Feb/March 2021

The diagram shows two congruent triangles joined at a point, creating a bow-tie shape.

Symmetry

Over 14 days, the number of passengers on a bus is noted each day: 15, 18, 22, 17, 35, 38, 24, 19, 19, 24, 25, 31, 36, 29.

Statistical charts and diagrams

The mean value of nine numbers is 17. Seven of these numbers have a total of 132. The remaining two numbers are 5 apart.

Averages and measures of spread

Factorise $9t^2w - 3t$ completely.

Algebraic manipulation

Saanvi prepares some biscuits. She sells $\frac{5}{13}$ of them. She is left with 96 biscuits.

Fractions, decimals and percentages

The sequence starts with these four terms: 29, 22, 15, 8.

Sequences

Find the lowest common multiple (LCM) for 18 and 21.

Types of number

Express 567000000 in standard form.

Standard form

The diagram shows two triangles, ABC and PQR, and it is marked NOT TO SCALE. In triangle ABC, AC measures 1.61 cm and CB measures 2.8 cm. In triangle PQR, RQ measures 3.2 cm and PR is labelled $x$ cm. Triangle ABC is mathematically similar to triangle PQR.

Similarity

Work out $x^{12} \div x^3$.

Indices I

Calculate $2\frac{1}{4} \times 3\frac{2}{3}$ without using a calculator. Show all your working, and present your answer as a mixed number in its simplest form.

Fractions, decimals and percentages

On the grid, draw a kite shape.

Geometrical terms

Solve the simultaneous equations. You must include all your working. $5x + 6y = 14$, $2x + 8y = 7$.

Equations

The diagram represents a figure formed by a quarter-circle, OAB, together with a right-angled triangle OBC. The diagram is marked NOT TO SCALE. The circle has radius 5 cm and $OC = 6$ cm.

Compound shapes and parts of shapes

Calculate the numerical value of $\sqrt{7.29}$.

Powers and roots

State a multiple of 9 that lies between 100 and 110.

Types of number

Explain why Rahul cannot be certain that Tanvi rounded 4896 correct to the nearest 100.

Limits of accuracy

The heights of four sisters are 1.61 m, 1.65 m, 1.53 m and 1.58 m.

Averages and measures of spread

Work out the value of $2 \begin{pmatrix}-3\\7\end{pmatrix}$.

Coordinates

Sahil and Anika divide $78$ in the ratio $5 : 8$.

Ratio and proportion

The diagram depicts a prism. Its cross-section is an equilateral triangle. The diagram includes dimensions marked 4 cm and 3 cm and is labelled NOT TO SCALE.

Surface area and volume

The diagram consists of two congruent triangles joined at a single point, giving an hourglass-like shape.

Symmetry

The towns $L$, $M$ and $N$ are marked on a map so that they make an equilateral triangle. The bearing of $M$ from $L$ is $103^{\circ}$. A diagram is provided, with North shown at $L$.

Angles

Determine the highest common factor (HCF) of 36 and 84.

Types of number

The diagram presents a composite shape formed by a quarter-circle $OAB$ together with a right-angled triangle $OBC$. The circle has radius $5\,\text{cm}$ and $OC = 6\,\text{cm}$.

Area and perimeter

The number of butterflies in one variety is falling exponentially by $34\%$ each year. By the end of 2014, the population had reached $125.9$ million.

Exponential growth and decay

Write down the following two terms.

Sequences

The points $E$, $F$, $G$ and $H$ all lie on the circle, with $EG = EH$. The lines $HF$ and $EG$ meet at $K$. $ET$ is tangent to the circle at $E$. Angle $FET$ is $47^{\circ}$ and angle $FEG$ is $25^{\circ}$.

Circle theorems I

Region $R$ consists of the points that satisfy all three inequalities: $y > 1$, $y < 2x + 2$, $x + y \leq 3$.

Drawing linear graphs

A group of students were asked how many books they had each placed in their school bags. The table contains some of the details. The mean number of books is $7.6$.

Averages and measures of spread

Simplify $(343x^{9})^{\frac{2}{3}}$.

Indices I

Solve the simultaneous equations. Show every stage of your working. $x - y = 7$, $x^{2} + y = 149$.

Equations

Sahil and Anika divide $78$ in the ratio $5 : 8$.

Ratio and proportion

Determine the value of $x$.

Similarity

Using the axes, sketch the graph of each function listed here.

Sketching curves

Calculate the lower bound for the total mass of 10 of these bags.

Limits of accuracy

The diagram depicts a pyramid $VABCD$ with a rectangular base. $V$ is directly above $M$, where the diagonals $AC$ and $BD$ intersect. $AB = 12\,\text{cm}$, $BC = 10\,\text{cm}$ and $VC = 14\,\text{cm}$.

Pythagoras' theorem and trigonometry in 3D

The curve is described by $y = x^{3} - 2x^{2} + 5$.

Differentiation

For 14 days, the number of passengers on a bus is counted each day. 15, 18, 22, 17, 35, 38, 24, 19, 19, 24, 25, 31, 36, 29

Averages and measures of spread

By rounding each number to 1 significant figure, determine an estimate for the value of $\frac{2.8 \times 82.6}{27.8 - 13.9}$.

Estimation

The number of bowls of hot soup sold falls when the temperature increases.

Scatter diagrams

Joseph uses $\frac{5}{24}$ of his one week’s earnings to buy a jacket. The jacket costs $56.50$.

Ratio and proportion

Without a calculator, calculate $2\frac{1}{4} \times 3\frac{2}{3}$. Show all your steps and write your answer as a mixed number in simplest form.

Fractions, decimals and percentages

Write $0.3\dot{7}$ in fraction form.

Fractions, decimals and percentages

Calculate $4.8 \times 10^{6} + 3.7 \times 10^{7}$. Write your answer in standard form.

Standard form

A group of 20 students each chose their favourite science subject. Their results are shown in the bar chart. Bar chart details: The vertical axis is marked "Frequency" and extends to 12. The horizontal axis lists the categories: Biology, Chemistry, Physics. Biology has a frequency of 11. Chemistry has a frequency of 3. Physics has a frequency of 6.

Interpreting statistical data

A family travel to America for a skiing holiday.

Limits of accuracy

The grid diagram contains three triangles $A$, $B$ and $C$. Triangle $A$ is shaded. The coordinate grid shows the x- and y-axes. Angle $w$ is labelled at the top vertex of triangle $B$.

Transformations

On the map, the scale drawing gives the locations of Kendra’s house, $K$, and Latika’s house, $L$. North arrows appear at both $K$ and $L$.

Scale drawings

Fill in the missing values in the table for $y = -x^2 - x + 14$.

Sketching curves

On a 1 cm$^2$ grid, the diagram shows point $P$, shape $S$ and lines $A$ and $B$.

Equations of linear graphs

Prakash purchases 45 flowers from a shop.

Ratio and proportion

Complete the clock diagram so that it shows the time when the cakes are ready.

Sets

On the $1 \text{cm}^2$ grid, sketch one rectangle with perimeter 22 cm and area 24 cm$^2$.

Area and perimeter

The rates below are what a painter, a plumber and an electrician charge for some work carried out for Mr Sharma. Painter: $35 per hour. Plumber: Fixed charge $40 plus $26.50 per hour. Electrician: $48 per hour for the first 2 hours then $32 per hour.

Rates

The coordinate grid contains triangle A, triangle B and triangle C plotted on one common set of axes.

Transformations

Find the values of $a$, $b$ and $c$ here.

Angles

Calculate how many of these 16500 people are expected to use their voucher.

Probability of combined events

The diagram depicts quadrilateral $ABCD$, together with the lengths and angles that are given.

Non-right-angled triangles

The grid displays the graph of $y = a + bx^2$. The curve passes through the points $(0,4)$ and $(1,1)$.

Differentiation