Oct/Nov 2020

State the mathematical name for an angle measuring less than $90^$.

Geometrical terms

Work out the sum $\begin{pmatrix}2\\-3\end{pmatrix} + \begin{pmatrix}5\\-1\end{pmatrix}$.

Coordinates

Rangan purchases $3.6\text{ kg}$ of potatoes together with $2.8\text{ kg}$ of leeks. Altogether, they cost $\$13.72$. The leeks are priced at $\$2.65$ per kilogram.

Money

$T = \dfrac{49.2 - 9.59}{4.085 \times 2.35}$

Estimation

Write $18$ as a product of prime factors.

Types of number

Calculate $2\dfrac{2}{3} \times 2\dfrac{3}{4}$ without a calculator. Show every step of your working and write your answer as a mixed number in the simplest form.

Fractions, decimals and percentages

Convert $4.37$ litres into cubic centimetres.

Units of measure

$2y = 5x - 7$

Algebraic manipulation

Trina places \$16\,000 into an account that earns compound interest at a rate of 5\% per year.

Percentages

Aisha keeps a record of the distance she runs and her average speed. These results are displayed in the scatter diagram. The vertical axis is labelled Average speed (km/h). The horizontal axis is labelled Distance (km).

Scatter diagrams

The circumference of a circle is $56\text{ mm}$.

Circles, arcs and sectors

isosceles, hexagon, regular, perpendicular, congruent

Geometrical terms

A graph with axes marked $x$ and $y$ shows a line named $L$.

Equations of linear graphs

Calculate $x$.

Equations

Express $\frac{60}{105}$ in its lowest terms.

Fractions, decimals and percentages

Calculate the value of $\sqrt{\frac{1}{0.01} - 8^2}$.

Powers and roots

In the diagram, draw every line of symmetry.

Symmetry

A figure is composed of rectangles. Its overall area is $517\text{ m}^2$. The diagram is marked with these lengths: the top is $24\text{ m}$, the right-hand side is $x\text{ m}$, the inner horizontal side is $17\text{ m}$, the inner vertical side is $19\text{ m}$, and the bottom-left side is $7\text{ m}$. NOT TO SCALE.

Compound shapes and parts of shapes

Hua rides her bicycle from home to the library. The journey is shown on the travel graph. The vertical axis is labelled Distance from home (km), and the horizontal axis is labelled Time. Home is at $0$ km, while Library is at $12$ km.

Graphs in practical situations

The triangular field $ABC$ has $AC = 500\text{ m}$ and $BC = 650\text{ m}$. Work to a scale where $1\text{ cm}$ stands for $100\text{ m}$. Side $AB$ has already been drawn.

Scale drawings

Alan and Beth divide $\$1190$ in the ratio Alan : Beth = $5 : 2$.

Ratio and proportion

Express two hundred thousand and seventeen in figures.

Types of number

A triangle is drawn between two parallel lines. The angle outside the triangle at the top is marked $x^\circ$, while the angle inside the triangle at the top is marked $y^\circ$. In the lower-left corner, the angle formed by the triangle side and the lower parallel line is $140^\circ$. In the lower-right corner, the matching angle is $120^\circ$. The diagram is NOT TO SCALE.

Angles

The diagram presents cuboid A and cuboid B. Cuboid A has measurements of 12 cm, 8 cm and 5 cm. Cuboid B has measurements of 16 cm, 10 cm and height $h$. Cuboid A has the same volume as cuboid B. The diagram is marked NOT TO SCALE.

Surface area and volume

Fernando notes the favourite sport for each of 20 people. The sports shown are: football, cricket, rugby, cricket, rugby, rugby, football, football, rugby, football, cricket, rugby, tennis, football, tennis, football, rugby, cricket, football, cricket.

Statistical charts and diagrams

Increase 42 by 16% to obtain the new value.

Percentages

The opening four terms in a sequence are 17, 10, 3, -4.

Sequences

Triangle $ABC$ is drawn. $AB = 6$ cm. The perpendicular from $C$ to the line through $AB$ is labelled $h$ cm. The diagram is marked NOT TO SCALE. The area of triangle $ABC$ is 27 cm$^2$.

Area and perimeter

A coordinate grid is displayed, with the $x$-axis and $y$-axis labelled. Point $A$ appears on the grid, and a straight line $L$ crosses the grid.

Equations of linear graphs

The expression to evaluate is $\frac{5}{6} \div 1\frac{1}{3}$.

Fractions, decimals and percentages

A pencil has length, $l$ cm, which is 18 cm when rounded to the nearest centimetre.

Standard form

One side of a rectangle has length 12 cm, and its diagonal has length 13 cm.

Pythagoras' theorem

Write $867$ rounded to the nearest ten.

Limits of accuracy

Alex and Chris divide sweets in the ratio Alex : Chris = 7 : 3, and Alex gets 20 more sweets than Chris.

Ratio and proportion

Express 825 as a product of prime factors.

Types of number

A right-angled triangle is displayed. Its base measures 22 cm. The angle at the lower-right corner is $36^\circ$. The hypotenuse has been labelled $x$ cm. The diagram is labelled NOT TO SCALE.

Right-angled triangles

The diagram depicts two similar triangles $TUV$ and $XYZ$. In triangle $TUV$, the side matching $XZ$ is 12 cm long. In triangle $XYZ$, $YX = 63$ cm and $XZ = 54$ cm. The diagram is labelled NOT TO SCALE.

Similarity

A regular octagon is illustrated.

Transformations

There are 20 balls in a bag, and 5 of them are red. One ball is chosen at random from the bag.

Introduction to probability

Find the total number of hours in 3 days.

Time

The four numbers listed are $\frac{11}{27}$, 41%, 0.4, and $\frac{16}{39}$.

Fractions, decimals and percentages

The relationship is expressed by $6 - 2x = 3x$.

Equations

Calculate the temperature difference between -6^{\circ}C and 5^{\circ}C.

The four operations

The formula can be written as $A = \frac{1}{4}bc^2$.

Introduction to algebra

This bar chart illustrates the rainfall amount, in mm, recorded in each month of one year in a city.

Statistical charts and diagrams

Ethan places $\$6400$ in an account paying simple interest at $2.6\%$ per year.

Percentages

The line $l$ is described by the equation $y = 5x + 12$.

Gradient of linear graphs

A cuboid measures $5\text{ cm}$ in length, $4\text{ cm}$ in width and $3\text{ cm}$ in height.

Surface area and volume

The trapezium and the parallelogram have equal areas.

Area and perimeter

The length, $l\text{ cm}$, of a line is measured as $18.3\text{ cm}$, accurate to the nearest millimetre.

Limits of accuracy

Use each number correct to $1$ significant figure to estimate $\dfrac{37.8 \times 13.2}{28.5 + 22.1}$. Show every step of your working.

Estimation

A bag contains $7$ red discs, $5$ green discs and $2$ pink discs. Helen chooses one disc at random, notes the colour and then puts it back into the bag. She repeats this $140$ times.

Relative and expected frequencies

Expand the brackets, then simplify: $4(2m + 3) - 5(m - 2)$.

Algebraic manipulation

Ramond covers $2460$ metres in $33$ minutes.

Rates

A regular polygon has an exterior angle measuring $20^{\circ}$.

Angles

Fill in this bill. 2.5 kg potatoes at $1.12 per kg $ [BLANK] [BLANK] kg bananas at $1.05 per kg $ [BLANK] Total = $ 4.69

Money

Without a calculator, calculate $1\dfrac{7}{10} \times 2\dfrac{1}{10}$. Show every step of your working and express your final answer as a mixed number in simplest form.

Fractions, decimals and percentages

$\xi = \{\text{children in a group}\}$ $R = \{\text{children who own a rabbit}\}$ $H = \{\text{children who own a hamster}\}$ The group contains $40$ children. $19$ of the children own a rabbit. $27$ of the children own a hamster.

Sets

Calculate the value of $PQ$.

Pythagoras' theorem

Solve the simultaneous equations below. You must show all of your working. $3x - 8y = 22$ $x + 4y = 4$

Equations

Write $97.4236$ rounded to $3$ decimal places.

Limits of accuracy

State the order of rotational symmetry of each shape.

Symmetry

Seven numbers have a mean of $16$. The six values given are $12, 20, 19, 10, 21$ and $13$.

Averages and measures of spread

In triangle $ABC$, $BC = 7.6\text{ cm}$ and $AC = 6.2\text{ cm}$. With a ruler and compasses only, construct triangle $ABC$. Keep your construction arcs visible. Side $AB$ has already been drawn for you.

Geometrical constructions

The table gives the temperatures, in $^{\circ}\text{C}$, at midnight and at $3\text{ pm}$ for four cities on one day.

The four operations

Calculate the value of $\dfrac{4}{\sqrt{0.0025}}$.

Powers and roots

Thor converts $40000$ Icelandic Krona into dollars at an exchange rate of $1$ krona = $0.0099$ dollars.

Rates

Simplify the expression $3a + 7b - 4a + b$.

Algebraic manipulation

A town begins with a population of 45 000. That population grows exponentially by 1.6% each year.

Exponential growth and decay

In the diagram, a rectangle has a line of symmetry at $x = 2$. Two of the rectangle's vertices lie at $(-1,1)$ and $(-1,4)$. The shaded area is given by the inequalities $a \le x \le b$ and $c \le y \le d$.

Coordinates

The interior angle of a regular polygon that has $n$ sides is $156^\circ$.

Angles

Express the recurring decimal $0.1\dot{7}$ as a fraction in its simplest form. You must show all your working.

Fractions, decimals and percentages

Determine the gradient of a line perpendicular to $8y + 4x = 5$.

Perpendicular lines

The diagram presents the speed-time graph for the first 100 seconds of a journey made by a car and a motorbike. Diagram text: The vertical axis is labelled "Speed (m/s)" and extends to 20. The horizontal axis is labelled "Time (s)" and extends to 100. A solid line marked "Car" remains at 18 m/s from 0 to 60 s, then drops in a straight line to 6 m/s at 100 s. A dashed horizontal line labelled "Motorbike" is drawn at 12 m/s.

Graphs in practical situations

Factorise the expression $6x^2 + 7x - 20$.

Algebraic manipulation

Find what $a$ is.

Functions

The figure represents a solid formed by a cylinder and a hemisphere, each with radius 7 cm. The cylinder’s length is 12 cm. [The surface area, $A$, of a sphere with radius $r$ is $A = 4\pi r^2$.]

Surface area and volume

The Venn diagram contains three intersecting circles, $M$, $N$ and $P$, set inside a universal set.

Sets

A triangle-shaped field, $ABC$, is given. $AC = 500\text{ m}$ and $BC = 650\text{ m}$. With only a ruler and compasses, finish the scale drawing of field $ABC$. Keep the construction arcs visible. Work to a scale where 1 cm represents 100 m. The side $AB$ has already been drawn. Diagram text: A straight line joins the points marked $A$ and $B$. The label says: "Scale: 1 cm to 100 m".

Geometrical constructions

The figure represents a cyclic quadrilateral. The angles are marked as $(4x - 87)^\circ$, $(x + 60)^\circ$, $2x^\circ$ and $y^\circ$.

Circle theorems I

The diagram depicts a cuboid $PQRSTUVVW$. $PV = 17.2 \text{ cm}$. The angle formed by the line $PV$ and the base $TUVW$ of the cuboid is $43^\circ$.

Pythagoras' theorem and trigonometry in 3D

Simplify $\frac{x^2 - 5x}{2x^2 - 50}$.

Algebraic fractions

The diagram depicts a parallelogram $CDEF$. $\overrightarrow{FE} = m$ and $\overrightarrow{CE} = n$. $B$ lies at the midpoint of $CD$. $\overrightarrow{FA} = 2\overrightarrow{AC}$.

Vector geometry

Rangan purchases 3.6 kg of potatoes together with 2.8 kg of leeks. The overall cost comes to $13.72. Leeks are priced at $2.65 per kilogram.

Rates

Aisha keeps track of the distance she runs and her average speed. The outcomes are displayed in the scatter diagram. Axes text: The vertical axis is labelled "Average speed (km/h)" and runs from 5 to 16. The horizontal axis is labelled "Distance (km)" and runs from 0 to 10.

Scatter diagrams

Let $T = \frac{49.2 - 9.59}{4.085 \times 2.35}$.

Estimation

Without a calculator, calculate $2\frac{2}{3} \times 2\frac{3}{4}$. Show every step of your working and give your answer as a mixed number in simplest form.

Fractions, decimals and percentages

Rearrange this formula so that $x$ is the subject: $2y = 5x - 7$.

Algebraic manipulation

State the digit that both numbers must finish with.

Types of number

From the options below, place a ring around the correct calculation.

The four operations

Write two hundred thousand and seventeen using figures.

Types of number

Calculate $\frac{5}{6} - 1\frac{1}{3}$ without a calculator. Show every stage of your working and write your answer as a fraction in its simplest form.

Fractions, decimals and percentages

Simplify the expression $2x^{2} \times 5x^{5}$.

Indices I

The sweets are divided between Alex and Chris in the ratio Alex : Chris $= 7 : 3$. Alex gets 20 more sweets than Chris.

Ratio and proportion

One side of a rectangle measures 12 cm. Its diagonal measures 13 cm.

Pythagoras' theorem

Find the value of $(3 \times 10^{19}) + (2 \times 10^{20})$. Write your answer in standard form.

Standard form

A circle sector is depicted with a central angle of $60^\circ$ and a radius measuring $7.5\text{ cm}$. The drawing is not drawn to scale.

Circles, arcs and sectors

A shirt costs $26.50, and that amount already includes 6% tax.

Percentages

The diagram presents the speed-time graph for the first 40 seconds of a cycle ride. Speed is measured in m/s and time is measured in seconds.

Graphs in practical situations

The sides of an isosceles triangle are measured to the nearest millimetre. One side measures 8.2 cm, and another side measures 9.4 cm.

Limits of accuracy

A triangle is drawn with one side measuring 8 cm, the base measuring 9 cm, the angle at the top equal to $100^\circ$, and the lower-right angle marked as $x^\circ$. The figure is not drawn to scale.

Non-right-angled triangles

Add one pair of brackets so that this calculation is correct: $7 - 5 - 3 + 4 = 9$.

The four operations

A scale model of a statue is 4 cm tall. Its volume is $12\text{ cm}^3$. The statue itself has a volume of $40500\text{ cm}^3$.

Ratio and proportion

Differentiate the expression $6 + 4x - x^{2}$.

Differentiation

The figure contains triangle $OAB$ together with the straight line $OAC$. The ratio $OA : OC = 2 : 5$, and $M$ is the midpoint of $AB$. Also, $\vec{OA} = \vec{a}$ and $\vec{OB} = \vec{b}$. The diagram is not drawn to scale.

Vector geometry

Put into one fraction in its simplest form: $2 - \frac{2x - 1}{x + 1}$.

Algebraic fractions

A line passing through the point $(2, 3)$ is perpendicular to the line $y = \frac{1}{3}x + 1$. The lines intersect at the point $P$.

Perpendicular lines

Solve the equation $\tan x = 2$ within $0^\circ \leq x \leq 360^\circ$.

Trigonometric functions

Simplify the expression $\frac{ux - 2u - x + 2}{u^{2} - 1}$.

Algebraic fractions

Solve $6 - 2x = 3x$.

Equations

The figure presents a triangle set between two parallel lines. The angle at the top is divided into two parts, marked $y^\circ$ and $x^\circ$. Along the bottom, the left exterior angle is $140^\circ$ and the right exterior angle is $120^\circ$. The diagram is not drawn to scale.

Angles

Calculate 42 after a 16% increase.

Percentages

Factorise completely the expression $4 - 8x$.

Algebraic manipulation

Triangle $ABC$ is illustrated. The length of $AB$ is $6\text{ cm}$. From $C$, a perpendicular is drawn to the line containing $AB$ and meets it at right angles, with the height labelled $h\text{ cm}$. The diagram is not drawn to scale.

Pythagoras' theorem

Calculate the measure of one interior angle in a regular polygon that has 40 sides.

Angles

Solve these simultaneous equations: $2x + y = 7$ and $3x - y = 8$.

Equations

State the cube number that is above 50 but below 100.

Powers and roots

Solve the simultaneous equations by showing all of your working. The equations are $3x - 8y = 22$ and $x + 4y = 4$.

Equations

A bag has 7 red discs, 5 green discs and 2 pink discs inside it.

Relative and expected frequencies

A straight line, $l$, is defined by $y = 5x + 12$.

Gradient of linear graphs