intercept form" in the US. This requires terminology localization. Verifier: The term "gradient-intercept form" is the standard Australian curriculum term for what is known as "slope-intercept form" in the US, requiring terminology localization. |
mqn_01JT5FXQKKMBW8QG90CRMVEK4R |
Localize | Units (simple) | Multiple Choice
Which of the following is not numerical data?
Options:
|
Multiple Choice
Which of the following is not numerical data?
Options:
|
Classifier: The text contains the metric unit 'km/h' in one of the answer choices, which requires conversion to US customary units (mph). Verifier: The text contains the metric unit "km/h" in one of the answer choices, which requires conversion to US customary units (mph). |
mqn_01JSXK9REH4JHGX8T3NWK6PVC4 |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
Depreciation refers to the $[?]$ in the value of an asset over time due to wear and tear or obsolescence.
Options:
|
Multiple Choice
Fill in the blank:
Depreciation refers to the $[?]$ in the value of an asset over time due to wear and tear or obsolescence.
Options:
|
Classifier: The answer choice "Stabilisation" uses the AU/UK 's' spelling, which requires conversion to the US 'z' spelling ("Stabilization"). Verifier: The answer choice "Stabilisation" uses the AU/UK 's' spelling, which requires localization to the US 'z' spelling ("Stabilization"). |
mqn_01JT2SAJP12VD107CQCFBS18GM |
Localize | Units (simple) | Multiple Choice
A jug has a capacity of $1.5$L.
Which of the following best explains what this means?
Options:
|
Multiple Choice
A pitcher has a capacity of $1.5$ gal.
Which of the following best explains what this means?
Options:
|
Classifier: The question and answers contain multiple metric units (L, m, kg) which require conversion for a US audience. Verifier: The question and answers contain multiple metric units (L, m, kg) which require conversion for a US audience. |
mqn_01JT2NY7KGRKSBB6TTKCS8ZBMP |
Localize | Terminology | Multiple Choice
What does the A stands for in BODMAS?
Options:
|
Multiple Choice
What does the A stand for in PEMDAS?
Options:
|
Classifier: BODMAS is the standard acronym for order of operations in Australia/UK. In the US, PEMDAS is the standard acronym. This requires terminology localization. Verifier: BODMAS is the standard acronym in Australia, whereas PEMDAS is used in the US. This is a school-context terminology difference. |
mqn_01JT0JZG44ZQ618XJV643DP8F5 |
Localize | Cultural refs | Multiple Choice
Which of the following best describes GST?
Options:
|
Multiple Choice
Which of the following best describes sales tax?
Options:
|
Classifier: GST (Goods and Services Tax) is the specific consumption tax system used in Australia. The US uses "Sales Tax" which is structured differently (state-level vs national). This is a distinct cultural/economic reference. Verifier: GST (Goods and Services Tax) is a specific tax system used in Australia (and other countries like NZ/Canada), whereas the US uses Sales Tax. This is a cultural/economic reference requiring localization. |
mqn_01JTHYVQNVFNWPFEGDGF7BX0QA |
Localize | Terminology | Multiple Choice
Classify the solution(s) to the following simultaneous equations, where $a \ge 2$ and $ b > 0$:
$ a(2x - y) + b(x + y) = 3a + b$
$ 2ax + bx + (b - a)y = 5$
Options:
|
Multiple Choice
Classify the solution(s) to the following system of equations, where $a \ge 2$ and $ b > 0$:
$ a(2x - y) + b(x + y) = 3a + b$
$ 2ax + bx + (b - a)y = 5$
Options:
|
Classifier: The term "simultaneous equations" is the standard AU/UK term for what is typically called a "system of equations" in US curriculum. Verifier: The term "simultaneous equations" is the standard AU/UK terminology for what is called a "system of equations" in the US. |
mqn_01JT7TKS5B3P5XTM0KTPQD1GTY |
Localize | Terminology | Multiple Choice
Line segments connecting the points $A(-10, 6)$, $B(4, 6)$, $C(8, -4)$, and $D(-10, -4)$ form a trapezium.
Which statement about the gradients of the sides is true?
A) All sides have gradient $0$
B) The gradients of $AB$ and $CD$ are $0$
C) The gradients of $AD$ and $BC$ are undefined
D) Only $BC$ has an undefined gradient
Options:
|
Multiple Choice
Line segments connecting the points $A(-10, 6)$, $B(4, 6)$, $C(8, -4)$, and $D(-10, -4)$ form a trapezoid.
Which statement about the slopes of the sides is true?
A) All sides have slope $0$
B) The slopes of $AB$ and $CD$ are $0$
C) The slopes of $AD$ and $BC$ are undefined
D) Only $BC$ has an undefined slope
Options:
|
Classifier: The text uses the term "trapezium", which in the US refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to a quadrilateral with at least one pair of parallel sides (which the US calls a "trapezoid"). This requires terminology localization. Verifier: The text uses the term "trapezium", which in the US refers to a quadrilateral with no parallel sides, whereas in AU/UK it refers to a quadrilateral with at least one pair of parallel sides (US "trapezoid"). This requires terminology localization. |
mqn_01JTHBJY4043252919RT3X74YT |
Localize | Units (simple) | Multiple Choice
The area of a rectangular garden is given by the expression $ (2x+5)(x-3)+(x+2)^2- (3x-4)^2$ square metres.
Expand and simplify the expression.
Options:
|
Multiple Choice
The area of a rectangular garden is given by the expression $ (2x+5)(x-3)+(x+2)^2- (3x-4)^2$ square feet.
Expand and simplify the expression.
Options:
|
Classifier: The text contains the metric unit "metres" (square metres), which requires conversion to US customary units (square feet/yards) and also contains AU-specific spelling ("metres" vs "meters"). Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains "square metres", which is both a metric unit requiring conversion and an AU-specific spelling. Per rule 5, units conversion takes precedence over spelling. |
mqn_01JTHXCX7NW3GAEGFDMJR518QB |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(3a - 4b)(3a + 4b)(9a^2 + 16b^2)$?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(3a - 4b)(3a + 4b)(9a^2 + 16b^2)$?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
mqn_01JTN6YP391SYTV6FZBB5JNYNM |
Localize | Terminology | Multiple Choice
A linear equation passes through the point $\left(-\frac{2}{5},\ \frac{7}{4}\right)$ and has a gradient of $-\frac{5}{3}$.
What is the equation of the line in general form?
Options:
|
Multiple Choice
A linear equation passes through the point $\left(-\frac{2}{5},\ \frac{7}{4}\right)$ and has a slope of $-\frac{5}{3}$.
What is the equation of the line in general form?
Options:
|
Classifier: The term "gradient" is standard in AU/UK for the steepness of a line, whereas "slope" is the standard term in US school mathematics. Additionally, "general form" in the US usually refers to Ax + By + C = 0, but the terminology preference (slope vs gradient) is a clear localization signal. Verifier: The term "gradient" is the standard AU/UK term for the US "slope", which is a school-context terminology difference. |
mqn_01JTHGP5JX6JNKPSRFFKJJ4HMY |
Localize | Spelling (AU-US) | Multiple Choice
Write $2ax - 3bx + 4ay - 6by + ax - \dfrac{3}{2}bx$ in factorised form.
Options:
|
Multiple Choice
Write $2ax - 3bx + 4ay - 6by + ax - \dfrac{3}{2}bx$ in factored form.
Options:
|
Classifier: Contains the AU spelling "factorised". Verifier: The text contains the AU spelling "factorised" (US: factorized). |
mqn_01JTHG94JSJ5D1J2815DJ7E4ND |
Localize | Spelling (AU-US) | Multiple Choice
Write $12x^3 - 6y - 18x^2y + 4x + 8x^2 - 12xy $ in factorised form.
Options:
|
Multiple Choice
Write $12x^3 - 6y - 18x^2y + 4x + 8x^2 - 12xy $ in factored form.
Options:
|
Classifier: Contains the AU spelling "factorised". Verifier: The text contains the AU spelling "factorised" (US: factorized). |
mqn_01JTHXEQVKXBN29WFMYPH1N415 |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(5m - 2n)(5m + 2n)(25m^2 + 4n^2)$?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(5m - 2n)(5m + 2n)(25m^2 + 4n^2)$?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
mqn_01JTHXGFCWHCAFBNQV8V67NYDW |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following expressions can be factorised as $(6x - 7y)(6x + 7y)(36x^2 + 49y^2)$?
Options:
|
Multiple Choice
Which of the following expressions can be factored as $(6x - 7y)(6x + 7y)(36x^2 + 49y^2)$?
Options:
|
Classifier: The word "factorised" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("factorized"). Verifier: The text contains "factorised", which is the AU/UK spelling. US spelling is "factorized". |
mqn_01JTJJ9NP69ZH9SH38QKHKWSR2 |
Localize | Terminology | Multiple Choice
At $5\%$ p.a. compound interest, an investment grows from $\$2000$ to $\$6000$ in $x$ years.
At $8\%$ p.a., the same growth happens in $y$ years.
Which is true about $x$ and $y$?
Options:
|
Multiple Choice
At $5\%$ APR compound interest, an investment grows from $\$2000$ to $\$6000$ in $x$ years.
At $8\%$ APR, the same growth happens in $y$ years.
Which is true about $x$ and $y$?
Options:
|
Classifier: Contains "p.a." (per annum), which is an AU/UK convention for interest rates that requires localization for US students. Verifier: Contains "p.a." (per annum), which is an AU/UK convention for interest rates that requires localization for US students. |
mqn_01JTJJ6HDNCZRNYKQTWAJSGYHT |
Localize | Terminology | Multiple Choice
At $5\%$ p.a. compound interest, an investment grows from $\$2000$ to $\$6000$ in $x$ years.
At $10\%$ p.a., the same growth happens in $y$ years.
Which is true about $x$ and $y$?
Options:
|
Multiple Choice
At $5\%$ APR compound interest, an investment grows from $\$2000$ to $\$6000$ in $x$ years.
At $10\%$ APR, the same growth happens in $y$ years.
Which is true about $x$ and $y$?
Options:
|
Classifier: The text contains the abbreviation "p.a." (per annum), which is common in AU/UK contexts but typically replaced with "per year" or "annually" in US K-12 math. While the dollar sign is used, "p.a." is a distinct terminology marker. Verifier: The abbreviation "p.a." (per annum) is a common AU/UK convention for interest rates and is rarely used in US K-12 mathematics, where "per year" or "annually" is preferred. |
mqn_01JTHF4A2Q8PZH4XT49B7FWY4Y |
Localize | Spelling (AU-US) | Multiple Choice
Write $x^2(x+y)^4 - \dfrac{1}{16}y^2(2x+2y)^4$ in factorised form.
Options:
|
Multiple Choice
Write $x^2(x+y)^4 - \dfrac{1}{16}y^2(2x+2y)^4$ in factored form.
Options:
|
Classifier: Contains the AU spelling "factorised". In the US, "factorized" is used. Verifier: The text contains the AU spelling "factorised" (US: factorized). |
mqn_01JTN7J518VDT6SNZBQ5G22DKR |
Localize | Terminology | Multiple Choice
A line has gradient $m = \dfrac{2a}{3b}$ and passes through the point $\left(-\dfrac{3b}{2a},\ 0\right)$.
Write its equation in general form in terms of $a$ and $b$.
Options:
|
Multiple Choice
A line has slope $m = \dfrac{2a}{3b}$ and passes through the point $\left(-\dfrac{3b}{2a},\ 0\right)$.
Write its equation in general form in terms of $a$ and $b$.
Options:
|
Classifier: Contains the term "gradient", which is the AU/UK equivalent of the US "slope". Verifier: The term "gradient" is used, which is a specific AU/UK terminology preference over the US "slope". |
mqn_01JW8DRCEG131JXJD4875DJ40J |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following questions cannot be asked about an expression?
Options:
|
Multiple Choice
Which of the following questions cannot be asked about an expression?
Options:
|
Classifier: The text contains the AU spelling "factorised", which requires conversion to the US spelling "factorized". Verifier: The text contains the AU spelling "factorised" in the third answer choice, which requires localization to "factorized". |
mqn_01JVSJ4SQHD0F1G31RQPM8AVNB |
Localize | Units (simple) | Multiple Choice
There are $100$ centimetres in a metre.
Convert $3.25$ metres to metres and centimetres.
Options:
|
Multiple Choice
There are $12$ inches in a foot.
Convert $3.25$ feet to feet and inches.
Options:
|
Classifier: The text contains metric units (centimetres, metre) and AU-specific spelling (metres, centimetres). Per decision rule 6, units conversion takes precedence over spelling. Verifier: The text contains metric units (metres, centimetres) and AU-specific spelling (metres). Per rule 5, units conversion takes precedence over spelling. |
mqn_01JVY3T91YPFF64QM031MAJGQM |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is least appropriate for a scatterplot?
A) Exploring the relationship between heart rate and running speed
B) Displaying the number of students enrolled in each subject
C) Comparing temperature and ice cream sales
D) Analysing hours of sleep and concentration levels
Options:
|
Multiple Choice
Which of the following is least appropriate for a scatterplot?
A) Exploring the relationship between heart rate and running speed
B) Displaying the number of students enrolled in each subject
C) Comparing temperature and ice cream sales
D) Analyzing hours of sleep and concentration levels
Options:
|
Classifier: Contains the AU spelling "Analysing", which needs to be converted to the US spelling "Analyzing". Verifier: The text contains the AU spelling "Analysing" in option D, which requires localization to "Analyzing". |
mqn_01JV3Q7GM7MTM38VA115M6SN6D |
Localize | Terminology | Multiple Choice
A school excursion includes $112$ Year $10$, $86$ Year $9$, and $74$ Year $8$ students. Later, $38$ more Year $9$ students join the group.
What is the ratio of Year $10$ students to the new total number of students?
Options:
|
Multiple Choice
A school field trip includes $112$ Grade $10$, $86$ Grade $9$, and $74$ Grade $8$ students. Later, $38$ more Grade $9$ students join the group.
What is the ratio of Grade $10$ students to the new total number of students?
Options:
|
Classifier: The text uses "Year 10", "Year 9", and "Year 8" to refer to grade levels, which is standard Australian school terminology. In the US, these are referred to as "Grade 10", "Grade 9", and "Grade 8". Verifier: The text uses "Year 10", "Year 9", and "Year 8" to refer to grade levels, which is specific to Australian/British school terminology. In the US, these are "Grade 10", etc. |
mqn_01JWNQAYE862ZVA3DTEYYRWEB5 |
Localize | Terminology | Multiple Choice
A line passes through points where the $y$-value decreases by $6$ for every increase of $3$ in the $x$-value.
What word best describes the gradient of this line?
Options:
|
Multiple Choice
A line passes through points where the $y$-value decreases by $6$ for every increase of $3$ in the $x$-value.
What word best describes the slope of this line?
Options:
|
Classifier: The term "gradient" is the standard AU/UK term for what is referred to as "slope" in US school mathematics. Verifier: The term "gradient" is the standard AU/UK term for what is referred to as "slope" in US school mathematics, requiring localization for US audiences. |
mqn_01JWNQCRYWX2Z2QENV4SNERYG2 |
Localize | Terminology | Multiple Choice
A line passes through points where the $y$-value increases by $12$ every time the $x$-value increases by $4$.
What word best describes the gradient of this line?
Options:
|
Multiple Choice
A line passes through points where the $y$-value increases by $12$ every time the $x$-value increases by $4$.
What word best describes the slope of this line?
Options:
|
Classifier: Uses the AU term "gradient" (US: slope). Also contains a typo "Unchnaged" in the answer set, though terminology is the primary classification driver. Verifier: The term "gradient" is used, which is a specific school-context terminology difference (AU: gradient, US: slope). |
mqn_01JWA4PDWZQWB04SADWPKJGWVQ |
Localize | Units (simple) | Multiple Choice
A data set of $500$ student heights, in cm, is normally distributed.
If each height is squared and then displayed in a histogram, how does the shape change?
Options:
|
Multiple Choice
A data set of $500$ student heights, in in, is normally distributed.
If each height is squared and then displayed in a histogram, how does the shape change?
Options:
|
Classifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units (inches/feet) for a US audience. Verifier: The text contains the metric unit "cm" (centimetres), which requires conversion to US customary units. The conversion is a simple numeric change in context. |
mqn_01JX7Y7P3173FAVQRGJWYAMNC6 |
Localize | Units (simple) | Multiple Choice
Two distances are $4.8$ km and $3200$ m.
Write the ratio in kilometres, in simplest form.
Options:
|
Multiple Choice
Two distances are $4.8$ mi and $3200$ ft.
Write the ratio in miles, in simplest form.
Options:
|
Classifier: The text contains metric units ("km", "m", "kilometres"). Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains metric units ("km", "m", "kilometres") and the AU spelling "kilometres". Per rule 5, units conversion takes precedence over spelling. |
mqn_01JX7YG8F72XYRFWSEX54CK5MH |
Localize | Units (simple) | Multiple Choice
A recipe uses $900$ g of flour and $2.7$ kg of sugar.
Express the ratio in grams, in simplest form.
Options:
|
Multiple Choice
A recipe uses $900$ oz of flour and $2.7$ lb of sugar.
Express the ratio in ounces, in simplest form.
Options:
|
Classifier: The text contains metric units ("g", "kg"). Verifier: The text contains metric units ("g", "kg"). Per rule 3, any metric unit requires at least RED.units_simple_conversion. |
mqn_01JWA4J9JQH8NA9AYAJAV2C3RQ |
Localize | Spelling (AU-US) | Multiple Choice
A data set of $200$ lap times is normally distributed with a mean of $130$ and standard deviation of $10$.
If all values below $120$ are removed, which of the following best describes the new distribution?
A) Symmetrical, centred at $130$
B) Right-skewed, peak near $130$
C) Left-skewed, peak near $120$
D) Uniform, spread evenly from $120$ to $150$
Options:
|
Multiple Choice
A data set of $200$ lap times is normally distributed with a mean of $130$ and standard deviation of $10$.
If all values below $120$ are removed, which of the following best describes the new distribution?
A) Symmetrical, centered at $130$
B) Right-skewed, peak near $130$
C) Left-skewed, peak near $120$
D) Uniform, spread evenly from $120$ to $150$
Options:
|
Classifier: The text contains the AU spelling "centred", which requires conversion to the US spelling "centered". Verifier: The text contains the AU spelling "centred" in option A, which requires localization to "centered". |
mqn_01JX7Y4FCJMJ18RXM4M42PNMHM |
Localize | Units (simple) | Multiple Choice
A tank holds $3$ litres of oil and $750$ mL of water.
Express their amounts as a ratio in litres, in simplest form.
Options:
|
Multiple Choice
A tank holds $3$ gallons of oil and $750$ fl oz of water.
Express their amounts as a ratio in gallons, in simplest form.
Options:
|
Classifier: The text contains metric units ("litres", "mL") and the AU spelling "litres". Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains metric units ("litres", "mL") and the AU spelling "litres". Per rule 5, units conversion takes precedence over spelling. |
mqn_01JWN0J4P0CPF4XH2R83NNRV1R |
Localize | Units (simple) | Multiple Choice
A data set contains distances between $300$ km and $900$ km for $50$ trucks.
If one additional value of $1600$ km is added, what will happen?
Options:
|
Multiple Choice
A data set contains distances between $300$ mi and $900$ mi for $50$ trucks.
If one additional value of $1600$ mi is added, what will happen?
Options:
|
Classifier: The text contains the metric unit "km" (kilometres), which requires conversion to US customary units (miles) for a US audience. Verifier: The text contains the metric unit "km" (kilometres) multiple times, which requires conversion to US customary units (miles). The conversion is a simple numeric change in a statistical context. |
mqn_01JXCF5T09ST4JMSAM22GKMPJ2 |
Localize | Units (simple) | Multiple Choice
True or false:
Shape A has side lengths $4$ cm and $8$ cm.
Shape B has side lengths $5$ cm and $8$ cm.
Shape B could be a dilation of Shape A.
Options:
|
Multiple Choice
True or false:
Shape A has side lengths $4$ in and $8$ in.
Shape B has side lengths $5$ in and $8$ in.
Shape B could be a dilation of Shape A.
Options:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires conversion for US localization. Verifier: The text contains the metric unit "cm", which requires conversion for US localization. |
mqn_01JX7Y17S2EPQ096X5AB7GY9D9 |
Localize | Units (simple) | Multiple Choice
The lengths of two ropes are given as $2.5$ m and $150$ cm
Express their lengths as a ratio in metres, in simplest form.
Options:
|
Multiple Choice
The lengths of two ropes are given as $2.5$ ft and $150$ in
Express their lengths as a ratio in feet, in simplest form.
Options:
|
Classifier: The text contains metric units ("m", "cm", "metres") and the AU spelling "metres". Per rule 6, units conversion takes precedence over spelling. Verifier: The text contains metric units ("m", "cm", "metres") and the AU spelling "metres". Per rule 5, units conversion takes precedence over spelling. |
mqn_01JXHWCEJG9Q0CAHCAXZEVF28F |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is the correct factorisation of $a^2x^2 - (b + c)ax + bc$ using the cross method?
Options:
|
Multiple Choice
Which of the following is the correct factoring of $a^2x^2 - (b + c)ax + bc$ using the cross method?
Options:
|
Classifier: The text contains the AU spelling "factorisation", which requires conversion to the US spelling "factorization". Verifier: The text contains "factorisation", which is the AU/British spelling. This requires localization to "factorization". |
mqn_01JZMXRW5N75RDD5PJPD1JE1H7 |
Localize | Spelling (AU-US) | Multiple Choice
What is the correct factorisation of $-6a^2bc + 3abc^2 - 9ab$ ?
Options:
|
Multiple Choice
What is the correct factoring of $-6a^2bc + 3abc^2 - 9ab$ ?
Options:
|
Classifier: Contains the AU spelling "factorisation", which needs to be converted to the US spelling "factorization". Verifier: The text contains "factorisation", which is the AU/British spelling. US English uses "factorization". |
mqn_01JXHW1BTVKEPVZ791SFC8XQ0M |
Localize | Spelling (AU-US) | Multiple Choice
Using the cross method, factorise $21x^2 - 47x + 10$.
What are the two binomial factors?
Options:
|
Multiple Choice
Using the cross method, factor $21x^2 - 47x + 10$.
What are the two binomial factors?
Options:
|
Classifier: The text contains the AU spelling "factorise", which requires conversion to the US spelling "factorize". While "cross method" is a specific pedagogical term, it is used in various regions and the spelling change is the primary localization requirement here. Verifier: The text contains "factorise", which is the AU/British spelling. This requires localization to "factorize". |
mqn_01JXVBZG7STA73ZG835P4SMYPK |
Localize | Units (simple) | Multiple Choice
A rectangle has a perimeter of $60$ m, and the length is $4$ metres less than twice the width.
Which equation represents this situation?
Options:
|
Multiple Choice
A rectangle has a perimeter of $60$ ft, and the length is $4$ feet less than twice the width.
Which equation represents this situation?
Options:
|
Classifier: The text contains metric units ("m" and "metres"). Per the decision rules, any metric unit found anywhere in the text requires classification into a units category. "metres" also constitutes an AU spelling. Verifier: The text contains metric units ("m" and "metres"). "metres" is also an AU spelling. Per rule 3 and 5, this is correctly classified as units_simple_conversion. |
mqn_01JX813WZ4DZER2GDXFJQ7R5BA |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
Two triangles have side lengths of $8$, $12$, $16$ cm and $4$, $6$, $8$ cm.
The triangles are similar by the $[?]$ similarity test.
Options:
|
Multiple Choice
Fill in the blank:
Two triangles have side lengths of $8$, $12$, $16$ in and $4$, $6$, $8$ in.
The triangles are similar by the $[?]$ similarity test.
Options:
|
Classifier: The text contains the metric unit "cm", which requires conversion to US customary units (e.g., inches) or a generic "units" label per localization policy. Verifier: The text contains the metric unit "cm", which requires conversion to US customary units or generic units. |
mqn_01JZMXW8YYMF4GH5Y6JXETHB7Z |
Localize | Spelling (AU-US) | Multiple Choice
What is the correct factorisation of $-8x^3y^2z^2 + 12x^2yz^2 - 4x^2y^2z$ ?
Options:
|
Multiple Choice
What is the correct factoring of $-8x^3y^2z^2 + 12x^2yz^2 - 4x^2y^2z$ ?
Options:
|
Classifier: Contains the AU spelling "factorisation", which requires conversion to "factorization" for a US audience. Verifier: The text contains "factorisation", which is the AU/British spelling. US English uses "factorization". |
mqn_01JZMY0BRYQDBBXNV7GJNRXMJC |
Localize | Spelling (AU-US) | Multiple Choice
What is the correct factorisation of $-9pqr + 3pq^2 - 6pq$ ?
Options:
|
Multiple Choice
What is the correct factoring of $-9pqr + 3pq^2 - 6pq$ ?
Options:
|
Classifier: Contains the AU spelling "factorisation". Verifier: The text contains "factorisation", which is the AU/British spelling. US English uses "factorization". |
mqn_01JZPQK1CN867TXZYAF1GT8ARD |
Localize | Units (simple) | Multiple Choice
Mel buys $6$ kg of apples for $\$13.50$.
What is the cost per kg?
Options:
|
Multiple Choice
Mel buys $6$ lbs of apples for $\$13.50$.
What is the cost per lb?
Options:
|
Classifier: Contains metric units "kg" and "g". Any metric unit requires localization to US customary units. Verifier: The text contains metric units "kg" and "g", which require conversion to US customary units (e.g., pounds/ounces). |
mqn_01JZMY3F0NRPQ1XNRKJM30W5D9 |
Localize | Spelling (AU-US) | Multiple Choice
What is the correct factorisation of $-12x^2y + 6xy^2 - 18x^2y^2$ ?
Options:
|
Multiple Choice
What is the correct factoring of $-12x^2y + 6xy^2 - 18x^2y^2$ ?
Options:
|
Classifier: Contains the AU spelling "factorisation". Verifier: The text contains "factorisation", which is the AU/British spelling. US English uses "factorization". |
mqn_01JZPQF5N8H5FC0Y7ZRD4DZR5Q |
Localize | Units (simple) | Multiple Choice
A car travels $450$ metres in $3.6$ minutes.
What is the distance per minute?
Options:
|
Multiple Choice
A car travels $450$ feet in $3.6$ minutes.
What is the distance per minute?
Options:
|
Classifier: Contains the metric unit "metres" (both a metric unit and AU spelling) and abbreviations like "m/h" and "m/min". Units conversion takes precedence over spelling. Verifier: The text contains the metric unit "metres" (which is also an AU spelling) and abbreviations "m/h" and "m/min". Metric units require conversion to US customary units. |
mqn_01JZSQYJQJX7FB622EMW9N0GXK |
Localize | Units (simple) | Multiple Choice
In a kite $ABCD$, sides $AB = AD = 8\text{ cm}$ and $BC = CD = 5\text{ cm}$.
Which diagonal will be bisected?
Options:
|
Multiple Choice
In a kite $ABCD$, sides $AB = AD = 8\text{ in}$ and $BC = CD = 5\text{ in}$.
Which diagonal will be bisected?
Options:
|
Classifier: The text contains the metric unit "cm", which requires localization to US customary units. Verifier: The text contains the metric unit "cm", which requires localization. It is a simple conversion as it involves basic side lengths. |
mqn_01JZVW85TVAVHPW4FX4DX14F3X |
Localize | Units (simple) | Multiple Choice
What is the best unit to measure the volume of an eyelash?
Options:
|
Multiple Choice
What is the best unit to measure the volume of an eyelash?
Options:
|
Classifier: The question and answer set are entirely based on metric units (mm, km, m, cm), which requires localization for a US audience. Verifier: The question and answer set rely entirely on metric units (mm, km, m, cm), requiring localization to US customary units. |
mqn_01JZPXCE6CB1N09PYM5W219K8A |
Localize | Units (simple) | Multiple Choice
A car uses $41.6$ litres of fuel over $347.2$ km.
How much distance can be covered per litre of fuel?
Options:
|
Multiple Choice
A car uses $41.6$ gallons of gas over $347.2$ miles.
How much distance can be covered per gallon of gas?
Options:
|
Classifier: Contains multiple metric units ("litres", "km", "L") and AU spelling ("litres"). Units conversion is the highest priority. Verifier: The text contains metric units "litres" (AU spelling), "km", and "L". These require conversion to US customary units (gallons/miles). |
mqn_01K071MVB852YJ2JZEX5M4BMBD |
Localize | Answer set | Multiple Choice
True or false:
If a trapezium has equal-length diagonals and one line of symmetry, it must be isosceles.
Options:
|
Multiple Choice
True or false:
If a trapezoid has equal-length diagonals and one line of symmetry, it must be isosceles.
Options:
|
Classifier: The term "trapezium" is used, which requires localization to "trapezoid" for the US market. Verifier: The term "trapezium" is used, which requires localization to "trapezoid" for the US market. |
mqn_01JZWF0NRSGK8M5E12M77HJRXQ |
Localize | Units (simple) | Multiple Choice
Which holds more water: a $19$ L cooler or $30$ bottles of $750$ mL each?
Options:
|
Multiple Choice
Which holds more water: a $19$ gal cooler or $30$ bottles of $750$ fl oz each?
Options:
|
Classifier: The text contains metric units "L" and "mL", which require localization. Verifier: The text contains metric units "L" and "mL", which require localization. |
mqn_01K08R3WZ1S9X30QHWSR9H2JPE |
Localize | Spelling (AU-US) | Multiple Choice
A rectangle is rotated about its centre.
Which of the following properties remain unchanged?
Options:
|
Multiple Choice
A rectangle is rotated about its center.
Options:
|
Classifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". Verifier: Contains the AU spelling "centre", which requires conversion to the US spelling "center". |
mqn_01JZWGTA5JPWMCP95C86799AGC |
Localize | Units (simple) | Multiple Choice
Which option has the greater total capacity?
A: $10$ test tubes of $75$ mL and $1$ large measuring cup of $2.5$ L
B: $4$ jugs of $200$ mL and $5$ cups of $250$ mL
Options:
|
Multiple Choice
Which option has the greater total capacity?
A: $10$ test tubes of $75$ fl oz and $1$ large measuring cup of $2.5$ gal
B: $4$ jugs of $200$ fl oz and $5$ cups of $250$ fl oz
Options:
|
Classifier: The text contains metric units "mL" and "L", which require localization. Verifier: The text contains metric units "mL" and "L", which require localization. |
mqn_01K05WKKGEN5SPH6SS6J6AFZ4V |
Review | Policy | Multiple Choice
Which of these is measured in months?
Options:
|
Multiple Choice
Which of these is measured in months?
Options:
|
Classifier: The term "school term" is used. In the US, this is typically referred to as a "semester" or "quarter" depending on the specific school's policy/system. This requires a policy decision on the preferred US equivalent. Verifier: The term "school term" is a specific educational structure term that maps to "semester" or "quarter" in the US, fitting the specific GRAY category for this policy ambiguity. |
mqn_01K05ZHGE22M3HFNXDQZB6TSCX |
Localize | Terminology | Multiple Choice
Which of these cannot be measured in years?
Options:
|
Multiple Choice
Which of these cannot be measured in years?
Options:
|
Classifier: The term "primary school" is used, which in the US is typically "elementary school". Verifier: The term "primary school" is used in the answer options, which requires localization to "elementary school" for a US audience. |
mqn_01K05ZR88R69K04PBP9J5C2T59 |
Localize | Spelling (AU-US) | Multiple Choice
Which activity cannot be measured in weeks?
Options:
|
Multiple Choice
Which activity cannot be measured in weeks?
Options:
|
Classifier: The word "Practising" is the AU/UK spelling of the verb. In US English, "practicing" is used for both the noun and the verb. Verifier: The word "Practising" is the AU/UK spelling for the verb form. In US English, "practicing" is used for both noun and verb. |
mqn_01JZWGZB184EM8RMD8YSP59P4H |
Localize | Units (simple) | Multiple Choice
Which option has the greater total capacity?
A: $3$ large cans of $1.5$ L and $6$ glass cups of $200$ mL
B: $2$ containers of $2$ L and $5$ baby bottles of $180$ mL
Options:
|
Multiple Choice
Which option has the greater total capacity?
A: $3$ large cans of $1.5$ gal and $6$ glass cups of $200$ fl oz
B: $2$ containers of $2$ gal and $5$ baby bottles of $180$ fl oz
Options:
|
Classifier: The text contains multiple metric units (L and mL) which require conversion to US customary units. Verifier: The text contains metric units "L" (litres) and "mL" (millilitres) which require conversion to US customary units (e.g., gallons, quarts, or fluid ounces). The math is a simple comparison of total volumes, making it a simple conversion. |
mqn_01K06TG7R144AHCAE336KY3Q7X |
Localize | Answer set | Multiple Choice
True or false:
If a quadrilateral has exactly one pair of parallel sides, then it is a trapezium.
Options:
|
Multiple Choice
True or false:
If a quadrilateral has exactly one pair of parallel sides, then it is a trapezoid.
Options:
|
Classifier: The text uses the term "trapezium", which requires localization to "trapezoid" in the US. Verifier: The term "trapezium" is used in the question, which requires localization to "trapezoid" for US English. |
mqn_01K08WY9T03SSB6Q9D75TKVB4F |
Localize | Terminology | Multiple Choice
Which change in compounding would triple the interest rate per period, assuming the annual interest rate stays the same?
Options:
|
Multiple Choice
Which change in compounding would triple the interest rate per period, assuming the annual interest rate stays the same?
Options:
|
Classifier: Contains the term "fortnightly", which is a distinct AU/UK term. In a US school context, this is typically replaced with "every two weeks" or "bi-weekly". Verifier: Contains the term "fortnightly", which is a distinct AU/UK term. In a US school context, this is typically replaced with "every two weeks" or "bi-weekly". |
mqn_01K06T9XMJSVK8N6YJCPARZEBE |
Localize | Answer set | Multiple Choice
Which of the following statements is always true?
A) All kites are rhombuses
B) All rhombuses are kites
C) All trapeziums are parallelograms
D) All parallelograms are kites
Options:
|
Multiple Choice
Which of the following statements is always true?
A) All kites are rhombuses
B) All rhombuses are kites
C) All trapezoids are parallelograms
D) All parallelograms are kites
Options:
|
Classifier: The text contains the term "trapeziums", which must be localized to "trapezoids" for a US audience. Verifier: The text contains "trapeziums", which is the AU/UK term for the US "trapezoids". |
mqn_01K06T455CQQF4XPJWFJAYYNZM |
Localize | Answer set | Multiple Choice
Which of the following quadrilaterals must have perpendicular diagonals?
Options:
|
Multiple Choice
Which of the following quadrilaterals must have perpendicular diagonals?
Options:
|
Classifier: The term "Trapezium" is used in the answer set, which requires localization to "Trapezoid" for a US audience. Verifier: The term "Trapezium" requires localization to "Trapezoid" for a US audience. |
mqn_01K03JZBMD33N0BEDC4DZWEAA3 |
Localize | Answer set | Multiple Choice
Which of the following best describes a trapezium?
A) A shape with all sides equal
B) A quadrilateral with no parallel sides
C) A quadrilateral with one pair of parallel sides
D) A triangle with one long base
Options:
|
Multiple Choice
Which of the following best describes a trapezoid?
A) A shape with all sides equal
B) A quadrilateral with no parallel sides
C) A quadrilateral with one pair of parallel sides
D) A triangle with one long base
Options:
|
Classifier: The term "trapezium" in AU/UK refers to a quadrilateral with one pair of parallel sides, which is called a "trapezoid" in the US. This requires localization of the term in both the question and the answer logic. Verifier: The term "trapezium" is used in AU/UK to describe a quadrilateral with one pair of parallel sides. In the US, this shape is called a "trapezoid". Because the question asks for the definition of the term itself, it requires localization to ensure the term and the logic (Option C) remain correct for a US audience. |
mqn_01K06T05FY1JJCEJ283HAB5CRN |
Localize | Answer set | Multiple Choice
Which shape always has exactly one pair of parallel sides?
Options:
|
Multiple Choice
Which shape always has exactly one pair of parallel sides?
Options:
|
Classifier: The term "Trapezium" in AU/UK refers to a quadrilateral with exactly one pair of parallel sides. In the US, this shape is called a "Trapezoid". Verifier: The term "Trapezium" is used in the AU context to describe a quadrilateral with one pair of parallel sides; in the US, this is called a "Trapezoid". |
mqn_01K03WMXH0PGQR8QJ0HXPN2K0Z |
Localize | Units (simple) | Multiple Choice
On a map, the scale is $1$ cm = $2$ km.
What is the length on the map for a distance of $10$ km?
Options:
|
Multiple Choice
On a map, the scale is $1$ in = $2$ mi.
What is the length on the map for a distance of $10$ mi?
Options:
|
Classifier: The text contains metric units "cm" and "km" which require conversion to US customary units (inches/miles) for a US audience. Verifier: The question uses metric units "cm" and "km" in a simple scale context. Conversion to inches/miles is required for US localization. |
mqn_01K06T8481XA7FBRCPBT0NK0J0 |
Localize | Answer set | Multiple Choice
Which of the following quadrilaterals must have opposite angles equal?
Options:
|
Multiple Choice
Which of the following quadrilaterals must have opposite angles equal?
Options:
|
Classifier: The answer set contains the term "Trapezium", which in the US is "Trapezoid". Additionally, "Arrowhead" is a common AU/UK term for a concave kite (often just called a "concave kite" or "dart" in US geometry). Verifier: The answer choices include "Trapezium" (US: Trapezoid) and "Arrowhead" (US: Concave kite or Dart), which are regional geometric terms requiring localization. |
mqn_01K071JQ2MWVT50FA6ZS5X93AW |
Localize | Answer set | Multiple Choice
Which of these must be true for an isosceles trapezium?
A) All angles are equal
B) Non-parallel sides are equal
C) Diagonals are perpendicular
D) All sides are equal
Options:
|
Multiple Choice
Which of these must be true for an isosceles trapezoid?
A) All angles are equal
B) Non-parallel sides are equal
C) Diagonals are perpendicular
D) All sides are equal
Options:
|
Classifier: The term "isosceles trapezium" is used, which in the US is referred to as an "isosceles trapezoid". Verifier: The term "isosceles trapezium" is used, which is "isosceles trapezoid" in US English. |
mqn_01K042ATQGVAAW64BQQSDP7T7G |
Localize | Units (simple) | Multiple Choice
Kai is drawing a $200$ km long highway on a map.
He needs it to fit within $20$ cm of space.
Which scale works best?
Options:
|
Multiple Choice
Kai is drawing a $200$ mi long highway on a map.
He needs it to fit within $20$ in of space.
Which scale works best?
Options:
|
Classifier: The text contains metric units "km" and "cm" which require conversion. Verifier: The question uses metric units "cm" and "km" for map scale calculations. |
mqn_01K09HFKTH6RWDY16B27SBTP7F |
Localize | Units (simple) | Multiple Choice
Which of the following sets of side lengths could represent the sides of a square?
A) $4$ cm, $4$ cm, $4$ cm, $6$ cm
B) $6$ cm, $6$ cm, $6$ cm, $6$ cm
C) $5$ cm, $5$ cm, $10$ cm, $10$ cm
D) $3$ cm, $3$ cm, $4$ cm, $4$ cm
Options:
|
Multiple Choice
Which of the following sets of side lengths could represent the sides of a square?
A) $4$ in, $4$ in, $4$ in, $6$ in
B) $6$ in, $6$ in, $6$ in, $6$ in
C) $5$ in, $5$ in, $10$ in, $10$ in
D) $3$ in, $3$ in, $4$ in, $4$ in
Options:
|
Classifier: The text contains the metric unit "cm" multiple times, which requires conversion for US localization. Verifier: The text contains the metric unit "cm" multiple times, which requires conversion for US localization. |
mqn_01K071PT57TNXSKD6SQS0ZV8SZ |
Localize | Answer set | Multiple Choice
Which of the following cannot be a trapezium?
A) A shape with two right angles
B) A shape with both pairs of opposite sides parallel
C) A shape with exactly one line of symmetry
D) A shape with non-equal diagonals
Options:
|
Multiple Choice
Which of the following cannot be a trapezoid?
A) A shape with two right angles
B) A shape with both pairs of opposite sides parallel
C) A shape with exactly one line of symmetry
D) A shape with non-equal diagonals
Options:
|
Classifier: The term "trapezium" is used in the question stem, which maps to "trapezoid" in US English. Verifier: The term "trapezium" is used in the question stem, which maps to "trapezoid" in US English. |
mqn_01K2Q2ASH5E3Y47SBTDX5MFA7R |
Localize | Units (simple) | Multiple Choice
True or false:
$4$ km $ +\,\,\,500$ m $+\,\,\,2500$ cm $=\,\,\,4550$ m
Options:
|
Multiple Choice
True or false:
$4$ mi $ +\,\,\,500$ ft $+\,\,\,2500$ in $=\,\,\,4550$ ft
Options:
|
Classifier: Contains multiple metric units (km, m, cm) which require conversion for US localization. Verifier: The question contains metric units (km, m, cm) which require conversion to US customary units. |
mqn_01K1FXPMND0TV2F1JW07F21N7B |
Localize | Spelling (AU-US) | Multiple Choice
Which sentence shows subtraction?
Options:
|
Multiple Choice
Which sentence shows subtraction?
Options:
|
Classifier: The text contains the Australian spelling "colour", which requires localization to the US spelling "color". Verifier: The text contains the word "colour", which is the Australian/British spelling. This requires localization to "color" for a US context. |
mqn_01K2Q2H5HHC2AEXN842MBPS1WT |
Localize | Units (simple) | Multiple Choice
True or false:
$1$ km $ +\,\,\,800$ m $+\,\,\,5000$ cm $=\,\,\,1850$ m
Options:
|
Multiple Choice
True or false:
$1$ mi $ +\,\,\,800$ ft $+\,\,\,5000$ in $=\,\,\,1850$ ft
Options:
|
Classifier: Contains metric units (km, m, cm) requiring conversion to US customary units. Verifier: The question contains metric units (km, m, cm) which require conversion to US customary units. |
mqn_01K2Q2F0GMX9NT24ZX0CK380XY |
Localize | Units (simple) | Multiple Choice
True or false:
$2$ km $ +\,\,\,1500$ m $+\,\,\,300$ cm $=\,\,\,3503$ m
Options:
|
Multiple Choice
True or false:
$2$ mi $ +\,\,\,1500$ ft $+\,\,\,300$ in $=\,\,\,3503$ ft
Options:
|
Classifier: Contains metric units (km, m, cm) used in a mathematical equality check. Verifier: The question contains metric units (km, m, cm) which require conversion to US customary units. |
mqn_01K4QFF5JX5YD0ZQN7KDR8CDAR |
Localize | Units (simple) | Multiple Choice
True or false:
A delivery service charges a $\$10$ delivery fee plus $\$2$ per kilometre travelled, but caps the maximum fee at $\$50$.
The graph of cost $C$ against distance $d$ is a straight line rising from $(0,10)$ to $(20,50)$, and then continues rising beyond this point.
Options:
|
Multiple Choice
True or false:
A delivery service charges a $\$10$ delivery fee plus $\$2$ per mile traveled, but caps the maximum fee at $\$50$.
The graph of cost $C$ against distance $d$ is a straight line rising from $(0,10)$ to $(20,50)$, and then continues rising beyond this point.
Options:
|
Classifier: Contains the metric unit "kilometre" and the AU spelling "kilometre" (vs US "kilometer"). Per rule 1 and 5, any metric unit requires conversion. Verifier: The text contains the metric unit "kilometre" and the AU spelling "kilometre". Per the decision rules, any metric unit requires at least RED.units_simple_conversion. |
mqn_01K6YJYPB1JW0WHKZ4ERSX2HXS |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
$(x - 1)(x - 2)(x - 3)(x - 4) = 0$ is a quartic equation in $[ ? ]$ form.
Options:
|
Multiple Choice
Fill in the blank:
$(x - 1)(x - 2)(x - 3)(x - 4) = 0$ is a quartic equation in $[ ? ]$ form.
Options:
|
Classifier: The answer choice "Factorised" uses the Australian 's' spelling; the US equivalent is "Factorized". Verifier: The answer choice "Factorised" uses the Australian/British 's' spelling. The US equivalent is "Factorized". |
mqn_01K6VSDDMNNZP9YHTHTR0HWWP4 |
Localize | Spelling (AU-US) | Multiple Choice
Using the cross method, factorise $15x^2−11x−4$.
What are the two binomial factors?
Options:
|
Multiple Choice
Using the cross method, factor $15x^2−11x−4$.
What are the two binomial factors?
Options:
|
Classifier: Contains the AU spelling "factorise". Verifier: The text contains the AU/British spelling "factorise" (US: "factor"). |
mqn_01K6VTWW77HTBVX3RYCMD050S2 |
Localize | Spelling (AU-US) | Multiple Choice
Using the cross method, factorise $8x^2−22x+15$.
What are the two binomial factors?
Options:
|
Multiple Choice
Using the cross method, factor $8x^2−22x+15$.
What are the two binomial factors?
Options:
|
Classifier: Contains the AU spelling "factorise". Verifier: The text contains the AU/British spelling "factorise" (US: "factor"). |
mqn_01K6W2TNA82SGPJQRX0PG4VBBQ |
Localize | Units (simple) | Multiple Choice
A rectangle has a length that is $4$ m more than its width.
If the area is $77$ m$^2$, which equation represents this situation?
Options:
|
Multiple Choice
A rectangle has a length that is $4$ ft more than its width.
If the area is $77$ ft$^2$, which equation represents this situation?
Options:
|
Classifier: Contains metric units "m" (metres) and "m^2" (square metres) which require conversion to US customary units. Verifier: The text contains metric units "m" (metres) and "m^2" (square metres) which require conversion to US customary units. |
mqn_01K7366AK0GKW67SX0C8PF80C2 |
Localize | Terminology | Multiple Choice
Which of the following is not a cubic equation in point inflection form?
Options:
|
Multiple Choice
Which of the following is not a cubic equation in inflection point form?
Options:
|
Classifier: Uses "point inflection form", which is an AU-specific pedagogical term for cubic equations. Verifier: The term "point inflection form" is specific to the Australian mathematics curriculum for cubic equations. |
mqn_01K735YNGRRPZR2SDPFDPNKP7E |
Localize | Terminology | Multiple Choice
Which of the following is a cubic equation written in point inflection form?
Options:
|
Multiple Choice
Which of the following is a cubic equation written in inflection point form?
Options:
|
Classifier: The term "point inflection form" (or "point of inflection form") is the standard Australian curriculum term for what is typically called "vertex form" or "standard form" for cubics in the US. Verifier: The term "point inflection form" is a specific pedagogical term used in the Australian curriculum for the vertex form of a cubic function. In the US, this is typically referred to as "vertex form" or "standard form". |
mqn_01K736FA5W6TC1SW7KJH99NFX6 |
Localize | Terminology | Multiple Choice
A cubic equation is written in point of inflection form as $a(x - h)^3 + k = 0$.
Which of the following must be true?
Options:
|
Multiple Choice
A cubic equation is written in inflection point form as $a(x - h)^3 + k = 0$.
Which of the following must be true?
Options:
|
Classifier: Uses "point of inflection form", which is the AU-specific terminology for the vertex form of a cubic. Verifier: The term "point of inflection form" is the standard Australian curriculum terminology for the vertex form of a cubic equation. |
mqn_01KG263ZW9M87EV2HAQSGDGT40 |
Localize | Spelling (AU-US) | Multiple Choice
Why does a sphere roll in a straight line when pushed on a flat surface?
Options:
|
Multiple Choice
Why does a sphere roll in a straight line when pushed on a flat surface?
Options:
|
Classifier: Contains the AU spelling "centre", which needs to be converted to "center". Verifier: Contains the AU spelling "centre" in the third answer choice, which requires localization to "center". |
mqn_01K6VSVWQKX5S0PPRW84KSD8MG |
Localize | Spelling (AU-US) | Multiple Choice
Using the cross method, factorise $6x^2-\frac{19}{2}x+\frac{5}{2}$.
What are the two binomial factors?
Options:
|
Multiple Choice
Using the cross method, factor $6x^2-\frac{19}{2}x+\frac{5}{2}$.
What are the two binomial factors?
Options:
|
Classifier: Contains the AU spelling "factorise". Verifier: The text contains the AU/British spelling "factorise" (US: "factor"). |
mqn_01K6VT4RH924YQDJF796NAZT3X |
Localize | Spelling (AU-US) | Multiple Choice
Using the cross method, factorise $4x^2−\frac{11}{3}x+\frac{5}{6}$.
What are the two binomial factors?
Options:
|
Multiple Choice
Using the cross method, factor $4x^2−\frac{11}{3}x+\frac{5}{6}$.
What are the two binomial factors?
Options:
|
Classifier: Contains the AU spelling "factorise". Verifier: The text contains the AU/British spelling "factorise" (US: "factor"). |
mqn_01K87AF5VW76CKNQSR0Y5BRZAZ |
Localize | Units (simple) | Multiple Choice
A water tank holds $60$ litres.
Each bottle can hold $1.5$ litres.
Which two expressions both show how many bottles can be completely filled with the water left after filling $x$ bottles?
Options:
|
Multiple Choice
A water tank holds $60$ gallons.
Each bottle can hold $1.5$ gallons.
Which two expressions both show how many bottles can be completely filled with the water left after filling $x$ bottles?
Options:
|
Classifier: The text contains the metric unit "litres", which requires both spelling localization (to "liters") and unit conversion to US customary units (e.g., gallons or quarts) per localization standards. Units take precedence over spelling. Verifier: The text contains the metric unit "litres", which requires both spelling localization and unit conversion to US customary units. |
mqn_01K8QP64MEP953NYHKRAAD2MWR |
Localize | Terminology | Multiple Choice
The equation of a line is $(2p−1)x+(3q+4)y=6$, where $p\neq\frac{1}{2}$ and $q\neq\frac{-4}{3}$.
A second line is perpendicular to this one.
What is the gradient of the second line in terms of $p$ and $q$ ?
Options:
|
Multiple Choice
The equation of a line is $(2p−1)x+(3q+4)y=6$, where $p\neq\frac{1}{2}$ and $q\neq\frac{-4}{3}$.
A second line is perpendicular to this one.
What is the slope of the second line in terms of $p$ and $q$ ?
Options:
|
Classifier: The text uses the term "gradient", which is the standard AU/UK term for what is referred to as "slope" in US school mathematics. Verifier: The text uses "gradient", which is the standard AU/UK term for "slope" in US school mathematics. |
mqn_01K87AYZP8S236ECGT2G7BTFMR |
Localize | Units (simple) | Multiple Choice
A delivery company charges a flat fee of $\$15$ plus $\$5$ for every kilometre travelled.
If a $10\%$ discount is given on the total cost, which two expressions both represent the final amount to pay for $x$ kilometres?
Options:
|
Multiple Choice
A delivery company charges a flat fee of $\$15$ plus $\$5$ for every mile traveled.
If a $10\%$ discount is given on the total cost, which two expressions both represent the final amount to pay for $x$ miles?
Options:
|
Classifier: The text contains the metric unit "kilometre" (and "kilometres"), which requires localization to US customary units (miles) or at least a spelling change to "kilometer" per the decision rules where any metric unit triggers a RED category. Verifier: The text contains the metric unit "kilometre" (AU spelling) and "kilometres". Per rule 3, any metric unit requires at least RED.units_simple_conversion. Since the conversion is a straightforward replacement of the unit/variable context without complex re-derivation of formulas, simple conversion is appropriate. |
mqn_01K9BY9PTY4AYRBSWKN05HFJ2F |
Localize | Spelling (AU-US) | Multiple Choice
Using $A = 3^{4} \times 5^{2} \times 11^{1}$ and $B = 3^{2} \times 5^{3} \times 7^{4}$, find the prime factorisation of their lowest common multiple.
Options:
|
Multiple Choice
Using $A = 3^{4} \times 5^{2} \times 11^{1}$ and $B = 3^{2} \times 5^{3} \times 7^{4}$, find the prime factorization of their least common multiple.
Options:
|
Classifier: Contains the AU spelling "factorisation", which needs to be converted to "factorization" for a US audience. Verifier: Contains the AU spelling "factorisation", which requires localization to "factorization". |
mrT0YqBW2kKYx9ngaVbF |
Localize | Units (simple) | Question
Fill in the blank:
Density $=7.8$ g/m$^3$
Mass $=[?]$
Volume $=5$ m$^3$
Answer:
|
Question
Fill in the blank:
Density $=7.8$ oz/ft$^3$
Mass $=[?]$
Volume $=5$ ft$^3$
Answer:
|
Classifier: The question contains metric units (grams and cubic metres) which require localization to US customary units or a US-centric metric context per policy. Verifier: The question uses metric units (grams and cubic metres) which require localization. It is a simple calculation (Density * Volume), so simple_conversion is correct. |
mqn_01KHSETSVAS6B81293ZF4F2PGW |
Localize | Units (simple) | Multiple Choice
Mia runs $\dfrac{3}{4}$ km each day for $6$ days.
Noah runs $\dfrac{5}{6}$ km each day for $5$ days.
Who runs further?
Options:
|
Multiple Choice
Mia runs $\dfrac{3}{4}$ mi each day for $6$ days.
Noah runs $\dfrac{5}{6}$ mi each day for $5$ days.
Who runs farther?
Options:
|
Classifier: Contains the metric unit "km" (kilometers), which requires conversion to US customary units (e.g., miles) for US localization. Verifier: Contains the metric unit "km" (kilometers), which requires conversion to US customary units. |
mrX6W3BpQq6DiZk3meTY |
Localize | Spelling (AU-US) | Multiple Choice
Factorise the polynomial $x^3-27$.
Options:
|
Multiple Choice
Factor the polynomial $x^3-27$.
Options:
|
Classifier: The word "Factorise" uses the AU/UK 's' spelling and needs to be converted to the US 'z' spelling ("Factorize"). Verifier: The word "Factorise" is AU/UK spelling; US spelling is "Factorize". |
n8vuikIpIZBD1hT72h5N |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following pairs of variables is not suitable for a scatterplot?
Options:
|
Multiple Choice
Which of the following pairs of variables is not suitable for a scatterplot?
Options:
|
Classifier: Contains the AU spelling "colour" which needs to be converted to "color". "Travelled" is also AU spelling (US: traveled). Verifier: The text contains "travelled" (US: traveled) and "colour" (US: color), which are AU/British spellings. |
nAxbRBDmTHrK2VaTN9LQ |
Localize | Terminology | Multiple Choice
As Maira practised more maths problems, her test scores improved.
What is the response variable in this situation?
Options:
|
Multiple Choice
As Maira practiced more math problems, her test scores improved.
What is the response variable in this situation?
Options:
|
Classifier: Contains "maths" (US: math) and "practised" (US: practiced). Terminology "maths" takes priority over spelling. Verifier: Contains "maths" (US: math) and "practised" (US: practiced). Per rule 5, terminology/school context takes priority over spelling. |
mqn_01KHSF18DE602DEMRD9HPJEZWD |
Localize | Units (simple) | Multiple Choice
Tank A fills at $\dfrac{11}{12}$ kL per hour for $4$ hours. Tank B fills at $\dfrac{5}{7}$ kL per hour for $5$ hours.
Which tank holds more water after filling?
Options:
|
Multiple Choice
Tank A fills at $\dfrac{11}{12}$ gal per hour for $4$ hours. Tank B fills at $\dfrac{5}{7}$ gal per hour for $5$ hours.
Which tank holds more water after filling?
Options:
|
Classifier: Contains the metric unit "kL" (kiloliters), which requires conversion to US customary units for US localization. Verifier: Contains the metric unit "kL" (kiloliters), which requires conversion to US customary units. |
nFH36vXggi7WOEotSqYp |
Localize | Terminology | Multiple Choice
True or false:
Hire-purchase agreements allow buyers to purchase expensive goods, but they do not own the goods until the last installment has been paid.
Options:
|
Multiple Choice
True or false:
Installment loans allow buyers to purchase expensive goods, but they do not own the goods until the last installment has been paid.
Options:
|
Classifier: "Hire-purchase agreements" is a term primarily used in Commonwealth countries (UK, AU). In the US, this is typically referred to as "rent-to-own" or "installment plans/contracts". Additionally, "installment" is spelled with two 'l's here, which is acceptable in both but often "instalment" in AU; however, the term itself is the primary trigger for localization. Verifier: "Hire-purchase agreements" is a specific financial/legal term used in Australia and the UK, whereas the US equivalent is typically "rent-to-own" or "installment plan". This requires terminology localization. |
myPfTM1EK00LkqhE0XlF |
Localize | Spelling (AU-US) | Multiple Choice
You are booking a theatre show ticket.
Tickets are only sold in batches of $2$ tickets or more in one booking, and one ticket costs $\$30$.
If you purchase $5$ or more tickets though, each ticket will cost $\$28$.
Represent the cost of tickets $f(x)$ if a person buys $x$ tickets.
Options:
|
Multiple Choice
You are booking a theater show ticket.
Tickets are only sold in batches of $2$ tickets or more in one booking, and one ticket costs $\$30$.
If you purchase $5$ or more tickets though, each ticket will cost $\$28$.
Represent the cost of tickets $f(x)$ if a person buys $x$ tickets.
Options:
|
Classifier: Contains the AU spelling "theatre", which needs to be converted to the US spelling "theater". Verifier: Contains "theatre", which is the AU/British spelling; US spelling is "theater". |
q0L1MTfzp1fi56qimS5l |
Localize | Spelling (AU-US) | Multiple Choice
True or false:
Amortising loans are loans paid in full to make the balance owed zero.
Options:
|
Multiple Choice
True or false:
Amortizing loans are loans paid in full to make the balance owed zero.
Options:
|
Classifier: The word "Amortising" uses the AU/UK 's' spelling. In US English, this is spelled "Amortizing". Verifier: The word "Amortising" uses the AU/UK 's' spelling, which requires localization to "Amortizing" for US English. |
nT70ZiWTvbm3n0jkgLzu |
Localize | Units (simple) | Question
A cylindrical water tank has a height of $20$ m and a radius of $10$ m. The tank is closed at both ends.
What is the tank's surface area?
Answer:
|
Question
A cylindrical water tank has a height of $20$ ft and a radius of $10$ ft. The tank is closed at both ends.
What is the tank's surface area?
Answer:
|
Classifier: The text contains metric units ("m" for metres and "m^2" for square metres) which require conversion for US localization. Verifier: The question uses metric units ("m" for metres and "m^2" for square metres) which require conversion to US customary units. |
q6PSxYrUknVCTiDEk5iO |
Localize | Cultural refs | Question
What is the time difference between Melbourne $(37^\circ{S},144^\circ{E})$ and Brisbane $(27^\circ{S},153^\circ{E})$ ?
Give your answer to the nearest minute.
Answer:
|
Question
What is the time difference between New York $(41^\circ{N},74^\circ{W})$ and Boston $(42^\circ{N},71^\circ{W})$ ?
Give your answer to the nearest minute.
Answer:
|
Classifier: The question references specific Australian cities (Melbourne and Brisbane) and their coordinates to calculate time differences. This is a distinct AU cultural/geographic reference. Verifier: The question uses specific Australian geographic locations (Melbourne and Brisbane) as the basis for the calculation, which constitutes a cultural/geographic reference. |
q10vA27rV2RnaJxOJ9N9 |
Localize | Units (simple) | Question
A man shares $12$ hectares of land equally between his $3$ children.
What share of land will each child get?
Answer:
|
Question
A man shares $12$ acres of land equally between his $3$ children.
What share of land will each child get?
Answer:
|
Classifier: The text contains the metric unit "hectares". According to the decision rules, any metric unit found anywhere in the text requires at least RED.units_simple_conversion. Verifier: The text contains the metric unit "hectares". According to rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. |
p5wJGJNYnmt1F2P2sq8w |
Localize | Units (simple) | Question
Find the area of a parallelogram with a height of $3$ cm and a base twice the length of its height.
Answer:
|
Question
Find the area of a parallelogram with a height of $3$ in and a base twice the length of its height.
Answer:
|
Classifier: The text contains the metric unit "cm" and "cm$^2$", which requires conversion to US customary units (inches). Verifier: The question contains metric units "cm" and "cm$^2$" which require conversion to US customary units. This is a simple numeric conversion. |
piil0wI0zfFWcYVGNFcy |
Review | Review | Question
Find the effective annual interest rate equivalent to a nominal rate of $11\%$ per annum, compounded quarterly.
Answer:
|
Question
Find the effective annual interest rate equivalent to a nominal rate of $11\%$ per year, compounded quarterly.
Answer:
|
Classifier: The text contains the term "quarterly". While common in finance in both regions, the decision rules suggest using GRAY for terms like "quarter" where policy might dictate specific localization or review, although in a financial context it is likely neutral. Verifier: The term "quarterly" in a financial context (compounding interest) is standard international English and does not fall under the GRAY.term_semester_quarter_policy which is intended for academic calendar terms (semesters vs quarters). There is no AU-specific content here. |
pjyR417jchv20q46eNv2 |
Localize | Spelling (AU-US) | Question
Lily has a $22\%$ stake in an organisation that earned a profit of $\$34509$ last year.
How much of last year's profit is Lily entitled to?
Give your answer to the nearest dollar.
Answer:
|
Question
Lily has a $22\%$ stake in an organization that earned a profit of $\$34509$ last year.
How much of last year's profit is Lily entitled to?
Give your answer to the nearest dollar.
Answer:
|
Classifier: The text contains the AU spelling "organisation", which needs to be converted to the US spelling "organization". Verifier: The text contains the AU spelling "organisation", which needs to be converted to the US spelling "organization". |
o4aAUMZYVlRp4zSsXy0G |
Localize | Units (simple) | Question
A round trip from Sydney to Brisbane covers a distance of approximately $1800$ km.
If you drive at an average speed of $60$ km/h, how long will it take you to drive from Sydney to Brisbane?
Assume that the time taken on either trip is the same.
Answer:
|
Question
A round trip from New York to Boston covers a distance of approximately $1800$ mi.
If you drive at an average speed of $60$ mph, how long will it take you to drive from New York to Boston?
Assume that the time taken on either trip is the same.
Answer:
|
Classifier: The question contains metric units (km, km/h) and Australian geographic references (Sydney, Brisbane). Per rule 8, units categories take precedence over cultural references. Verifier: The question contains metric units (km, km/h) and Australian geographic references (Sydney, Brisbane). Per Rule 5, units conversion takes precedence over cultural references. |
o1eLlfpXPMCwbzcntSzm |
Localize | Cultural refs | Multiple Choice
Fill in the blank:
GST is the $[?]\%$ tax applied to the value of goods and services.
Options:
|
Multiple Choice
Fill in the blank:
Sales tax is the $[?]\%$ tax applied to the value of goods and services.
Options:
|
Classifier: The term "GST" (Goods and Services Tax) is a specific tax system used in Australia (at a 10% rate). The US uses "Sales Tax", which varies by state and is not referred to as GST. Verifier: GST (Goods and Services Tax) is a specific tax system used in Australia (at a 10% rate), whereas the US uses "Sales Tax". This is a clear cultural/geographic reference. |
o9esXV43QAPrarhgKmYQ |
Localize | Units (simple) | Question
The lengths of two parallel sides of a trapezium are $12$ cm and $8$ cm, respectively. The distance between the parallel sides is $10$ cm.
What is the area of the trapezium?
Answer:
|
Question
The lengths of two parallel sides of a trapezoid are $12$ in and $8$ in, respectively. The distance between the parallel sides is $10$ in.
What is the area of the trapezoid?
Answer:
|
Classifier: The question contains metric units ("cm") and the term "trapezium", which is the AU/UK term for the US "trapezoid". Per decision rules, the presence of metric units triggers the units category as a priority. Verifier: The question contains metric units ("cm") which requires RED classification. It also uses "trapezium", which is the standard term in Australia (vs "trapezoid" in the US), but per rule 5, units conversion takes priority. |
nkitICzvQLwVSxLiRi2B |
Localize | Units (simple) | Question
An object starts from $2$ m to the right of the origin and moves in a straight line with velocity $v(t)=12t+2$ m/s for $t\geq0$.
Find the change in displacement of the object between $t=2$ and $t=5$ seconds.
Answer:
|
Question
An object starts from $2$ ft to the right of the origin and moves in a straight line with velocity $v(t)=12t+2$ ft/s for $t\geq0$.
Find the change in displacement of the object between $t=2$ and $t=5$ seconds.
Answer:
|
Classifier: The text contains metric units ("m" for meters and "m/s" for meters per second) which require conversion to US customary units (feet or miles). Per the decision rules, any metric unit found anywhere in the text triggers a RED units category. Verifier: The text contains metric units "m" (metres) and "m/s" (metres per second). According to decision rule 3, any metric unit found anywhere requires at least RED.units_simple_conversion. The conversion is a straightforward numeric change for displacement, so simple_conversion is correct. |
nj82IUmBbZHweOamJubW |
Localize | Units (complex) | Question
A toy car moves in a straight line with a velocity $v(t)=9t^2-12$ cm/s for $t\geq0$.
Find the distance travelled by the toy car in the first two seconds.
Answer:
|
Question
A toy car moves in a straight line with a velocity $v(t)=9t^2-12$ in/s for $t\geq0$.
Find the distance traveled by the toy car in the first two seconds.
Answer:
|
Classifier: The text contains metric units ("cm/s" and "cm") which require localization for a US audience. Verifier: While the classifier correctly identified the need for unit conversion (cm/s, cm), this is a kinematics problem where the velocity is defined by a function v(t) = 9t^2 - 12. According to rule 4, equations defining quantities in metric or problems requiring integration/derivation of metric functions should be classified as RED.units_complex_converted. |
nVGw1CAzb6Hz07MhdFqg |
Localize | Units (simple) | Question
The longitudes of point $A$ and point $B$ are $15^\circ E$ and $75^\circ E$ respectively.
Find the distance between them if they both lie on the equator, given that the Earth's radius is 6400 km.
Answer:
|
Question
The longitudes of point $A$ and point $B$ are $15^\circ E$ and $75^\circ E$ respectively.
Find the distance between them if they both lie on the equator, given that the Earth's radius is 6400 miles.
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers) multiple times, which requires conversion for US localization. Verifier: The question uses "km" (kilometers) which is a metric unit requiring conversion for US localization. It is a simple conversion as it involves a single distance calculation based on a given radius. |
oVBQYMchyEXkjLPafPwI |
Localize | Units (simple) | Multiple Choice
A particle moves in a straight line and its position at time $t$ seconds is given by $s(t)=2t^3-8t$ m for $0\leq t\leq 5$.
How many times did the particle change its direction in the given time interval?
Options:
|
Multiple Choice
A particle moves in a straight line and its position at time $t$ seconds is given by $s(t)=2t^3-8t$ ft for $0\leq t\leq 5$.
How many times did the particle change its direction in the given time interval?
Options:
|
Classifier: The text contains the metric unit "m" (metres) for position and "seconds". Per the decision rules, any metric unit found anywhere requires classification into a units category. Verifier: The text contains the metric unit "m" (metres). Per rule 3, any metric unit requires at least RED.units_simple_conversion. Since it is a single unit-bearing value in a simple context, simple_conversion is appropriate. |
o3cQ5nOiq7hNVCsAgeEU |
Localize | Units (simple) | Multiple Choice
Fill in the blank:
$1$ micrometre $=[?]$ metres
Options:
|
Multiple Choice
Fill in the blank:
$1$ micrometer $=[?]$ meters
Options:
|
Classifier: The text contains the metric unit "metres" and "micrometre", which also uses the AU/UK spelling "metres". Per rule 1 and 5, any metric unit requires at least RED.units_simple_conversion. Verifier: The text contains "micrometre" and "metres", which are metric units and use AU/UK spelling. Per Rule 1 and Rule 3, this requires a RED classification. |
osb8svVv78V7hsmTeHJz |
Localize | Units (simple) | Multiple Choice
A body moves in a straight line with velocity $v(t)=-2t+15$ m/s for time $t\geq0$ (seconds).
Is the speed of the body increasing or decreasing at $t=5$ ?
Hint: Find instantaneous velocity and acceleration at $t=5$ s and check their sign.
Options:
|
Multiple Choice
A body moves in a straight line with velocity $v(t)=-2t+15$ ft/s for time $t\geq0$ (seconds).
Is the speed of the body increasing or decreasing at $t=5$ ?
Hint: Find instantaneous velocity and acceleration at $t=5$ s and check their sign.
Options:
|
Classifier: The text contains the metric unit "m/s" (metres per second). According to the decision rules, any metric unit requires classification into a units category, which takes precedence over terminology or spelling. Verifier: The text contains the metric unit "m/s" (metres per second) and "s" (seconds). Per rule 3, any metric unit requires a RED classification. Since it is a single linear velocity function, simple_conversion is appropriate. |
oUT8fpX2Y6Hv58cmHcGK |
Localize | Spelling (AU-US) | Question
Factorise $f(x)=x^3 + 9 x^2 + 11 x - 21$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Question
Factor $f(x)=x^3 + 9 x^2 + 11 x - 21$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be localized to "Factorize" for a US audience. Verifier: The text contains "Factorise", which is the AU/UK spelling. Per rule 1, this requires RED classification. |
pBGHGzSSYTa7QkUV4Xb5 |
Localize | Spelling (AU-US) | Question
Factorise $x^3 + 4 x^2 + x - 6$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Question
Factor $x^3 + 4 x^2 + x - 6$.
Express your answer in the form $(x\pm a)(x\pm b)(x\pm c)$.
Options:
|
Classifier: The text uses the AU/UK spelling "Factorise", which requires conversion to the US spelling "Factorize". Verifier: The word "Factorise" is the AU/UK spelling; US English uses "Factorize". |
oFcGmkB0kBxi9iMpT2uK |
Localize | Spelling (AU-US) | Multiple Choice
Factorise $64+8x^3$.
Options:
|
Multiple Choice
Factor $64+8x^3$.
Options:
|
Classifier: Contains the AU spelling "Factorise", which needs to be localized to the US spelling "Factorize". Verifier: The text contains "Factorise", which is the AU/British spelling. The US spelling is "Factorize". |
qE2DBR9UZPcyGz6ra5lN |
Localize | Spelling (AU-US) | Multiple Choice
Which of the following is not an imperial unit of volume?
Options:
|
Multiple Choice
Which of the following is not a US customary unit of volume?
Options:
|
Classifier: Contains the AU spelling "Millilitre" which requires conversion to the US spelling "Milliliter". While it mentions units, the primary action is a spelling correction for a metric term in a multiple-choice list. Verifier: The answer choice "Millilitre" uses AU/British spelling. Since the question asks to identify a non-imperial unit, the word itself is the object of the question, but the spelling "re" vs "er" is the primary localization trigger. |
r5bqq7Bf5bk6LdSU16yg |
Localize | Cultural refs | Question
How many different uniform combinations can a football coach choose from if he has $3$ guernsey colours, $3$ shorts colours and $2$ sock options?
Answer:
|
Question
How many different uniform combinations can a football coach choose from if he has $3$ jersey colors, $3$ shorts colors and $2$ sock options?
Answer:
|
Classifier: The term "guernsey" is a distinctly Australian/British term for a sports jersey, particularly in the context of Australian Rules Football. Additionally, "colours" uses the AU spelling. While spelling is present, the cultural context of "guernsey" makes this a cultural reference. Verifier: The text contains "guernsey" (an Australian term for a sports jersey) and "colours" (AU spelling). Per rule 8, "guernsey" is a distinct AU cultural reference. |
qs0xTM3Wj49PC0e84oVt |
Localize | Units (simple) | Question
A sector has a central angle of $2.5$ radians and an arc length of $20$ m.
Find its area.
Answer:
|
Question
A sector has a central angle of $2.5$ radians and an arc length of $20$ ft.
Find its area.
Answer:
|
Classifier: The text contains the metric unit "m" (metres) and "m^2" (square metres), which requires conversion for US localization. Verifier: The text contains the metric unit "m" (metres) and "m^2" (square metres), which requires conversion for US localization. |
r0v96UxLPibqNQ1QRsZB |
Review | Review | Multiple Choice
True or false:
When a person borrows $\$1000$ for a $5$-year term with annual compound interest, the total amount owed changes after the first year.
Options:
|
Multiple Choice
True or false:
When a person borrows $\$1000$ for a $5$-year period with annual compound interest, the total amount owed changes after the first year.
Options:
|
Classifier: The text uses the word "term" in the context of a loan duration ("5-year term"). While common in both dialects, the decision rules suggest using the GRAY category for "term" to allow for policy-based review. Verifier: The word "term" in the context of a "5-year term" for a loan is standard financial English in both the US and AU. The category GRAY.term_semester_quarter_policy is specifically intended for school/academic calendar divisions (semesters vs terms), not for the duration of a financial contract. Since there are no other localization triggers, this is GREEN. |
qzGRrFZITvgxSsXpCdLz |
Localize | Units (simple) | Question
A square with an area of $25$ m$^2$ is scaled up by a factor of $4$, what is the side length of the new square?
Answer:
|
Question
A square with an area of $25$ ft$^2$ is scaled up by a factor of $4$, what is the side length of the new square?
Answer:
|
Classifier: The text contains metric units ("m^2" and "m") which require conversion to US customary units. Verifier: The question contains metric units ("m^2" and "m") which require conversion to US customary units. It is a simple conversion as it involves a single geometric shape and a scaling factor. |
qNE7EBW9fXpSHqLQEJ6W |
Localize | Spelling (AU-US) | Multiple Choice
Tiphany’s Jewellery is selling a $\$2000$ necklace for $35\%$ off.
Lorentz Jewels sells the same necklace for $\$2000$, but with a $25\%$ discount, plus an extra $10\%$ off the reduced price.
Which store offers the lower final price?
Options:
|
Multiple Choice
Tiffany’s Jewelry is selling a $\$2000$ necklace for $35\%$ off.
Lorentz Jewels sells the same necklace for $\$2000$, but with a $25\%$ discount, plus an extra $10\%$ off the reduced price.
Which store offers the lower final price?
Options:
|
Classifier: Contains the AU spelling "Jewellery", which should be "Jewelry" in US English. Currency symbols ($) are neutral. Verifier: The text contains "Jewellery", which is the AU/UK spelling. The US spelling is "Jewelry". |
rExZW8QuMUsIE4skcqLj |
Localize | Units (simple) | Question
The velocity of an object is $v(t)=8t^2+4$ m/s for $t\geq0$ (seconds).
Find its average velocity over the first $6$ seconds.
Answer:
|
Question
The velocity of an object is $v(t)=8t^2+4$ ft/s for $t\geq0$ (seconds).
Find its average velocity over the first $6$ seconds.
Answer:
|
Classifier: The text contains the metric unit "m/s" (metres per second). According to the decision rules, any metric unit found anywhere in the text requires classification into a units category, and "m/s" is a standard simple metric unit. Verifier: The text contains the metric unit "m/s" (metres per second). According to rule 3, any metric unit requires at least RED.units_simple_conversion. |
qklWHre0vNZHEMiWPsW5 |
Localize | Units (simple) | Question
Find the distance of Lebanon$(34^\circ{N},36^\circ{E})$ from the South Pole.
Give your answer to the nearest whole number.
Hint: Take Earth's radius to be $6371$ km
Answer:
|
Question
Find the distance of Lebanon$(34^\circ{N},36^\circ{E})$ from the South Pole.
Give your answer to the nearest whole number.
Hint: Take Earth's radius to be $3959$ miles
Answer:
|
Classifier: The text contains the metric unit "km" (kilometers) in both the hint and the suffix, which requires conversion to US customary units (miles) for a US audience. Verifier: The question uses "km" (kilometers) in the hint and suffix, which requires conversion to US customary units (miles). It is a simple conversion as it involves a single constant (Earth's radius) and a numeric answer. |
rRz1GLuinTSQZPPBpIvR |
Localize | Units (simple) | Question
Find the area of an isosceles triangle with one side of length $8$ m and two sides of length $5$ m.
Answer:
|
Question
Find the area of an isosceles triangle with one side of length $8$ ft and two sides of length $5$ ft.
Answer:
|
Classifier: The text contains metric units "m" (metres) and "m$^2$" (square metres), which require conversion to US customary units. Verifier: The text contains metric units "m" and "m$^2$" which require conversion to US customary units. |
qMFKCQ0WN74TzIMTqCLM |
Localize | Terminology | Multiple Choice
Which number greater than $30$ completes the Pythagorean triple?
$\{16, 30, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Options:
|
Multiple Choice
Which number greater than $30$ completes the Pythagorean triple?
$\{16, 30, [?]\}$
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Options:
|
Classifier: Contains the AU-specific term "right-angled triangle", which should be localized to "right triangle" in a US context. Verifier: The term "right-angled triangle" is the standard AU/UK term, whereas "right triangle" is the standard US term. This requires localization under terminology_school_context. |
ra0v0EafFr2XcVBV5igk |
Localize | Units (simple) | Question
Find the density of a spherical metal ball with a mass of $64$ g and a radius of $2$ cm.
Answer:
|
Question
Find the density of a spherical metal ball with a mass of $64$ oz and a radius of $2$ in.
Answer:
|
Classifier: Contains metric units (g, cm, g/cm^3) which require localization to US customary units or a decision on metric usage in US science context. Per rules, any metric unit triggers a RED category. Verifier: The question contains metric units (g, cm, g/cm^3) which require localization. |
qFtkwli10KusxhWPFkHB |
Localize | Terminology | Multiple Choice
Which of the following is not a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right-angled triangle.
Options:
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Multiple Choice
Which of the following is not a Pythagorean triple?
Hint: A Pythagorean triple is a set of integer side lengths that make up a right triangle.
Options:
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Classifier: The hint contains the term "right-angled triangle", which is the standard Australian/British term. The US equivalent is "right triangle". Verifier: The hint uses the term "right-angled triangle", which is the standard Australian/British terminology. The US equivalent is "right triangle". This requires localization for the US market. |
rdnQwYSklSpNuArPi20U |
Localize | Units (simple) | Question
An object moves in a straight line and its displacement function is given by $s(t)=t^2-t$ m for $0\leq t\leq 12$ s.
Find its average velocity over the first $7$ seconds.
Answer:
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Question
An object moves in a straight line and its displacement function is given by $s(t)=t^2-t$ ft for $0\leq t\leq 12$ s.
Find its average velocity over the first $7$ seconds.
Answer:
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Classifier: Contains metric units (m, s, m/s) used in a physics/calculus context. Verifier: Contains metric units (m, s, m/s) which require localization. |
rRriEmf1dR24HhiLnb79 |
Localize | Units (simple) | Multiple Choice
A particular bouncy ball will always bounce to half the height that it attained before dropping.
If this ball is thrown to a height of $50$m, what is the total distance that the ball will have travelled before it stops bouncing?
Options:
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Multiple Choice
A particular bouncy ball will always bounce to half the height that it attained before dropping.
If this ball is thrown to a height of $50$ ft, what is the total distance that the ball will have traveled before it stops bouncing?
Options:
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Classifier: The text contains the metric unit "m" (metres) in both the question and the answer choices, which requires conversion to US customary units (feet/yards). It also contains the AU spelling "travelled". Verifier: The text contains the metric unit "m" (metres) multiple times and the AU spelling "travelled". Per rule 5, units conversion takes precedence over spelling. |
rHWKz5Db4t3pKRzNtNlA |
Localize | Units (simple) | Multiple Choice
A particle moves in a straight line with the displacement function $s(t)=2t^3+6t^2+6t$ cm where time $t\geq0$ s.
Which of the following is the instantaneous velocity function?
Options:
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Multiple Choice
A particle moves in a straight line with the displacement function $s(t)=2t^3+6t^2+6t$ in where time $t\geq0$ s.
Which of the following is the instantaneous velocity function?
Options:
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Classifier: The text contains metric units "cm" and "m/s". Per the decision rules, any metric unit requires a RED units classification. While the math involves a derivative, the units themselves are simple metric units. Verifier: The text contains metric units "cm" and "m/s". Per rule 3, any metric unit requires a RED units classification. Since the units are standard and the conversion is straightforward (not involving complex re-derivation of coefficients in the formula itself), simple_conversion is appropriate. |
rk11VXQ83XO9g7fuPiTa |
Localize | Spelling (AU-US) | Multiple Choice
Fill in the blank:
Footwear colour is an example of $[?]$ data.
Options:
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Multiple Choice
Fill in the blank:
Footwear color is an example of $[?]$ data.
Options:
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Classifier: Contains the AU spelling "colour", which needs to be localized to "color". Verifier: Contains the AU spelling "colour", which requires localization to "color". |
rkKfBVZqkHvIR6NFkHbC |
Localize | Terminology | Question
Calculate the annual simple interest rate at which $\$7230$ amounts to $\$8856.75$ in $5$ years.
Answer:
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Question
Calculate the annual simple interest rate at which $\$7230$ amounts to $\$8856.75$ in $5$ years.
Answer:
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Classifier: The term "p.a." (per annum) is standard in AU financial math contexts but is less common in US K-12/undergraduate math compared to "per year" or simply omitting it when "annual" is already present. More importantly, the suffix format is a specific convention. Verifier: The abbreviation "p.a." (per annum) is a specific AU/UK financial math convention that requires localization for US school contexts. |
rhs9P6Xjbf4ZRZQdjdD3 |
Localize | Units (simple) | Question
The velocity function of a car is $v(t)=2t+50$ km/h for $0\leq t\leq5$, where $t$ is in hours.
Find the total distance travelled by the car in $5$ hours.
Answer:
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Question
The velocity function of a car is $v(t)=2t+50$ mi/h for $0\leq t\leq5$, where $t$ is in hours.
Find the total distance traveled by the car in $5$ hours.
Answer:
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Classifier: Contains metric units (km/h, km) which require conversion to US customary units (mph, miles). Also contains AU spelling "travelled". Units take precedence. Verifier: Contains metric units (km/h, km) and AU spelling "travelled". Units conversion is the primary driver for RED. |
raMqcHHV0IoyX8ryEndz |
Localize | Units (simple) | Multiple Choice
Maria runs a bakery that makes a profit of $\$10$ per strawberry cake sold and $\$14$ per Belgian cake sold.
Each strawberry cake uses $1$ kg of flour and takes $1.5$ hours, while each Belgian cake uses $1.5$ kg of flour and takes $1$ hour.
With a daily limit of $8$ hours and $10$ kg of flour, how many of each cake should she bake to maximise profit?
Options:
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Multiple Choice
Maria runs a bakery that makes a profit of $\$10$ per strawberry cake sold and $\$14$ per Belgian cake sold.
Each strawberry cake uses $1$ lb of flour and takes $1.5$ hours, while each Belgian cake uses $1.5$ lb of flour and takes $1$ hour.
With a daily limit of $8$ hours and $10$ lb of flour, how many of each cake should she bake to maximize profit?
Options:
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Classifier: Contains metric units (kg) and the AU spelling "maximise". Units conversion takes precedence over spelling. Verifier: Contains metric units (kg) and AU spelling (maximise). Units conversion is the primary driver for the RED classification. |