May/June 2024

Write 0.8 in fraction form.

Fractions, decimals and percentages

The cuboid is drawn with side lengths of $15\text{ cm}$, $6\text{ cm}$ and a height of $h\text{ cm}$. NOT TO SCALE.

Surface area and volume

Geetha has a box full of toys. She chooses one toy at random from the box. The probability that the toy she chooses is wooden is $0.6$.

Introduction to probability

The table gives some details about two sequences. Sequence A has nth term $60 - 4n$. Sequence B has nth term $n^2 - 300$. The 5th-term column is left blank.

Sequences

State the coordinates of the point at which the line $y = 3x - 5$ intersects the $y$-axis.

Equations of linear graphs

Use each number in the calculation rounded to 1 significant figure to find an estimate for the value of $\frac{28.2 - 5.6}{4.2 \times 1.68}$. You must show all your working.

Estimation

Factorise $36x^2 + 40x$ completely.

Algebraic manipulation

The figure depicts a rectangle whose length is $3x - 12$ and whose width is $x + 7$. It is not to scale.

Algebraic manipulation

A circle with centre $O$ is shown. Point $P$ lies on the circle, and the line $OP$ has been drawn.

Geometrical terms

Find the largest odd factor that is common to both 140 and 210.

Types of number

Calculate the value of $\sqrt[3]{343} - \sqrt{40.96}$.

Powers and roots

A straight line is drawn from point A to point B.

Units of measure

Find $137^0$.

Indices I

Calculate $1.827 \times 10^6 \div 9000$. State your answer in standard form.

Standard form

You are required to show all of your working.

Equations

Express $9.6\text{ km/h}$ in $\text{m/s}$.

Units of measure

The sequence starts with these five terms: 11, 18, 25, 32, 39.

Sequences

The diagram represents a figure formed by triangle JKL together with a semicircle whose diameter is JL. JKL is an isosceles right-angled triangle with $JK = JL = 12.8\text{ cm}$. The semicircle has radius $12.8\text{ cm}$. NOT TO SCALE.

Area and perimeter

The travel graph illustrates a bus trip. The vertical axis is labelled Distance (km), while the horizontal axis is labelled Time and runs from 14 00 to 16 00. The distance rises from 0 km at 14 00 to 12 km at 15 00, stays at 12 km until around 15 30, and then falls to 0 km again at 16 00.

Graphs in practical situations

State the order of rotational symmetry for a rhombus.

Symmetry

A shape is drawn on a $1\text{ cm}^2$ grid.

Area and perimeter

Work out the value of $28 - 16 \div 2$.

Fractions, decimals and percentages

On Monday, the temperature is $-27^\circ\text{C}$. On Tuesday, it is $15^\circ\text{C}$ higher than Monday.

The four operations

A figure in the form of a cross is shown.

Symmetry

The diagram plots two sides of parallelogram ABCD on a coordinate grid, with point A located at about $(-7,5)$, point B at $(-1,1)$ and point C at $(3,3)$.

Coordinates

Write 3127200 using words.

Types of number

The vectors are defined by $\mathbf{a} = \begin{pmatrix}5\\-7\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}6\\-7\end{pmatrix}$.

Coordinates

The sequence starts with these four terms: 23, 17, 11, 5.

Sequences

Write $0.04628$ correctly to $2$ significant figures.

Limits of accuracy

The Venn diagram shows a universal set that contains two overlapping circles labelled A and B.

Sets

Factorise fully: $20x - 90x^2$.

Algebraic manipulation

Describe the correlation pattern between the speed of runners and the time needed to finish a race.

Scatter diagrams

The area of a circle is given as $36\pi\text{ cm}^2$.

Surface area and volume

Write 174000 in standard form using powers of 10.

Standard form

In the diagram, a right-angled triangle has a side of 8.5 cm, a hypotenuse of 14 cm, and the base angle is marked $x^{\circ}$. The drawing is not to scale.

Right-angled triangles

Work out $2\frac{1}{4} \div 1\frac{7}{8}$ without a calculator. Show all your working, and write your answer as a mixed number in simplest form.

Fractions, decimals and percentages

The diagram contains two straight lines, AB and AC, which meet at A; B is placed to the right of A and C is positioned above A. The angle at A between AB and AC is labelled x.

Geometrical constructions

Expand, then simplify $(x-4)(x-7)$.

Algebraic manipulation

The equation $5^7 \div 5^x = 5^3$ is provided.

Indices I

A piece of material has length, $l$ metres, given as 4.5 m to the nearest 10 cm.

Limits of accuracy

$\mathcal{E}=\{x:x\text{ is a natural number less than }12\}$. $S=\{1,4,7,10\}$. $T=\{1,3,5,7,9,11\}$. The Venn diagram has circles labelled S and T. The number 10 appears in S only, while 2 is placed outside both circles, and 8 is also placed outside both circles.

Sets

Out of 30 students in the class, 13 go to school by bus. The school has 570 students in total.

Ratio and proportion

The figure depicts a flagpole, BD, supported by two ropes, AD and CD. ABC lies on a straight line, and angle ABD = $90^{\circ}$. $AD=21.2$ m, $AB=16.5$ m and angle BCD = $48^{\circ}$. The diagram is not drawn to scale.

Right-angled triangles

Work out the reciprocal of 0.4.

Fractions, decimals and percentages

Put these values in ascending order, beginning with the smallest: $\frac{6}{7}$, $8.6 \times 10^{-1}$, $\frac{11}{13}$, $86.5\%$.

Ordering

The diagram depicts a square.

Symmetry

At midnight, the temperature is $-4^{\circ}\text{C}$. By noon, it rises to $25^{\circ}\text{C}$.

The four operations

He sets his price at $\$6.55$ for every hour worked, together with a flat fee of $\$15.50$.

Money

Jonah begins with $\$750$. He uses $\frac{1}{4}$ of the money for travel, and some of the money on food. He is then left with $\$437.50$.

Fractions, decimals and percentages

A pizza delivery driver notes how many pizzas he delivers each month over one year: 48, 44, 39, 28, 57, 22, 36, 41, 54, 57, 49, 52. A stem-and-leaf diagram is displayed with stems 2, 3, 4, and 5. The key says that $4|8$ stands for 48 pizzas.

Statistical charts and diagrams

Put the number two million two thousand and two into figures.

Types of number

State the next term.

Sequences

Determine the value of $x$.

Equations

On the 1 cm$^2$ grid, finish a net for this cuboid. One face has already been drawn.

Surface area and volume

Completely factorise $4x^2y - 5xy^2$.

Algebraic manipulation

Calculate the actual separation between the two villages. Give your answer in kilometres.

Scale drawings

Without a calculator, calculate $\frac{3}{7} - \frac{1}{14}$. Show every step in your working and write your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Calculate the percentage increase in the price.

Percentages

Calculate $AB$.

Pythagoras' theorem

Complete the statement below about the value of $s$: $\ldots \le s < \ldots$.

Limits of accuracy

Solve these simultaneous equations.

Equations

Insert one pair of brackets into this calculation so that it is correct: $5 + 4 \times 3 + 9 = 53$.

The four operations

Find the bearing of town C as measured from town B.

Angles

Complete the Venn diagram shown.

Sets

Write $0.007$ in standard form.

Standard form

Calculate how many complete times the jug may be filled with water from the tank.

Surface area and volume

Simplify the expression $7x - 8y - x - y$.

Algebraic manipulation

Write 164703 rounded to the nearest thousand.

Limits of accuracy

On the diagram, draw any lines of symmetry.

Symmetry

Arrange these numbers from the smallest to the largest.

Ordering

Calculate the height of the cuboid.

Surface area and volume

Find the probability that it will not rain today in this city.

Introduction to probability

Calculate the difference between these two temperatures.

The four operations

The diagram illustrates two edges of a parallelogram $ABCD$.

Coordinates

Amir places $1500$ into an account. The account earns compound interest at a rate of $r\%$ per year. After 8 years, the investment is worth $1656.73$.

Exponential growth and decay

State the inequalities that define the unshaded region, $R$.

Inequalities

Solve the simultaneous equations. Show every step of your working. $\frac{3x}{2} + 5y = 5$ and $4x - 3y = 46$.

Equations

The diagram represents a cyclic quadrilateral.

Circle theorems I

The diagram illustrates a circle with a radius of 9 cm.

Circles, arcs and sectors

Write $0.146\overline{6}$ as a fraction in simplest form, showing every step of your working.

Fractions, decimals and percentages

In the Venn diagram, shade the area $M' \cap N'$.

Sets

Calculate the area of triangle $ABC$.

Area and perimeter

The graph of $y = x^3 + 4x^2 - 2$ is shown in the diagram for $-3 \le x \le 1.5$.

Graphs of functions

Factorise $12m^2 - 75t^2$ into brackets.

Algebraic manipulation

Geetha owns a box filled with toys. She selects one toy at random from the box. The probability that the toy is wooden is 0.6.

Introduction to probability

Solve the equation $8\sin x + 6 = 1$ for values of $x$ in the interval $0^\circ \le x \le 360^\circ$.

Trigonometric functions

The diagram depicts a cuboid. $HD = 4$ cm, $EH = 6.5$ cm and $EF = 9.1$ cm.

Pythagoras' theorem and trigonometry in 3D

Bag $A$ and bag $B$ contain only red counters and blue counters. Stephan selects a counter at random from bag $A$, and Jen selects a counter at random from bag $B$. The probability that Stephan selects a red counter is 0.4. The probability that both Stephan and Jen select red counters is 0.25.

Probability of combined events

The table gives some details for two sequences.

Sequences

Identify the largest odd factor of 140 that also divides 210.

Types of number

Calculate the value of $\sqrt[3]{343} - \sqrt{40.96}$.

Powers and roots

The figure illustrates 5 kites that are congruent to kite $ABCD$. Each kite is connected to the following kite along one edge. Angle $DAB = 40^\circ$ and $DCE$ is a straight line.

Angles

The figure is built from triangle $JKL$ and a semicircle whose diameter is $JL$. Triangle $JKL$ is an isosceles right-angled triangle with $JK = JL = 12.8$ cm.

Compound shapes and parts of shapes

The sequence begins with these five terms: 11, 18, 25, 32, 39.

Sequences

A car is worth $8000$. After each year, its value falls exponentially by 25%.

Exponential growth and decay

Determine the difference between these two temperatures.

Units of measure

Express 174000 in standard form.

Standard form

Determine the expected number of employees in the company who walk to work.

Relative and expected frequencies

The diagram depicts a right-angled triangle drawn to no scale. Its hypotenuse measures 14 cm, the base measures 8.5 cm, and the angle at the base is $x^\circ$.

Trigonometric functions

Without a calculator, find $2\frac{1}{4} \div 1\frac{7}{8}$. Show all of your working, and write your answer as a mixed number in simplest form.

Fractions, decimals and percentages

A is the point $(0, 2)$, while B is the point $(8, 6)$.

Equations of linear graphs

Three towns, A, B and C, are all the same distance apart from one another. The bearing of C from A is $104^\circ$.

Angles

A speed–time graph is used to give details of a car journey. Speed is in m/s and time is in seconds. The car increases speed from 0 to 16 m/s in 30 s, then continues at a steady speed up to 240 s, before slowing down to 0 by 320 s.

Graphs in practical situations

$W = \{$students who walk to school$\}$ $G = \{$students who wear glasses$\}$ There are 20 students in the class. 8 of them walk to school. 3 both wear glasses and walk to school. 2 neither wear glasses nor walk to school.

Sets

The graph for $y = f(x)$ is plotted on the grid.

Differentiation

Find the value of $y$ when $x = 7$.

Proportion

Calculate the total he charges for 4 hours of work.

Rates

Calculate the smaller parcel’s height.

Similarity

Solve the simultaneous equations below. You must show every step of your working. $4y + 3x = 13$ $y = x^2 - 18$

Equations

For the sketch, place a ring around the function type shown: linear, cubic, quadratic, reciprocal or exponential.

Trigonometric functions

The Venn diagram gives data on how many students are in a class. Some take English (E), some take French (F), some take Spanish (S), and some take none of these languages.

Sets

O is the origin, and OPQR forms a parallelogram. M lies halfway along PQ, while N divides QR in the ratio $2 : 1$. $\vec{OP}=\mathbf{a}$ and $\vec{OR}=\mathbf{b}$.

Vector geometry

A delivery driver keeps a monthly record of how many pizzas she delivers over one year. 48, 44, 39, 28, 57, 22, 36, 41, 54, 57, 49, 52

Statistical charts and diagrams

Work out what fraction of the $750 is spent on food.

Fractions, decimals and percentages

The table gives part of a tram timetable. Newpoint - Westhill times: 10 30 → 11 17 12 18 → (missing) 13 30 → 14 17 Every tram takes the same number of minutes to travel from Newpoint to Westhill.

Time

Round 0.04628 to 2 significant figures.

Limits of accuracy

A Venn diagram contains two overlapping circles, A and B, placed within the universal set.

Sets

Determine the value of $r$.

Equations

The coordinate grid displays triangle A and triangle B.

Transformations

Express two million two thousand and two in digits.

Types of number