True or false: In any simple graph with $n$ vertices, at least $\dfrac{n}{2}$ edges are needed to guarantee that no vert

The perimeter of an equilateral triangle is $123$ cm. What is the length of one side?

True or false: $0.005$ kL + $50000$ mL is greater than $0.1$ m$^3$.

The system of symbols used to represent sets is called set $\fbox{\phantom{4000000000}}$

Convert $3.75$ litres to millilitres.

Which of the following is a unit of length in the metric system?

Determine the general term formula for the given arithmetic sequence. $6,2,-2,-6,\dots$

Which asset is likely to depreciate the fastest?

Find the volume of the composite solid shown below. Image description: A cylinder with radius $5$ cm and height $18$ c

How can subgraphs help analyse specific components of a larger graph?

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

Which recurrence relation represents a geometric sequence with first term $5$ and common ratio $3$?

How many cubic millimetres are there in $10$ cubic centimetres ?

What makes $r^2$ represent the squared radius in the circle $(x-h)^2+(y-k)^2=r^2$?

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 $\times$ $

To find the next shape in a growing pattern, look for the $\fbox{\phantom{4000000000}}$ in how the shapes grow.

How do you know $y=3(2^x)+2$ has asymptote $y=2$?

How do you know a shape with base area $42$ cm$^2$ and height $4$ cm cannot have a volume of $200$ cm$^3$?

A spinner has $8$ equal sections numbered $1$ to $8$. A card is drawn from a deck containing $10$ cards numbered $1$ to

Why can an equation containing a term with an even exponent have two real solutions?

What is the next term in the sequence? $10.5, 25.5, 54.5, 97.5, \dots$

The $\fbox{\phantom{4000000000}}$ of rotation refers to how many degrees an object is turned.

How many cubic metres are there in $7$ kL?

Let $X$ be a binomial random variable with variables $n=5000$ and $p=0.67$. Using the normal approximation of the binom

Express $\log_{5}{3}+\log_{5}{2}+\log_{5}{6}+\log_5{1}$ as a single logarithm.

Why can’t a shape with $5$ corners be a square?

What is the next term in the given sequence below? $-10, -6, -2, \cdots$

A student picked up $12$ pieces of rubbish on Monday and $25$ pieces on Tuesday. How many pieces of rubbish did they pic

What is $43.8-13.5$ ?

Fill in the blank. The shortest distance along a meridian between two points $A$ and $B$ on the Earth's surface is given

True or false: $0.6$ is smaller than $6\%$

Why do we use powers in the rule $T_n = a \times r^{n-1}$ for a geometric sequence?

Show why $\{1, 2\} \cup \{2, 3\} = \{1, 2, 3\}$.

True or false: The displacement of air particles in a sound wave is given by $y = 10\cos\left(\frac{\pi}{5}t\right)$, w

Which option has the greater total capacity? A: $10$ test tubes of $75$ mL and $1$ large measuring cup of $2.5$ L B: $4$

Explain why $0.7 \times 0.5$ equals $0.35$.

In any right-angled triangle, why is the sine of one acute angle equal to the cosine of the other?

If $2x^2 + 3x + k$ and $2x^2 + ax + 5$ are equal, why can you find $a$ and $k$ by comparing their coefficients instead o

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 fr

Show why doubling the number of times interest is compounded in a year increases the amount.

Explain why the graph of a geometric sequence $a_n = a_1 r^{n-1}$ curves upwards if $a_1 > 0$ and the common ratio $r >

Express $15$ g in kilograms.

Write $ 529630$ in words.

A die is rolled, and a coin is flipped. The outcome of each is recorded. How many elements are in the sample space?

Area is measured in $\fbox{\phantom{4000000000}}$ units, such as square centimetres or square metres.

The sample variance ($s^2$) for a set of measurements is calculated to be $2.25$ m$^2$. What is the sample standard devi

How would you represent $2 \frac{2}{5}$ using rectangles?

What are the correct dimensions of a rectangle where the numerical value of its perimeter equals twice its area?

A bottle contains $94$ mL of juice. If $7$ mL is poured into a glass, how much juice is left in the bottle?

Fill in the blank: If the $n^\text{th}$ term of a geometric sequence is $6(-2)^{n-1}$, the common ratio is $[?]$.

What is the missing term in the given equation? $x^3-2y^3+[?]=x(x^2+y)-2y^3$

The coordinates of point $A$ and point $B$ are $(15^\circ N,50^\circ E)$ and $(15^\circ N, 90^\circ E)$ respectively. Fi

Explain why a triangle with sides $5$ cm, $7$ cm, and an included angle $60^\circ$ has an area of approximately $15.2$ c

Why is the year split into four seasons?

Find the $11^{th}$ term of the geometric sequence $2,2\sqrt{2},4,\dots$.

In a triangle, two adjacent sides are $15$ cm and $18$ cm long with an obtuse angle, $x$, between them. If the area is $

The minute hand of a watch is $15$ cm long. How far does its tip move in $40$ minutes?

What is the next term in the given sequence below? $309, 301, 293, \dots$

What is $5028+1230-1675$ ?

How do you know that halving the diameter halves the circumference? Use an example to explain.

Identify the base in $k^m$.

What is the missing term in the given sequence? $1, 0.75, [?], 0.25, 0$

What is the seventh month of the year?

Explain why increasing the rate increases the total simple interest using an example.

Convert $2.6$ L into mL.

Which of the following correctly splits the middle term in $x^2 + 5x +6$ so it can be factorised by grouping?

The perimeter of a regular octagon is $904$ cm. What is the length of its side?

Why do you separate numerical from categorical data?

True or false: A small circle can pass through the centre of the Earth.

Find the density of an ice cube of mass $2$ g and volume $0.27$ cm$^3$.

Determine the formula for the arithmetic sequence $t_n$ whose fourth term is $1$ and whose fifteenth term is $-32$.

What is the next term in the sequence? $1,10,100,1000,\dots$

Find the volume of a piece of metal with a mass of $100$ g and density of $1.80$ g/cm$^3.$

The $8$th term in a pattern is $9.2136$. Each term increases by $0.8012$. What is the first term?

Find the perimeter of a rectangular block of land that is $2$ km long and $0.6$ km wide.

Find the $18$th term in the arithmetic sequence $-2,-7,-12,-17,. . . $

Fill in the blank: $4.5$ m$^2 = [?] $ cm$^2$

Determine the next term in the sequence $ \frac{2}{3}, \frac{5}{3}, \frac{8}{3}, \frac{11}{3}, [?]$.

Why do we divide annual interest rate by number of periods?

What is the next term in the sequence ? $-3, 9, -27, \dots$

What is the missing term in the given sequence? $-3.75$, $-3.45$, $[?]$, $-2.85$

Fill in the blank: $15600$ kilograms $+[?]$ megagrams $=17900$ kilograms

Consider the sequence where $n^2$ is the rule and $n$ is the position of the term. If the $4$th term is $16$, which ter

Which of the following is not true with respect to the interest rate of a fixed interest rate personal loan?

How do you check if a number can be shared equally into groups of $5$ and groups of $10$? Why does this work?

Find the coordinates of the centre of the rectangular hyperbola $y = \frac{-3}{2x+1} + 2$. What is the sum of these coor

Find the area of a circle whose circumference is $44$ cm.

What is $42 \div 6$ ?

After $500$ rotations, a wheel has travelled $1.06$ km. Find the diameter of the wheel in metres.

Bernadette's invests $\$10000$ for $n$ years on a $6.8\%$ interest rate compounded annually. The recurrence relation for

What is the $7^\text{th}$ term in Lucas sequence?

Find the total surface area of a hemisphere of radius $8$ cm.

A swimming pool has a capacity of $120$ kilolitres. How many litres is this?

The thickness of a piece of paper is approximately $1$ mm. If a book contains $500$ pages, what is the most appropriate

Find the area of a parallelogram with a height of $3$ cm and a base twice the length of its height.

Why might different points reveal important polynomial features?

A swimmer moves at a speed of $2.5$ metres per second. Convert this speed to kilometres per hour.

How can choosing the right unit of volume make calculations easier?

What is $13 \times 10$?

Divide the numbers: $235689\div19$

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 startin

How does understanding the unit circle relate to predicting sine curve behaviour?

Write the second smallest of the following fractions. $\frac{11}{20}, \frac{9}{16}, \frac{5}{8}, \frac{7}{12}, \frac{13}

There are $60$ minutes in one degree. An angle measures $78.833^\circ$. Convert this to degrees and minutes, rounding th

A sequence increases by $7$ each time. If the $10$th term is $200$, what is the value of the $2$nd term?

A water tank fills at a rate of $120$ litres per minute. What is this rate in litres per hour?

Convert $1$ cubic metre to litres.

The number of leaves, $N$, on a tree after $t$ years is given by $N(t) = 20000t + t^5 - 21t^2$. Given that $N'(t) = 200

Which of the following is an example of categorical data?

In an equilateral triangle $ABC$ with side length $10$ cm, the angle bisector from $A$ meets $BC$ at point $D$. What is

True of false: A parallelogram with a perpendicular height of $2$ cm and a base length $5$ cm has an area of $10$ cm$^2$

Which of these can't be represented by a binomial random variable?

Which operation would turn $6m$ into a like term with $-2mn$?

The cost of a $2$ litre can of paint is $\$6$. What will the cost of $24$ litres of paint be?

Why must we consider time period in compound curves?

A positive gradient indicates an $\fbox{\phantom{4000000000}}$ line, while a negative gradient indicates a downward sl

A wizard wears a conical hat with a circular base of radius $3$ cm and a height of $4$ cm. What is the curved surface a

A boat sails $12$ km on a bearing of $126^\circ \text{T}$, then $68$ km on a bearing of $216^\circ \text{T}$. Find the

What makes tree diagrams useful for multi-step probability problems?

What is the coefficient of the $x^2$ term in the expansion of the polynomial $P(x) = (4x^2 - 3)(x+2)$?

Which of the following statements best describes the behaviour of the graph of $y = \cos(x)$ over the interval $0^\circ

Fill in the blank: Co-interior angles are always $[?]$.

A rectangular garden has a length of $4\sqrt{3}$ metres. The area of the garden is $24\sqrt{3}$ square metres. Find the

A right circular cylinder has height equal to its base radius. Point $V$ lies halfway up the side, directly above a poin

Why does a frequency table help organise data into categories?

An additional monthly payment of $\$1000$ is being made on a sum of $\$500$, initially invested at $5.5\%$ per annum, co

Convert $0.075$ cm$^3$ to mm$^3$.

Consider the function $h(x) = \sqrt{4-x^2}$ with domain $[-2, 2]$. Is this function one-to-one or many-to-one?

Explain why $A=P(1+\frac{R}{n})^{nt}$ calculates the total amount

The highest score on a maths test is $95$ and the lowest is $60$. What is the range?

A student says the only solution to $\tan^2 x = 1$ between $0^\circ$ and $360^\circ$ is $x = 45^\circ$. Explain why this

Fill in the blank: The highest or lowest point on the graph of a parabola is called the $[?]$.

Find the next term in the given sequence. $ 0.02, 0.04, 0.06,\dots$

A random survey of $500$ people was conducted, and their responses recorded, with $369$ people agreeing that maths was t

How many mL are there in $0.1$ L ?

In Melbourne, $120$ schools are randomly surveyed to study the effects of remote learning. Which group is the population

A graph with $4$ vertices, $6$ edges and $5$ faces is a connected graph.

In a number pattern, each term is given by the rule: $\text{term} = 6 - 2n$, where $n$ is the position in the pattern. W

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

Which of the following pairs of variables is not suitable for a scatterplot?

The lines $y = (k - 2)x + (3k + 1)$ and $y = (k + 1)x + (k - 5)$ intersect at $x = 1$. Find the value of $k$.

Find the general term of the arithmetic sequence. $ \frac{1}{2}, 1, \frac{3}{2}, 2, \dots $

What is the distance along $26^\circ$N between ($26^\circ$N, $150^\circ$W) and ($26^\circ$N, $112^\circ$W), rounded to t

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

Fill in the blank: $10$ nanometres $=[?]$ metres

Drivers must travel slower than $40$ km/h in a certain zone. Which inequality represents this if $v$ is the car's speed

Why is the radius one unit for a unit circle?

The density $D$ of a metal block varies inversely with its volume $V$ when mass is fixed. When the volume is $4.8$ cm$^

What makes height numerical data?

The SI base unit for length is the metre (m). Which of these is a derived SI unit for area?

A box has a volume of $2$ m$^3$. How many smaller boxes with a volume of $4000$ cm$^3$ can fit inside it?

Which of the following is the general equation of a semicircle with a centre at the origin and radius $r$ units?

Explain why a parallelogram with base $3$ cm and perpendicular height $6$ cm cannot have an area of $9$ cm$^2$.

At which points do the equations $y=-2x^2+1$ and $y=x$ intersect?

The value of an investment triples after $x$ years at an interest rate of $r\%$ per year, compounded annually. The same

Andrew wants to take a loan of $\$20000$ from a bank. He has been provided two loan options in that bank: Loan A $:4\%$

Find the circumference of a circle with a radius of $4.5$ cm.

How does finding $100\%$ relate to understanding percentage change?

Explain why the $3$rd term in a sequence with recurrence relation $V_0 = 15$, $V_{n+1} = V_n - 4$ is positive.

An amount of money was invested at an $11\%$ simple interest rate per year. It grew to $\$5988$ in $2$ years and $3$ mon

Show why doubling the diameter doubles the circumference of a circle. Use an example to explain.

Calculate $x + y + z$ by simplifying the ratio of the given quantities, ensuring all values are in grams: $0.64$ kg to $

Explain why the next term in the sequence $5, 15, 25...$ cannot be $45$

The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$. If the container initially has $

It is observed that $20\%$ of cars entering a car park are red. What is the probability that the next three cars enterin

Why do grams change to kilograms the same way millilitres change to litres?

Bernadette's invests $\$10000$ for $n$ years on a $6.8\%$ interest rate compounded annually. The recurrence relation for

Find the missing term in the sequence. $0.010, 0.030, 0.050, [?], 0.090, 0.110$

Explain why $p_{7}=-3$ if $p_{1}=-3$ and $p_{n+1}=-p_{n}$

True or false: The centre of the rectangular hyperbola $y=\frac{2}{x-1}+1$ is $(1,1)$.

In $\triangle PQR$, $PQ = 152$ cm, $QR = 207 $ cm, $\angle QRP = 36^\circ$ and $\angle PQR = 112^\circ$. Find the lengt

By the SAS congruency rule, $\Delta ABC \cong \Delta PQR$. For $\angle A=30^\circ$, $\overline{AB}=15$ cm and $\overlin

A period of twelve months is called a $\fbox{\phantom{4000000000}}$

Which of the following is not numerical data?

You are booking a theatre show ticket. Tickets are only sold in batches of $2$ tickets or more in one booking, and one

Centimetres and millimetres are $\fbox{\phantom{4000000000}}$ of length.

Why do we need different units to measure weight?

A cylinder has a radius of $r$ and height $h$. The area of its two circular ends is $2\pi r^2$. If $r=2\text{ cm}$, wha

Your friend thinks that an angle the same as a right angle can also be called acute or obtuse. Why is this wrong?

Why does a negative exponent result in a reciprocal?

Which of the following statements defines a chord?

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, fin

Convert $5$ L into mL.

The $\fbox{\phantom{4000000000}}$ is the distance from the centre of a circle to any point on its circumference.

In triangle $ABC$, $\overline{BC} = 153$ cm, $\overline{AB} = 128$ cm, and $\angle{ABC} = 47.3^\circ$. Find $\overline{A

$\fbox{\phantom{4000000000}}$ form is a way of writing a linear equation that shows the gradient and $y$-intercept.

Which among these statements is true?

Express $0.006$ cubic metres in cubic centimetres.

How can you confirm a shape has been rotated $90^\circ$ clockwise around a specific point?

In a circle with diameter $AB = 10$ cm, point $C$ lies on the circle, forming $\triangle ACB$. If $BC = 6$ cm, what is

If the inflation rate is $2\%$ per year, calculate the value of $\$2000$ indexed for inflation over $2$ years.

Fill in the blank. The $12^\text{th}$ term of the arithmetic sequence whose first term is $1$ and the common difference

Fill in the blank: The total surface area of a closed cylinder with radius $r$ cm and height $h$ cm is given by $[?]$.

Why do we multiply by $1000$ when changing cubic metres into litres?

An equilateral triangle has a perimeter of $36$ cm. If the perpendicular height of the triangle is $10.4$ cm, what is i

How many centimetres are in $2$ metres?

Fill in the blank: $5a+6ab-b$ is an example of $[?]$.

Show why doubling the time doubles the simple interest earned.

When should you measure something in mm and when in cm?

A circular pizza has a diameter of $30$ cm. There is a circular hole at the centre of the pizza with a diameter of $4$ c

Tim says 'miles' is not a metric unit used to measure length. How do you know he is correct?

Which of the following is equal to $67$ L ?

Which number is the same as $\frac{1}{10}$?

At a car service centre, $58\%$ of vehicles are petrol and $42\%$ are diesel. $12\%$ of petrol vehicles and $23\%$ of d

David found the 13th term ($a_{13}$) for the arithmetic sequence $21, 26, 31...$ to be $86$. Show that he is incorrect.

What is the period of $2\tan{6x}$ ?

A number is divisible by $2$. Which of the following must also be divisible by $2$?

Which units are most appropriate for measuring a small amount of cooking oil in a recipe?

In how many ways can $6$ different books be arranged on a shelf if a specific book must always be placed last?

The volume of water $(V)$ in a container increases by a factor of $2$ every hour $(t)$. If the container initially has $

True or false: The angle subtended by a chord at the centre of the circle is equal to the angle subtended by the same c

A rectangle has a perimeter of $60$ m, and the length is $4$ metres less than twice the width. Which equation represents

Maira bought a gold chain for $\$600$ ten years ago and it now costs $\$1500$. She wants to investigate whether inflatio

What is the next term in the given sequence? $1,\ 3,\ 11,\ 123,\ \cdots$

True or false: The perimeter of a two-dimensional shape is equal to the sum of the length of all the sides.

Find the simple interest if $P = \$200$, $R = 3\%$ p.a., and $T = 1$ year.

What is the missing term in the given sequence? $-4.75$, $-4.25$, $[?]$, $-3.25$

Convert $4.5$ tonnes : $750$ kg : $300000$ g into a simplified ratio.

A water tank holds $60$ litres. Each bottle can hold $1.5$ litres. Which two expressions both show how many bottles can

Why is it important to understand parallelograms in maths or in real-life designs?

Fill in the blank. The slope of a simple interest graph equals the $[?]$.

A drone flies at a speed of $15$ metres per second. Convert this speed to kilometres per minute.

The radius of a circular track is increased by $5$ cm, and its diameter becomes $40$ cm. What was the original radius of

Fill in the blank: A water tank is filled at a constant rate of $8$ litres per hour. After $6$ hours, the tank will hav

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 d

How do you know that combining two $3$ m by $2$ m spaces needs square metres to show the total area?

Show that $12.25$ m$^3$ plus $750$ millilitres is not the same as $13$ litres.

The total surface area of a cone is $90\pi$ cm$^2$. If its radius is $5$ cm, what is its slant height?

Joe invested $\$20,000$ in an annuity which earns an interest of $12\%$ per annum compounding quarterly. He wants to rec

Which of the following is equal to $\$3.50$ ?

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

A sum of $\$2000$ amounts to $\$2101.25$ in one year when the interest of $5\%$ is compounded half-yearly. What will the

What makes rounding to significant figures different from decimal places?

The perimeter of a regular hexagon is $564$ cm. What is the length of one of its sides?

A particle moves in a straight line and its velocity after $t$ seconds is given by $v(t)=3t^2+t$ m/s for $0\leq t\leq 12

A rectangle has a length that is $3$ metres more than its width. If the area of the rectangle is equal to its perimeter

The radius of a spherical asteroid is $10$ km. Find its surface area in terms of $\pi$.

Which of the following is not a unit for measuring the velocity of an object?

A rock has a mass of $90$ g and a volume of $3$ cm$^3$. What is its density?

What is the value of $\sqrt[3]{-216}$?

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

An $\fbox{\phantom{4000000000}}$ interest rate is the interest rate for a full year.

Fill in the blank: $3.2$ litres $+\ 0.175$ litres $+\ 250$ cm$^3\ = [?]$ cm$^3$

True or false: The total surface area of a cube of side length $0.2$ cm is $2.4$ cm$^2$

The volume of a sphere is $288\pi$ cm$^3$. What is its radius?

The lengths of two parallel sides of a trapezium are $12$ cm and $8$ cm, respectively. The distance between the parallel

Fill in the blank: Two triangles have side lengths of $8$, $12$, $16$ cm and $4$, $6$, $8$ cm. The triangles are similar

Does adding any two odd numbers always give an even answer? Explain using two examples.

Consider $f(x)=x^2+ax+5$ and $g(x)=x^2-x+5$ and $f(x)=g(x)$. Find the value of $a$.

The volume of the square pyramid is $48$ cm$^3$ and the cube has side length $6$ cm. What is the volume of the composite

What is $10$ m$^2$ in cm$^2$ ?

A delivery truck travels at $90$ kilometres per hour. Convert this speed to metres per minute.

Let $P(x) = x^{4} + ax^{3} + bx^{2} + cx + d$. When divided by $(x+1)^{2}$, the quotient is monic with no constant term,

Why do you need to divide the interest rate by the number of times it is compounded in a year when calculating compound

What is the $11^{th}$ term of the arithmetic sequence whose first term is $10$ and its common difference is $10$?

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, wh

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

Which of the following is an example of categorical data?

How many grams are in $2$ kg and $45$ g of peanuts?

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 f

Which of the following is the correct rule of the density function for $\frac{1}{5}X+6$ if $f$ is the probability densit

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 r

Which of the following can be represented by a discrete random variable?

A water tank contains $85$ litres of water. If $8$ litres are used for irrigation, how much water is left in the tank?

How many mL are there in $40$ cm$^3$ ?

How is changing $1$ m$^2$ into cm$^2$ different from changing $1$ m into cm?

Fill in the blank: $4.5$ mm$^2=[?]$ cm$^2$

Why are road distances measured in km and not m?

How do you know that the length of a rectangle with area $32$ cm$^2$ and width $4$ cm will be twice the width?

Fill in the blank. A common ratio of $[?]$ results in a $10\%$ increase from one term of a geometric sequence to the nex

The area of a kite is $2528.75$ cm$^2$. The length of the shorter diagonal is $70\%$ of the length of the longer diagona

Why must both quantities in the ratio $3$ km$:$ $600$ m be written in the same units before simplifying?

How do you know that the $7$th term in the geometric sequence $4, 8, 16...$ is $256$, not $2^7$?

Why do we multiply by $10\ 000$ and not $100$ when changing $1$ m$^2$ into cm$^2$?

A company defines a week as $6$ days for their roster. Based on a $365$-day year, how many full company weeks fit into

What is $\frac{7}{8}-\frac{4}{8}$ ?

Fill in the blank: $1.5$ ML $- \,\,950$ kL $=[?]$ L

The setup cost of a fitness centre is $\$24000$. Maintenance costs $\$12.50$ per member per month, and membership revenu

Describe the two main steps to find the inverse of a function, such as $y = \frac{2x}{x-1}$.

Why do we group items in sets?

A bike is purchased for $\$9,000$. The value of the bike decreases by $20\%$ each year. Find the value the bike value af

A round trip from Sydney to Brisbane covers a distance of approximately $1800$ km. If you drive at an average speed of

What does the M stand for in BODMAS?

Which statement about simple random sampling is false?

A tap fills at $0.5$ litres per second. Sam says this equals $30$ litres per minute. How can you prove if he is correc

Why are different units of mass used for objects of different size?

Which of the following is the imperial unit of mass?

What is $75.254$ $\div \ 100$ ?

The highest power of the variable in a $\fbox{\phantom{4000000000}}$ is $1$

How do you know $\$1000$ at $5\%$ simple interest gives $50$ yearly?

A rectangular signboard has a width of $x$ metres and its height is twice the width. Write an expression for the area.

Why does changing from kilometres per hour to metres per second change the number but not the speed?

In $\triangle ABC$, $\angle A = 40^\circ$, $BC = 13$ cm, and $AC = 19$ cm. Determine how many distinct triangles can be

$3$ kg of oranges and $4$ kg of apples cost $\$24$. $4$ kg of oranges and $3$ kg of apples cost $\$22$. Which statement

Write the fifth term, $t_5$, of the sequence given by the recurrence relation $t_0=-2$, $t_{n+1}=-t_{n}$

Explain why shoe size is a type of discrete data but the length of a shoe is continuous.

How does understanding vertical lines relate to identifying functions?

The volume of a cone is $75\pi$ cm$^3$. If its radius is $5$ cm, what is its perpendicular height?

What is $2000$ litres in m$^3$ ?

How do you know that a rectangle with its length and width in centimetres will have its area in square centimetres?

Why does the $90$th percentile represent a higher score than the $10$th percentile?

Fill in the blank: If a plant grows linearly by $2$ cm each week, after $10$ weeks, it will have grown an additional $[?

Why do quadratic functions curve instead of forming lines?

How many millilitres are in $1$ cubic centimetre?

A sum $P$ is invested for one year. Account $1$ pays $4\%$ simple interest, earning $I_1$. Account $2$ pays $3\%$ in si

A wheel of radius $35$ cm is rolled. How far will it move after $10$ rotations?

A student factorises $-6x - 12$ as $-(6x - 12)$. How would you explain why this is incorrect?

Four bakeries produce dough at different rates. Which bakery produces the most dough per minute?

Write $y^2 + 4y + 3y + 12$ in factorised form.

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 me

What is $\Large\frac{0}{0.5}$ ?

What is $\frac{3}{4} \times \frac{5}{4}$ ?

Find the total length, in metres, of the following: $1.25$ km, $38\ 500$ cm and $72\ 000$ mm

Why does the value of $a$ in $y=a(x-h)^2+k$ decide whether the parabola opens up or down?

Mary borrowed $\$4000$ at an annual interest rate of $10\%$, compounded monthly, with monthly payments of $\$351.60$. F

Explain why each term in the sequence $3,7,11,15...$ increases by $4$

Evaluate $\int{e^{-mx}}dx$ where $m$ is a constant term.

Convert $90000$ mL into L.

Why do we use similar steps to long division with numbers when dividing polynomials?

What is the next term in the sequence ? $5, 10, 20, ...$

A company's profit increases by $1.08$ times every year. If the profit generated in the first year was $\$10$ Million, h

Calculate the volume (in litres) of a cylindrical tank with a height of $5$ m and a base area of $4$ m$^2$.

In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 10$ cm, and $AC = 16$ cm. Determine how many distinct triangles can be

What is the total surface area of a $35$ cm long closed cylinder with a diameter of $13$ cm?

Find the $5$th term of the geometric sequence $3, 6, 12, 24,\dots$

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

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?

An architect is designing a triangular roof. The base of the roof is $19$ metres and the height is $22$ metres. What is

Mia puts $\$500$ into a savings account. The bank pays $4\%$ simple interest each year. How much interest will she earn

True or false: Cubic centimetres is an appropriate unit to measure the volume of a wooden plank.

How do you know $3^n$ triples from one term to the next?

Which statement best explains why compound interest causes exponential growth? A) The interest rate increases each year

Why does compound interest grow faster than simple interest?

An exterior angle of an isosceles triangle is $100^\circ$, and this exterior angle is adjacent to one of the base interi

In $\triangle ABC$, $\angle A = 30^\circ$, $BC = 7$ cm, and $AC = 16$ cm. Determine how many distinct triangles can be

Fill in the blank: $\frac{3}{4}$ kg $=[?]$ g

The volume of the cylinder is $540$ cm$^3$ and the volume of the cone is $180$ cm$^3$. What is the volume of the composi

Why do we complete the square to convert a quadratic to turning point form?

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

Hannah started a job in $2010$ with an annual salary of $\$35000$. Each year, she received a pay increase of $\$200$. Wh

Convert $0.65$ L into mL.

Why is it important to understand decimal shifts when solving measurement problems?

A rectangular garden has an area of $120$ m$^2$ and a perimeter of $52$ m, with length $𝑙$ metres and width $𝑤$ metres.

Solve for $x$: $\dfrac{1}{x-2}= \dfrac{3x+1}{x^2-4}$

What is the next term in the sequence? $1,5,13,25,41,\dots$

A delivery route has three segments. The first segment is $2.8$ km, the next is $1550$ m, and the last is $35000$ cm.

A cyclist travels $12.6$ kilometres in $1.5$ hours. Find the speed in metres per hour.

A floor is in the shape of a rectangle. It has a length of $8.12$ metres and a width of $7.54$ metres. Calculate the a

Complete the statement below. The sum of an $n$-term geometric series with first term $a$ and common ratio $r$ is given

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

Why does $1$ hour equal $3600$ seconds?

Olivia borrows $\$5000$ from the bank at a simple interest rate of $6\%$ per annum. After $4$ years, will the amount of

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

Fill in the blank: A cyclist rides $5$ km every day. After $14$ days, the total distance travelled will be $[?]$ km.

Fill in the blank: $20060$ g $=20$ kg and $[?]$ g

Evaluate $(-1)^{100}$

Convert $7$ kg and $409$ g into grams.

A rectangular prism with dimensions $6$ cm $\times$ $4$ cm $\times$ $3$ cm is enlarged by a scale factor of $3$. What i

A sequence decreases by $\dfrac{2}{9}$ each time. If the $15$th term is $-\dfrac{5}{3}$, what is the first term?

Why does multiplying two polynomial functions increase the degree of the result?

Explain why the $5$th term in the sequence $2, 6, 18,...$ is $162$

Why does changing the centre angle affect both the sector and triangle areas differently?

A gardener uses $0.125$ kg of fertiliser per square metre. She fertilises $1000$ m$^2$ of the garden. How much fertilise

Is $\begin{bmatrix} 1&0&0\\0&0&1\end{bmatrix}$ an identity matrix?

Find the missing term in the given sequence. $10, 9.8, [?], 9.4, 9.2$

How do you know the discriminant $b^2-4ac=0$ means there is one repeated real root?

How many litres are there in $6$ m$^3$ ?

Fill in the blank: $(-4)^{-2}=[?]$

The area of a sector is $\frac{132}{7}$ cm$^2$ and the central angle is $60^\circ$. What is the diameter of the entire

Fill in the blank: Two lines have the same gradient but different $y$-intercepts. These lines are $[?]$

Why is it important to organise $x$ and $y$ values in a table?

A recipe uses $900$ g of flour and $2.7$ kg of sugar. Express the ratio in grams, in simplest form.

A basket has $16$ apples. How do you know there will be $10$ apples if $6$ are taken away?

True or false: ${11}$ is the constant term in $t^2+{11}t-{11}$.

Fill in the blank. $745.98$ mL$=[?]$ cm$^3$

Fill in the blank: $0.003$ ML $+ 4.2$ kL $=[?]$ L

A triangle has a base length of $15$ cm and a height of $8$ cm. Find the area of the triangle.

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 ha

Water is flowing at a rate of $300$ millilitres per second. How many litres flow in one minute?

Fill in the blank: The point at which both axes intersect is called the $[?]$ on the Cartesian plane.

Fully factorise the following expression: $-2x^6y^7z^3-4x^3y^3z$

True or false: $1$ year is the same as $12$ months.

Explain why subtracting $0.25$ from each term creates a sequence in $2.0, 1.75, 1.5, 1.25,...$.

How do you know the $5$th term in the geometric sequence $2, 10, 50...$ is $1250$, not $500$?

A city had a population of $54302$ people. In the first half of the year, $12678$ people left. In the second half of t

A sphere has a diameter of $8$ cm. Calculate its volume, leaving the answer in terms of $\pi$.

Find the distance of Miami$(26^\circ{N},80^\circ{W})$ from the equator.

Fill in the blank: $1$ micrometre $=[?]$ metres

How do asymptotes relate to understanding graphs?

For a random variable $F$ , it is known that $Var(F)=9$ . Calculate $sd(5F-11)$ .

Delhi, India and Xinjiang, China have coordinates $(29^\circ N,77^\circ E)$ and $(41^\circ N,77^\circ E)$. Calculate th

How do you know millilitres is not an imperial unit of volume?

How does finding equivalent fractions relate to comparing $\frac{2}{3}$ and $\frac{3}{4}$?

Why is Pythagoras’ theorem only applicable for right triangles?

Convert $2$ L into mL.

A library initially has $10\ 000$ books. Each year, $500$ are added and $150$ are removed. Which recurrence relation des

A delivery company charges a flat fee of $\$15$ plus $\$5$ for every kilometre travelled. If a $10\%$ discount is given

Suppose that a bicycle costs $\$3,450$ today. If inflation averages $1.5\%$ per year, calculate the value of the bicycle

A large jug holds $2.25$ L. How many $250$ mL cups can be filled from the jug?

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?

$\fbox{\phantom{4000000000}}$ growth is a type of growth where the quantity increases by a constant amount per unit of

Explain why $I = P \times R \times T$ is used for simple interest.

Find the volume of the composite solid shown below. Image description: A rectangular prism measuring $10$ cm by $8$ cm

Explain why Quadrant I has positive $x$ and $y$ values, while Quadrant III has negative $x$ and $y$.

If $A=$$\begin{bmatrix} 0&0&1\\ 0&1&0\\ 1&0&0\\ \end{bmatrix}$ and $B=$$\begin{bmatrix} 1&4&-1\\ 2&-2&2\\ 1&-2&0\\ \end{

How many litres are there in $7$ m$^3$ ?

A student has mastered $50.2\%$ of $500$ maths skills. How many skills remain to be mastered?

Explain why the circle $(x + \frac{3}{2})^2 + (y - 3)^2 = 36$ has centre $\left(-\frac{3}{2}, 3\right)$.

Find the volume of the composite solid shown below. Image description: The solid is made from two rectangular prisms. T

For two disjoint sets $P$ and $Q$, we know that $P\cup{Q}=U$, where $U$ is the universal set, which of these statements

Which of the following gives the $n^\text{th}$ term of the geometric sequence whose fourth and seventh terms are $24$ an

Which of the following statements is true?

Location coordinates are given as: Point $X$ $=42^\circ{N},170^\circ{E}$ Point $Y$ $=60^\circ{N},170^\circ{E}$ Wha

Fill in the blank: $600$ cm$^3$ $+\ 0.001$ m$^3=[?]$ cm$^3$

For two places lying on a meridian, their coordinates of the location are $36^\circ{N}$ and $12^\circ{S}$. What is the

What makes the form $y=a(x-h)^3+k$ useful for graphing cubics?

Why must we analyse real situations to identify mutually exclusive events?

In a geometric sequence, the $k^{th}$ term is $T_k$ and the $(k+2)^{th}$ term is $T_{k+2}$. If $T_k \cdot T_{k+2} = (T_{

A fish tank has dimensions $80$ cm $\times$ $50$ cm $\times$ $40$ cm. What is its volume in litres?

True or false: $4\times(20+8)= (4\times 20 ) + (4\times 8)$

I take two and a half hours to run $1.5$ km. What is my average speed in km per hour?

Choose the correct symbol to fill in the blank. $9$ $[?]$ $9$

Bill makes a purchase of $\$2000$ and pays a deposit of $\$500$ and agrees to pay the rest in $7$ instalments, each wort

The price of an electronic bicycle is represented by the regression line: Price $= 900 - 10 \times$ quarter of a year Wh

A $\fbox{\phantom{4000000000}}$ is a fixed numerical value.

A total of $\$328.80$ including GST was paid for public transport last year. What was the cost excluding GST?

A jug has a capacity of $1.5$L. Which of the following best explains what this means?

Cubic metres and cubic centimetres are units of $\fbox{\phantom{4000000000}}$

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

What makes monthly compounding use $12$ periods?

Why does multiplying litres by $1000$ always give the number of millilitres?

Which of the following will not maintain mathematical equivalence?

Which recurrence relation represents a geometric sequence with first term $81$ and common ratio $\dfrac{1}{3}$?

Creating tables of values helps in understanding the $\fbox{\phantom{4000000000}}$ between variables.

Which of the following is the general term $u_n$ of the geometric sequence in which $u_5=\frac{3}{16}$ and $u_8=\frac{3}

Fill in the blank: $1.25$ ML $+ \,\,1500$ L $+ \,\,2.75$ kL $=\ [?]$ ML

Explain why $30$ months equals $2$ years and $6$ months

The latitude and longitude of Beijing, China is $40^\circ N$ and $116^\circ E$ respectively. Find its distance from the

A man bought a laptop costing $\$15000$. He pays a deposit of $\$3000$. He must pay the remaining amount by making month

What is the least possible number of edges in a connected graph having three vertices?

Fill in the blank: Footwear colour is an example of $[?]$ data.

A triangular prism has a right-angled triangle base with $\angle C = 90^\circ$, $AC = 6$ cm, and $BC = 8$ cm. The hypote

A rectangular box has dimensions of $2$ cm, $3.3$ cm, and $10$ cm. What is the total surface area of the box?

Which of the following is the equation of a semicircle with centre at $(1,1)$ and radius $2$ units with its base on $y-$

How many years will it take for $\$1500$ to double if it is invested at an annual interest rate of $6\%$, compounded con

A chemical solution is $1200$ ml. Each hour, $75$ ml evaporates, and $15$ ml is added. Which recurrence relation repres

True or false: Single-stage experiments involve only one action or trial.

Which of the following is not a key property of the function $y = \frac{1}{x^2}$ ?

An amount $P$ is invested for $3$ years at $R\%$ simple interest. The same $P$ is invested for $2$ years at $(R + 2.5)\

In a particular geometric sequence, the second term is $2\sqrt{2}$ and the ninth term is $32$. What is the $14^\text{th}

What is the total surface area of a cone if $l$ is slant height, $r$ is the radius of the circular base and $h$ is the v

Find the smallest distance between the centre of the circle of radius $12$ cm and a chord of length $18$ cm.

Fill in the blank: A team of talented maths students being selected to represent a school in an interschool maths compet

Which of the following numbers is larger than $11111$ ?

What is the correct factorisation of $-12x^2y + 6xy^2 - 18x^2y^2$ ?

True or false: A continuous random variable can represent the amount of iron contained in a beaker containing $250$ ml o

Solve for $x$: $\frac{4.8}{5}-\frac{x}{4}=6$

Why does multiplying every term of an equation by the same number not change the solutions of the system?

A grocery store sells milk in cartons of $1$ litre. A customer wants to purchase a total of $3000$ millilitres of milk.

A plane flies $100$ km on a bearing of $025^\circ \text{T}$. How far east does the plane fly?

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?

Why does solving a logarithmic equation often involve rewriting it in exponential form?

How does understanding percentages help you make sense of different interest rates?

Explain why $x$ in $\frac{7}{x} = 2$ can be found by multiplying both sides by $x$ and then dividing by $2$.

Fill in the blank. The solutions to the quadratic equation $x^2 - 2x - 3 = 0$ are $x = \frac{2 \pm \sqrt{[?]}}{2}$.

Find the value of $m$ such that the equation $mx^2 - 2x + 1 = 0$ has exactly one solution.

Why do we subtract the discount from the original price to get the final price?

Convert $7000$ mL into L.

How many months in a year have exactly $31$ days?

A scale using exponential increases is called a $\fbox{\phantom{4000000000}}$ scale.

A rectangular billboard is built with $100$ metres of framing. Its area is modelled by $A = -x² + 50x$ What is the maxim

What is the next term in the sequence? $0.6, 1.2, 2.4, \dots$

Map A uses a scale of $1$ cm = $1$ km. Map B uses a scale of $1$ cm = $0.5$ km. A road appears $6$ cm long on Map A. How

An architect is designing a triangular balcony. The base of the balcony is $15$ metres, and the height is $20$ metres. W

Express $\log_{3}{5}+\log_{3}{2}+\log_{3}{4}$ as a single logarithm.

True or false: The cubic metre (m$^3$), is a base SI unit.

Convert $3.9$ kg into grams.

How do you know that a square with area $16$ cm$^2$ cannot have a side length of $5$ cm?

How many mL are there in $3.5$ L ?

John borrowed $\$4000$ at $10\%$ annual interest, compounded monthly, with monthly payments of $\$351.60$. What is his

Find the radius of the circle in which the central angle of $\frac{\pi}{3}$ intercepts an arc of length $37.4$ cm.

What factor does the SI prefix ‘kilo-’ represent in terms like kilogram or kilometre?

Why does converting from a smaller unit (like mL) to a larger unit (like L) make the number smaller, even though the amo

Find the missing term in the sequence: $1.50, 2.50, 6.50, 13.50, 23.50, 36.50, [ ? ]$

Naruto runs a total distance of $800$ meters while using his Sage Mode. How long did it take him to cover this distance

True or false: In reducing balance loans, the balance owed is reduced by half after every depreciation term.

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 neare