Oct/Nov 2017

The sketch represents a quadrilateral. NOT TO SCALE. Its interior angles are labelled 83^{\circ}, 104^{\circ}, 72^{\circ} and $x$^{\circ}.

Angles

The diagram displays two sides of the rhombus $ABCD$ on a coordinate grid, with points A, B and C marked.

Coordinates

Simplify the fraction $\frac{30}{54}$ to its lowest form.

Fractions, decimals and percentages

Without a calculator, calculate $1\frac{2}{3} - \frac{11}{15}$. Show every step of your working and give your answer as a fraction in its lowest terms.

Fractions, decimals and percentages

The numbers listed are $\sqrt{5}$, $-7$, $343$, $-11$, $0.4$, $2.5$, $\frac{1}{3}$.

Types of number

Find $\begin{pmatrix} 3 \\ 2 \end{pmatrix} + \begin{pmatrix} -1 \\ 5 \end{pmatrix}$.

Coordinates

The figure depicts a regular pentagon. $AB$ serves as a line of symmetry. The angle at A formed with one side is marked $d$^{\circ}.

Angles

The figure depicts a right-angled triangle $ABC$, with $AB = 8$ cm, $AC = 18$ cm, and the right angle at $B$.

Pythagoras' theorem

Simplify the expression $(m^{5})^{2}$.

Indices I

Solve the simultaneous equations. You must present all of your working: $3x + 4y = 6$ and $6x - y = -15$.

Equations

Juan surveys 40 people about the language spoken at home. The results are shown in the table: English 18 (162^{\circ}), French 11, Spanish 7, Other 4. Juan intends to use a pie chart to display this information.

Statistical charts and diagrams

A watch is priced at $80. The exchange rate is $1 = 124.3 Japanese Yen.

Rates

Determine the shaded area.

Surface area and volume

The figure depicts rectangle $ABCD$.

Geometrical constructions

Find the value of $2^{-4} \times 2^{5}$.

Indices I

Amber’s average score over five tests is 80. Her scores in four of those tests are 68, 81, 74 and 89.

Averages and measures of spread

Express $18.766$ correct to 1 decimal place.

Limits of accuracy

Calculate $\sqrt{2 + \frac{0.2}{1.7 - 0.9}}$.

Powers and roots

Factorise $12x^{2} + 15xy - 9x$ completely.

Algebraic manipulation

Jade’s race time, $t$ seconds, is 14.3 seconds, accurate to 1 decimal place.

Limits of accuracy

Calculate the area of a circle whose diameter is 9 cm.

Circles, arcs and sectors

Express fourteen thousand and twenty seven in figures.

Types of number

Express $55\,\text{g}$ as a percentage of $2.2\,\text{kg}$.

Percentages

A triangle has area $528\,\text{cm}^2$, and its base measures $33\,\text{cm}$.

Area and perimeter

What sort of correlation is shown here?

Scatter diagrams

Bastian has a bag with four different kinds of sweet inside. He chooses one sweet from the bag at random.

Introduction to probability

The ship’s length, $l$ metres, is stated as $362\,\text{m}$ when rounded to the nearest metre.

Limits of accuracy

The figure shows a right-angled triangle. Its left-hand vertical edge measures $6.4\,\text{cm}$. The slanted side, which is the hypotenuse, measures $8.1\,\text{cm}$. The angle between the bottom horizontal side and the hypotenuse is labelled $x^{\circ}$. The diagram is marked NOT TO SCALE.

Right-angled triangles

The diagram shows a coordinate grid with the $x$-axis running horizontally and the $y$-axis running vertically. Point $A$ is marked at $(2,5)$. Point $B$ is marked at about $(-3,-2)$.

Coordinates

$AB$ lies on a straight line. The diagram shows a horizontal line segment with point $A$ at the left-hand end and point $B$ at the right-hand end.

Geometrical constructions

Determine the measure of the interior angle of a regular hexagon.

Angles

A cuboid with dimensions $5\,\text{cm}$ by $4\,\text{cm}$ by $3\,\text{cm}$ is shown. On the $1\,\text{cm}^2$ grid, construct an accurate net of the cuboid. One face has already been drawn.

Surface area and volume

On one day in Maseru, the temperature at noon was $17\,^{\circ}\text{C}$. By midnight, it had dropped by $20\,^{\circ}\text{C}$.

The four operations

Express $\frac{11}{3}$ as a mixed number.

Fractions, decimals and percentages

The diagram displays a straight line $l$. It meets the $y$-axis at about $y=2$ and passes through the point near $(6,5)$.

Equations of linear graphs

Write down the term that comes next.

Sequences

Solve $7 - 3n = 11n + 2$.

Equations

The diagram shows two shapes. For the first shape, the base is $15\,\text{cm}$, the upper side is $12\,\text{cm}$, and the sloping left side is marked $x\,\text{cm}$. For the second shape, which is similar to the first, the base is $12.5\,\text{cm}$, the sloping left side is $5\,\text{cm}$, and the upper side is marked $y\,\text{cm}$. The diagram is not drawn to scale.

Similarity

State the value of $12^0$.

Powers and roots

Express $5.17 \times 10^{-3}$ in ordinary form.

Standard form

Arrange the following from least to greatest, beginning with the smallest: $\frac{31}{50}$, $64\%$, $\frac{5}{8}$, $0.63$.

Fractions, decimals and percentages

A taxi fare consists of a fixed charge of $\$4.50$, together with $80$ cents for every kilometre completed. Julianna goes $7\,\text{km}$.

Rates

Calculate $\frac{6.32 + 2.06}{4.15 - 0.12}$. Write your answer correct to $1$ decimal place.

Fractions, decimals and percentages

List every other factor of $12$.

Types of number

In the diagram, $AB$ is a straight line. The figure places point $A$ on the left and point $B$ on the right along a horizontal straight line. Starting from point $A$, a sloping line rises to a vertex where the interior angle is $80^{\circ}$. From that vertex, another sloping line descends to meet the straight line segment between $A$ and $B$. At that intersection, the angle above the straight line is marked $x^{\circ}$, while the exterior angle on the right-hand side of the straight line is $120^{\circ}$. At point $A$, the angle between the straight line and the sloping line is marked $y^{\circ}$. The diagram is NOT TO SCALE.

Angles

Ahmed is driving his car from London to Cambridge. He sets off from London at 0745 and reaches Cambridge at 1017.

Time

Use values rounded to 1 significant figure to estimate $\frac{59.2 \times 1.97}{2.04 + 3.85}$.

Estimation

From a survey of 40 workers, 6 cycle to the office. The office employs 800 workers altogether.

Ratio and proportion

Adilla places $\$1200$ into an account earning compound interest at a yearly rate of $2.6\%$.

Percentages

The table gives the midday temperatures in several cities on 1st February.

The four operations

The mass of each of 20 potatoes, accurate to the nearest gram, is given below: 85, 97, 125, 100, 90, 102, 116, 89, 96, 104, 89, 107, 106, 93, 84, 118, 120, 98, 112, 109.

Classifying statistical data

Calculate the measure of one interior angle in a regular 12-sided polygon.

Geometrical terms

Find $3\frac{1}{7} - 1\frac{4}{9}$ and give your answer as a mixed number in its lowest terms. Do not use a calculator, and show every step of your working.

Fractions, decimals and percentages

The diagram depicts triangle $ABC$. $ABC$ is a right-angled triangle. At $C$, the angle is $52^{\circ}$. The vertical side from $A$ to $B$ measures $8.6\text{ cm}$. The sketch is labelled NOT TO SCALE.

Right-angled triangles

Express $1.8 \times 10^4$ as an ordinary number.

Standard form

Alvin exchanges some dollars ($) for euros (€). When he exchanges $\$100$, he is given €60.

Graphs in practical situations

Calculate the amount represented by $16\%$ of $\$525$.

Percentages

Write down the term that comes next.

Sequences

A park $ABCD$ is shown in the scale drawing. The scale means 1 centimetre stands for 20 metres. A North arrow is included, and the points are marked $A, B, C, D$.

Geometrical constructions

The diagram presents a shape assembled from a square and a semi-circle. The square’s bottom edge is labelled 10 cm. The diagram is NOT TO SCALE.

Compound shapes and parts of shapes

A quadrilateral has a single line of symmetry and no rotational symmetry. Write down the name given to this quadrilateral.

Symmetry

Simplify the expression $y^4 \times y^5$.

Indices I

A scale is labelled with 0, 0.1 and 0.2, and an arrow is shown pointing somewhere between 0.1 and 0.2.

Fractions, decimals and percentages

A bag holds 16 counters. 3 are red, 6 are blue, and the rest are yellow. Jay chooses a counter from the bag at random.

Introduction to probability

Complete the table shown.

Graphs of functions

The vectors are specified as $s = \begin{pmatrix}3\\-1\end{pmatrix}$ and $t = \begin{pmatrix}4\\2\end{pmatrix}$.

Coordinates

Solve for $x$ in $5x + 4 = 19 + 2x.$

Equations

The figure depicts a quadrilateral. The interior angles marked are 83^{\circ}, 104^{\circ}, 72^{\circ}, together with an angle labelled $x^{\circ}$. It is stated that the diagram is NOT TO SCALE.

Angles

Work out $1\dfrac{2}{3} - \dfrac{11}{15}$ without a calculator. Show all your working clearly and give your answer as a fraction in its lowest terms.

Fractions, decimals and percentages

A regular pentagon is shown. $AB$ serves as the line of symmetry, and the top central angle is marked $d^{\circ}$. The diagram is not drawn to scale.

Symmetry

The numbers in the list are $\sqrt{5},\ -7,\ 343,\ -11,\ 0.4,\ 2.5,\ \dfrac{1}{3}$.

Types of number

Work out $(m^{5})^{2}$.

Indices I

Determine the coordinates of point $E$.

Vector geometry

Write down a set $P$ for which $P \subset Q$.

Sets

A coordinate grid displays triangle $A$ and triangle $B$; triangle $A$ is the larger shaded shape, whereas triangle $B$ is the smaller one.

Transformations

$y$ varies inversely with $(x+1)^{2}$. $y = 50$ when $x = 0.2$.

Ratio and proportion

The diagram is a scale drawing of Tariq’s garden. The scale is 1 centimetre represents 2 metres. It shows two points labelled Tree and one point labelled Bird bath.

Geometrical constructions

Express as one fraction in simplest form $\dfrac{5}{x-3} + \dfrac{3}{x+7} + \dfrac{1}{2}$.

Algebraic fractions

Calculate $2^{-4} \times 2^{5}$.

Indices I

Calculate the volume of this cylinder.

Surface area and volume

The figure represents a square-based pyramid $ABCDE$. The square’s diagonals intersect at $M$. $E$ is directly above $M$ on a vertical line. $AB = BC = 12\ \text{cm}$ and $EM = 9\ \text{cm}$. The figure is not drawn to scale.

Pythagoras' theorem and trigonometry in 3D

Simon measures the heights, $h$ cm, of 200 sunflowers in his garden, and this information is displayed on the cumulative frequency diagram.

Cumulative frequency diagrams

Across one week, Neha spends $x$ hours cooking and $y$ hours cleaning. The time she spends cleaning is at least as much as the time she spends cooking. This may be written as $y \ge x$. In total, she spends no more than 16 hours cooking and cleaning. She spends at least 4 hours cooking.

Inequalities

Use a calculator to calculate $\dfrac{5^{0.4}-\sqrt{3}}{0.13-0.015}$. Record every digit that appears on the calculator screen.

Using a calculator

Amber’s mean score over five tests is 80. Her results in four of those tests are 68, 81, 74 and 89.

Averages and measures of spread

Factorise fully $12x^2 + 15xy - 9x$.

Algebraic manipulation

The grid diagram shows two sides of rhombus $ABCD$ on a coordinate plane. The points visible are marked $A$, $B$ and $C$.

Coordinates

Petra sets off in her car and starts from rest. She speeds up at a constant rate of $0.4\ \text{m s}^{-2}$ for 30 seconds. After that, she continues moving at a steady speed for 40 seconds.

Graphs in practical situations

Three identical cuboids are stacked to make a tower. The height of a single cuboid is $6.5\ \text{cm}$, accurate to the nearest millimetre. The diagram is NOT TO SCALE.

Limits of accuracy

A motorbike is priced at $12\,400$. Its value falls exponentially by 15% each year.

Exponential growth and decay

Work out what the temperature was at midnight.

Graphs in practical situations

A triangle has side lengths of 5.2 cm, 6.3 cm and 9.4 cm, and each measurement is rounded to the nearest millimetre.

Limits of accuracy

Express the recurring decimal $0.\dot{4}\dot{8}$ as a fraction. Include all your working.

Fractions, decimals and percentages

Expand the brackets, then simplify $(5 - n)(3 + n)$.

Algebraic manipulation

Write $\frac{11}{3}$ in mixed-number form.

Fractions, decimals and percentages

Find the integers that satisfy the inequality $-5 < 2n - 1 \leq 5$.

Inequalities

Write $\frac{x+1}{x} - \frac{y-1}{y}$ as one fraction and reduce it to simplest form.

Algebraic fractions

The first four terms of this sequence are 23, 17, 11, 5.

Sequences

The diagram shows one part of a regular polygon. The exterior angle is $x^\circ$. The interior angle is $29x^\circ$.

Angles

Solve the simultaneous equations. Show all your working. $y = \frac{x}{2}$ and $2x - y = 1$.

Equations

Rearrange the formula $y = \sqrt{x^2 + 1}$ so that $x$ is the subject.

Algebraic manipulation

Express $5.17 \times 10^{-3}$ as a decimal number.

Standard form

The figure presents a speed-time graph.

Graphs in practical situations

O denotes the origin, and K lies on AB such that AK : KB = 2 : 1. $\overrightarrow{OA} = a$ and $\overrightarrow{OB} = b$.

Vectors in two dimensions

A, B, C and D are located on the circle with centre O. BCE is a straight line. Angle AOC = 108^{\circ} and angle DCE = 60^{\circ}.

Circle theorems I

The diagram depicts a sector of a circle, with centre O and radius 6 cm. Its sector angle measures 30^{\circ}. The area of the shaded segment is $(k\pi - c)$ cm$^2$, with $k$ and $c$ being integers.

Circles, arcs and sectors

Solve the equation $7 - 3n = 11n + 2$.

Equations

Factorise completely the expression $x^2 - x - 132$.

Algebraic manipulation

The prism has a length of 4 cm. Its cross section is a right-angled triangle. BC = 3 cm and CQ = 2 cm.

Pythagoras' theorem and trigonometry in 3D

Simplify the expression $81^{\frac{3}{4}}$.

Indices II

On the diagram, BL bisects angle ABC, while MN is the perpendicular bisector of AB.

Geometrical constructions

State every other factor of 12.

Types of number

The diagram shows AB lying on a straight line.

Angles

Express 55 g as a percentage of 2.2 kg.

Percentages

A triangle has an area of 528 cm$^2$, and its base measures 33 cm.

Area and perimeter

Amar rides his bicycle at 18 km/h, and he needs 55 minutes to go from one village to the other.

Rates

Find, giving your answer in standard form: $1.2 \times 10^{40} + 1.2 \times 10^{41}$.

Standard form

Ahmed sets off in his car from London towards Cambridge. He departs London at 0745 and gets to Cambridge at 1017.

Time

A house model is constructed to a scale of $1 : 30$. Its volume is $2400\text{ cm}^3$.

Scale drawings

Calculate the measure of one interior angle in a regular 12-sided polygon.

Angles