Feb/March 2024

Write thirty thousand and fifty in figures.

Types of number

The numbers in the list are: -9, -7, -3, -1, 0, 2, 5, 6, 8.

The four operations

Sarah notes the number of people who play golf on each of 14 days: 28, 46, 54, 71, 70, 65, 49, 50, 64, 77, 68, 72, 45, 58.

Averages and measures of spread

The diagram shows a cuboid net. The labelled measurements are 10 cm across the top rectangle, 4 cm for the vertical side of that rectangle, and 5 cm for the vertical side of the rectangle on the right. The diagram is marked NOT TO SCALE.

Surface area and volume

A car park contains 20 cars, and 3 of them are blue.

Statistical charts and diagrams

Factorise $3x^3 - 7xy$ completely.

Algebraic manipulation

A coordinate grid is displayed, with point $A$ positioned at about $(7, 1)$ and point $B$ positioned at about $(-3, 4)$.

Coordinates

The exchange rates are 1 euro = 1.05 dollars and 1 rupee = 0.013 dollars. Vani converts $x$ euros into dollars, and then changes those dollars into 17850 rupees.

Money

The lines $y = 2x - 5$ and $y = 3$ meet at point $P$.

Equations of linear graphs

The diagram displays two shapes, $A$ and $B$, plotted on a grid.

Transformations

The diagram depicts a smaller circle with radius 7 cm and a larger circle with radius $R$ cm. It is marked NOT TO SCALE. The total area of 16 small circles is equal to the area of one large circle.

Area and perimeter

Write 5926 rounded to the nearest 10.

Limits of accuracy

Work out the first three terms in this sequence.

Sequences

The rope length, $l$ m, is stated to be 18.7 m, accurate to the nearest 10 centimetres.

Limits of accuracy

$6.5 \times 10^{19} \times n = 5.46 \times 10^{23}$.

Standard form

Triangle $ABC$ is similar, in the mathematical sense, to triangle $DEF$. For triangle $ABC$, $AC = 118.9$ cm and $AB = h$ cm. For triangle $DEF$, $DF = 159.9$ cm and $DE = 97.5$ cm. The diagram is labelled NOT TO SCALE.

Similarity

Work out $1\frac{1}{4} - \frac{5}{6}$ without a calculator. Show all of your working and write your answer as a fraction in simplest form.

Fractions, decimals and percentages

The highest common factor (HCF) of two numbers is 6, and their lowest common multiple (LCM) is 90. Each number is greater than 6.

Types of number

Draw a straight line joining point S to point T.

Geometrical constructions

A square grid figure is displayed.

Percentages

The night bus operates from 21 50 until 05 18 on the following day.

Time

Using this list of numbers, write down every multiple of 11.

Types of number

The difference between the largest and smallest of the eight numbers is 31. Seven of the numbers are 28, 36, 42, 24, 38, 16 and 21.

Averages and measures of spread

Calculate $\sqrt{5.76} + 2.8^3$.

Powers and roots

Simplify the expression $4m + 7k - m + 3k$.

Algebraic manipulation

The night bus operates from 21 50 until 05 18 on the following day.

Time

The diagram displays trapezium $PQRS$. Its pair of parallel sides are $SR = 5.3$ cm and $PQ = 8.7$ cm. One side that is not parallel is $PS = 4.4$ cm. The indicated height is $3.8$ cm, and a right angle is shown at the base. The figure is labelled NOT TO SCALE.

Area and perimeter

Calculate $1\frac{1}{4} - \frac{5}{6}$. Show every step of your working and present your answer as a fraction in simplest form.

Fractions, decimals and percentages

Farid uses a spinner with three sides labelled $A$, $B$ and $C$. The chance that it lands on $C$ is $0.35$. Farid then spins the spinner 40 times.

Relative and expected frequencies

From A, the bearing to B is $107^\circ$.

Angles

A train that is 1750 metres in length is moving at 55 km/h.

Rates

The coordinate grid displays triangles labelled $A$, $B$ and $C$.

Transformations

$x$ is an integer. $\mathcal{E} = \{x : 1 \le x \le 10\}$, $P = \{x : x$ is an even number$\}$, $Q = \{x : x$ is a multiple of $5\}$. The Venn diagram below shows sets $P$ and $Q$ within the universal set $\mathcal{E}$.

Sets

Heights were measured for 200 people. The table summarises the outcomes. Height $h$ (cm): $100 < h \le 120$, $120 < h \le 130$, $130 < h \le 150$, $150 < h \le 190$. Frequency: $32, 55, 64, 49$.

Averages and measures of spread

Find the highest common factor (HCF) shared by $28x^5$ and $98x^3$.

Algebraic manipulation

The speed-time graph provides data for a bus journey. The vertical axis is Speed (m/s) and the horizontal axis is Time (seconds). Speed rises linearly from 0 to 15 m/s during the first 20 seconds, remains constant at 15 m/s until 140 seconds, then falls linearly to 0 by 190 seconds. The graph is labelled NOT TO SCALE.

Graphs in practical situations

Calculate the value of $\sqrt{5.76} + 2.8^3$.

Powers and roots

The figure shows triangle $ABC$ with $AB = 4.9$ cm, $BC = 5.6$ cm, and angle $ABC = 23^\circ$. It is labelled NOT TO SCALE.

Non-right-angled triangles

State the value of $h$.

Indices I

$y$ varies inversely with the square of $(x + 3)$. If $x = 5$, then $y = 0.375$.

Ratio and proportion

Sketch the graph of $y = \cos x$ over $0^\circ \le x \le 360^\circ$.

Trigonometric functions

$x^2 - 16x + a$ may be expressed in the form $(x + b)^2$.

Algebraic manipulation

A bag holds 2 green buttons, 5 red buttons and 6 blue buttons. Two buttons are chosen at random from the bag without replacement.

Probability of combined events

$A$ is the point $(6, 1)$ while $B$ is the point $(2, 7)$.

Equations of linear graphs

Simplify $4m + 7k - m + 3k$ into its simplest form.

Algebraic manipulation

The figure is the net of a cuboid, and the base is shaded. The cuboid has length 10 cm, width 4 cm and height 5 cm. The lengths on the diagram are marked as $a$ cm, $b$ cm, $c$ cm and $d$ cm. The shaded rectangle is labelled Base. The diagram is drawn NOT TO SCALE.

Surface area and volume

A car park contains 20 cars, and 3 of them are blue.

Introduction to probability

The coordinate diagram displays points $A$ and $B$ on axes named $x$ and $y$.

Vectors in two dimensions

When the temperature rises, the number of people going swimming also rises.

Scatter diagrams

Work out the sequence’s first three terms.

Sequences

The line $y = 2x - 5$ meets the line $y = 3$ at the point $P$.

Equations of linear graphs

Draw a line through point $P$ so that it is perpendicular to line $l$.

Symmetry

Garage A charges $1.41 per litre. Garage B charges $1.50 per litre.

Money

Using only a ruler and compasses, construct triangle $DEF$. Keep the construction arcs on your drawing.

Geometrical constructions

State how many televisions the shop sells on Monday.

Probability of combined events

Complete the table for the values of $y = -x^2 + 5x + 7$.

Graphs of functions

With $1\text{ cm}$ representing 8 km, plot the position of town $S$.

Scale drawings

For $P = 3a + 5$, determine the value of $P$ at $a = 2$.

Equations

A university mathematics department employs 120 people to teach. Some details are displayed in the table. One fifth of the people are professors. 30% of the people work part-time.

Sets

The grocer sells potatoes, mushrooms, and carrots.

Percentages

The table gives some values for $y = 2x^3 + 6x^2 - 2.5$. $x$: -3, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1 $y$: , 3.75, 5.5, 4.25, 1.5, , -2.5, -0.75,

Sketching curves

$f(x)=\frac{1}{x},\; x\ne0 \qquad g(x)=3x-5 \qquad h(x)=2^x$

Functions

The diagram depicts a circle with radius 12 cm, from which a sector has been cut out. The angle of the missing sector is $50^\circ$.

Circles, arcs and sectors

A, B, C and D lie on a circle. ADX and BCX are straight lines. $\angle BAD = x^\circ$ and $\angle DCX = y^\circ$.

Circle theorems I

The table gives the marks scored by each of 10 students in a test. Mark: 15, 16, 17, 18, 19, 20 Frequency: 4, 1, 2, 1, 0, 2

Averages and measures of spread

The figure depicts a pyramid with square base $BCDE$. The diagonals $CE$ and $BD$ meet at $M$, and vertex $F$ is vertically above $M$. $BE = 12$ cm and $FM = 9$ cm.

Surface area and volume

Factorise the expression. $x^2 - x - 12$

Algebraic manipulation

The diagram represents triangle $ABC$ with $AB=17.2$ cm. The angle at $B$ is $54^\circ$ and the angle at $C$ is $68^\circ$.

Non-right-angled triangles

The vectors are $p = \begin{pmatrix}8\\-5\end{pmatrix}$ and $q = \begin{pmatrix}-4\\5\end{pmatrix}$.

Vectors in two dimensions

Sketch the graph of $y = 4 - 3x$ on the axes.

Differentiation

Janna and Kamal each put in $8000. At the end of 12 years, both amounts are $12\,800.

Exponential growth and decay