Feb/March 2025

Express twenty thousand in figures.

Types of number

A shape has been drawn on a grid with 1 $\text{cm}^2$ squares.

Area and perimeter

Multiplying 19.5 by 20.4 gives 397.8.

Fractions, decimals and percentages

Kat uses a rule for finding the difference of two square numbers, $a^2 - b^2$. Her rule is to multiply the sum of $a$ and $b$ by the difference between $a$ and $b$. She demonstrates this for $17^2 - 13^2$: $17^2 - 13^2 = (17 + 13) \times (17 - 13) = 30 \times 4 = 120$.

Algebraic manipulation

Convert 8 litres into $\text{cm}^3$.

Units of measure

The diagram depicts a triangular prism. $ABC$ is an isosceles triangle with $AC = BC$. The perpendicular height of triangle $ABC$ measures 4 cm. $AB = 6$ cm and $BD = 6$ cm.

Surface area and volume

The figure contains triangle $BCD$ and also the straight line $ABC$. In addition, $DB = DC = BC$.

Geometrical terms

Over ten days, Jill notes both the temperature and how many people are on a beach, and the findings are presented in the scatter diagram.

Scatter diagrams

The grid shows line $L$.

Equations of linear graphs

Complete the table by filling in the values for $y = \frac{12}{x}$.

Graphs of functions

State the values of $n$ that satisfy $7 < n \leq 15$.

Inequalities

Write 0.07 in percentage form.

Fractions, decimals and percentages

The height of a building, $h$ metres, is 635 m when rounded to the nearest metre.

Limits of accuracy

$X=\frac{1}{3}w^2p$

Algebraic manipulation

Calculate $1 \frac{7}{15} - \frac{4}{5}$. Express your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Mai purchases two batteries. The probability that a battery is faulty is $\frac{1}{10}$.

Probability of combined events

A circle with radius 7 cm is compared with a square whose side is x cm. The circle’s circumference has the same length as the square’s perimeter.

Area and perimeter

Triangles $ABC$ and $PQR$ are mathematically similar.

Similarity

Solve these simultaneous equations: $4t - 3w = 11$ and $6t + 2w = -3$.

Equations

List all the factors of 18.

Types of number

Find $10^3$.

Powers and roots

Draw every line of symmetry on the diagram.

Symmetry

Calculate the reciprocal of 0.25.

Fractions, decimals and percentages

Calculate $-6 \times -3 + 7 \times 2$.

The four operations

Arrange these numbers from least to greatest, beginning with the smallest: $34\%$, $\pi$, $\frac{1}{3}$, $3$, $\frac{3}{10}$.

Ordering

A film begins at 19 35 and runs for 70 minutes.

Time

The oranges are priced at 220 rupees per kilogram. Find the cost of 9 kg of these oranges.

Rates

Three regular polygons $A$, $B$ and $C$ are joined at one point. Their interior angles are in the ratio $a : b : c = 3 : 4 : 5$. The diagram labels the angles at the shared point as $a^\circ$, $b^\circ$ and $c^\circ$.

Angles

This company sells goods either through a website or in shops. The composite bar chart illustrates the percentages of sales made on the website and in shops in January, February and March. The key for the bar chart is: white = sales in shops, shaded = sales on website.

Statistical charts and diagrams

Express $\dfrac{x}{4} + \dfrac{3x}{8} - \dfrac{x+2}{12}$ as a single fraction in its simplest form.

Algebraic fractions

The sketch depicts a cylinder with radius $r$ cm and height $16$ cm. A sphere with radius $3$ cm is also given. The cylinder and the sphere have equal volumes.

Surface area and volume

The points $A$, $B$, $C$, $D$ and $E$ all lie on one circle. $FG$ is tangent to the circle at $C$. $angle BAD = 110^\circ$, $angle ADB = 20^\circ$ and $angle BEC = 45^\circ$.

Circle theorems II

Point $A$ is located at $(-4, 1)$, and the vector $\vec{BA}$ is given by $\begin{pmatrix}-5\\-12\end{pmatrix}$.

Vectors in two dimensions

The stem-and-leaf diagram gives the mass of each of 13 packets. The stems are 3, 4 and 5, and the leaves are: for 3, 1, 2, 8; for 4, 0, 1, 2, 3, 3, 8; for 5, 1, 2, 3, 4. Key: $3|1$ stands for $31$ g.

Averages and measures of spread

Work out $\dfrac{5}{9} + 0.2\dot{8}$. Write your answer as a fraction in its simplest form.

Fractions, decimals and percentages

The quadrilateral $ACDE$ is made up from two right-angled triangles, $ABE$ and $BCD$. The given lengths are $AC = 17$ cm, $AE = 18$ cm and $BD = 6$ cm, and the diagram shows an angle of $60^\circ$ at $A$.

Right-angled triangles

A Venn diagram displays three intersecting sets $A$, $B$ and $C$ within the universal set $\xi$.

Sets

Aryan makes a journey. He sets off from home at 11 40 and gets there at 14 18. Determine the duration of the journey in hours and minutes.

Time

Simplify $\sqrt{300} + \sqrt{48}$.

Surds

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

Equations of linear graphs

The curve is defined by $y = x^3 + x^2 - x$. One stationary point occurs at $\left(\dfrac{1}{3}, -\dfrac{5}{27}\right)$.

Differentiation

Simplify the expression $\left(\dfrac{x^2}{4}\right)^{\frac{3}{2}}$.

Indices I

A quadrilateral has one line of symmetry. Its diagonals meet at right angles. Write down the mathematical name of the quadrilateral.

Symmetry

$V=4mp^2$

Algebraic manipulation

Arrange these lengths by size, beginning with the smallest: 0.03 m, 2.9 cm, 32 mm, 0.000 02 km.

Units of measure

A trapezium is drawn, not to scale, and the labels show a left vertical side of 15 cm, an upper sloping side of 10 cm, a right vertical side of 9 cm, and a bottom base of 8 cm. The lower left and lower right corners are right angles.

Area and perimeter

The number line extends from -6 to 6. An unfilled circle is marked at $x = -3$ and a solid circle is marked at $x = 4$, with a solid segment joining them.

Inequalities

Priyanka takes part in a game that can end in a win, lose or draw. The table lists the probabilities for winning and losing a game. Outcome of game: win, lose, draw. Probability: win 0.3, lose 0.25, draw blank.

Introduction to probability

The relation is $D = \sqrt{\dfrac{1.95 \times 9.92^2}{8.07}}$.

Estimation

Taj is $3\frac{1}{4}$ years old. Calculate her age in months.

Time

The table presents a stem-and-leaf diagram arranged in order. Stem 0: leaves 2, A Stem 1: leaves 1, 3, B, 7 Stem 2: leaves 0, 4, 6, C Key: $1|3$ represents 13. For the ten numbers: the range is 27, the median is 16, and the mean is 16.5.

Averages and measures of spread

Two lighthouses, $P$ and $Q$, are shown on this scale drawing. The scale is 1 centimetre represents 0.8 kilometres. A north arrow is drawn upwards at each lighthouse. Scale: 1 cm to 0.8 km.

Scale drawings

Mo asks a group of people whether they prefer sun, rain or wind. The pie chart gives the results. The sectors are marked Sun, Wind and Rain. The Wind sector has an angle of $95^\circ$ and the Rain sector has an angle of $80^\circ$. 45 more people choose wind than rain.

Statistical charts and diagrams

Xie converts 2000 dollars into krona. $1$ dollar $= 0.615$ euros. $1$ krona $= 0.087$ euros.

Ratio and proportion

Factorise the expression $8x^2 - 2x$.

Algebraic manipulation

A car covers 95 km in 2 hours and 15 minutes. Calculate the average speed of the car in km/h.

Rates

Chi divides $480$ according to the ratio $2:3:7$. Find the size of the largest share.

Ratio and proportion

Solve $\frac{x}{3} = 18$.

Indices II

Clare puts $12000$ into an investment for 3 years at $8\%$ per year compound interest. Calculate the value of her investment after the 3 years. Give your answer correct to the nearest $10$.

Percentages

Write 2025 as the product of its prime factors.

Types of number

Div has $25 to spend on cups that cost $4.25 each. Calculate how many cups he can buy at most and the change he gets back.

Money

The diagram depicts three shapes, $A$, $B$ and $C$, on a $\text{cm}^2$ grid. The coordinate axes carry the labels $x$ and $y$.

Transformations

Show that the interior angles of a pentagon add up to $540^\circ$.

Angles

The diagram illustrates angle A, which is made by two straight lines.

Angles

The items in the list are 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39.

Types of number

A farmer plants $t$ trees each day. Give an expression for the number of trees he plants in $d$ days.

Introduction to algebra

Raj is thinking of a negative number $n$. He adds 10 to $n$ and then multiplies the result by 5. This gives 30. Find the value of $n$.

Equations

The diagram depicts a straight transversal cutting across two parallel lines. The angles at the upper intersection are marked $b$, $c$, $A$, $d$, and those at the lower intersection are marked $h$, $e$, $g$, $f$.

Angles

The sequence begins with these four terms: 31, 24, 17, 10.

Sequences

A cuboid has dimensions 3 cm, 7 cm and 11 cm. Calculate its surface area.

Surface area and volume

State a factor of 28 that is a prime number.

Types of number

A coordinate grid is displayed, and triangles $A$ and $B$ are marked on it.

Transformations

Midhil puts $\$1500$ into an account earning $4.2\%$ compound interest each year. Determine the value of the investment after $5$ years.

Exponential growth and decay

The cone’s sloping edge measures $12\text{ cm}$, and its base radius is $5\text{ cm}$.

Surface area and volume

The table presents the first $5$ terms of sequences $A$, $B$ and $C$.

Sequences

The function is defined by $f(x)=5-4x$.

Functions

Virat measures the height of each of $80$ sunflowers. The results are given in the table.

Averages and measures of spread

The graph plots a cyclist’s speed over a $30$ second journey. The vertical axis is labelled Speed (m/s), while the horizontal axis is Time (seconds).

Differentiation

The diagram places three points $A$, $B$ and $C$ on level ground. The bearing of $C$ from $A$ is $145^\circ$ and $\angle ACB = 38^\circ$. Also, $AC = 65\text{ m}$ and $BC = 95\text{ m}$. A north arrow is included. The diagram is marked NOT TO SCALE.

Non-right-angled triangles

Factorise $18a^2 - 98$ into its fully factorised form.

Algebraic manipulation

Solve the equation $2 + 5 \cos x = 0$ for $0^\circ \le x \le 360^\circ$.

Trigonometric functions

Simplify $4y^2 + 3y - y^2 + 2y$.

Algebraic manipulation

A metal sample has a volume of $1240\text{ cm}^3$, to the nearest $20\text{ cm}^3$. Its mass is $7800\text{ g}$, to the nearest $100\text{ g}$. [Density = mass \div volume.]

Limits of accuracy

The figure depicts triangle $OAB$. $C$ is placed at the midpoint of $OA$. $OC = m$ and $CB = n$. $E$ is situated on $AB$ and $AE : EB = 4 : 5$. The figure is marked NOT TO SCALE.

Vector geometry

The line $y = 4x + 12$ meets the curve $y = 2x^2 - x - 3$ at points $P$ and $Q$.

Graphs of functions

The diagram depicts the larger segment of a circle with centre $O$ and radius $2.5\text{ m}$. This segment forms the cross-section of a tunnel whose height is $3\text{ m}$. The tunnel is $800\text{ m}$ long and its cross-section is constant along the whole length. The diagram is marked NOT TO SCALE.

Circles, arcs and sectors

A display of small square cells is shown, with some of the squares already shaded.

Symmetry

Calculate $\dfrac{20.24 - \sqrt[3]{30}}{6.5}$. State your answer correct to 1 decimal place.

Powers and roots

A figure is made from 3 congruent rectangles. Starting from the rectangle beside it, each rectangle is turned through $90^\circ$ about one vertex. Point $A$ is at $(2, 5)$. Point $B$ is at $(4, 1.5)$. A coordinate diagram is displayed and marked NOT TO SCALE. The diagram includes points $A$, $B$, $C$ and $D$.

Transformations

In each week, Nisha earns $12$ per hour for the first $40$ hours she works. For any additional hours, her hourly rate is $30\%$ higher. In one week, she works $45.5$ hours.

Percentages

The table lists the age and mass for each of 10 babies.

Scatter diagrams

The scale plan indicates where boat $A$ and boat $B$ are located. On the scale, $1\text{ cm}$ stands for $0.5\text{ km}$. A north arrow is included. The sketch labels the points $A$ and $B$.

Scale drawings

In standard form, write $0.00709$.

Standard form