May/June 2025

Write 10069 in word form.

Units of measure

Ky rides from his office to a meeting and then travels back again. The travel graph illustrates the time he spends at the meeting and his return journey. Time is shown from 09:00 to 12:00 along the horizontal axis, while distance from the office (km) goes from 0 to 15 on the vertical axis. A flat section at 14 km represents the time at the meeting, followed by a straight downward-sloping line to show the journey back to the office.

Graphs in practical situations

Calculate the volume for a cube with a side length of 3 cm.

Surface area and volume

Solve the equation $5x + 8 = 3x - 2$.

Equations

Calculate $-5 \times -4$.

The four operations

Using $3^p \times 3^4 = 3^{10}$, find the value of $p$.

Indices I

A cuboid is displayed, not to scale, with the dimensions marked as length 6 cm, height 4 cm and width 3 cm.

Surface area and volume

Simplify $6a + 4b - a - 5b$.

Algebraic manipulation

By first rounding each number in the calculation correctly to 1 significant figure, find an estimate for the value of $\frac{42.8 + 17.4}{1.97 \times 5.79}$.

Estimation

The diagram depicts two parallel lines crossed by two straight lines. The angles marked are $x^\circ$, $y^\circ$, $z^\circ$, $110^\circ$ and $50^\circ$. The drawing is not drawn to scale.

Angles

A box holds 10 counters, and each counter is either red or green. The ratio of red counters : green counters is $1 : 4$. Shareen selects one counter at random, records its colour and replaces it in the box. She then selects a second counter at random. A tree diagram is provided with branches headed First counter and Second counter, and outcomes Red and Green, but the probabilities are blank.

Probability of combined events

One bag of sweets is priced at $0.34. Arun purchases 10 bags of sweets.

Money

The scatter diagram compares the price of petrol per litre with the number of litres sold at a petrol station over ten days. The vertical axis, Number of litres sold, runs from 0 to 500. The horizontal axis, Price per litre ($), spans 1.40 to 1.70.

Scatter diagrams

Points $A$, $B$ and $C$ are on a circle with centre $O$. The diagram indicates an angle of $39^\circ$ at the circumference between the line $AB$ and the line $AO$. The diagram is not drawn to scale.

Circle theorems I

Let $A = 2^3 \times 3$ and $B = 3^2 \times 5$.

Types of number

The diagram shows a coordinate grid with triangles marked $A$, $B$ and $T$.

Transformations

Work out $1\frac{1}{3} + 1\frac{3}{4}$. Write your answer as a mixed number in the simplest form.

Fractions, decimals and percentages

Write $32\,500$ in standard form.

Standard form

Solve for $x$ and $y$ using the simultaneous equations $2x + 5y = 5$ and $3x + 4y = 11$.

Equations

Two numbers have a total of $-2$ and a product of $-15$.

Equations

The numbers in the list are 7, 27, 39, 49, 99, 112.

Types of number

State the reciprocal of 5.

The four operations

Insert a single pair of brackets into $7 - 5 \times 4 + 8 = 16$ so that the calculation becomes correct.

The four operations

Write an expression, in dollars, for the cost of $t$ tickets.

Introduction to algebra

Express $90\%$ as a fraction in lowest terms.

Fractions, decimals and percentages

Write down the rule from one term to the next for this sequence.

Sequences

Give the figure form of sixteen thousand and sixty-two.

Types of number

The cuboid measures 5 cm in length, 2 cm in width and 3 cm in height.

Surface area and volume

The six numbers are 0, 2, 2, 3, 4, 7.

Averages and measures of spread

Tim uses a technique for multiplying a number by 99. He demonstrates it with $53 \times 99$: $53 \times 99 = 53 \times 100 - 53 = 5300 - 53 = 5247$.

The four operations

Write down the mathematical name for this quadrilateral.

Geometrical terms

Complete the value table for $y = (x + 3)(x - 2)$.

Sketching curves

Beth considers a positive number $n$. She squares $n$ and then subtracts 55. The result is 9.

Equations

A point P together with three triangles, A, B and C, is shown on a $1\text{ cm}^2$ grid.

Transformations

Estimate the value of $\frac{17.8 + 10.3}{5.5}$ by first changing each number in the calculation to 1 significant figure.

Estimation

Determine the highest common factor (HCF) of 66 and 110.

Types of number

State the value of $P$ that satisfies the inequality $13 < P < 19$.

Inequalities

Write three-quarters in decimal form.

Fractions, decimals and percentages

The universal set $\mathcal{E}$ is displayed. Sets J and K overlap, and the shaded part covers every point in circle J or circle K, including the common region.

Sets

Calculate $2\frac{7}{9} \times 1\frac{1}{5}$. Write the answer as a mixed number in simplest form.

Fractions, decimals and percentages

The mass, $m$ kg, of a stone is $3.2$ kg when rounded to the nearest 100 g.

Limits of accuracy

Factorise the expression $9x - 6xy$.

Algebraic manipulation

Solve the simultaneous equations $5x + 2y = 3$ and $3x + 4y = 27$.

Equations

The diagram depicts a figure formed from two semicircles that share a common centre. The radius of the larger semicircle is 7 cm, and the radius of the smaller semicircle is 4 cm.

Circles, arcs and sectors

State the value of $\sqrt{36}$.

Powers and roots

The diagram contains line AB and point P.

Geometrical constructions

Complete this sentence. 10 weeks is ................ days.

Units of measure

Shade the part of the rectangle that represents $\frac{2}{5}$ of it.

Fractions, decimals and percentages

Find the reciprocal value of $\frac{1}{3}$.

Indices I

Insert a single pair of brackets into $-12 + 4 \div 2 - 3 = -16$ so that the calculation becomes correct.

The four operations

Place these fractions in order, beginning with the smallest.

Ordering

Give the word form of 70 000 000.

Fractions, decimals and percentages

The equation of Line A is $y = 3x + 1$. The equation of Line B is $y = 3x - 1$.

Parallel lines

Jo surveys 90 people to see whether they like pop, rock, classical, jazz or folk music. The pie chart presents some of the outcomes. The sector angles given are Pop = 120^{\circ} and Rock = 100^{\circ}.

Statistical charts and diagrams

A music group contains 30 members. 7 members play a flute (F) and play a clarinet (C). 12 members play a flute. 1 member does not play a flute and does not play a clarinet.

Sets

Using 1 significant figure for each number in the calculation, estimate the value of $\dfrac{62.5}{9.7 \times 0.52}$.

Estimation

The sketch depicts a trapezium and is NOT TO SCALE. Its area equals $42\text{ cm}^2$. The two parallel sides measure 4 cm and 10 cm, while the perpendicular height is $h$ cm.

Area and perimeter

A number line has a filled dot at $-4$ and a hollow circle at $3$, with the section between them shaded.

Inequalities

On Monday, a concert ticket costs $\$x$. On Tuesday, a ticket for that same concert costs 20% more than it did on Monday. Jack purchases 4 tickets on Monday and 5 tickets on Tuesday, and he pays $\$270$ altogether.

Percentages

Simplify this expression.

Indices I

The diagram depicts a circle with centre $O$. $P$ and $S$ lie on the circle. $POR$ is a straight line. $QRST$ is tangent to the circle at $S$. The marked angles are $25^{\circ}$ at $P$, $x^{\circ}$ at $S$, and $y^{\circ}$ at $R$ on the tangent.

Circle theorems I

A diagram illustrates a sector of a circle with radius 3 cm and sector angle 60^{\circ}. It is not drawn to scale.

Circles, arcs and sectors

Write down the mathematical term for an angle that lies between 90^{\circ} and 180^{\circ}.

Geometrical terms

Find the highest common factor (HCF) between 36 and 54.

Types of number

All measurements in this question are given in centimetres. The triangle’s perimeter is equal to the rectangle’s perimeter.

Area and perimeter

The equation can be written as $g = \dfrac{h}{3} - 8$.

Algebraic manipulation

Rectangle A is similar, in the mathematical sense, to rectangle B.

Similarity

Calculate $3\dfrac{1}{2} - 1\dfrac{4}{7}$. State your answer as a mixed number in its simplest form.

Fractions, decimals and percentages

Solve these simultaneous equations: $8x + 5y = 4$ and $2x - y = 10$.

Equations

State the value of $\sqrt{169}$.

Powers and roots

The figure is a quadrilateral whose sides all have the same length. NOT TO SCALE. The two interior angles at the bottom are marked $a^\circ$ and $2a^\circ$.

Geometrical terms

Find the term that comes next in the sequence: 1, 5, 10, 16, 23, …

Sequences

These are the lengths, in minutes, of seven phone calls: 10, 22, 5, 7, 35, 8, 75.

Averages and measures of spread

There are 70 students taking one of French, Spanish and German. The ratio of the number who study French to the number who study Spanish is 3 : 7. 15 students take French.

Ratio and proportion

The diagram displays two faces from a cuboid net on a 1 $\text{cm}^2$ grid.

Surface area and volume

The net of a square-based pyramid is shown in the diagram. NOT TO SCALE. Each triangular face has a perpendicular height of 4 cm. The square base has side length 5 cm.

Surface area and volume

Simplify the expression $7c - 5d + c + 3d$.

Algebraic manipulation

Points A, B and C lie on a circle with centre O. DE is a tangent to the circle at A. Angle $ACO$ is $35^{\circ}$ and angle $BCO$ is $40^{\circ}$. The diagram is marked NOT TO SCALE.

Circle theorems II

The diagram presents two parallel lines cut by two straight lines. The angles indicated are labelled $w^{\circ}$, $x^{\circ}$, $y^{\circ}$, $76^{\circ}$ and $158^{\circ}$. It is marked NOT TO SCALE.

Angles

Sally places $1500 at $3\% per year simple interest. Find the total value of her investment after 6 years.

Money

Calculate $\frac{5}{6} - \frac{2}{3} \times \frac{3}{8}$.

Fractions, decimals and percentages

The interior angle of a regular polygon measures $150^{\circ}$. Find how many sides this polygon has.

Angles

The graph of $x + y = 7$ has been drawn on the grid.

Drawing linear graphs

Express the recurring decimal $0.2\dot{6}$ as a fraction. State it in lowest terms.

Fractions, decimals and percentages

$m = \begin{pmatrix}11 \\ 5\end{pmatrix}$ and $n = \begin{pmatrix}8 \\ -3\end{pmatrix}$.

Vectors in two dimensions

The table presents information about the marks obtained by a group of students in a test. Test marks: 4, 5, 8. Frequencies: 2, 4, $n$. The mean mark equals 6.

Averages and measures of spread

Shade one additional small square so that the diagram has a single line of symmetry.

Symmetry

The diagram depicts a sector of a circle with centre $O$. The arc length is $n\pi$ cm.

Circles, arcs and sectors

Write $0.00708$ in standard form.

Standard form

$P$, $Q$ and $R$ are points on a circle, and $QR$ is a diameter.

Circle theorems I

A group of 100 students each solved a puzzle. The table gives the time each student needed to complete it.

Cumulative frequency diagrams

Write $0.25$ in fraction form.

Fractions, decimals and percentages

The diagram presents the graph of $y = \frac{2}{x} - 1$.

Graphs of functions

The solid is formed by attaching a hemisphere to a cylinder. Both the hemisphere and the cylinder have radius 6 cm. The cylinder has height 5 cm.

Surface area and volume

Determine the value of

Indices II

Rationalise the denominator in $\frac{9}{\sqrt{3}}$. Write your answer in the simplest form.

Surds

Express the result as one fraction in lowest terms.

Algebraic fractions

The scale diagram marks the locations of villages P and Q, with $1\text{ cm}$ standing for $0.5\text{ km}$.

Scale drawings

This gives $y \propto \frac{1}{\sqrt{x}}$.

Ratio and proportion

The diagram displays the graph of $y = 3x - x^3$. It meets the $x$-axis at $A$, $O$ and $B$, and its turning points are $P$ and $Q$.

Differentiation

State the exact value of $\tan 60^\circ$.

Exact trigonometric values

In the diagram, $OA$ runs parallel to $BC$. $BC = 3OA$. $M$ is the midpoint of $AC$. The position vector of $A$ is $\mathbf{a}$ and the position vector of $B$ is $\mathbf{b}$.

Vector geometry

The line $y = 7x + 3$ meets the curve $y = x^2 + 5x - 12$ at points $A$ and $B$.

Equations

The diagram depicts two straight lines that intersect two parallel lines.

Angles

Samira chooses one of these cards at random and then puts it back.

Relative and expected frequencies

Translate triangle $T$ using the vector $\begin{pmatrix}0\\-2\end{pmatrix}$.

Transformations

Solve for $x$ in $8x + 7 = 39$.

Equations

The sequence begins with these 4 terms: 11, 8, 5, 2.

Sequences

State the highest common factor (HCF) shared by 36 and 54.

Types of number

$A$ is located at $(3,-1)$. The vector $verrightarrow{AB} = \begin{pmatrix}2\\-4\end{pmatrix}$.

Vectors in two dimensions

The probability of selecting a green pen from a box is 0.17. Find the probability that a green pen is not selected from the box.

Introduction to probability

Solve the simultaneous equations $4x - 5y = 13$ and $3x - 2y = 8$.

Equations

Angela chooses one number randomly from 1, 2 and 3. She then chooses another number randomly from 4, 5 and 6. She adds these two numbers to get the total.

Conditional probability

Calculate $5\mathbf{v}$.

Vectors in two dimensions

Points A, B, C and D lie on a circle. EF touches the circle at A. AB is parallel to DC. The diagram shows angles 35^{\circ} and 60^{\circ} at A. Diagram not to scale.

Circle theorems I

Work out the lowest common multiple (LCM) of $15xy^3$ and $18x^4y$.

Indices II

Simplify the expression $\sqrt{27} + \sqrt{12}$.

Surds

Write $0.32\dot{8}$ as a fraction in simplest form.

Fractions, decimals and percentages

Solid A and solid B are mathematically similar. Solid A has height 7 cm and surface area 60 cm$^2$, whereas the surface area of solid B is 540 cm$^2$. A diagram of both solids is shown, not drawn to scale.

Similarity

Rearrange the formula $2 = \frac{m(1 - t)}{pt}$ so that $t$ is the subject.

Algebraic manipulation