Oct/Nov 2018

Work out the value of $8\%$ of $140$.

Percentages

The grid shows shape $A$.

Transformations

Find $6\begin{pmatrix}2\\-1\end{pmatrix}$.

Coordinates

Triangle $ABC$ and triangle $PQR$ are similar. In triangle $ABC$, $AB = 8\text{ cm}$ and $BC = 12\text{ cm}$. In triangle $PQR$, $PQ = 14\text{ cm}$ and $QR = x\text{ cm}$. The diagram is not drawn to scale.

Similarity

Calculate the measure of a single exterior angle in a regular $15$-sided polygon.

Angles

Shohan rides his cycle from home to the library, stopping at the post office along the way. His trip is shown on the distance-time graph. The vertical axis is marked "Distance from home (km)" and the horizontal axis is marked "Time" from $10\,00$ to $12\,00$. Home is at $0$ km and Library is at $10$ km.

Graphs in practical situations

The sketch depicts the top view of a table. The shape has right angles marked on it. The upper horizontal side measures $1.2\text{ m}$. The left vertical side drops $0.4\text{ m}$. The right vertical side drops $0.9\text{ m}$. The lower horizontal side measures $0.7\text{ m}$. Diagram not drawn to scale.

Area and perimeter

Without a calculator, calculate $\frac{3}{8} \div 2\frac{1}{4}$. Show all your working and give your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Each week, a teacher sets her Spanish students a test. The scatter diagram shows some of the marks the students achieved over two weeks. The horizontal axis is labelled "Mark in week 1" and the vertical axis is labelled "Mark in week 2".

Scatter diagrams

Jan places $800$ into an investment that earns simple interest at $3\%$ per year.

Percentages

The sequence starts with these five terms: $8,\ 11,\ 14,\ 17,\ 20$.

Sequences

The dollar-to-euro exchange rate is $1 = €0.88.$

Rates

A cuboid-shaped water tank measures $1.5$ metres in length and $1$ metre in width. The water in the tank is $60$ centimetres deep.

Surface area and volume

Express $187\,000\,000$ in standard form.

Standard form

The diagram depicts an isosceles triangle $ABC$ in which $AB = AC$. $LCM$ and $BCN$ are straight lines, and $LCM$ is parallel to $AB$. The angle $ACL$ is $56^{\circ}$. The diagram is not drawn to scale.

Angles

Expand each bracket, then simplify fully: $5(x-3)+2(3x+1)$.

Equations

Calculate the value of $\frac{a^5}{a^2}$.

Indices I

Arrange these values from least to greatest, beginning with the smallest: $0.38$, $\frac{3}{8}$, $30\%$, $\frac{7}{20}$.

Ordering

Find the radius of the circle with centre $O$. State your answer in centimetres.

Geometrical terms

Write $257\,964$ correct to the nearest thousand.

Limits of accuracy

Draw the line of symmetry on the shape below.

Symmetry

A bag holds $50$ counters, and $10$ of them are red. A counter is then chosen at random from the bag.

Introduction to probability

Calculate the difference between these temperatures.

Interpreting statistical data

State the type of angle represented in the diagram.

Angles

The scale diagram gives the locations of town $A$ and town $B$. The scale is 1 centimetre represents 12 kilometres.

Scale drawings

Mark the probability scale with an arrow (↓) to show the chance of selecting a blue counter.

Introduction to probability

Find the value of his investment after 4 years.

Percentages

The diagram presents a conversion graph linking pounds (£) and dollars ($).

Graphs in practical situations

Calculate the third term of this sequence.

Sequences

Among 120 students deciding what to do after they leave school, the choices are listed in the table: University 57, Training 45, Work 18.

Statistical charts and diagrams

Calculate the value of $4.1^3$.

Powers and roots

Write 56 as a prime-factor product.

Types of number

The diagram displays pentagon $ABCDE$.

Geometrical constructions

Solve the simultaneous equations below. Show all your working. $2x + 5y = 60$ and $3x - 2y = 14$.

Equations

State the measure of one angle in an equilateral triangle.

Angles

State the coordinates of point $A$.

Equations of linear graphs

Write $23\,000$ in standard form.

Standard form

Work out the value of $\begin{pmatrix}-2 \\ 5\end{pmatrix} - \begin{pmatrix}-1 \\ 1\end{pmatrix}$.

Coordinates

Expand the expression $2x(3 - x^2)$.

Algebraic manipulation

Triangle $ABC$ is similar to triangle $DEF$.

Similarity

The diagram depicts a right-angled triangle.

Right-angled triangles

$T = a^2 + 4b$

Introduction to algebra

Fill in the table.

Graphs of functions

Determine the length of this line in centimetres.

Units of measure

Simplify the expression $2p - q - 3q - 5p$.

Algebraic manipulation

Write $0.076499$ correct to 2 significant figures.

Limits of accuracy

Calculate $\frac{1}{4} \div \frac{2}{3}$ without using a calculator.

Fractions, decimals and percentages

Express the number five million, two hundred and seven as figures.

Standard form

State all the factors of 30.

Types of number

Ethan owns a box filled with toys, and he picks one toy at random.

Introduction to probability

State the gradient of the line $y = 4x - 6$.

Gradient of linear graphs

Katy’s suitcase has mass $m$ kilograms, and this is 31 kg when rounded to the nearest kilogram.

Limits of accuracy

The numbers in the list are: 16, 7, 23, 18, 73, 20, 95, 17, 89, 54.

Averages and measures of spread

Find the value of $x$.

Equations

Determine $\frac{7}{11}$ of 198 kg.

Fractions, decimals and percentages

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

Angles

The table gives the number of pets owned by each of the 95 students at a school.

Averages and measures of spread

The diagram shows two triangles. In triangle $ABC$, the base has length $BC = 8$ cm and the height is marked $x$ cm. In triangle $PQR$, the base is $QR = 20$ cm and one side is marked $23$ cm. The diagrams are not drawn to scale.

Similarity

The diagram shows a coordinate grid with the $x$-axis running horizontally and the $y$-axis running vertically. Point $A$ lies in the first quadrant, while point $B$ lies in the second quadrant.

Coordinates

Calculate the distance covered by the car. Give your answer in metres.

Rates

Jo places $5000 into an investment that earns compound interest at 2% per year.

Money

Solve the equation $3w - 7 = 32$.

Equations

Determine $1.45$ as a percentage of $72.50$.

Percentages

Calculate $\dfrac{5.39 - 0.98}{0.743 - 0.0743}$.

Fractions, decimals and percentages

Factorise the expression $y - 2y^2$.

Algebraic manipulation

Determine $(2,5) - (-3,4)$.

Coordinates

The diagram shows a shape in the form of a cross.

Symmetry

Split $72$ in the ratio $5 : 4$.

Ratio and proportion

Find the temperature at midnight.

Graphs in practical situations

Carlos begins work at 21 20 and ends at 06 15 the next day. Calculate how long Carlos is at work.

Time

A cuboid-shaped water tank measures 1.5 metres in length and 1 metre in width, and the water in it is 60 centimetres deep.

Surface area and volume

The sequence begins with these five terms: 8, 11, 14, 17, 20.

Sequences

Find the integer values of n for which the inequality $15 \leq 4n < 28$ is true.

Inequalities

The diagram displays triangle ABC and an arc centred at C with radius 6.5 cm.

Geometrical constructions

Without using your calculator, calculate $\frac{3}{8} \div 2\frac{1}{4}$. Show all your working and give your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Write the expression as a single fraction in its simplest form: $\frac{x - 5}{3} + \frac{6}{x + 2}$.

Algebraic fractions

The diagram depicts isosceles triangle ABC, where AB = AC. LCM and BCN are straight lines, and LCM is parallel to AB. Angle ACL = $56^\circ$.

Angles

From $t^x \times t^2 = t^{10}$, determine the value of x.

Indices I

Solve the simultaneous equations. Show all your working. The equations are $2x + 3y = -12$ and $5x + 2y = 14$.

Equations

Solve the equation $3x^2 + 7x - 11 = 0$ by using the quadratic formula. Show every stage of your working, and give your answers correct to 2 decimal places.

Equations

The diagram indicates that AB = AC and BN = NC.

Geometrical terms

Here, $M = \begin{pmatrix}8 & 2\\7 & 3\end{pmatrix}$ while $N = \begin{pmatrix}4 & -1\\-3 & 5\end{pmatrix}$.

Algebraic manipulation

As soon as Heidi was born, her grandfather placed some money into an account that paid compound interest. The graph illustrates the exponential increase of this investment.

Exponential growth and decay

A sample of 200 people was surveyed about which city they would most like to visit next. The table records the results.

Probability of combined events

The functions are given by $f(x) = 7 + 3x$, $g(x) = x^4$ and $h(x) = 3^x$.

Functions

The scatter diagram has Energy plotted on the vertical axis and Time plotted on the horizontal axis.

Scatter diagrams

Calculate $(6.4 \times 10^7) + (9.6 \times 10^6)$. Give your answer in standard form.

Standard form

Expand and simplify the expression $(3x - 7)(2x + 9)$.

Algebraic manipulation

From B, the bearing to A is $227^\circ$.

Angles

The quantity y is inversely proportional to $x^3$. At $x = 2$, the value of $y$ is $0.5$.

Proportion

Saafia has a barrel that contains 6000 millilitres of oil, accurate to the nearest 100 ml. She uses this oil to fill bottles, and each bottle holds exactly 50 ml.

Limits of accuracy

Jan puts $800$ into an investment that earns simple interest at 3% per year.

Percentages

Express $23000$ in standard form.

Standard form

Find the midpoint of $AB$ when $A = (w, r)$ and $B = (3w, t)$. Write your answer in simplest form using $w$, $r$ and $t$.

Length and midpoint

An equilateral triangle has a side length of $12\text{ cm}$, correct to the nearest centimetre. Find the lower bound and the upper bound of its perimeter.

Limits of accuracy

$x^\circ$ is an obtuse angle, and $\sin x^\circ = 0.43$. Find $x$.

Trigonometric functions

The initial five terms of a sequence are $-4, 2, 8, 14, 20$.

Sequences

A coordinate plane is displayed with the $x$-axis running from $0$ to $4$ and the $y$-axis running from $0$ to $8$. The lines drawn are $y = 2x + 1$, $y = 4 - x$, together with the vertical lines $x = 2$ and $x = 3$. The axes are marked $x$ and $y$.

Inequalities

Given that $M = \begin{pmatrix}5 & -3 \\ -1 & 2\end{pmatrix}$.

Algebraic manipulation

$x^2 - 12x + a = (x + b)^2$. Determine the values of $a$ and $b$.

Algebraic manipulation

The diagram displays the points $C(-1, 2)$ and $D(9, 7)$. A coordinate grid with $x$- and $y$-axes is shown, and the diagram is labelled NOT TO SCALE.

Perpendicular lines

A total of 120 students decide what they will do after leaving school. The table shows their choices: Choice: University $57$, Training $45$, Work $18$.

Statistical charts and diagrams

The figure depicts a pentagon $ABCDE$.

Geometrical constructions

A circle with centre $O$ is shown. $AB$ and $DE$ are chords of the circle. $M$ is the midpoint of $AB$ and $N$ is the midpoint of $DE$. Also, $AB = DE = 9\text{ cm}$ and $OM = 5\text{ cm}$. The figure is labelled with the points $A, B, C, D, E, M, N$ and centre $O$, and it is marked NOT TO SCALE.

Circle theorems I

Rearrange the formula $x = \frac{3m}{2 - m}$ to express $m$ as the subject.

Algebraic manipulation

The figure depicts an equilateral triangle $ABC$ with each side measuring $10\text{ cm}$. $AMN$ is a sector of a circle, centred at $A$. $M$ is the midpoint of $AC$. The diagram is labelled NOT TO SCALE.

Circles, arcs and sectors

A cuboid is illustrated with side lengths $5.5\text{ cm}$, $8\text{ cm}$ and $16.2\text{ cm}$. Line $AB$ is drawn on the cuboid, and the figure is labelled NOT TO SCALE.

Pythagoras' theorem and trigonometry in 3D

Write $56$ in prime-factor form.

Types of number

The time, $t$ minutes, taken by each of the $80$ students to finish their homework is recorded. The cumulative frequency diagram displays the outcomes. The axes are labelled Time (minutes) on the horizontal axis and Cumulative frequency on the vertical axis.

Cumulative frequency diagrams

For part (a), $f(x) = x^3$ and $g(x) = 5x + 2$.

Functions

Calculate the value of $0.125^{-\frac{2}{3}}$.

Indices I

Expand the expression $2x(3 - x^2)$.

Algebraic manipulation

Working without a calculator, find $\frac{1}{15} + \frac{2}{5}$. Show every stage of your calculation and give your result as a fraction in simplest form.

Fractions, decimals and percentages

Solve the inequality $7m - 2 \ge 19$.

Inequalities

$C = \{x : x \text{ is an integer and } 5 \le x \le 12\}$ together with $D = \{5, 10\}$.

Sets

Factorise $xy + 5y + 2x + 10$ into its bracket form.

Algebraic manipulation

Africa has $30000$ lions. The lion population in Africa falls exponentially by $2\%$ per year.

Exponential growth and decay

Calculate $\frac{7}{11}$ of $198\text{ kg}$.

Fractions, decimals and percentages

Solve for $w$ in $3w - 7 = 32$.

Equations

Rearrange the formula so that $l$ is the subject.

Algebraic manipulation