Oct/Nov 2019

Convert 4.6 metres into centimetres.

Units of measure

Divide 518 in the ratio $2:5$.

Ratio and proportion

Write 15060 as words.

Standard form

Simplify the expression $5c - d - 3d - 2c$.

Algebraic manipulation

Calculate the area of a circle whose radius is 12 cm.

Circles, arcs and sectors

Levante converts 24650 Hungarian forints into dollars. The exchange rate given is $1 = 290$ forints.

Money

Paula puts in $600 at a yearly simple-interest rate of $r\%$. After 10 years, the interest gained totals $90$.

Percentages

Without a calculator, calculate $\frac{5}{16} \times 1\frac{1}{7}$. Show every step of your working and express your answer as a fraction in simplest form.

Fractions, decimals and percentages

Simplify the expression $2x^3 \times 3x^2$.

Indices I

A table listing Fraction, Decimal and Percentage is provided.

Fractions, decimals and percentages

The numbers in the list are 27, 14, 8, 93, 32, 55, 14, 38, 73, 47.

Averages and measures of spread

The diagram depicts a regular pentagon.

Symmetry

Juan goes from his home to a shop. The travel graph represents his journey. The vertical axis is Distance (km). The horizontal axis is Time. Home is at 0 km and the shop is at 14 km. The graph shows travel starting from 13:00 onwards.

Graphs in practical situations

The diagram, which is not drawn to scale, shows a right-angled triangle with base 12 cm, hypotenuse $x$ cm, and a $43^\circ$ angle at the base.

Right-angled triangles

Solve the equation $8(w + 11) = 120$.

Equations

The two simultaneous equations are $5x + 4y = 10$ and $7x - 6y = 43$.

Equations

The equation can be written as $y = \frac{8}{x}$.

Graphs of functions

Calculate $5\%$ of $25$.

Percentages

Factorise $5p + pt$.

Algebraic manipulation

Rui has a bag with only 5 black pens, 8 red pens and 3 blue pens inside it. He selects one pen from the bag at random.

Probability of combined events

Give 8473 correct to the nearest ten.

Limits of accuracy

The values given are $\frac{9}{19}$, $\frac{3}{7}$, $37\%$, $0.43$.

Fractions, decimals and percentages

The diagram shows the triangle’s base. The other two sides are 6 cm and 4 cm long.

Geometrical constructions

Calculate $\frac{16.379 - 0.879}{4.2} \times 1.241$. State your answer correct to 2 significant figures.

Limits of accuracy

Simplify the expression $5t + 4t - 2t$.

Algebraic manipulation

Fill in the missing values: $3.5\text{ kg} = [\,] \text{ g}$ and $1.4\text{ m}^2 = [\,] \text{ cm}^2$.

Units of measure

Kiran sets off from home at 9.45 am. She travels 135 km to see a friend, reaching her friend’s house at 11.15 am.

Rates

The scatter diagram plots the age and value of each of ten cars of the same model. The horizontal axis runs from 0 to 12 for Age (years). The vertical axis runs from 0 to 14 000 for Value ($). Ten points are shown.

Scatter diagrams

Find the value obtained from $6^0 + 6^2$.

Indices I

In part (a), a $4 \times 4$ array of small squares is shown, with some of them shaded. In part (b), a square is split by a diagonal into four triangular areas, with some of those shaded.

Symmetry

On one day, each of 10 students sent these numbers of texts: 18, 13, 15, 8, 9, 17, 12, 8, 6, 14.

Averages and measures of spread

The sketch shows a cuboid with dimensions 15 cm by 12 cm by 4 cm. It is not drawn to scale.

Surface area and volume

Do not use a calculator. Work out $3\frac{5}{8} - 1\frac{2}{3}$. Show all your working and present your answer as a mixed number in its simplest form.

Fractions, decimals and percentages

Javier places $750 in an investment for 3 years, earning compound interest at a rate of 1.8% per year.

Percentages

The figure is a right-angled triangle. Its vertical side measures 3.9 cm, the hypotenuse measures 8.5 cm, and the base is marked $x$ cm. The figure is not drawn to scale.

Pythagoras' theorem

At Scott Base in Antarctica, the lowest temperature that was recorded was $-57.0\degree\text{C}$. The highest temperature recorded there was $63.8\degree\text{C}$ above this.

The four operations

On the grid, the line $L$ is plotted. The $x$-axis runs from $-4$ to $4$, while the $y$-axis runs from $-5$ to $5$. Line $L$ passes through $(0,1)$ and slopes upwards to the right.

Equations of linear graphs

The grid contains several quadrilaterals, each labelled A, B, C, D, E, F, G and H.

Similarity

Esme purchases $x$ magazines costing $2.45$ each and $y$ cards costing $3.15$ each.

Introduction to algebra

The diagram is a scale drawing of Lei’s garden, $PQRS$. The scale is 1 centimetre represents 2 metres.

Geometrical constructions

The diagram shows point A and point B, each with a north arrow pointing straight up, and a straight line joining A to B.

Angles

Find the numerical value of $24^2$.

Powers and roots

A bag contains only 3 green balls, 4 red balls and 1 blue ball. Matt selects one ball from the bag at random. Some probabilities are indicated on the probability scale. The scale has letters A, B, C, D, E, F, G, H, I placed at equal intervals between 0 and 1, with 0.5 marked in the middle.

Introduction to probability

Sara travels from home to school on foot. Her journey is represented on the distance–time graph. On the vertical axis, Distance (km) is labelled from 0 to 3. On the horizontal axis, Time runs from 08:00 to 09:00. The graph has a line sloping upwards from home at 08:00 to about 1.2 km at 08:10, then a flat section until about 08:25, then another upward line to about 2.4 km at about 08:45, and finally a horizontal line to 09:00 at school.

Graphs in practical situations

Put these in order of size, beginning with the smallest: $\frac{7}{8}$, $\frac{5}{7}$, $0.8$, $78\%$.

Fractions, decimals and percentages

The table gives the ways children in Ivan’s class get to school: Walk 12; Car 7; Bicycle 9; Bus 4.

Statistical charts and diagrams

Rashid converts 30 000 rupees into dollars at an exchange rate of $1 = 68.14$ rupees.

Rates

Write down the mathematical term for this kind of angle.

Geometrical terms

Calculate the circumference of a circle whose radius is 4.5 cm.

Circles, arcs and sectors

Express $72\,000$ in standard form.

Standard form

Expand then simplify $(x + 3)(x + 5)$.

Algebraic manipulation

In $x^{3} \times x^{6} = x^{m}$, determine the value of $m$.

Indices I

The diagram depicts a right-angled triangle. The horizontal side measures 31 cm, the vertical side measures 28 cm, and the hypotenuse is $x$ cm.

Pythagoras' theorem

Davina notes the colour of every car that passes her house on one morning as follows: red, grey, black, red, grey, white, white, black, black, white, grey, red, grey, white, grey, black, grey, black, white, grey.

Classifying statistical data

The cuboid has dimensions of 5 cm, 7 cm and 9.5 cm.

Surface area and volume

Calculate:

Coordinates

To make 12 pancakes, you will need these ingredients: 110 g flour, 2 eggs, 200 ml milk, 50 g butter.

Ratio and proportion

The mean value of three numbers is 150. Those numbers are 361, $2n$ and $(n - 1)$.

Equations

Convert 560 metres into kilometres.

Units of measure

The diagram displays points $A$, $B$ and $C$ on a coordinate grid.

Coordinates

The diagram displays a conversion graph between dollars and Kenyan shillings.

Graphs in practical situations

The scatter diagram displays the results for ten athletes in both the 100 metre race and the triple jump.

Scatter diagrams

The scale diagram represents triangle $ABC$. The scale is 1 centimetre represents 8 kilometres.

Geometrical constructions

Write forty thousand three hundred as figures.

Types of number

Write $12x + 15$ in factorised form.

Algebraic manipulation

Insert one pair of brackets into the calculation $8 + 6 - 2 \times 5 = 28$ so that it becomes correct.

Algebraic manipulation

State the temperature that lies $7^{\circ}\text{C}$ below $-3^{\circ}\text{C}$.

Types of number

This is a list of numbers: 87, 77, 57, 47, 27.

Types of number

A bag contains 6 red balls and 10 blue balls only. On the probability scale, draw an arrow to show the probability that a ball chosen at random is:

Introduction to probability

A television costs $560. In a sale, this price is cut by 18%.

Percentages

Calculate 5% of $25.

Percentages

Simplify $\left(\frac{x^3}{8}\right)^{\frac{4}{3}}$.

Indices II

$P = 2r + \pi r$. Rearranging the equation gives $r$ in terms of $P$ and $\pi$.

Algebraic manipulation

A square has side lengths of 15.1 cm, correct to 1 decimal place. Find the upper bound of the area of the square.

Limits of accuracy

The diagram shows a triangle, NOT TO SCALE. Two sides measure 11 cm and 13 cm, and the angle enclosed by them is $39^{\circ}$.

Non-right-angled triangles

The map is drawn to a scale of 1 : 10 000 000, and Slovakia covers 4.9 $\text{cm}^2$ on the map.

Scale drawings

$y$ varies inversely with $x^2$. When $x = 4$, $y = 2$.

Ratio and proportion

A triangle is drawn, and it is NOT TO SCALE. The side lengths are marked 8 cm and 12 cm, and one angle measures $39^{\circ}$. The obtuse angle is labelled $x$.

Non-right-angled triangles

The figure has two sectors of circles that share the same centre. The angle is $45^{\circ}$. The inner radius is 3 cm and the outer radius is 5 cm. The shaded part lies between the two sectors. NOT TO SCALE.

Circles, arcs and sectors

Express $\frac{x}{2} - \frac{2x + 4}{x + 1}$ as one fraction, and give it in simplest form.

Algebraic fractions

Let $M = \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}$ together with $P = \begin{pmatrix}5 & 6\\7 & 8\end{pmatrix}$.

Algebraic manipulation

Factorise the expression $5p + pt$.

Algebraic manipulation

The chance that the school bus arrives late is $\frac{9}{10}$. When the school bus is late, the chance that Seb goes on the bus is $\frac{15}{16}$. When the school bus is on time, the chance that Seb goes on the bus is $\frac{3}{4}$.

Conditional probability

The diagram shows two shapes on a coordinate grid. The top shape is labelled $T$, and the lower shape is labelled $A$. The horizontal and vertical axes are marked $x$ and $y$.

Transformations

A pipe is entirely filled with water. Water moves through the pipe at a speed of $1.2\,\text{m s}^{-1}$ into a tank. The pipe’s cross-sectional area is $6\,\text{cm}^2$.

Rates

The universal set is $\xi = \{0, 1, 2, 3, 4, 5, 6\}$, while $A = \{0, 2, 4, 5, 6\}$ and $B = \{1, 2, 5\}$.

Sets

The functions are defined by $f(x) = 3x - 5$ and $g(x) = 2^x$.

Functions

A triangle is drawn and it is NOT TO SCALE. $O$ denotes the origin, $\overrightarrow{OP} = 2\overrightarrow{OA}$, $\overrightarrow{OQ} = 3\overrightarrow{OB}$ and $\overrightarrow{PM} = \overrightarrow{MQ}$. $\overrightarrow{OP} = \mathbf{p}$ and $\overrightarrow{OQ} = \mathbf{q}$.

Vector geometry

A speed-time graph is shown, and it is not drawn to scale. A car travels at 20 m/s for 15 seconds before it comes to rest by slowing down at $2.5\,\text{m s}^{-2}$.

Graphs in practical situations

Calculate $\frac{16.379 - 0.879}{4.2} \times 1.241$. Your answer should be given correct to 2 significant figures.

Limits of accuracy

Express 15 060 in words.

Standard form

Simplify the expression $5c - d - 3d - 2c$.

Algebraic manipulation

Solve for $x$ in $\frac{x - 2}{3} = 3$.

Equations

Simplify the expression $2x^3 \times 3x^2$.

Indices II

Without a calculator, Calculate $\frac{5}{16} \times 1\frac{1}{7}$. Show every step in your working and write your final answer as a fraction in lowest terms.

Fractions, decimals and percentages

Paula puts $600 into an investment earning simple interest at a rate of $r\%$ each year. After 10 years, the interest collected is $90. Find the value of $r$.

Percentages

State the highest temperature recorded at Scott Base.

Units of measure

Rewrite the recurring decimal $0.\dot{6}\dot{7}$ as a fraction. Include all your working and present your answer in simplest form.

Fractions, decimals and percentages

Calculate $3\frac{5}{8} - 1\frac{2}{3}$ without a calculator. Show all your working and express your answer as a mixed number in its simplest form.

Fractions, decimals and percentages

The interior angle of a regular polygon is $176^{\circ}$.

Angles

Two containers that are mathematically similar have heights of 30 cm and 75 cm. The larger one has a capacity of 5.5 litres.

Similarity

Show that $4y = 5x - 10$ and $5y + 4x = 35$ are perpendicular lines.

Gradient of linear graphs

Esme purchases $x$ magazines priced at \$2.45 each, together with $y$ cards costing \$3.15 apiece.

Introduction to algebra

A coordinate grid is displayed, together with a straight line labelled $2x + y = 6$.

Inequalities

The diagram presents a scale drawing of Lei’s garden, $PQRS$. The scale is 1 centimetre to 2 metres.

Geometrical constructions

Harris is sitting a driving test. The result of each attempt does not depend on what happened in earlier attempts. The chance that he passes at the first attempt is 0.6. If he is unsuccessful, the chance that he passes any later attempt is 0.75.

Probability of combined events

In the circle shown, $A$, $B$, $C$ and $D$ all lie on the circumference, with centre $O$. Angle $ACD = x^{\circ}$ and angle $OAB = 2x^{\circ}$. The sketch is marked NOT TO SCALE.

Circle theorems II

Calculate the value of $\frac{5}{8} + \sqrt[3]{340}$.

Powers and roots

Factorise $18y - 3ay + 12x - 2ax$

Algebraic manipulation

From $3^{-2} \times 3^x = 81$, determine the value of $x$.

Indices II

The matrices are defined by $A = \begin{pmatrix} 3 & 2 \\ -5 & 0 \end{pmatrix}$, $B = \begin{pmatrix} -2 & 5 \\ 4 & 1 \end{pmatrix}$ and $C = (-1\ \ k)$.

Algebraic manipulation

The speed-time graph provides details of a train journey. Speed is given in km/min and time is measured in minutes.

Differentiation

Expand the expression $a(a^3 + 3)$.

Algebraic manipulation

The Venn diagram depicts a universal set $\xi$ that contains two overlapping circles labelled $A$ and $B$.

Sets

The masses, accurate to the nearest kilogram, of the 11 parcels are given below: 24, 23, 23, 26, 25, 27, 18, 96, 16, 17, 32.

Averages and measures of spread

The table gives the ways children in Ivan’s class go to school. Walk: 12 Car: 7 Bicycle: 9 Bus: 4 Ivan intends to draw a pie chart to represent this data.

Statistical charts and diagrams

Rashid converts 30 000 rupees into dollars when the exchange rate is $\$1 = 68.14$ rupees.

Money

The diagram indicates point $B$ and includes an arrow showing north. The bearing of $P$ from $B$ is $102^{\circ}$. The figure is labelled NOT TO SCALE.

Angles

Solve this inequality: $\frac{x}{2} - 13 > 12 + 3x$.

Inequalities

State the temperature that is $7 ^{\circ}C$ lower than $-3 ^{\circ}C$.

The four operations