Oct/Nov 2025

Write four hundred and sixty thousand and five as a numeral.

Limits of accuracy

The bar chart displays how many books were sold in a shop across five months.

Averages and measures of spread

At midnight, the temperature is -2^{\circ}C. By noon, it has risen to 5^{\circ}C.

The four operations

This cuboid measures 5 cm, 4 cm and 3 cm. Finish the cuboid net on the 1 cm^{2} grid. One face is already shown.

Surface area and volume

This scale drawing gives the locations of town A and town B. Its scale is 1 centimetre represents 10 kilometres.

Scale drawings

The ages of the 12 children, measured in months, are 11, 27, 8, 10, 26, 17, 28, 12, 9, 13, 22 and 12.

Interpreting statistical data

ABC forms a straight line, and ABD is an isosceles triangle. The exterior angle at B measures 140^{\circ}, while the angle at D is x^{\circ}.

Angles

Fill in the value table for $y=\frac{9}{x}$.

Graphs of functions

State a prime number from between 20 and 30.

Types of number

Work out $\frac{11}{18}-\frac{2}{9}$. Write your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Using each number in the calculation rounded correctly to 1 significant figure, estimate the value of $\frac{5.3\times19.5}{2.49}$.

Estimation

The diagram displays a circle with centre O.

Geometrical terms

A group of students sit a test. 75 of them pass the test. This represents $\frac{3}{5}$ of the students who sit the test.

Ratio and proportion

Shapes A and B are displayed on the grid.

Transformations

For chocolate cookies, the recipe makes 12. Ingredients: 100 g flour, 55 g butter, 55 g sugar, 20 g cocoa, 1 egg.

Ratio and proportion

Determine the value for x.

Equations

E = {students in a year group}, H = {students who study History}, G = {students who study Geography}. There are 80 students in the year group altogether. 40 students study History. The Venn diagram shows 10 in the History-only region and 15 outside both sets.

Sets

Expand the brackets and simplify $(x+3)(x-2)$.

Algebraic manipulation

Write $1.753\times10^8$ in ordinary form.

Standard form

The diagram depicts a semicircle. Its radius measures 8 cm.

Circles, arcs and sectors

Find $8\frac{2}{3}\div1\frac{5}{8}$. Write your answer as a mixed number in its simplest form.

The four operations

Jim purchases 15 apples and 10 pears for $42.50. Li purchases 4 apples and 5 pears for $16.

Equations

State the mathematical name of this polygon.

Geometrical terms

List all the factors of 24.

Types of number

In triangle ABC, AB = 8 cm and BC = 6.4 cm. With only a ruler and compasses, construct triangle ABC. Keep the construction arcs visible. AC has already been drawn.

Geometrical constructions

Shade one square so that the diagram has rotational symmetry of order 4.

Symmetry

These are the first four terms of a sequence: 9, 5, 1, -3

Sequences

$p = 3q - 2r$

Equations

Colour in $\frac{3}{4}$ of this grid.

Percentages

State the value of the 3 in the number 23 679.

Types of number

A bag has red balls and green balls in it. The ratio of red balls : green balls is 2 : 3. One ball is chosen at random.

Introduction to probability

The stem-and-leaf diagram presents how many customers went into a shop on each of 20 days.

Interpreting statistical data

The sketch depicts a parallelogram. The angles labelled are $(x-30)^{\circ}$ and $(3x+10)^{\circ}$.

Angles

The diagram depicts a right-angled triangular prism. The dimensions indicated are 3 cm, 4 cm, 4 cm and 5 cm.

Surface area and volume

The sketch depicts a smaller triangle DEF, with its vertices positioned on the sides of a larger triangle ABC. The angles labelled are A = 100^{\circ}, B = 50^{\circ}, C = 30^{\circ}, at D = 25^{\circ}, and at F = 45^{\circ} and 35^{\circ}.

Angles

The sum $n is divided between three sisters in the ratio 10 : 3 : 2. The smallest portion is $120.

Ratio and proportion

$9.857\times10^{-2}$, $3.5\times10^{2}$, $1.54\times10^{1}$, $6.5\times10^{-2}$. Arrange these numbers from the smallest upwards.

Ordering

A trapezium whose parallel sides are 8 cm and 14 cm, with a height of 6 cm.

Compound shapes and parts of shapes

Calculate $2\frac{5}{6} \div 4\frac{1}{4}$. Give your answer as a fraction in its simplest form.

The four operations

The grid contains two flags, F and A.

Transformations

Determine how much change he receives from $20$.

Money

The universal set is $\xi = \{1,2,3,4,5,6,7,8,9,10\}$, with $A=\{1,3,5,7,9\}$ and $B=\{1,3,6,10\}$.

Sets

Simplify the expression $\frac{18x^8}{9x^2}$.

Algebraic manipulation

Determine the size of one interior angle of a regular hexagon.

Geometrical terms

Two different charges are charged for using a bridge. Cars are charged $a. All other vehicles are charged $b. On Monday, 4 cars and 20 other vehicles together pay $130. On Tuesday, 6 cars and 15 other vehicles together pay $105.

Equations

B is a point on the circle with centre O. ABC is tangent to the circle at B, and angle OAB = 36^{\circ}.

Circle theorems I

Expand the expression $(x-5)(x+2)$ and then simplify it.

Algebraic manipulation

The rope has length, l metres, of 16.32 metres, rounded to 2 decimal places.

Limits of accuracy

Find the nth term for this sequence.

Sequences

Write 17469 rounded to the nearest ten.

Limits of accuracy

State the value of $\sqrt{144}$.

Powers and roots

The diagram consists of equilateral triangles.

Symmetry

Write $\frac{3}{4}$ in decimal form.

Fractions, decimals and percentages

A bag holds 8 discs numbered from 1 to 8, and one disc is chosen at random from the bag.

Introduction to probability

The number n is a divisor of 144 and a multiple of 9.

Types of number

At midday on Monday, the temperature is -3^{\circ}C, whereas at 10 pm on Monday it is -15^{\circ}C.

The four operations

Measure the distance of line AB in centimetres.

Geometrical constructions

The sketch shows an isosceles triangle set between two parallel lines. The apex angle is 40^{\circ}. The angles x^{\circ} and y^{\circ} are marked.

Angles

Determine the cost of 1 peach.

Introduction to algebra

Simplify the expression $3y-4y+2y$.

Equations

A number line has a filled circle at -5 and an unfilled circle at 1, with the stretch between those points shaded.

Inequalities

Victoria places $2000$ in an investment earning simple interest at 5% per year.

Percentages

Fill in each statement.

Units of measure

Kai, Jo and Liz divide some money in the ratio Kai : Jo : Liz = 4 : 7 : 13, and Jo is given $1400.

Ratio and proportion

From $k^x \times k^5 = k^{20}$, determine the value of x.

Algebraic manipulation

A circle has a diameter of 16 cm.

Circles, arcs and sectors

Find the number of sides in a regular polygon that has an interior angle of 160^{\circ}.

Angles

Express the number 83 042 in words.

Ordering

The door’s height, h cm, is 180 cm, accurate to the nearest centimetre.

Limits of accuracy

The sequence begins with these four terms: -6, 1, 8, 15.

Sequences

The diagram displays triangles A and B on coordinate axes.

Transformations

In part (a), a Venn diagram is shown for sets A and B, and the overlapping section is shaded. Part (b): E = {people in a club}, T = {people who play tennis}, S = {people who go swimming}. The club has 60 people in total. 36 people go swimming. The Venn diagram shows 10 outside both sets and 30 in the S-only region.

Sets

Express this as the ratio 1 : n.

Ratio and proportion

Calculate $\frac{3}{4} \times 1\frac{2}{3}$. Present the result as a mixed number in its simplest form.

The four operations

On Li’s trip to work, there are 2 sets of traffic lights. The chance that he stops at the first set is 0.4, while the chance that he stops at the second set is 0.7.

Probability of combined events

Sam expresses 851000 in standard form as $85.1 \times 10^4$.

Standard form

Measure the angle a.

Angles

Ben writes down the favourite sport for each of the 20 students: Football, Cricket, Hockey, Rugby, Football, Tennis, Rugby, Football, Football, Rugby, Tennis, Football, Rugby, Football, Cricket, Football, Rugby, Football, Cricket, Cricket.

Classifying statistical data

The diagram displays quadrilateral ABCD on a 1 cm^{2} grid.

Coordinates

Anna picks a number, multiplies it by 2, and then takes the square root. The result is 12.

Powers and roots

The journey begins at 10 55 and finishes at 16 10.

Time

The masses, measured in kg, of these 11 bags are: 23, 16, 8, 10, 27, 19, 4, 17, 13, 4, 14.

Statistical charts and diagrams

Find the value of $2^5$

Indices I

Divide $90$ into the ratio $2:3$.

Ratio and proportion

$\mathcal{E}=\{n:n\text{ is an integer and }1\le n\le 8\}$, $A=\{\text{values that are factors of }12\}$, $B=\{\text{odd numbers}\}$.

Sets

Write $0.\dot{2}\dot{4}$ as a fraction in lowest terms.

Fractions, decimals and percentages

The diagram depicts a sector of a circle with centre $O$ and radius $9\text{ cm}$. Its perimeter is $(18+2\pi)\text{ cm}$.

Circles, arcs and sectors

Rahul’s 10 test scores are $9, 8, 9, 10, 7, x, 9, 9, x, 7$. Their mean equals 8.

Averages and measures of spread

$A$, $B$, $C$, $D$ and $E$ are on the circle. $AC$ and $BD$ meet at $X$. Angle $ACD=55^{\circ}$ and angle $CXD=88^{\circ}$.

Circle theorems I

Write the number $66000$ in standard form.

Standard form

The graph encloses region $R$ with boundaries at $y=4$, $y=3$, $x=2.5$ and $y=2x$.

Inequalities

This gives $I=M(k^2+c^2)$.

Algebraic manipulation

Using $f(x)=2x+5$, the expression $f(x)f(x)-f(f(x))=ax^2+bx+c$ is obtained.

Functions

Solve for $x$ in $\left(\frac{1}{3}\right)^x=9^{x+4}$.

Indices II

Calculate angle $CAB$.

Angles

Bag A has 5 white balls and 3 black balls, whereas bag B has 3 white balls and 1 black ball.

Probability of combined events

$(3-\sqrt5)(2+3\sqrt5)=a+b\sqrt5$. Find $a$ and $b$.

Powers and roots

Solve the equation $\frac{2}{x-1}=\frac{x}{x+2}$.

Equations

Find the coordinates of the turning point for the graph of $y=7-2x-x^2$.

Sketching curves

The diagram indicates that $OBD$ and $ACD$ are straight lines. $O$ is the origin, the position vector of $A$ is $\mathbf a$ and the position vector of $B$ is $\mathbf b$. $\overrightarrow{BC}=\frac13\overrightarrow{OA}$. $M$ is located at the midpoint of $CD$.

Vectors in two dimensions

Simplify $\frac{10ax+6bx-25a-15b}{4x^2-25}$.

Algebraic fractions

Solve $\tan x=\frac{1}{\sqrt3}$ over $0^{\circ}\le x\le360^{\circ}$.

Trigonometric functions

Determine the interior angle of a regular 20-sided polygon.

Geometrical terms

Find the height of the triangle.

Pythagoras' theorem

The coordinate grid displays triangles $P$ and $T$.

Transformations

Calculate the value of $5^{-5} \times 5^{5}$.

Indices I

Simplify $\frac{p}{t} \div \frac{2}{t}$ by writing the result in its simplest form.

Algebraic manipulation

The price of one orange is $t$ cents. The price of one apple is $w$ cents. Altogether, 3 oranges and 1 apple cost 51 cents. Altogether, 6 oranges and 5 apples cost 129 cents.

Equations

Nina’s average speed is $5\text{ km/h}$, rounded to the nearest km/h. She walks for exactly 2 hours.

Limits of accuracy

Find the size of the temperature increase from 4 am to 4 pm, given that the temperature was -12^{\circ}C at 4 am and 21^{\circ}C at 4 pm.

The four operations

$b=dm+2mk$

Algebraic manipulation

The diagram shows S on PQ and T on PR. ST runs parallel to QR.

Similarity

A fitness club contains 100 members. 60 swim (S). 70 cycle (C). 25 do not swim or cycle.

Introduction to probability

\(M=2^7\times3^3\times5^2\)

Indices I

Determine the value of $3^2 \div 3^{-2}$.

Indices I

Factorise the expression $x^2-64$.

Algebraic manipulation

AB and BD are two sides of a regular 15-sided polygon, while AB and BC are two sides of a regular n-sided polygon. Angle DBC = 14^{\circ}.

Angles

B has coordinates (-3, 1) and D has coordinates (-5, 9). BD is one diagonal of kite ABCD. The ratio of the diagonal lengths BD : AC = 2 : 3.

Length and midpoint

Rationalise the denominator, then simplify $\frac{20}{4+\sqrt{6}}$.

Surds

The diagram depicts a box shaped as a cuboid with side lengths 5 cm, 5 cm and 7 cm. Mala has a straight rod measuring 10 cm.

Pythagoras' theorem