Igcse Revision

iContents

Contents Exam questions

MathematicsA

1 Working with numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Angles, triangles and quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Solving problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5 Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6 Fractions and mixed numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

7 Circles and polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

MathematicsB

1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

2 Algebra 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

3 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4 Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

5 Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

6 Equations 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

7 Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

8 Statistical calculations 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

9 Sequences 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

10 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

11 Constructions 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

12 Using a calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

13 Statistical diagrams 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

14 Integers, powers and roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

15 Algebra 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

16 Statistical diagrams 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

17 Equations 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

18 Ratio and proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

19 Statistical calculations 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

20 Pythagoras’ theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

21 Planning and collecting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

22 Sequences 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

23 Constructions 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

24 Rearranging formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

ii Contents

1 Two-dimensional representation of solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2 Probability 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3 Perimeter, area and volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 The area of triangles and parallelograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 Probability 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7 Perimeter, area and volume 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

8 Using a calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

9 Trial and improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

10 Englargement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

11 Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

12 Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

MathematicsC

8 Powers and indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

9 Decimals and fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

10 Real-life graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

11 Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

12 Percentages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

13 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

14 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

15 Enlargement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

16 Scatter diagrams and time series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

17 Straight lines and inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

18 Congruence and transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Unit A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Unit B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

Unit C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18

Answers to exam questions

1 IntegersHere is an exam question …

Look at these numbers.6, 8, 9, 11, 14, 15, 18, 27From this list, write down a two odd numbers. [1]b a multiple of 5. [1]c a prime number. [1]d two consecutive numbers. [1]e a factor of 30. [1]

… and its solutiona Any two of 9, 11, 15 and 27b 15c 11d 8 and 9 or 14 and 15e 6 or 15

Here is an exam question …Three friends had a meal together. They had three ‘Chef’s specials’ at £8.99 each, two drinks at £1.45 each, one drink at £1.75 and two puddings at £2.49 each. They agreed to share the bill equally. How much did each friend pay? Write down your calculations. [4]

… and its solution3 × 8.99 = 26.972 × 1.45 = 2.901 × 1.75 = 1.752 × 2.49 = 4.98 Total = 36.60Each paid £36.60 ÷ 3 = £12.20

3 × 5 = 15

30 ÷ 6 = 5 and 30 ÷ 15 = 2

Now try these exam questions

1 a Write 478 correct to the nearest 10. [1]b Write 4290 correct to the nearest 1000. [1]

2 Look at these numbers. 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 From this list choose

a an even number. [1]b a multiple of 7. [1]c a factor of 24. [1]d a prime number. [1]e a square number. [1]

3 Write these numbers in order, smallest first.a 2164, 3025, 4047, 1987, 2146, 3332, 1084 [1]b −3, 6, −8, 4, −2, 1, 0, −4 [1]

4 At a weather station, the temperature is recorded every six hours.

Noon 6 p.m. Midnight

–3 ºC 2 ºC

a How many degrees has the temperature risen between noon and 6 p.m.? [1]

b The temperature falls 9 degrees between 6 p.m. and midnight. What is the temperature at midnight? [1]


1 Solve this puzzle using trial and improvement. ‘I think of a number, then divide it by 1.5. I then square the result. The answer is 49. What number am I thinking of?’ The working has been started for you.

Trial Working out Result

Too small Too large

6 6 ÷ 1.5 = 4 42 = 16

12

[3]2 A magazine advert costs £20, plus 50 pence

per word. Graham paid £48 for an advert. How many words did it have? [3]

3 A train from Birmingham to Newcastle had 14 coaches. Each coach had 56 seats. There were 490 seats occupied.

How many spare seats were there? [3]

1© Hodder Education 2011 Unit A

2 Revision Notes © Hodder Education 2011

Exam

que

stio

ns:U

nitA 2 Algebra 1

Here is an exam question … Simplify these.a k + k + k + k [1]b 8n − 5n [1]c 4 × f × g [1]

… and its solutiona 4kb 3nc 4fg

3 Data collectionHere is an exam question ...

The staff of a shoe shop counted how many pairs of shoes they had left in stock after a sale. Draw a bar chart to show the following information.

Shoe size Number of pairs

3–5 3

6–8 4

9–11 8

12 and over 5

[3]

... and its solution


1 a Write as simply as possible p + p + p + p [1]

b Write down, in terms of x, the perimeter of this rectangle as simply as possible.

[1]

2 Simplify these.a 5m + 3m − 4m [1]b 6k − 3k + 2k [1]c 4d + 3d − 5d + 2d [1]

3 a Sam has 4 dogs, x cats and y rabbits. Write an expression for the total number of pets he has. [1]b Lee has x CDs. Chloe has 7 more than Lee.

Write an expression for the number of CDs they have in total. [1]

4 Simplify these.a 3 × a × 5 × a [2]b 7x + 3y − 2x + 5y [2]

5 A rectangle is 3x units wide and 2y units high. Write down expressions for the perimeter and the

area of the rectangle. Give each answer in its simplest form.

[4]

2x

3x

3x

3x

2y2y

00 3 to 5 6 to 8

Shoe size

Freq

uenc

y

9 to 11 12 andover

123456789


1 Pali did a survey about school meals. He included the following questions amongst others.

State one thing that is wrong with each question.a Don’t you think they should serve fish on Fridays?b Would you like to see more salads and more

burgers?


4 DecimalsHere is an exam question ...

In one day, Dave uses 13.8 units of electricity. The price of electricity is 17.5p per unit.Calculate the cost of the electricity Dave uses that day. [2]

... and its solutionCost = 13.8 × 17.5p = 241.5p = £2.42 to nearest penny

2 The table shows the number of passengers travelling on bus number 38B into town during one day.

Number of passengers on bus

Number of buses (frequency)

Less than 10 5

10−19 24

20−29 19

30−39 12

40–49 7

50–59 3

Draw a bar chart to illustrate this information. [3]3 Amelia surveyed some students in her school to

find out each student’s favourite pet. Here are her results.

Dog Cat Other Total

Boys 24 17

Girls 27 62

Total 38 45

a Copy and complete the table. [3]b How many students did she ask? [1]c How many girls chose ‘cat’? [1]

4 These data show the number of text messages received by each of 80 people in a single week.

27 56 32 8 31 90 24 48 52 31 18 34 56 73 52 55 19 18 3 67 56 13 28 35 69 27 38 59 21 53 36 34 71 57 32 43 65 48 33 29 16 36 47 78 41 60 74 36 22 41 25 29 13 27 55 43 32 4 37 63 47 81 92 78 41 57 34 28 19 62 64 24 14 7 34 35 49 36 29 84

a Using groups of 1 to 20, 21 to 40, 41 to 60, 61 to 80, and so on, produce a frequency table to show the data. [2]

b Draw a bar chart to illustrate the results. [2]5 Anil and Ben carried out a survey to find the

number of absences per week in their school year group over a period of 40 weeks. The results are shown below.

15 20 31 27 39 52 31 16 17 8 22 31 17 21 16 34 26 27 11 6 4 45 57 31 24 23 22 15 14 43 41 32 27 24 35 18 29 31 23 44 To analyse their results they each decided to group

their data and make a frequency table.

a Anil chose these groups: 0−10, 10−20, 20−30, 30−40, 40−50, 50−60.

Explain why these groups are unsuitable. [1]b Ben chose these groups: 0−9, 10−19, 20−29,

30−39, 40−49, 50−59. Complete the following frequency table using

Ben’s groups of number of absences.

Absences Tallymarks Frequency

0−9

10−19

20−29

30−39

40−49

50−59

[2]c On the grid below draw a bar chart to show the

distribution of number of absences.

[3]

0Number of absences

Freq

uenc

y

12345678

10111213

9


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5 FormulaeHere is an exam question …

a K = 5p − 8. Find K when p = 3. [2]b L = 3q + 2r. Find L when q = 4 and r = 5. [2]

… and its solution a K = 5 × 3 − 8 = 7b L = 3 × 4 + 2 × 5 = 12 + 10 = 22

Here is another exam question … The diagram shows an isosceles triangle whose base is f and whose other two sides are g.

a Write a formula for the perimeter (p) in terms of f and g. [1]

b Work out the value of p when f = 1.7 m and g = 2.4 m. [2]

… and its solution a p = f + 2gb p = 1.7 + 2 × 2.4 = 1.7 + 4.8 = 6.5 m

More exam practice

1 For the formula G = 12 x − 3, work out the value

of G whena x = 12. [1]b x = 4. [1]

2 For the formula K = 25 − 7g, work out the value of K whena g = 3. [1]b g = −2. [1]

3 For the formula H = 0.5a, work out the value of H whena a = 12. [1]b a = 4. [1]

4 If Q = 7xy, find Q whena x = 5 and y = 2. [1]b x = 6 and y = 1.5. [1]


1 Sunita checks her bank balance. It is −£43.75. She pays £100 into this account, then uses her

account to pay a phone bill of £15.32. What is her bank balance after this? [2]2 Robert is buying presents for his friends. He buys 6 DVDs at £5.59 each and 9 CDs at 3.49

each. He pays with 7 £10 notes. How much change

should he get? [3]3 Work out these.

a 0.3 × 40 b 0.1 × 0.1 [2]4 a Work out these.

i 0.36 × 1000 ii 0.45 × 100 iii 45.6 ÷ 1000 iv 8563 ÷ 10 000 [4]b A school orders 1000 pens. Each one costs £0.32. Find the total cost. [1]

5 Where possible, match a fraction with its equivalent decimal.

One has been done for you.

5100

14 0.1

150 0.2

12 0.25

1325 0.5

110 0.52

420

25

[4]

g g

f


1 A single textbook costs £9. Write down a formula for the cost, £C, of n

textbooks. [1]2 For the formula F = 7x + 5, work out the value

of F whena x = 2. [1]b x = 5. [1]

3 If P = 8a + 3b, find P whena a = 5 and b = 4 [2]b a = 4 and b = 2.5 [2]

4 P and k are connected by the formula P = 20 + 4k. Find the value of P when

a k = 2. [2]b k = 5.5. [2]


6 Equations 1Here is an exam question …

a Find the values of a and b.

[2]b Solve the following equations. i 6x = 30 [1] ii x + 5 = 3 [1]

iii x4

= 5 [1]

… and its solutiona a = 5, b = 9b i x = 30 ÷ 6 = 5 ii x = 3 − 5 = − 2 iii x = 5 × 4 = 20

7 CoordinatesHere is an exam question …

a Plot the following points on the grid. [3]

A(3, 1), B(7, 3), C(5, 7), D(3, 5), E(2, 3), F(5, 1), G(2, 7)b Points A, B and C are three corners of a square. Write down the coordinates of a point P that

would be the fourth corner of the square. [1]

… and its solutiona

b (1, 5)

�51531

�4ab

Chief Examiner saysx4 means x ÷ 4 and the inverse of ÷ is ×.


1 For the given inputs, find the output from these number machines.

a

[3]

b

[4]2 Solve the following equations.

a 8x = 32 [1]b x − 6 = 9 [1]c x

5 = 7 [1]

3 Given that x = 9 and y = 7, calculate the value of x2 − 5y. [2]

4 The formula t = v u

a–

may be used to find the time taken for a car to accelerate from a speed u

to speed v with acceleration a. Find t when v = 11.9, u = 5.1 and a = 1.7. [3]5 The cost, C pence, of printing n party invitations is

given by C = 120 + 4n. Find a formula for n in terms of C. [2]

�616 94

iiiiii

�51019

�2iii

4

y

x

5678

321

0 1 2 3 4 5 6 7 8

4

y

x

5678

321

0 1 2 3 4 5 6 7 8

G C

D

E

A F

B


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8 Statistical calculations 1Here is an exam question …

Twelve pupils did a piece of maths work.It was marked out of 8. The results are shown below.3 4 4 4 4 55 6 6 7 7 8a Find the mode of these marks. [1]b Find the median of these marks. [1]

… and its solutiona Mode = 4 b Median = 5


1

a State the coordinates of point A.b Plot the points B(−2, 4), C(−2, −3) and D(5, −3).c Join A to B, B to C, C to D and D to A. What

type of quadrilateral is ABCD? [4]2 The three points A, B and C are joined to form a

triangle. A is (2, 1), B is (14, −2) and C is (3, 7). Work out the coordinates of the midpoint ofa side AC. [2]b side AB. [2]

3 A is the point (2, 4).

a Write down the coordinates of i B ii C. [2]b Point D is such that ABCD is a square. Plot

point D on the grid. [1]4 ABCD is a trapezium.

�5�4�3�2�1

12345y

x�5�4�3�2�1 10 2 3 4 5

A

�5�6�7

�4�3�2�1

12345

y

x

67

�5�6�7 �4�3�2�1 10 2 3 4 5 6 7

A

BC

�4�3�2�1

123

x�3�2�1 10 2 3 4

A

D

B

C

y

a Write down the coordinates of A, B, C and D. [4]b Write down the equations of the lines passing

through the following points. i A and B ii B and C [2]

5

a Write down the equation of line a. [1]b Write down the equation of line b. [1]c On the grid draw and label the line x = −3. [1]d On the grid draw and label the line y = 0. [1]

�5�4�3�2�1

12345y

x�5�4�3�2�1 10 2 3 4 5

a

b

The value that occurs most often.

There are two middle values, 5 and 5, so the median must be 5.


9 Sequences 1Here is an exam question …

a These are the first four terms of a sequence. 2, 9, 16, 23

i Write down the term-to-term rule. [1]ii Find the sixth term of this sequence. [1]

b These are the first four terms of a sequence. 29, 25, 21, 17

i Find the seventh term. [1]ii Explain how you worked out your answer. [1]

c Here is the term-to-term rule for another sequence. Multiply the previous term by 4 then subtract 1. The first term of the sequence is 2. Find the third term. [1]

… and its solutiona i the rule is + 7 ii 37 b i 5 ii The rule is −4 and

17 − 4 − 4 − 4 = 5c 27


1 The following paragraph is taken from the introduction to this book.

‘If you know that your knowledge is worse in certain topic areas, don’t leave these to the end of your revision programme. Put them in at the start so that you have time to return to them nearer the end of the revision period.’

Complete the grouped frequency table for the number of letters in the words in the above paragraph. [3]

Number of letters in a word

Number of words

Class interval Tally Frequency

1−3

2 The weights, in kilograms, of a rowing crew are as follows.

80 83 83 86 89 91 93 99 Calculate

a the mean. [3]b the range. [2]

3 The following data shows the number of people using a particular footbridge on each day in June.

7 12 14 5 3 6 8 2 13 17 7 1 3 9 5 17 22 7 7 6 8 10 23 18 6 4 1 9 7 19

a Calculate the range of these data. [2]b Calculate the mean number of people per day. [4]c Find the mode. [1]

4 The data below shows the time taken, in minutes, by each of 30 students to solve a puzzle.

3 6 14 18 20 14 6 16 13 7 15 8 15 10 14 10 15 5 4 9 16 9 15 12 14 10 6 13 15 12 What is the modal class? [1]5 A school has to select one student to take part in

a general knowledge quiz. Kim and Pat took part in six trial quizzes. The

following table shows their scores.

Kim 28 24 21 27 24 26

Pat 33 19 16 32 34 16

a Calculate Pat’s mean score and range. [2]b Which student would you choose to represent

the school? Explain the reason for your choice, referring to

the mean scores and ranges. [2]

6 The table below shows the number of letters per word in the first paragraph of two books.

Number of letters (n)

Frequency

Book 1 Book 2

0 < n < 5 38 35

5 < n < 10 29 21

10 < n < 15 7 13

15 < n < 20 0 2

Compare the median, mean and range in the number of letters per word of the two paragraphs. [4]

23 + 7 + 7 = 37

2 × 4 − 1 = 7, 7 × 4 − 1 = 27


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10 MeasuresHere is an exam question …

For each of these, write the most suitable metric unit to use for measuring.a The length of a football pitch [1]b The amount of liquid that a teaspoon can hold [1]c The area of a square with side 5 cm [1]

… and its solutiona metres (m)b millilitres (ml)c square centimetres (cm2)


1 For each of these sequences, the numbers are the number of lines in each picture.a

b

c

i Draw the next two pictures in each of the sequences. [1][1][1]

ii Explain what you need to do to the previous number to get the next number. [1][1][1]

2 The sequence below starts 1, 2, 1. The next term is the previous three terms added together.

1, 2, 1, 4, 7, 12, 23, …a Write down the next two terms of the

sequence. [2]b There seems to be another pattern in this

sequence, involving odd and even numbers. 1 (odd), 2 (even), 1 (odd), 4 (even), … Does this ‘odd, even’ pattern continue for the

next few numbers? [1] Give examples to support your answer. [2]

3 Match these sequences to the correct nth terms. [3]

3, 4, 5, 6, 7 3n

3, 6, 9, 12, 15 2n + 1

15, 12, 9, 6, 3 n + 2

3, 5, 7, 9, 11 6 − n

5, 4, 3, 2, 1 18 − 3n

4 a Find the first 5 terms in each of these sequences. i First term 4, term-to-term rule: add 5 [1] ii First term 13, term-to-term rule: subtract 4 [1]b Find the term-to-term rule for each of these

sequences. i 2 5 8 11 … [2] ii 30 23 16 9 … [2]

3 5 7 9

4 7 10

13

8 15 22

29

c Find the term-to-term rule for the number of squares in this sequence of patterns.

[2]5 For each of these sequences:

i write down the next two terms of the sequence. [1+1+1]

ii write down the term-to-term rule for the sequence. [1+1+1]a 1, 6, 11, 16, 21, …b 18, 15, 12, 9, …c 1, 3, 9, 27, …


1 a Pat weighs 106 pounds. Estimate her weight in kilograms.

b Pat is 5 feet tall. How tall is this in metres? [4] 2 Write down the temperature shown on these scales. a

40 5060

7080

90

30

2010

0

Temp°C


11 Constructions 1Here is an exam question …

Simon went orienteering. This is a sketch he made of part of the course.

a Draw an accurate plan of this part of the course. Use a scale of 1 cm to 50 m. [3]

b Use your drawing to find the bearing of C from A. [1]


b 069º

Here is another exam question … Two buoys are anchored at A and B. B is due East of A.A boat is anchored at C.

a Using a scale of 1 cm to 2 m, draw the triangle ABC. [2]

b Measure the bearing of the boat, C, from buoy A. [2]

… and its solutiona Step1: Draw the line AB 7.5 cm long. Step2: Using compasses, draw an arc 10 cm from A,

and an arc 4 cm from B. Step3: Mark the point C where the arcs cross and

join to A and B to complete the triangle.b To measure the bearing, use your protractor, to draw

the North line at A, at right-angles to AB.

Note: the diagram above is not to scale.

Now use your protractor, with the zero line along the North line, to measure the bearing. It should be between 069º and 070º.

b

c

[3]

3 Write these measurements in order of size, smallest first.

1234 ml 2.59 l 0.375 l 4.68 l 579 ml [2]4 a Jim travelled 20 miles home from work. Approximately how many kilometres is this? [2]

b On his way home, Jim bought a 5 kilogram bag of potatoes.

Approximately how many pounds of potatoes did he buy? [2]

5 a Estimate the height of a typical house front door. [1]b Estimate the length of a family car. [1]

Temp °C60 70 8050

Temp °C100 2000

N

A

B

C

47°

125°

300 m

200 m

A

C

Scale � 1 cm to 50 m

NB

Diagram shown half size.

N

N

20 m

15 m

8 m

A B

C

A B

C

N

Scale 1 cm to 2 m


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1 This is a sketch of triangle ABC.

a Make an accurate drawing of the triangle. [4]b Measure the length of CB and the size of angle BAC. [2]

2 a Draw angles of the following sizes. i 63° ii 109° iii 256° [3]b Measure these angles. i ii iii

[3]3 Measure these angles.

a b

[2]

5.3 cm

9.1 cm

148°

C

B A


12 Using a calculatorHere is an exam question …

Work out the following. Give your answers to 2 decimal places.a 4.24 [1]

b3 9 0 533 9 0 53

2. .. .+× [2]

c 350 × 1.00512 [1]

… and its solutiona 311.17

b 7.61

c 371.59

4 P is 8 km from O on a bearing of 037° and Q is 7 km due East of O.a Make a scale drawing showing O, P and Q. Use a scale of 1 cm to 2 km.b Find the distance between P and Q.c Find the bearing of P from Q. [5]

5 The diagram shows a triangle ABC. The bisector of the angle at A meets line BC at X.

a Construct the triangle and the bisector of angle A.b Measure the distance AX. [5]

A

C

X

B120°

12 cm

8 cm

Key in

4 . 2 xy 4 =

311.1696

Key in

( 3 . 9 x2 +

0 . 5 3 ) ÷ ( 3 . 9 × 0 . 5 3 ) =

7.614 900 ...

Key in

3 5 0 × 1 . 0 0 5 xy

1 2 = 371.587 234 ...


Give your answers to 2 decimal places where appropriate. 1 Work out these.

a 283 103

360–

[1]

b 3.2(5.2 − 11 6. ) [2]

c 1

4 5 6 8. .+ [2]

2 Work out these.

a 25 of 65 g [2]

b 35% of £720 [2] 3 Work out these.

a 1.6 − 2.8 × 0.15 [2]

b 14 3 9 42 2. – . [2]

4 a Work out 23 of £4.56. [2]

b A travel firm offers a discount of 12% on a holiday costing £490.

How much is the discount? [2]c Three tins of dog food cost £1.38. What will eight tins of the same dog food

cost? [2] 5 Work out these.

a 4 6 3 92 5

. – .. [1]

b 14

2 5 7 3. .+ [2]

c 13 69. [1]6 A recipe for 4 people uses 360 g of flour and

60 g of butter. How much flour and butter is needed for 6

people? [2]


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More exam practice1 Work out these, giving the answers to 2 decimal

places.a 3.45 [1]b (5.1 + 3.7) × 4.2 [1]

c5 1 2 614 2 6 3. .. – .

× [2]

2 Work out the reciprocal of each of these. Give your answers to 2 decimal places where

appropriate.a 50 [1]b 0.75 [1]c 32 [1]

3 Work out these.

a 35 of 200 g [1]

b 234 − 145 [2]

c 47 of £26.60 [1]

4 Work out these, giving your answers to 2 decimal places where appropriate.

a 730 × 1.0115 [1]

b 1413 [1]

c 840 1 03840 1 03

×+

.

. [2]

13 Statistical diagrams 1Here is an exam question …

The manager of the Metro cinema records the number of people watching each of two films for 25 days.The frequency diagram is for Film A.

The table shows the numbers of people who watched Film B.

Number of people, Film B Frequency

0–99 5

100–199 12

200–299 6

300–399 2

400–499 0

500–599 0

Compare the two distributions. [2]

… and its solutionThe average attendance for Film A was much higher (more people watched Film A). The numbers attending Film A were more varied (the number watching Film B each night was more consistent).

7 Work out these.

a 27 of £19.60 [2]

b 12.5% of £980 [2] 8 Work out these.

a 14 6 12 44. .+ [2]b 14.52 − 12.62 [2]

9 To fly to America, Bernard bought a ticket for £748. He had to pay a surcharge of 2.5%.

How much was the surcharge? [2]10 Work out these.

a 4.7 × 3.9 − 2.6 [1]b (14.6 − 8.6) × 3.5 [1]

c 4 051 5

15 126 3

..

.

.+ [2]

4

Freq

uenc

y 6

8

2

0 200 300Number of people (Film A)

400 500 600100


14 Integers, powers and rootsHere is an exam question …

a Find the HCF and LCM of 12 and 16. [4]b Work out these, writing each answer as a whole

number.i 56 ÷ 54 [1]ii 23 × 25 ÷ 27 [1]iii 62 × 52 ÷ 22 [2]

… and its solutiona 12 = 2 × 2 × 3 16 = 2 × 2 × 2 × 2 HCF = 2 × 2 = 4 LCM = 2 × 2 × 2 × 2 × 3 = 48b i 56 ÷ 54 = 52

= 25 ii 23 × 25 ÷ 27 = 21

= 2 iii 62 × 52 ÷ 22 = 36 × 25 ÷ 4 = 225


1 Harry finds out what types of car his neighbours have and makes a table of his results.

Draw a pie chart to represent this data.

Type of car Frequency

Saloon 18

Hatchback 11

MPV 7

4x4 4

[4]2 The pie chart shows the number of local councillors

in 2008 for the main political parties.

a The Liberal Democrats had 4534 councillors. Approximately how many councillors were ‘Others’? [1]

b Measure the angle that the sector of the pie chart forms for ‘Conservatives’. [1]

c The Conservatives had roughly the same number of councillors as the total for Labour and the Liberal Democrats. Approximately how many councillors did Labour have? [2]

Conservative

Labour

OtherNationalist

LiberalDemocrats

Two 2s are common to both.

Four 2s and one 3 are in at least one of the numbers.

6 − 4 = 2

3 + 5 − 7 = 1

Chief Examiner says

There are different numbers so do not try to collect the indices.


1 Write the following as whole numbers.a 26 [1]b 53 [1]c 45 × 42 ÷ 43 [2]

2 a Write 30 as the product of its primes. [2]b Write down the prime factor of 30 that is

also a prime factor of 21. [1]3 Find the HCF and LCM of 10, 12 and 20. [5]4 Find the value of (−5)2 + 4 × (−3). [2]5 a The area of a square is 49 cm2. Work out the

length of one side of the square. [1]b Work out 43. [1]c If the reciprocal of a number is 2.5, what is

the number? [1]


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Here is an exam question … a Expand the brackets and write this expression as

simply as possible. 2(3x − 4) − 5(x + 3) [4]b Factorise this expression completely. 3a2 + 6ab [2]c For the formula H = 17 − 0.5a, work out the

value of H when a takes each of these values. i a = 12 ii a = −4 [4]d Simplify 2a4 × 4a2. [2]

… and its solutiona 6x − 8 − 5x − 15 = x − 23

b 3a(a + 2b)

c i H = 17 − 6 = 11ii H = 17 − −2 = 19

d 8a6

4 a Multiply out 2(3x + 1). [2]b Factorise completely 12p2 − 15p. [2]

5 Factorise completely 3a2 + 6ab. [2]6 For the formula S = at + bt2, work out the value

of S whena a = 3, b = 2, t = 5. [2]b a = 2, b = 3, t = −4. [2]

16 Statistical diagrams 2Here is an exam question ...

The numbers below list the ages of the members of a tennis club. a Construct a stem-and-leaf diagram with these

ages. [3] Use it to find out the following.b How many members the club has [1]c The modal age of the members [1]d Their median age [1]e The range in their ages [1]f The fraction of members who are veterans

(over or equal to 40) [1]

71 39 40 16 57 12 63 34 41 45 17 52

27 16 59 40 60 14 22 48 43 38 65 16

35 23 25 52 36 38 26 31 27

... and its solutiona Put the data into groups by tens, column by column. This is an unordered stem-and-leaf diagram.

1 6 6 2 4 7 6

2 7 3 5 2 6 7

3 5 9 6 8 4 1 8

4 0 0 8 1 3 5

5 9 2 7 2

6 0 3 5

7 1

Then put each row into order.

Take care with the signs. −5 × +3 = −15

3a is common to both terms.

Multiply the numbers and add the indices.


1 a Write down the perimeter of this rectangle in terms of x, as simply as possible.

[1]b P = ab + b2. Work out the value of P when

a and b take these values.i a = 2 and b = 3 [2]ii a = 4 and b = −5 [2]

2 a Simplify 2a + 3b + 3a − 3b. [2]b Multiply out 3(x + 2y). [2]c Factorise completely 3a + 6ab. [2]

3 Which of these are correct?i 3(5a + 2b) = 35a + 32bii 3(5a + 2b) = 15a + 6biii 3(5a + 2b) = 15a + 2biv 3(5a + 2b) = 8a + 5b [1]

2x

3x


1 2 4 6 6 6 7

2 2 3 5 6 7 7

3 1 4 5 6 8 8 9

4 0 0 1 3 5 8

5 2 2 7 9

6 0 3 5

7 1

Finally add a key.

b 33 c The modal age (age with the highest frequency) is 16.d The median age is 38. e The oldest member is 71 and the youngest is 12, so

the range is 71 − 12 = 59. f There are 14 members aged 40 or more so the

fraction of veterans = 14/33.


1 Mrs Taylor and Mr Ahmed both work for the same company. In 2010 they each recorded the mileage of every journey they made for the company. The mileages for Mrs Taylor’s journeys are summarised in the frequency polygon below.

The mileages for Mr Ahmed’s journeys are summarised in this table.

Mileage (m miles) 0 < m < 10 10 < m < 20 20 < m < 30 30 < m < 40

Frequency 38 44 10 8

a Draw, on the same grid, the frequency polygon for the mileages of Mr Ahmed’s journeys. [2]b Make two comparisons between the mileages of Mrs Taylor’s and Mr Ahmed’s journeys. [2]

2 A class of 33 students sat a mathematics exam. Their results are listed below.

89 78 56 43 92 95 24 72 58 65 55

98 81 72 61 44 48 76 82 91 76 81

74 82 99 21 34 79 64 78 81 73 69

a Draw an ordered stem-and-leaf diagram for this information. [3]b Find the median mark. [1]

3 The table gives information about how much time was spent in a supermarket by 100 shoppers.

Time (t minutes) 0 < t < 10 10 < t < 20 20 < t < 30 30 < t < 40 40 < t < 50

Number of shoppers 6 21 15 33 25

Draw a frequency diagram to represent this information. [4]

0

10

Num

ber o

f jou

rney

s(fr

eque

ncy)

20

30

40

50

10 20 30 40 50Mileage (m miles)

6 3 = 63


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17 Equations 2Here is an exam question …

Solve the following equations.a 2(3 − x) = 1 [3]

b 5 83

6x + = [3]

c 4(x + 7) = 3(2x − 4) [4]

… and its solutiona 2(3 − x) = 1 6 − 2x = 1 −2x = −5

x = 212

b 5 83

6x + =

5x + 8 = 18 5x = 10 x = 2c 4(x + 7) = 3(2x − 4) 4x + 28 = 6x − 12 40 = 2x x = 20

4 Bob and Eddie each collect pebbles from two different places on a beach. They measure the maximum diameter of 20 pebbles they have collected and record the data. All the measurements are in centimetres.

Bob records his measurements in a stem-and-leaf diagram:

1 0

2 0 1 2 2 5 5 7 8

3 0 0 1 1 3 4 7 8 9

4 0 6

Key 1 9 means 1.9 cm

a Write down the range and the median diameter of Bob’s pebbles. [2] Eddie’s pebbles have the following measurements.

1.2 5.5 2.2 2.1 3.4

1.8 4.5 3.2 3.0 1.4

3.3 4.9 2.1 2.1 2.8

4.8 4.2 1.9 3.8 1.1

b Draw a stem-and-leaf diagram for Eddie’s pebbles and find the range and median. [2+2+1]c Compare the two distributions. [2]

5 The numbers below show how many correct answers each person had in a quiz.

23 12 21 24 18 15 20 19 22 21 17 16

9 20 23 21 18 27 25 28 29 23 14 23

21 25 19 23 20 30 24 2 26 13 27 18

a Draw an ordered stem-and-leaf diagram to show this information. [3]b What was the range of the scores? [1]c What was the modal score? [1]


1 Solve these.a 3x = x + 1 [2]b 3p − 4 = p + 8 [3]

c 34m = 9 [2]

2 Solve 3(p − 4) = 36. [3]3 Solve 4(x − 1) = 2x + 3. [3]


18 Ratio and proportionHere is an exam question …

John and Peter did some gardening. They shared the money they were paid in the ratio of the number of hours they worked.John worked for 5 hours. Peter worked for 7 hours. They were paid a total of £28.80.How much did each one receive? [2]

… and its solutionRatio is 5 : 7Total = 12One share = 28.8 ÷ 12 = £2.40John receives 5 × 2.40 = £12Peter receives 7 × 2.40 = £16.80

19 Statistical calculations 2Here is an exam question …

A wedding was attended by 120 guests.The distance, d miles, that each guest travelled was recorded in the frequency table.Calculate an estimate of the mean distance travelled. [5]

Distance (d miles) Number of guests (f)

0 < d < 10 26

10 < d < 20 38

20 < d < 30 20

30 < d < 50 20

50 < d < 100 12

100 < d < 140 4

4 The longer side of a rectangle is 2 cm longer than its shorter side.

Its perimeter is 36 cm. Let x cm be the length of the shorter side.

a Write down an equation in x. [2]b Solve your equation to find x. [2]c Find the area of the rectangle. [1]

5 Solve these equations.a 3x2 = 27 [2]b 4x + 1 = 7 − 2x [3]

Check: £12 + £16.80 = £28.80


1 Some of the very first coins were made with 3 parts silver to 7 parts gold.a How much gold should be mixed with 15 g of

silver in one of these coins? [2]b Another coin made this way has a mass of 20 g.

How much gold does it contain? [2]2 A recipe for rock cakes uses 100 g of mixed fruit

and 250 g of flour. This makes 10 rock cakes. Jason wants to make 25 rock cakes. How much mixed fruit and flour does he need? [2]

3 A car park contains vans and cars. The ratio of the vans to cars is 1 : 6. There are 420 vehicles in the car park. a How many vans are there?b How many cars? [2]

4 Adrian, Penelope and Gladys shared a lottery win in the ratio 2 : 5 : 8.

They won £7000. How much did each receive, correct to the nearest

penny? [3]5 The table shows the prices of different packs of

chocolate bars.

Pack Size Price

Standard 500 g £1.15

Family 750 g £1.59

Special 1.2 kg £2.49

Find which pack is the best value for money. You must show clearly how you decide. [4]


Exam

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Distance (d miles) Number of guests (f) Mid-interval values df

0 < d < 10 26 5 26 × 5 = 130

10 < d < 20 38 15 38 × 15 = 570

20 < d < 30 20 25 20 × 25 = 500

30 < d < 50 20 40 20 × 40 = 800

50 < d < 100 12 75 12 × 75 = 900

100 < d < 140 4 120 4 × 120 = 480

Total 120 3380

Mean = 3380120

= 28.2 miles


1 An orchard contains young apple trees. The 150 apples from the trees were picked and weighed. Their weights are shown in the table opposite.

Calculate an estimate of the mean weight of an apple. [4]

2 FreeTel allows its customers to make free telephone calls at the weekend as long as the call is less than 1 hour long. The table shows the length of calls in minutes that Jessica made in one month.

Find the mean length, in minutes, of the telephone calls that Jessica made.

[5]

3 The frequency table shows the number of weeks’ holiday taken by 90 different families in one year.

a Draw a frequency diagram to show this information. [2]b Find the median number of weeks’ holiday. [1]c Calculate the mean number of weeks’ holiday taken by these families. [3]

Weight (w grams) Number of apples Mid-interval value

50 < w < 60 23 55

60 < w < 70 42

70 < w < 80 50

80 < w < 90 20

90 < w < 100 15

Minutes (m) Frequency

0 < m < 9 23

10 < m < 19 16

20 < m < 29 9

30 < m < 39 17

40 < m < 49 14

50 < m < 59 11

Weeks Frequency

0 2

1 31

2 37

3 16

4 3

5 1


20 Pythagoras’ theoremHere is an exam question ...

a Find the area of this triangle.

b Calculate the length of the hypotenuse of this triangle. Give your answer to a sensible degree of accuracy. [5]


a Area of triangle = 12 base × height

= 12 × 4.6 × 5.0

= 11.5 cm2

b a2 = b2 + c2

= 4.62 + 5.02

= 46.16

a = 46 16. a = 6.8 cm (to 1 d.p.)

4 ‘Doggy Planet’ sell pet goods by post. They record the weight of each package sent by post one day.

Calculate an estimate of the mean weight of a package.

[4]

5 The table shows the number of text messages received by each of 80 people in a single week.

Number of messages received Frequency

1 to 20 12

21 to 40 31

41 to 60 22

61 to 80 11

81 to 100 4

Calculate an estimate of the mean number of messages received per person during the week. [4]

Weight of package (w kg) Frequency

0 < w < 5 6

5 < w < 10 11

10 < w < 15 23

15 < w < 20 8

20 < w < 25 2

5.0 cm

4.6 cm


1 The diagram shows the cross section of the end of a shed.

The shed is 180 cm wide at ED and AC. The length of the roof AB is 110 cm. The height of the side AE is 2 m.

What is the maximum height of the shed? [5]

A C

E D

B


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nitA 21 Planning and

collectingHere is an exam question …

Amy is going to do a survey to find out if people like the new shopping centre in her town. She writes these two questions.a How old are you?b This new shopping centre appears to be a success.

Do you agree?Re-write each question and explain why you would change it. [4]

… and its solutiona The question may be thought to be personal – some

people may not answer. Change to: What is your age? Tick the appropriate box. 10–19 20–29 30–39 40–49 50–59 60+ b This is a leading question. Change to: Do you think the new shopping centre is a success?

Tick the appropriate box. Yes No Don’t know

2

Calculatea BD [2]b AB [2]

3 Find the length of the side marked x.

[3]4 Calculate the length of this ladder.

[3]

5

a Show, by calculation, that angle X is not a right angle. [3]

b Is angle X greater than 90° or less than 90°? Use your calculations from part a to support your decision. [2]

A

B

D

11 cm

5 cm

8 cmC

7.8 cm

9.1 cmx

4.2 m

1.8 m

X

12

10

6

A leading question is one that encourages you to give a particular answer. Amy’s question encourages you to say ‘Yes’.


1 You have been asked to select a small sample of the population of your district in order to find out what leisure facilities should be available locally. Here are three possible methods.a Select at random from the telephone directory.b Ask people leaving the local swimming pool.c Deliver questionnaires to houses near where

you live. In each case, explain why these methods do not

avoid bias. [3] 2 Henry wants to find out about how people exercise.

a In each case say why the question is a bad question and write a better one.A Do you agree that it is good idea to exercise

regularly? Yes No Don’t know [2]B How many hours each week do you exercise? 2–4 6−8 more than 8 [2]


b Now write a question to find out how (where) people mostly do their exercise. [1]

3 Yolande is planning a survey. This is one of the questions she plans to ask.

How much do you expect to pay for a meal out? A: Less than £5 B: About £10 C: A lot more.

a Say what is wrong with the question. [1]b Write a better version of this question. [2]

4 Simon wants to find out what cat food cat owners buy and why.

Write down three questions he could ask. [3]

22 Sequences 2Here is an exam question …

a These are the first four terms of a sequence: 19, 15, 11, 7

i Find the seventh term. [1]ii Explain how you worked out your answer. [1]

b Here is another sequence. 3, 7, 11, 15, ...

i Write down the 10th term for the sequence. [1]ii Write down an expression for the nth term. [1]iii Show that 137 cannot be a term in this

sequence. [1]

… and its solutiona i −5 ii −4 each time.b i 39 ii 4n − 1

iii If 137 is in this sequence then 4n − 1 = 137 4n = 138 n = 138 ÷ 4 n = 34.5 34.5 is not a whole number. Therefore 137 cannot be in the sequence.

23 Constructions 2Here is an exam question …

This is the plan of a garden drawn on a scale of 1 cm to 2 m.

A pond is to be dug in the garden.The pond must be at least 4 m from the tree.It must be at least 3 m from the house.Shade the region where the pond can be dug. Show all your construction lines. [3]

7 − 4 − 4 − 4 = −5

3 + 9 × 4 = 39

The difference between terms is 4, giving 4n. If n = 1, 4n = 4, so you need to subtract 1.

Or, the first term is 3, add 4 (n − 1) times = 3 + 4n − 4 = 4n − 1.


1 a Write down the term-to-term rule of the following sequences.i 7, 13, 19, 25, 31 [1]ii 32, 25, 18, 11, 4 [1]

b Write down the first five terms of the following sequences.i n + 7 [2]ii 5n − 3 [2]

2 The first four terms of a sequence are 3, 8, 13, 18a Find the 20th term. [1]b Find the nth term. [2]

3 The first five terms of a sequence are 1, 3, 6, 10, 15a Find the eighth term. [1]b Is the number 55 one of the terms of this

sequence? Explain how you worked out your answer. [2]

4 a Write down the first five terms of the sequence whose rule is 4n − 1. [2]b Find the i 25th ii 50th term of the sequence. [2]

5 a Write down the term-to-term rule for this sequence of numbers.

25, 19, 13, 7, 1 [1]b Write down the fifteenth term for this sequence

of numbers. 1, 7, 13, 19, 25 [1]

c Write down the nth term for this sequence of numbers.

5, 11, 17, 24, 29 [2]

HouseTree


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nitA … and its solution

At least 4 m from the tree means it is outside a circle radius 2 cm, centre the tree.At least 3 m from the house means it is to the left of a line parallel to the house and 1.5 cm from it.

24 Rearranging formulaeHere is an exam question …

The price of a hand tool of size S cm is P pence.The formula connecting P and S is P = 20 + 12S.a Calculate the price of a hand tool of size 3 cm. [2]b Calculate the size of a hand tool whose price

is 95p. [2]c Rearrange the formula P = 20 + 12S to express S

in terms of P. [3]

… and its solutiona P = 20 + 12 × 3 = 20 + 36 = 56pb 20 + 12S = 95 12S = 75 S = 75 ÷ 12 S = 6.25 cmc P = 20 + 12S P − 20 = 12S

S = P – 2012

House

Scale 1 cm to 2 m

Tree


1 Ashwell and Buxbourne are two towns 50 km apart. Chris is house-hunting. He has decided he would like to live closer to Buxbourne than Ashwell but no further than 30 km from Ashwell.

Using a scale of 1 cm to represent 5 km, construct and shade the area in which Chris should look for a house. [4]

2 Ashad’s garden is a rectangle. He is deciding where to plant a new apple tree.

It must be nearer to the hedge AB than to the house CD. It must be at least 2 m from the fences AC and BD. It must be more than 6 m from corner A.

Shade the region where the tree can be planted. Leave in all your construction lines. Make the scale

of your drawing 1 cm to 2 m. [4]3 A furniture store will deliver purchases according to

the following information.

Free delivery Within 4 miles of the store

£10 Between 4 miles and 7 miles from the store

£25 Over 7 miles from the store

Draw three separate diagrams to show the three delivery areas.

Use a scale of 1 cm to represent 2 miles. [6]

24 m

Fence

Fence

Hedge House

A C

DB

10 m


1 Rearrange each of the following to give d in terms of e.a e = 5d + 3 [2]b e = 4(3d − 7) [3]

2 The pressure in a gas is given by the formula

P kNTV

=

Make k the subject of this formula. [2]3 Rearrange these formulae to make the letter in

the brackets the subject.a T = 25 + 20n (n) [1]b A = 5(a − b) (a) [1]c V = πr2h i (r) ii (h) [3]

1 Working with numbersHere is an exam question …

In a cricket match, England’s two scores were 326 and 397 runs.Australia’s two scores were 425 and 292 runs.a Which team had the higher total score? [3]b How many more runs did they score than the

other team? [2]

… and its solution

a England

326397723

+ Australia

425292717

+

England had the higher score.

b Difference

723717

6–

England’s score was higher by 6 runs.

More exam practice1 Work out these.

a 723 × 41 [3]b 918 ÷ 27 [3]

2 The average weight of a member of England’s rugby scrum was 128.825 kg. Round this toa the nearest whole number. [1]b one decimal place. [1]

3 a Write 572 to the nearest 100. [1]b Write 2449 to the nearest 1000. [1]c Work out 15.7 − 3.9 × 2. [2]

4 On their holidays, Sue and Pam drove 178 miles on the first day and 274 miles on the second day.a How far did they drive in those two days? [2]b How much further did they drive on the

second day? [2]5 Serina goes to a garden centre.

a She buys two bags of fertilizer at £2.27 each and a trowel at £4.56. Work out how much change she gets from a £20 note. [3]

b She later buys 18 packets of seeds at 82p a packet. Work out the total cost of the 18 packets of seeds. Give the answer in pounds. [3]

6 George buys 28 fencing panels for his garden. He pays £133. How much does one panel cost? [3]

7 Netty buys five pizzas for a party. It cost her £17.50. How much would it have cost for three pizzas? [3]

8 Albert is a bricklayer. When building a wall, he laid 138 bricks in 3 hours. If he kept working at the same rate, how many bricks would he lay in 8 hours. [3]

2 Angles, triangles and quadrilateralsHere is an exam question …

a Work out the size of angle A. [1]b Work out the size of angle B. [2] In each case, give reasons for your answer.


1 a John saves 10p each week.How many weeks will it take him to save £5? [1]

b Calculate 86 − 20 ÷ 2. [1]c Calculate 15.7 − (0.6 + 2.4). [1]

2 There are 4.546 09 litres in a gallon.Round 4.546 09 toa 1 decimal place. [1]b 2 decimal places. [1]

3 A theatre has 48 rows of seats. Each row has 31 seats. Work out the number of seats in a theatre. [3]

4 Anston takes part in a long jump competition. These are his four jumps, in metres.

4.58, 5.6, 5.02, 5.74a Write these in order, smallest first. [1]Anston’s personal best jump is 6.05 metres. His friend Salman has a personal best of 5.47 metres.b i Who can jump the furthest? ii By how much? [2]

5 Bella works out that 12 − 2 × 5 = 10 × 5 = 50 Explain why this is wrong [1] 34° A

B

23© Hodder Education 2011 Unit B


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The two diagonal lines on the sloping sides of the triangle tell you it is an isosceles triangle. The two marked sides are of equal length and the two angles at the end of these lines are equal.a As the two base angles are equal, angle A is 34°.b The sum of the angles in a triangle is 180°.

The sum of the two base angles is 34 + 34 = 68°.180 − 68 = 112 so angle B is 112º.

3 FractionsHere is an exam question …

Anna, Ben and Chris have 200 raffle tickets to sell.

Anna sells 15 of the tickets.

Ben sells 38 of the tickets.

Chris sells the rest.a How many raffle tickets does Chris sell? [5]b What fraction of the tickets does Chris sell?

Give your answer in its simplest form. [2]

… and its solutiona Anna sells 1

5 × 200 = 40

Ben sells 38 × 200

= 75Chris sells 200 − 40 − 75 = 85

b Fraction = 85200

=1740

Here is another exam question …a Convert 3

8 to a decimal. [2]b Add 3

8 and 15, giving your answer as a decimal. [3]


a )8 3 0 0 00 3756 4..

= 0.375

b 15 = 0.2

0.375 + 0.2 = 0.575


1 Name these shapes.a b

c

[1 + 1 + 1]2 a Sketch a rhombus and mark everything that is

equal.b Draw in all the lines of symmetry. [3]

3 In this trapezium, angle A is a right-angle.

a Which angle is obtuse?b Which sides are parallel?c Name two sides which are perpendicular. [3]

4 A quadrilateral has opposite sides which are parallel and diagonals which are not equal but bisect at 90°.a Make a sketch of this quadrilateral. [1]b Write down the name of this quadrilateral. [1]

5 a Work out the sizes of the angles in this triangle. [3]

b What type of triangle is this? [1]

A B

D C

37°

Not to scale

* + 37°

*°

Chief Examiner says

Divide numerator and denominator by 5.


1

a What fraction of this shape is shaded? [1]

b Shade some more squares so that 35 is now shaded. [1]

2

a What fraction of the shape is shaded? [1]b What fraction of the shape is not shaded? [1]

c Shade some more squares so that 58 of the

shape is shaded. [1]


More exam practice

1 Ordinary marmalade is 35 sugar. What mass of sugar is there in a 340 g jar of

marmalade. [2]2 In a hockey tournament, the Allstars had 48 corners.

They scored from 58 of them. How many corners did

they score from? [2]3 Jane buys a 3 metre piece of wood.

She cuts off 14 of it. How many centimetres of wood has she cut off? [2]4 Put these fractions in order of size, smallest first.

56

14

512

38, , , [2]

5 Which of the following fractions are equal to 23?

610

461015

4932, , , , [2]

4 Solving problemsHere is an exam question …

Three friends had a meal together. They had three ‘Chef’s specials’ at £8.99 each, two drinks at £1.45 each, one drink at £1.75 and two puddings at £2.49 each. They agreed to share the bill equally. How much did each friend pay? Write down your calculations. [4]

… and its solution3 × 8.99 = 26.972 × 1.45 = 2.901 × 1.75 = 1.752 × 2.49 = 4.98 Total = 36.60Each paid £36.60 ÷ 3 = £12.20

More exam practice1 Each week, Stephen earns £9.20 from his paper

round. His father gives him £10 and his grandma gives him £3.50. How much does he get altogether? [2]

2 Heather has to take two 5 ml teaspoons of medicine three times a day. She has a 300 ml bottle. How long will it last? [2]

3 These are some of the programmes on television on Sunday night.

5.40 p.m. Songs of Praise 6.15 p.m. When love comes in 6.45 p.m. Antiques Roadshow 7.35 p.m. News 8.00 p.m. Rough Diamond

David wants to record the Antique Roadshow.a What time does it start in the 24-hour clock? [1]b How long is the programme? [1]

4 To buy a lawn mower you can pay £120 cash or a deposit of £40 and £2.40 a week for 38 weeks. How much extra do you have to pay if you do so over 38 weeks? [3]

5 Mr and Mrs Davies have to catch an aeroplane at 15:30. They need to be at the airport at least 2 hours before the flight. The journey to the airport takes 1 hour 15 minutes. What is the latest time they can leave home to get to the airport on time? [3]

6 A footballer was paid £750 000 for playing a 90 minute game. How much was this a minute? Give the answer to the nearest penny. [3]

7 A company packs magazines ready for dispatch. They charge £60 plus £14 for every 100 magazines. One client paid £760 to have some magazines packed. How many magazines were packed? [3]

8 A sliced loaf is 24 cm long. Each slice is 8 mm thick. How many slices are there in the loaf? [2]


1 Bert went to the theatre. The show started at 7.30 p.m. The first act was 1 hour 10 minutes long, the interval lasted 25 minutes and the second act was 50 minutes long. What time did the show finish? [3]

2 a A train left Ashton at 11:34 and arrived at Stockdale at 13:22. How long did the journey take? [1]b The train remained at Stockdale for 8 minutes

and then continued to Deverton. The journey to Deverton took 1 hour 15 minutes. What time did the train arrive at Deverton? [2]

3 A supermarket offered bottles of elderflower cordial at 3 for the price of 2. The normal price was 67p for each bottle. How much did it work out per bottle with the special offer? Give the answer to the nearest penny? [3]


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Here is an exam question …

a i Work out the size of angle x. ii Complete this statement for angle x. The angles on a straight line …………………… . [3]b i Work out the size of angle y. ii Complete this statement for angle y. Opposite angles ……..………………………… . [2]

… and its solutiona i 180 − (62 + 45) = 73º ii …add to 180º.b i 45º ii …are equal.

6 Fractions and mixed numbersHere is an exam question …

a Work out 37 of 35 kilograms. [2]

b Which is the greater, 23 or 13

20 of an amount? [2]

45°62° x

y


1 Find the size of each of the angles marked a, b, c. In each case give a reason for your answer.

[3]2 Calculate the angles marked with letters. Explain

your reasoning.

[5]

66°

47°

ba

c

118°64°a d

c b e

3

In the diagram ABC is a straight line. AB is parallel to DE. BD = BA.

Find the value ofa x [1]b y [1]c z [2]

In each case, give a reason for your answer.4 Four lines meet at a point, as shown in the diagram.

Find the value of p. [2]5 Work out the size of the angles x, y and z in these

diagrams. Give reasons for your answers.

[6]

AB

C

D E

z ° x °

y °

136°

98°146°

pp

50° x112° 125°

y

135°z



a 37 of 35 kg = 3

7 × 35 = 15 kg

b 23

4060= , 13

203960=

2

3 is the greater.

More exam practice1 Work out these, giving your answers as fractions, as

simply as possible.

a 1 214

35+ [3]

b 35

49× [2]

2 Work out these.

a 4 2316

12– [3]

b 310

415÷ [2]

3 These are the lengths of four nails in inches.

1 1 1 112

716

14

38, , ,

Put them in order, smallest first. [2]4 Work out these.

a 45

59× [2]

b 38 6÷ [2]

7 Circles and polygonsHere is an exam question …

From the six words below, pick the correct one for each label on the diagram.

Diameter TangentArcChordRadiusCircumference

[3]

… and its solutiona Tangentb Arcc Diameterd Chord

Change both fractions to the same denominator.


1 Work out the following, giving your answers as simply as possible.

a 2345+ [2]

b 35

56× [2]

2 Put these fractions in order of size, smallest first.

34

710

3558, , , [2]

3 Work out these, giving your answers as simply as possible.

a 2 138

12– [3]

b 2345÷ [2]

4 A piece of metal is 2 14 inches long. Stuart cuts

off 716 of an inch. How much is left? [3]

a)

b)

c)

d)


1 A weighing machine has a dial which shows up to 5 kilograms.

a Explain how you can work out that the arrow turns through 72° for 1 kilogram. [1]

b On a copy of the diagram, mark accurately 1, 2, 3, 4 kg round the dial. [1]

c Draw accurately a line from the centre to show a weight of 3.5 kilograms. [1]

2 a How many sides does a quadrilateral have?b A polygon has five sides. What is its name? [2]

3 Draw a circle of radius 4 cm. On your circle, mark and label each of these.a An arcb A radiusc A tangent [3]

0

5 kg


Exam

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nitB More exam practice

1

a Find the size of angle a.b What type of triangle is ABC?c Find the size of angle b. [3]

2

Find the size of x and y. Give reasons for your answers. [4]

3 Here is a sketch of a regular pentagon, centre O.

a Work out x.b What type of triangle is OAB?c Draw a circle of radius 5 cm and construct

a regular pentagon with its vertices on the circle. [5]

4 The interior angle of a regular polygon is 168°. Find the number of sides of the polygon. [3]

8 Powers and indicesHere is an exam question …

a Expand the brackets and write this expression as simply as possible. 2(3x − 4) − 5 (x + 3) [4]

b Factorise this expression completely. 3a2 + 6ab [2]c For the formula H = 17 − 0.5a, work out the value

of H when a takes each of these values.i a = 12 ii a = −4 [4]

d Simplify 2a4 × 4a2. [2]

... and its solutiona 6x − 8 − 5x − 15 = x − 23

b 3a(a + 2b)

c i H = 17 − 6 = 11 ii H = 17 − −2 = 19d 8a6

9 Decimals and fractionsHere is an exam question ...

a Write the following decimals as fractions. i 0.2 ii 0.375 [3]b Find the sum of your fractions in part a.

Give your answer as a fraction. [3]

60°

40°

60°60°

A

B

D

C

ab

34°

x y

x

A

O

B

Take care with the signs. −5 × +3 = −15

3a is common to both terms.

Mulitply the numbers and add the indices.


1 Which of these are correct?i p3 = p × 3ii p3 = p + p + piii p3 = p × p × piv p3 = p2 + p [1]

2 Simplify these.a x4y3 × x3y2 [2]b 3x2y3 × 2xy2 [2]

3 a Explain how you know that 28 is about 5.3. [1]

b Estimate the value of 95 [1]4 a Work out.

i 173

ii 1225 [1 + 1]b Simplify.

i 87 ÷ 84

ii 3 33

7 5

6× [1 + 1]

5 a Put a circle round the term which is equal to r × r × r × r × r 5r r + 5 r5 r5 [1]

b Work out 7293 [1]



a i 15

ii 3751000

38

b 15

38+ = 0.2 + 0.375 = 0.575

Converting this to a fraction = 5751000

= 2340

10 Real-life graphsHere is an exam question …

The weight (T tonnes) of coal and its volume (V cubic metres) are related.100 m3 of coal weighs 600 tonnes.a Draw a conversion graph for volume (V) and

weight (T ). [3]b Use your graph to find i the weight of 25 m3 of coal. [1] ii the volume of 200 tonnes of coal. [1]c Use this information to estimate the volume of

1000 tonnes of coal. [1]


b i 150 tonnes ii About 33 m3

c About 167 m3

Divide numerator and denominator by 125, that is by 5 and by 5 and by 5.

Divide numerator and denominator by 25.


1 Write each of the following fractions as a decimal.a 2

5 b 29 [3]

2 a Work out 25 + 1

3 [2]

b Convert 25 and 1

3 to decimals and add them. [2]c What do the answers to parts a and b show? [1]

3 Using 0.1. = 1

9 , 0.0. 1. = 1

99, 0.0. 01

. = 1

999

write these decimals as fractions in their simplest terms.a 0.5

. [1]

b 0.5. 6. [1]

c 0.6. 12

. [2]

4 Convert these decimals into fractions.Write your answers in their lowest terms.a 0.55 [2]b 0.036 [2]c 0.2246 [2]

5 a Write these numbers in order, smallest first. 3.3 0.303 0.33 3.03 [2]b Write down a decimal which is between

0.207 and 0.27. [1]

400

Wei

ght

(T to

nnes

)

600

200300

500

100

0 20 40Volume (V m3)

60 80 10010 30

(i)(ii)

50 70 90

Draw a straight line from (0, 0) to (100, 600).

If the volume of coal is zero, weight will be zero.


1 The table below shows the distance in kilometres a car travels in given times (in hours).

Time (h) 0 1 2 3 4

Distance (km) 0 70 140 210 280

a i Draw a pair of axes. Put time on the horizontal axis using a scale of 2 cm to 1 hour. Put distance on the vertical axis using a scale of 2 cm to 50 km. [1]

ii Plot the points (0, 0) and (4, 280) and join them with a straight line. [1]

b Find the distance travelled after i 1.5 h. [1] ii 3.5 h. [1]c Find the time taken to travel i 100 km. [1] ii 250 km. [1]

2 This conversion graph is for pounds (£) and Australian dollars (AU$), for amounts up to £100.

100

Aus

tralia

n do

llars

(AU

$) 150

200

250

50

0 20 40Pounds (£)

60 80 10010 30 50 70 90


Exam

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1 The table shows the number of litres of fuel left after a car has travelled a certain number of kilometres.

Distance travelled (km) 0 50 100 200

Fuel left (litres) 50 45 40 30

a i Draw a pair of axes. Put distance on the horizontal axis, using a scale of 1 cm to 50 km. Put fuel left on the vertical axis, using a scale of 2 cm to 10 litres. [1]

ii Plot the points from the table and join them with a straight line. [1]

b Find the fuel left after travelling 75 km. [1]c Find the distance travelled when there is 35 litres

of fuel left. [1]d If the car continued travelling at the same rate

until it ran out of fuel, how far would it have travelled? [1]

2 This conversion graph is for pounds (£) to Hong Kong dollars (HK$), for amounts up to £50.

a Use the graph to find the number of Hong Kong dollars equal to

i £15. [1] ii £40. [1]b Use the graph to find the number of pounds

equal to i HK$400. [1] ii HK$75. [1]

a Use the graph to find the number of Australian dollars equal to

i £20. [1] ii £85. [1]b Use the graph to find the number of pounds

equal to i AU$100. [1] ii AU$175. [1]

3 Gayla records the temperature in the school garden every hour. Here is a graph showing some of her results on a particular day. She forgot to take the temperature at 4 p.m.

a At what time was the highest temperature recorded? [1]

b Estimate when the temperature was first 9 °C. [1]c The temperature fell steadily between 3 p.m. and

5 p.m. Estimate the temperature at 4 p.m. [1]4 Jim went out walking. In the diagram ABCD represents his walk.

a How far had Jim walked after 112 hours? [1]

b What does the part of the graph BC represent? [1]c After walking 9 km, Jim turned round and walked

straight back to his starting place without stopping. It took him 2 hours to get back.

Draw a line on a copy of the grid to show this. [2]d Work out his average speed on the return

journey. [2]

8

Tem

pera

ture

(°C

)

12

16

20

46

10

14

18

2

0 10 12

Time

a.m. p.m.noon

2 4 69 11 1 3 5

4

6789

10

Dist

ance

from

sta

rt (k

m)

23

5

1

0 2 3Time (hours)

4 5 61

BC

D

A

100

200

300

400

500

600

700

0 10 20 30Pounds (£)

Hon

g Ko

ng d

olla

rs (H

K$)

40 50


3 100 pints is approximately 55 litres.a i Draw a pair of axes. Put pints on the horizontal axis, using a scale of 1 cm to 10 pints. Put litres on the

vertical axis, using a scale of 1 cm to 5 litres. [1] ii Join the points (0, 0) and (100, 55). [1]b Use the graph to find the number of litres equal to i 20 pints. [1] ii 70 pints. [1]c Use the graph to find the number of pints equal to i 5 litres. [1] ii 35 litres. [1]

4 The temperature in the Namib Desert was measured every two hours through a 24 hour period. The results are shown on the line graph and in the table.

Time 2000 2200 2400

Temperature (°C) 18 3 −8

a Plot the three points from the table and complete the graph. [1]b i What was the highest temperature recorded? [1] ii What was the lowest temperature recorded? [1]c Work out the difference between the highest and lowest recorded temperatures. [2]d Estimate the temperature at 0700 on the day that these temperatures were taken. [1]e Estimate for how long the temperature was above 30°C on that day. [1]

5 This graph is used for converting degrees Celsius (°C) to degrees Fahrenheit (°F).

Use the graph to changea 30 °C to °F b 115 °F to °C. [2]

�20

�10

0

10

20

30

40

Time

Tem

pera

ture

(°C

)

0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200 2400

50

100

150

0 20 40 60 °C

°F


Exam

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6 This graph can be used to convert distances in miles to distances in kilometres.

Use the graph to changea 20 miles to kilometres.b 100 kilometres to miles.

7 This graph can be used to calculate the fare for a taxi ride.

Use the graph to finda the cost of a 16 mile taxi ride.b how far you could travel for £10.

8 Draw a pair of axes. Put gallons on the horizontal axis, using a scale of 1 cm to 2 gallons, up to 20 gallons. Put litres on the verical axis, using a scale of 1 cm to 10 litres, up to 100 litres. Draw a solid line from (0, 0) to (20, 90).

Use your graph to converta 5 gallons to litres.b 75 litres to gallons.

9 Draw a pair of axes. Put kilograms on the horizontal axis, using a scale of 1 cm to 5 kilograms, up to 50 kilograms. Put pounds on the vertical axis, using a scale of 1 cm to 10 pounds, up to 120 pounds. Draw a solid line from (0, 0) to (50, 110).

Use your graph to converta 5 kilograms to pounds.b 75 pounds to kilograms.

11 ReflectionHere is an exam question …

a Describe the transformation that mapsi B on to D ii A on to Ciii D on to E iv C on to D. [4]

b Explain why A does not map on to E using the transformation in part iv. [1]

… and its solutiona i Reflection in y = 3 ii Reflection in x = −1

iii Reflection in y = −12 iv Reflection in y = x

b E is closer to the line.

50

100

150

200

0 20 40 60Miles

Kilo

met

res

80 100

10

20

30

40

50

0 4 8 12Distance (miles)

Cos

t (£)

16 202 6 10 14 18

�5�4�3�2�1

12345y

x�5�4�3�2�1 10 2 3 4 5

A CB

D

E


1 Draw the image of shape A after reflection in the mirror line.

[2]

Mirror line

A


12 PercentagesHere is an exam question …

A school has 900 students. 42% of the students are boys.a What percentage of the students are girls? [1]b What fraction of the students are boys? [1]c 12% of the students are in year 11. How many students are in year 11? [2]

… and its solutiona 58% are girls

b 42% = 42100 = 21

50 c 0.12 × 900 = 108

2

a Reflect triangle A in the y axis. Label your triangle B. [2]

b Reflect triangle A in the line y = 1. Label your triangle C. [2]

3

The end of the prism in the diagram is an equilateral triangle.How many of planes of symmetry does the prism have? [1]

4 Complete the pattern so that the horizontal and vertical lines are lines of reflection.

[4]

5 a

Shade 1 more square to give the shape 2 lines of reflection symmetry. [1]

0 1–1–2–3–4–5–6–7 2 3 4 5 6 7 x

1

–1–2–3–4–5–6–7

2345

A

67y

b

Copy the diagram above and then draw on it all the lines of reflection symmetry. [1]

42 + 58 = 100

Cancel by 2.

12 × 900 = 10 800 and there are two figures after the decimal point, giving 108.00 = 108.


1 a Shade 75% of this shape. [1]

b Write 60%i as a decimal.ii as a fraction. [2]

2 List the following numbers in order, starting with the smallest.

66%, 35 , 0.62, 0.59, 55% [3]


Exam

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More exam practice1 Write each of these as a percentage.

a 0.06 [1]

b 25 [1]

2 When John booked his holiday he had to pay a deposit of 5%. The holiday cost £840. How much deposit did he have to pay? [2]

3 In a sale all the items were priced at 80% of the usual price. A skirt’s usual price was £45. What was it in the sale? [2]

4 The Candle Theatre has 320 seats. At one performance 271 seats were occupied.

What percentage of the seats was occupied? Give the answer correct to 2 decimal places. [2 + 1]

5 Mobina cut 90 cm off a piece of wood 2.5 m long. What percentage of the wood was left? [3]

6 Sarah earns £34 720 a year. After deductions she receives £26 734.40. What percentage was deducted from her pay? [3]

7 Joe bought a plane ticket for £570. Because he paid by credit card, a 1.5% charge was added to his bill. How much did he have to pay in total? [3]

13 RotationRotationsymmetry

Recognisinganddescribingrotations

Here is an exam question …a Triangle T is rotated 180° clockwise about the

point (0, 0). Its image is triangle R. Draw and label triangle R. [2]

b Triangle R is reflected in the y-axis. Its image is triangle S. Draw and label triangle S. [1]

c Describe the single transformation which would map triangle T on to Triangle S.

[3]

… and its solutionaandb

c Reflection in the x-axis.

3 In Year 11 of St Marie’s school there are 140 students. 15% of them study French. How many students in year 11 study French? [2]

4 Amanda receives an annual salary of £15 000. She pays 8% into a pension fund. How much does she pay into the pension fund? [2]

5 There are 630 people on a cruise. Of these, 67% are over 65. How many of them are over 65? [2]

6 At a football match, 68% of the spectators are male. Explain how you know that 32% are female. [1]

Try this exam question

For each of these shapes, statea how many lines of symmetry it has.b its order of rotational symmetry.

[4]

�4

�2

2

4y

x�4 �2 0 2 4

T

�4

�2

2

4y

x�4 �2 0 2 4

T

SR


1 Which two of these shapes are congruent?

[1]

A

D

G H

E F

B

C


14 EstimationHere is an exam question ...

Use estimation techniques to show that these sums are incorrect.

a 53 73 0 09719 4

2 6865. ..

.× = [2]

b 23.815 ÷ 0.85 = 20.242 75 [2]

... and its solutiona Rounding each number to 1 sf we get

50 0 120

520

0 25× = =. .

The answer is ten times this estimate and so is incorrect, the actual answer is probably 0.268 65.

b Dividing 23.815 by a number less than 1 should lead to an answer larger than 23.815 and as it is not then this answer is incorrect.

15 EnlargementHere is an exam question ...

Find the centre of enlargement and the scale factor for the transformation that maps the smaller rectangle on to the larger one. [3]

.

2 The diagram shows shapes A and B.

Describe fully the single transformation that maps shape A on to shape B.

3

a Describe fully the single transformation that maps triangle A on to triangle B. [2]

b Rotate triangle C through 90° clockwise about (−4, −1). Label the image D. [2]

�2�3

�1

21

3y

x�2�3 �10 2

A

B

1 3

�5�4�3�2�1

12345y

x�5�4�3�2�1 10 2

AC B

3 4 5


1 Use estimation techniques to show that these sums are incorrect.a 0.382 × 18.6 = 26.8584 [2]b 24.608 ÷ 1.2 = 25.5296 [2]

c 84 4567 824 4 6

16 8.. .

.+ = [2]

2 Look at these equations.Without doing any calculation, explain for each equation how you can tell that it is wrong.

a 14.67 × 0.247 = 36.2349

b 1 125

34

120÷ =

c −6.3 × −2.4 ÷ −1.5 = 10.08 [3]3 Estimate the answer to this calculation.

8 9350 017 6 914

.. .×

Show all the values you use and give your answer to 1 significant figure. [3]

4 The average weight of a member of England’s rugby scrum was 128.825 kg. Round this toa the nearest whole number. [1]b one decimal place. [1]

5 Francis has £45 to spend at the garden centre. He wants to buy a bird table costing £23.85 and six bags of birdseed costing £2.95 each. Show how he can work out in his head that £45 will be enough. Do not work out the exact amount. [2]

0 2 4 6 8 10 12 14 16 18 x

2468

101214

y


Exam

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nitB .. and its solution

The scale factor is 3, as you can see from comparing the lengths of sides of the smaller and larger rectangles.The lines drawn through corresponding points gives the centre of enlargement as (2, 3).

0 2 4 6 8 10 12 14 16 18 x

2468

101214

y


1 The diagram shows shape A.

Draw the shape A after an enlargement with centre (0, 0) and scale factor 3. Label the image B. Note that you will need an x-axis from −5 to 10 and a y-axis from −5 to 8. [3]

2 The diagram shows the shapes A and B and the line L.

a Shape B is an enlargement of shape A. For this enlargement, find

i the scale factor. ii the coordinates of the centre of enlargement.b Draw the image of shape B after reflection in

the line L. Note that you will need x- and y-axes from −7 to 7. [4]

�2�3

�1

21

3y

x�2�3 �10 2

A

1 3

4L

A

B567

23

1

�1�2

0 4 5 x

y

2 31�1�3�2�4

3 For this diagram, describe fully the single transformation that maps trapezium Q on to trapezium R. [3]

4

Find the centre and scale factor of the enlargement that maps shape A on to shape B. [3]

5

Rectangle B is an enlargement of rectangle A.Complete these statements.

a The scale factor of the enlargement is

……………… [1]

b The centre of the enlargement is

…………………… [2]c The area of rectangle B is ……….. times the

area of rectangle A. [2]

d The perimeter of rectangle B is ……….. times the perimeter of rectangle A. [2]

4

23

1

�1�2

0 4 5 6 x

y

2 3

RQ

1�1�2

4

2

0 4

A B

6 x

y

2�2

0 1–1–2–3–4 2 3 4 5 6 7 x

1

–1–2–3–4

2345

A

B

67

y

89

10

8 9 10 11


16 Scatter diagrams and time seriesHere is an exam question ...

This table shows the hours of sunshine during the day and the number of bikes hired out by a bike hire firm over a 10-day period.

Hours of sunshine 6 1 7 8 10 2 9 4 9 5

Bikes hired out 25 5 26 7 35 10 22 14 30 18

a Draw a scatter diagram to show this information. [2]b Describe the correlation shown in the scatter diagram. [1]c Draw a line of best fit on your diagram. [1]d Use your line of best fit to estimate how many bikes would be hired when there were 3 hours of sunshine. [1]

... and its solutionaandc

b Positive correlationd About 12 bikes

2 4 6 8 10 12Hours of sunshine

0

10Num

ber o

f bik

es h

ired

20

30

40

5

15

25

35

Exam Tip

Make sure your line is close to most of the points and that there are roughly the same number on each side of the line.

Exam Tip

Always show your working for part d. Even if your line of best fit is not correct you can still gain the marks for knowing (and showing the examiner) how to use it.


Exam

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nitB Now try these exam questions

1 The table shows the amount of coal used in blast furnaces and the iron produced in the years before the Second World War.

Year Coal used (million tons) Iron produced (million tons)

1929 14.5 7.6

1930 11.7 6.2

1931 7.1 3.8

1932 6.5 3.6

1933 7.4 4.1

1934 10.5 6.0

1935 10.8 6.4

1936 12.8 7.7

1937 14.8 8.5

1938 11.6 6.8

a Plot these data on a scatter graph. [3]

b Draw a line of best fit. [1]c i How much iron would you expect to be produced using 15 million tons of coal? [1] ii Why would it be unwise to use the graph to predict values for 1947? [1]

2 The table shows data about cinemas in 10 towns, all approximately the same size.

Number of screens 16 13 19 12 19 21 18 15 20 16

Weekly admissions (thousands)

9.5 7.8 11.0 7.3 12.4 12.3 9.8 7.7 11.5 8.5

86 10 12 14 16Coal used (million tons)

5

Iron

prod

uced

(mill

ion

tons

)

7

4

3

6

8

9


a Complete the scatter diagram. (The first 5 points have been plotted for you.) [2]

b Describe the correlation shown in the scatter diagram [1]c Draw a line of best fit. [1]d A new cinema is to be built in another town. It is to have 17 screens. Estimate the weekly audience. [1]

3 The table shows the daily audiences for three weeks at a cinema.

Mon Tue Wed Thu Fri Sat

Week 1 268 325 331 456 600 570

Week 2 287 359 391 502 600 600

Week 3 246 310 332 495 565 582

a Plot these figures in a graph. Use a scale of 1 cm to each day on the horizontal axis and 2 cm to 100 people on the vertical axis. You will need to have your graph paper ‘long ways’. [3]

b Comment on the general trend and the daily variation. [2]4 An orchard contains nine young apple trees. The table shows the height of each tree and the number of

apples on each.

Height (m) 1.5 1.9 1.6 2.2 2.1 1.3 2.6 2.1 1.4

Number of apples 12 15 20 17 20 8 26 22 10

a Draw a scatter graph to illustrate this information. Use a scale of 2 cm to 1 m on the horizontal axis and 2 cm to 10 apples on the vertical axis. [4]

b Comment briefly on the relationship between the height of the trees and the number of apples on the trees. [1]

c Add a line of best fit to your scatter graph. [1]d Explain why it is not reasonable to use this line to estimate the number of apples on a tree of similar type

but of height 4 m. [1]

1210 14 16 18 20 22Number of screens

8

Wee

kly

adm

issio

ns (t

hous

ands

)

9

10

11

12

13

7


Exam

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17 Straight lines and inequalitiesStraight-linegraphs

Here is an exam question …a i On the same grid, draw the graphs of

x + 2y = 4 and y = 2x − 3. [4] ii What are the values of x and y for which

x + 2y = 4 and y = 2x − 3?b Find the gradient of the straight line in the diagram.

[2]

… and its solutiona i

ii x = 2 and y = 1 (the coordinates of the point where the lines meet).

b Gradient = 34

More exam practice1 a Draw the graph of y = 3x − 1. [2]

b i Write down the gradient of the line. [1] ii Write down the equation of a line parallel

to y = 3x − 1. [1]2 Work out the gradient of this line. [2]

3 A line has the equation y = 7x + 3.a Write down the gradient of the line. [1]b Write down the equation of a line parallel to

y = 7x + 3. [1]

5 The table shows a company’s quarterly sales of umbrellas in the years 2007 to 2010. The figures are in thousands of pounds.

1st quarter 2nd quarter 3rd quarter 4th quarter

2007 153 120 62 133

2008 131 105 71 107

2009 114 110 57 96

2010 109 92 46 81

Plot these figures on a graph. Use a scale of 1 cm to each quarter on the horizontal axis and 2 cm to 20 thousand pounds on the vertical axis. [3]

�1

12345 (4, 5)

y

x10�1�2 2 3 4 5

1

�1

�2

�3

2y

y � 2x � 3

x � 2y � 4

x10 2 3 4


1 The three points A, B and C are joined to form a triangle. A is (2, 1), B is (14, −2) and C is (3, 7). Work out the coordinates of the midpoint ofa side AC. [2]b side AB. [2]

2 Write down the gradient of the line with equation y = 2x − 4. [1]

1

�1

2345y

x10

2 3


Inequalities

Here is an exam question …a Describe the inequality shown on these number

lines. i [1]

ii

[1]

b Solve the inequality 5x 3x + 8. [2]

… and its solutiona i 1 x 6 ii −2 x 3b 5x 3x + 8 2x 8

x 4

18 Congruence and transformationsHere is an exam question …

a Reflect shape A in the y-axis. Label the image B.b Reflect shape B in the line x = 3. Label the image C. [4]


Graphicalsolutionofsimultaneousequations

Now try this exam question

1 Solve these simultaneous equations graphically. y = 3x + 4 x + y = 2 [4]

0 1 2 3 4 5 6

�3 �2 �1 0 1 2 3 4


1 a Solve these inequalities.i 2x x + 7 [1]ii 5x 2x − 6 [2]

b Show the answers to part a on number lines. [1+2]

2 Solve these inequalities.a 8x + 5 25 [2]b 2x + 9 4x [2]

3 Solve the inequality −6 5x − 1 9. [3]4 Find all the integers that satisfy 5 2x + 1 15. [3]

4

2

�2

0 4 6 8 10 x

y

2

A

�2

�2

2

4y

x

x � 3

�2 0 2 4 6 8

CAB

10


Exam

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nitB Now try these exam questions

1 Which of these pairs of triangles are congruent?A B

C D

E F

G H

[3]2 The grid shows the position of shape A.

a Reflect shape A in the y-axis. Label the image B. [1]

b Rotate shape A 180° clockwise about the origin. Label the image C. [2]

c Describe the single transformation that maps shape B on to shape C. [1]

3 Which two of the triangles A, B, C and D are congruent to triangle X?

Explain why you chose these triangles.

NOT TO SCALE [4]4

a Reflect triangle A in the line x = 3. Label the image B. [2]

b Translate triangle A by 3

4–

Label the image C. [2]

0 1–1–2–3–4–5–6–7 2 3 4 5 6 7 x

1

–1–2–3–4–5–6–7

2345

A

67y

X

A

CD

67°

67°

67°

63°

70°

70°

70°43°

43°

43°

2.5 cm

2.5 cm

2.5 cm

2.5 cm

2.5 cm

B

�5�4�3�2�1

12345y

x�5�4�3�2�1 10 2

A

3 4 5

1 Two-dimensional representation of solidsHere is an exam question ...

The diagram represents a toilet roll.

a Draw a full-size accurate side elevation of the toilet roll. [2]b Draw a full-size accurate plan view of the toilet roll. [2]

... and its solutiona

6 cm12 cm

11 cm

43© Hodder Education 2011 Unit C


Exam

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1 This sweet box is in the shape of a prism. The base is an isosceles right-angled triangle.

Construct the net of the box. [4]2 a How many faces does this L-shaped prism have?

b How many vertices does it have?c Make an isometric drawing of this prism. [6]

3 Sketch the plan (P) and side elevation (S) of this shape. [3]

5.2 cm

7.4 cm

3 cm

3 cm

2 cm

2 cm1 cm

1 cm

P

S


More exam practice1 The diagram shows the net of a box.

Draw a sketch of the box. Mark on its length, width and height.

2 Draw a full-size net for a cuboid with length 4 cm, width 2 cm and height 3 cm. [3]

3 This shape is made from five centimetre cubes.

Make an isometric drawing of the shape. [3]

2 Probability 1Calculatingprobabilities

Here is an exam question …A compact disc player selects tracks at random from those to be played.a A disc has 9 tracks on it. The tracks are numbered 1,

2, 3, 4, 5, 6, 7, 8 and 9. What is the probability that the number of the first

track played is i 5? [1] ii 10? [1] iii a multiple of 4? [1]b Another disc has three tracks on it. The tracks are

numbered 1, 2 and 3. i List the different orders in which the tracks

can be played. Two have been done for you. 1, 2, 3 1, 3, 2 [2] ii What is the probability that the tracks are

not played in the order 1, 2, 3? [1]


a i 19

ii 0

iii 29

b i 1, 2, 3 1, 3, 2 2, 1, 3 2, 3, 1 3, 1, 2 3, 2, 1

ii 56

3 cm

2 cm 2 cm

2 cm 2 cm 2 cm2 cm

2 cm

8 cm

8 cm

8 cm

8 cm2 cm

3 cm

4 and 8 are both multiples of 4.

There are six ways of playing the three tracks.


1 Here is a fair spinner used in a game.

The score is the number where the arrow stops. Helen spins the spinner once.

a What score is she most likely to get? [1]b Mark with a cross (), on the scale below, the

probability that she gets a score of less than four. Explain your answer. [2]

c Mark with a cross (), on the scale below, the probability that she gets an even number score. Explain your answer. [2]

2 A manufacturer makes flags with three stripes.a Find all the different flags which can be made

using each of the colours amber (A), blue (B) and cream (C). The first one has been done already. [2]

b One of each of the different flags is stored in a box. Alan takes one out at random. What is the probability that its middle colour is blue? [2]

48

5

4

7

46

6

0 1

0 1

A

B

C


Exam

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nitC More exam practice

1 Choose the most appropriate word from this list to describe each of the events below.

Impossible Very unlikely Unlikely EvensLikely Very Likely Certain

a Valentine’s day will be on February 14 next year. [1]

b The next child born at the local hospital will be a boy. [1]

c The temperature in London will be above 30 °C every day in July. [1]

d February will have 30 days next year. [1]2 Lynn buys a bag of 20 sweets for Joseph. The bag

contains 1 orange, 3 white, 4 yellow, 5 green and 7 red sweets. Joseph takes one sweet out of the bag without looking. What is the probability that the sweet isa green? [1]b yellow or white? [1]c not green? [1]d black? [1]

3 The Oasis café sells sandwiches of various sorts. Three types of bread are used: brown (B), white (W) and granary (G). Three types of filling are also used: cheese (C), egg (E) and ham (H). Each sandwich has only one type of filling.

a Complete the table to show all the different sandwiches which could be made at the Oasis café.

[2]

b Explain why the probability that the first customer buys a brown bread and cheese sandwich does not have to be

1number of choices in the table

. [1]

c Peter says the probability that the first customer will buy a brown bread and cheese sandwich is 1

5. If he is correct, what is the probability that first customer will not buy a brown bread and cheese sandwich. [1]

Experimentalprobabilities

Here is an exam question ...Anwar did a survey on the colours of cars passing his house.Here are his results.

Colours Red Black Blue Silver Other

Number of cars

36 44 28 60 32

Estimate the experimental probability that the next car passing his house will bea silver.b blue.Give your answers as fractions in their lowest terms. [3]

... and its solutionThe total number of cars = 36 + 44 + 28 + 60 + 32 = 200.

a Experimental probability of a silver car 60200

310= .

b Experimental probability of a blue car 28200

750= .

Bread Filling

B C

B E


1 Janine has a biased coin. She tosses it 300 times and it comes down ‘heads’

190 times. Estimate the experimental probability that the coin

next comes downa heads.b tails. [2]

2 On an aircraft the number of passengers in each class is shown in this table.

Class First Business Economy

Number of passengers

15 65 420

Estimate the probability that one of the passengers chosen at random travelled ina first class.b business class. [3]


3 Perimeter, area and volume 1Here is an exam question ...

a Find the perimeter of this rectangle. [2]b Find the area of this rectangle. [2]

... and its solutiona 7 + 4 + 7 + 4 = 22 cmb 7 × 4 = 28 cm2

More exam practice1 Find the perimeter and area of each of these shapes.

a

b

[4]

3 Will carried out a survey on people’s favourite flavour of crisps.

He asked 200 people. These are his results.

Flavour Plain Salt & vinegar

Cheese & onion

Other

Number of people

35 72 38

a How many people chose cheese & onion flavour crisps?

b Estimate the experimental probability of someone choosing salt & vinegar. [2]

4 A certain type of moth on a tropical island has either two spots, three spots or four spots on its wings. The probability that a moth has two spots is 0.3. In a survey conducted by biologists, 1000 moths were examined and 420 moths with three spots were found. What is the probability of a moth, caught at random, having four spots? [4]

7 cm

4 cm


1 A rectangle has a length of 4.3 cm and a width of 2.6 cm.

Work out the following.a The perimeter of the rectangle [2]b The area of the rectangle [2]

2 a On centimetre squared paper, draw two different rectangles which each have an area of 12 cm2. [2]b Work out the perimeter of each of your

rectangles. [2]


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2 This is a map of the island of Alderney. The length of each square represents 1 km.

Work out an estimate of the area of Alderney. [2]3 A rectangle has an area of 36 cm² and a length

of 9 cm. Find the width of the rectangle. [2]4 This is a sketch of a rectangular school playing field.

Work out the area of the field. [2]5 Mr Chan has drawn this plan of his lounge floor.

What is the perimeter and area of his lounge floor? All lengths are in metres. [4]

Thevolumeofacuboid

Here is an exam question ...a Find the volume of this cuboid. [2]b Find the total surface area of this cuboid. [2]

... and its solutiona Volume of cuboid = length × width × height

= 40 × 20 × 30 = 24 000 cm3

b Surface area = 2 × top + 2 × side + 2 × front = 2(20 × 40) + 2 (40 × 30) + 2(20 × 40) = 1600 + 2400 + 1200 = 5200 cm2

4 MeasuresHere is an exam question ...

The dimensions of this rectangle are accurate to the nearest metre.a Give upper and lower bounds for the length, 5 m,

of the rectangle. [2]b Find an upper bound for the area of the rectangle

in square metres. [2]c Change your answer to part b into square

centimetres. [2]

41.2 m

79.6 m

6

4

22

1 1

20 cm

40 cm

30 cm


1 Calculate the volume of this cuboid. [2]

2 The volume of water in this fish tank is 10 000 cm3. All the sides and base of the tank are rectangles.

Calculate the depth of water in the tank. [3]

4.6 m 1.5 m

5.2 m

d

50 cm20 cm

5 m

3 m


... and its solutiona Upper bound 5.5 m Lower bound 4.5 mb 5.5 × 3.5 = 19.25 m² c 19.25 × 10 000 = 192 500 cm²

5 The area of triangles and parallelogramsHere is an exam question …

The area of this triangle is 48 cm².Calculate the value of h. [3]


Area = 12 × 12 × h = 48

So 6h = 48And h = 8 cm

Upper bound of width = 3.5 m


1 A rectangle has dimensions 354 cm by 64 cm.a Work out the area i in cm2. ii in m2.b The dimensions were measured to the nearest

centimetre. Write down the bounds between which the

dimensions must lie. [5]2 A block of wood is a cuboid measuring 6.5 cm

by 8.2 cm by 12.0 cm.a Calculate the volume of the cuboid.

The density of the wood is 1.5 g/cm3.b Calculate the mass of the block. [4]

3 A bicycle wheel has diameter 62 cm. When Peter is cycling one day, the wheel turns 85 times in one minute.a What distance has the wheel travelled in

1 minute?b Calculate Peter’s speed, in kilometres per hour. [5]

4 The population of Denmark is 5.45 million. The land area of Denmark is 42 400 km2. Calculate the population density of Denmark. Give your answer to a sensible degree of accuracy. [3]

5 The dimensions of this rectangle are given to the nearest cm.

Calculate upper and lower bounds for the perimeter. [4]

6 Bob travels the first 30 miles of a journey at 60 mph. He travels the next 15 miles at 20 mph.a Find the time, in hours, he took to travel the

first 30 miles. [2]b Find the average speed, in mph, for the whole

journey. [3]

18 cm

13 cm

h cm

12 cm


1 a Find the area of this triangle.

b Calculate the length of the hypotenuse of this triangle. Give your answer to a sensible degree of accuracy. [5]

2 Find the total area of this shape. [4]

5.0 cm

4.6 cm

5 cm

6 cm

4.6 cm

0.7 cm

Not to scale


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Here is an exam question …a Complete the table. [2]

Outcome Square Triangle Circle Star

Probability 0.2 0.35 0.3

b In a pack of cards, the cards are either red or blue. There are three times as many blue cards as red cards. What is the probability that a card drawn at random is red? [2]

… and its solutiona P(Circle) = 1 − (0.2 + 0.35 + 0.3)

= 1 − 0.85 = 0.15

b 3 parts blue, 1 part red. P(red) = 14

More exam practice1 Ahmed is counting vehicles passing a junction

between 8.00 a.m. and 8.30 a.m.

Vehicle Cars Motorcycle Lorries

Frequency 72 15 28

Vehicle Vans Buses

Frequency 33 12

3 The area of this triangle is 18.9 cm². The height, AD, = 4.5 cm. Calculate the base, BC, of the triangle.

4

ABCD is a parallelogram. AE = 3 cm, EB = 6 cm and DE = 5.2 cm. Calculate the following.

a The area of the parallelogram [2]b The perimeter of the parallelogram [4]

5

The two ends of this solid are parallelograms. The remaining faces are all rectangles with

length 8 cm. Calculate the following.

a The area of each of the parallelograms [2]b The total surface area of the shape [4]

6 This triangle and this parallelogram have the same area.

Calculate the height of the parallelogram. [4]

DB C

A

E

5.2 cm

3 cm 6 cmA B

D C

3 cm

8 cm

5 cm

4 cm

5.6 cm

8.5 cm 4.8 cm


1 The probability of getting a 2 with a spinner is 35.

What is the probability of not getting a 2? [1]2 Coloured sweets are packed in bags of 20. There are

five different colours of sweet. The probabilities of four colours are given in the table.

Colour Orange White Yellow Green Red

Probability 0.05 0.2 0.25 0.35

a Find the probability of picking a white sweet. [2]b Find the probability of not picking a green

sweet. [1]c How many sweets of each colour would you

expect to find in each bag? [3]


a Use these data to find the probability that the next vehicle to pass the junction

i is a car. [3] ii is a bus. [2] iii has more than two wheels. [2] Give your answers as fractions in their lowest

terms.b Will this give reliable results for vehicles passing

the junction at 11:00 p.m? Explain your answer. [1]

2 The probability that United will win any match is 0.65. The probability that they lose any match is 0.23.a What is the probability that United will draw

any match? [2]b Estimate the number of matches United will win

in a season of 46 games. [2]3 In tennis a draw is not possible. Roger says the probability that he will beat Andy in

their next match is 0.7. Andy says the probability that he will beat Roger in

their next match is 0.35. Explain why they cannot both be right. [2]4 Mosna throws a dice 10 times. These are her results.

Score 1 2 3 4 5 6

Number of times 1 3 1 2 3 0

Mosna says this is evidence that the dice is biased as the probability of getting a six is zero.

Is Mosna right? Explain your answer. [2]

7 Perimeter, area and volume 2Here is an exam question …

A heart shape is made from a square and two semi-circles. Find the area and perimeter of the heart shape.

[6]

… and its solutionShape = square of side 20 cm + one whole circle of radius 10 cmArea of shape = 20 × 20 + π × 102 = 714.2 cm2 (to 1 d.p.)Perimeter of shape = two semicircles + two sides of

square = circumference of whole circle +

40cm = π × 20 + 40 = 102.8 cm (to 1 d.p.)

Here is another exam question …Find the volume of this greenhouse.The ends are semi-circles. [3]

… and its

solution

Area of end = 12 × πr2

= 12 × π × 2.52

Volume = area of end × length

= (12 × π × 2.52) × 11

= 108 m3 (to 3 s.f.)

20 cm

11 m5 m


1 Work out the area of the lawn in this diagram. [4]

2 The circumference of a circle is 26 cm. Calculate the radius of this circle. [2]

3

The diagram shows a garden pond with a path round it.a A fence is to be made round the pond on the

inside of the path. Calculate the length of the fence. [2]b Find the area of the path. [4]

28 m

Lawn24 m Patio

2.5 m3 m


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a Calculate the perimeter of the shape. [1]b Calculate the area of the shape. [3]

5

a Find the area of this shape. [3]b Find the perimeter of this shape. [3]

6

The diagram shows a games presentation rostrum. Find the volume of the rostrum. [3]

7 This sweet box is in the shape of a prism. The base is an isosceles right-angled triangle.

Find the volume of the box. [3]8

Calculate the volume of this prism. [2]9 This is a triangular prism.

a Find its volume.b Find its surface area. [6]

10 Find the volume of coffee in this cylindrical tin. [3]

4

NOT TOSCALE

4

2

2

2

10

6

10 cm

3 cm4 cm

8 cm

1.5 m

1.5 m1.5 m

0.5 m 0.8 m2 1

34.5 m

0.2 m2 m

5.2 cm

7.4 cm

3 cm

3 cm

2 cm

2 cm1 cm

1 cm

7 cm

3 cm

4 cm

5 cm

14 cm

7.5 cm


8 Using a calculatorHere is an exam question …

Work out the following, giving your answers to 2 decimal places.a 5.62 [1]

b 16724 16+

[2]

c 2.72 + 8.32 [2]

d 3 5 7+ × [1]

… and its solutiona 31.36b 4.18c 76.18d 6.16

Here is another exam question …Work out the following. Give your answers correct to 3 significant figures.a 4.24 [1]

b 3 9 0 533 9 0 53

2. .. .+× [2]

c 350 × 1.00512 [1]

… and its solutiona 311

b 7.61

c 372

Key in

4 . 2 xy 4 =

311.1696

Key in

( 3 . 9 x2 +

0 . 5 3 ) ÷ ( 3 . 9 × 0 . 5 3 ) =

7.614 900 ...

Key in

3 5 0 × 1 . 0 0 5 xy

1 2 =

371.587 234 ...


Give your answers to 3 significant figures where appropriate.1 Round these numbers to the number of

significant figures shown in the brackets. [5]a 5678 (2)b 230 421 (3)c 0.005 69 (1)d 0.006 073 8 (4)e 0.898 (2)

2 Work out these.

a 4 2 1 71 252. – ..

[2]

b 5 122 2+ [1]3 Work out these.

a 43% of £640 [2]b 2

5 of 47.5 m [2]c 84.6 − 23.9 [2]

4 Work out these.

a 1 83 0 933 75

. – ..

[2]

b 4.6 × 5.2 − 17.1 [1]

c 3 7 2 14 8

. ..

+ [1]

5 Work out these.a 4.312 − 1.92 [1]

b 8 2 1 716 32. – .

. [2]

c 4 75 1 242 2. – . [2]

6 Work out these.a 4.12 [1]

b 9 63. [1]c 7.9 − 3.6 × 1.25 [2]d 3

7 of £164 [2]

7 £1627 is shared equally between five friends. How much does each one get? [2]

8 a A shopkeeper makes a special offer on fertilizer priced at £3.68. He reduces it by 83p. What is the new price? [2]

b At the garden centre they decide to charge 75% of the original price of £3.68. Whose price is cheaper and by how much? [3]

9 Twelve baking potatoes cost £2.76. How much would five cost? [2]

10 John worked out 4

2 3+ using a calculator and his

answer was 5. Explain what he did wrong. [1]


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1 Work out these.

a 423 + 234 [2]

b 247 – 12

3 [2]

c 35

37× [2]

2 Work out these.

a 56 [1]

b 31 (Give the answer 2 d.p.) [1+1]

c 3 842 19 1 59

.. – .

[1]

3 Jo invests £10 000 in a two stage bond. Jo uses the following calculations to find how much her bond will be worth after 6 years.

10 000 × (1.045)4 × (1.065)2

Work this out correct to the nearest pound. [2+1]

4 Work out these, giving the answers to 2 decimal places.

a 3.23 + 2.55 [1]

b 37.214 [1]

c 1.67−3 [1+1]

5 Work out these, giving the answers to 3 significant figures.

a 3 5 7+ + [2]

b 13

15

17

+ + [2]

6 Work out these, giving the answers to 3 significant figures.

a The square root of 7 [1]

b The cube of 2.3 [1]

c 1.43 − 0.84 [1+1]7 Work out these.

a 213 – 134 [2]

b 27 of £434 [1]

c 194485 , as a fraction in lowest terms [1]

9 Trial and improvementHere is an exam question …

A solution of the equation x3 + 4x2 = 8 lies between −3 and −3.5. Find this solution by trial and improvement. Give your answer correct to 2 decimal places. [4]

… and its solutionx = −3 –33 + 4 × −32 = 9 Too big.x = −3.5 −3.53 + 4 × −3.52 = 6.125 Too small. Try between −3.5 and −3.x = −3.3 −3.33 + 4 × −3.32 = 7.623 Too small. Try between −3.3 and −3.x = −3.2 −3.23 + 4 × −3.22 = 8.192 Too big. Try between −3.3 and −3.2.x = −3.25 −3.253 + 4 × −3.252 = 7.921 875 Too small. Try between −3.25 and −3.2.x = −3.23 −3.233 + 4 × −3.232 = 8.033 333 Too big. Try between −3.23 and −3.25.x = −3.24 −3.243 + 4 × −3.242 = 7.978 176 Too small.To 2 decimal places, either x = −3.23 or x = −3.24. Try halfway between to check.x = −3.235 − 3.2353 + 4 × −3.2352 = 8.005 897 Too big.So the answer is between −3.235 and −3.24 x = −3.24 (to 2 d.p.) This solution keeps several decimal places as a

check for you. There is no need to write them all down. For example, for x = −3.23, 8.03 is enough.


More exam practice1 The equation x3 − 15x + 3 = 0 has a solution

between 3 and 4. Use trial and improvement to find this solution. Give your answer to 1 decimal place. Show clearly the outcomes of your trials. [3]

2 Use trial and improvement to calculate, correct to 2 decimal places, the solution of the equation x3 − 5x − 2 = 0 which lies between 2 and 3. Show all your trials and their outcomes. [3]

3 a Show that the equation x3 − 8x + 5 = 0 has a root between x = 2 and x = 3. [3]b Use trial and improvement to find this root

correct to 1 decimal place. Show all your trials and their outcomes. [3]

4 The volume, V cm3, of this cuboid is given by V = x3 + 6x2.

a Complete the table of values of x from 1 to 6. [2]

x 1 2 3 4 5 6

V

b Use trial and improvement to find the dimensions of the cuboid if its volume is 200 cm3. Give your answer correct to 1 decimal place. Show all your trials. [3]

10 EnlargementHere is an exam question ...

Triangles ABC and ADE are similar.Calculate a CE b BC. [5]

... and its solutionFirst draw the triangles separately.

Scale factor = 85 = 1.6

AE = 6 × 1.6 = 9.6, so CE = 9.6 − 6 = 3.6 cm

BC = 121 6. = 7.5 cm


1 The volume of this cuboid is 200 cm3.

a Explain why x3 + x2 = 50. [2]b Find the solution of x3 + x2 = 50 that lies

between 3 and 4. Give your answer correct to 3 significant figures. You must show your trials. [3]

2 Use trial and improvement to find the solution of x 3 − 3x = 15 that lies between 2 and 3. Give your answer to 2 decimal places. Show clearly the outcomes of your trials. [3]

4x

x � 1

x

xx

x � 6

12 cm

3 cmD E

B C

A

5 cm 6 cm

B C

A

5 cm 6 cm

12 cmD E

A

8 cm

B C

A

5 cm 6 cm

12 cmD E

A

8 cm


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1 PQRS is an enlargement of ABCD.

Calculate the following.a PQ [3]b BC [2]

2 The triangles ABC and PQR are similar.

Calculate the lengths of the following.a QR [3]b AC [2]

3 Triangle EDC is similar to triangle ABC.

a Calculate the length of BD. [3]b Calculate the value of this fraction in its

simplest form: ∆

∆ [2]

4 Triangles AOB and DOC are similar.

AO = 3 cm, DO = 5 cm, AB = 7.5 cm and CO = 6 cm. Calculate the lengths of the following.

a CD [3]b BO [2]

5 These shapes are similar. The radius of the small circle is 5 cm. The radius

of the large circle is 8 cm.

a The length of the chord of the large circle is 11 cm. Calculate the length of the chord of the small

circle. [3]b Calculate the values of these fractions.

i Circumference of small circleCircumference of large ciircle

ii Area of small circleArea of large circle

[4]

D C S R

BA

P

Q

7 cm

10 cm 15 cm

9 cm

D C S R

BA

P

Q

7 cm

10 cm 15 cm

9 cm

RQ

P

B

A

C

5 cm

8 cm

7 cm 9.1 cm

RQ

P

B

A

C

5 cm

8 cm

7 cm 9.1 cm

BD

A

E

C

6 cm

12 cm

8 cm

Area of EDCArea of ABC

A B

OC D

7.5

36 5


11 Graphs

Here is an exam question …The graph shows Philip’s cycle journey between his home and the sports centre.

a Explain what happened between C and D. [1]b Explain what happened at B. [1]c Explain what happened at E. [1]d Work out the total distance that Philip travelled. [2]

… and its solutiona Philip was at the sports centre.b Philip’s speed changed, perhaps due to a steep hill.c Philip arrived home.d 12 km

Distance–timeandotherreal-lifegraphs

2

4

6

8

1

3

5

7

y

20A

BC D

E0 40 60

Time in minutes

Dist

ance

from

hom

ein

kilo

met

res

80 100 120

6 km there and 6 km back.


1 A rocket is fired out to sea from the top of a cliff. The graph shows the height of the rocket above sea level until it lands in the sea.

a How high is the rocket above sea level after 10 seconds. [1]b How long does it take before the rocket lands in the sea? [1]c Write down the time when the rocket is at the same height as it started. [1]d Write down the times when the rocket is 10 m above the cliff. [2]

50

60

70

80

40

Hei

ght i

n m

etre

s ab

ove

sea

leve

l

30

20

10

0 5 10 15Time in seconds

20 25 30


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More exam practice1 The graph can be used to divide people into three

groups – underweight, OK and overweight according to their height.

a Alphonse is 185 cm tall and weighs 80 kg. Which group is he in? [1]

b Hussain is 185 cm tall and is underweight. Complete this statement.

Hussain weighs less than ..... kg. [1]c George weighs 60 kg and is overweight.

Complete this statement. George is less than ..... cm tall. [1]d Betty is 155 cm tall. If she is in the OK group,

between what limits does her weight lie? [2]2 Tom leaves home at 8.20 a.m. and goes to

school on a moped. The graph shows his distance from the school in kilometres.

2 Katy needs new carpet for her kitchen. She measures the floor and draws a plan.

a Calculate the total area of the floor. State the units of your answer. [4]

b This is a graph for working out an approximate cost if Katy chooses a certain types of carpet.i Use the graph to find the cost of the carpet

for Katy’s kitchen. [1]ii Find the cost per square metre of this

carpet. [2]

c Another type of carpet costs £6 per square metre. Draw a line on a copy of the grid which can be used to find the cost of different sizes of this carpet. [1]

4.3 m

1.6 m

1.5 m

2 m

150

200

100Cos

t (£)

50

0 5 10 15Area (m2)

Wei

ght (

kg)

50

40

60

70

80

90

100

110

120

Height (cm)

Overweight

Underweight

OK

150140 160 170 180 190

Dist

ance

from

sch

ool (

km)

2

0

4

6

8

Time8.20 a.m. 8.30 a.m. 8.40 a.m. 8.50 a.m.


a How far does Tom live from school? [1]b Write down the time that Tom arrives at the

school. [1]c Tom stopped three times on the journey. For

how many minutes was he at the last stop? [1]d Calculate his speed in km/h between 8.20 a.m.

and 8.30 a.m. [3]3 Steve goes from home to school by walking to a

bus stop and then catching a school bus. Use the information below to construct a

distance–time graph for Steve’s journey. Steve left home at 8.00 a.m. He walked at 6 km/h for 10 minutes. He then waited for 5 minutes before catching the bus. The bus took him a further 8 km to school at a steady speed of 32 km/h. [4]

4 The graph below describes a real-life situation. Describe a possible situation that is occurring. [3]

Quadraticgraphs

Here is an exam question …a Make a table of values and draw the graph of

y = x2 − x − 3 for values of x from −2 to 4. [4]b Use your graph to solve the equation

x2 − x − 3 = 2. [2]


b x = −1.8 and x = 2.8

More exam practice1 a Complete the table and draw the graph of

y = x2 − 4 for values of x from −3 to 3. [4]

x −3 −2 −1 0 1 2 3

y 5 −3 −4 0

b Use your graph to find the solutions of the equation x2 − 4 = 0. [2]

Speed

Time

x −2 −1 0 1 2 3 4

x2 4 1 0 1 4 9 16

−x 2 1 0 −1 −2 −3 −4

−3 −3 −3 −3 −3 −3 −3 −3

y 3 −1 −3 −3 −1 3 9

5

6

7

8

9

4

3

2

1

0�1

�2

�3

y

y � 2

y � x2 � x � 3

x�1�2 1 2 3 4


1 a Complete the table of values and draw the graph of y = x2 − 2x + 1 for values of x from −1 to 3. [2]

x –1 0 1 2 3

y 1 4

b Use the graph to find the value of x when y = 3. [2]

2 a Complete the table for y = 4x − x2 and draw the graph. [4]

x −1 0 1 2 3 4 5

y 3 0

b Use your graph to find i the value of x when 4x − x2 is as large as

possible. [1] ii between which values of x the value of

4x − x2 − 2 is larger than 0. [2]


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2 a Draw the graph of y = x2 − 3x − 5 for values of x from −2 to 5. [4]b Use your graph to find the solutions of the

equation x2 − 3x − 5 = 0. [2]3 a Draw the graph of x2 + 4x − 4 for values of x

from −6 to 2. [4]b Use your graph to find the solutions of the

equation x2 + 4x − 4 = 0. [2]c On the graph, draw the line y = −5 and use

this to find the solutions of the equation x2 + 4x − 4 = −5. [3]

4

In the diagram each edge of the shape is parallel to one of the axes.

OE = 7 OA = 2 EF = 3 HJ = 3 FK = 1 Write down the coordinates of the following.

a The point K b The point Hc The midpoint of BC [3]

12 PercentagesPercentageincreaseanddecrease

Here is an exam question …Sian invested £5500 in a fund. 4% was added to the amount invested at the end of each year. What was the total amount at the end of the 5 years. [2]

… and its solutionTotal amount = £5500 × (1.04)5

= £6691.59 (to the nearest penny)

More exam practice1 A bath normally priced at £750 is offered with

a discount of 10%. What is the new price of the bath? [3]

2 In a sale, all the prices were reduced by 20%. A jumper was originally priced at £45. What was the sale price? [3]

3 A low-sugar jam claims to have 42% less sugar. A normal jam contains 260 g of sugar. How much sugar does the low-sugar jam contain? [3]

4 Stephen negotiated a 5% reduction in his rent. It originally was £140 a week. What was it after the reduction? [3]

5 A computer was advertised at £650 + 12.5% service change. What was the cost including the service charge? [3]

6 Jo bought a plane ticket for £570. Because she paid by credit card, a 1.5% charge was added to her bill. How much did she have to pay in total? [3]

7 Tess invested £5000 at 4% compound interest for five years. How much was the investment worth after five years? [3]

8 A computer cost £899. It decreased in value by 30% each year. What was its value aftera 1 year? [2]b 5 years? [2]

Solvingproblems

Here is an exam question ... The Retail Price Index in 1998 was 162.9.The Retail Price Index in 2008 was 214.8.a What was the percentage increase in prices

from 1998 to 2008? [2]b A washing machine cost £265 in 1998.

What would you expect it to cost in 2008? [2]


a Increase = 51.9 % increase = 51 9162 9

..

× 100 = 31.86%

b 265 × 1.3186 = £349.43 (approx £350)

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1 A calculator was sold for £6.95 plus VAT when VAT was 17.5%. What was the selling price of the calculator including VAT? Give the answer to the nearest penny. [3+1]

2 All clothes in a sale were reduced by 15%. Mark bought a coat in the sale that was usually priced at £80. What was its price in the sale? [3]

3 A house went up in value by 1% per month in 2007. At the beginning of the year it was valued at £185 000. What was its value six months later? Give the answer to the nearest pound. [2+1]


1 In 2002 the Average Earnings Index in an industry was 106.2.

In 2007 the Average Earnings Index was 122.0. By what percentage did average earnings increase

from 2002 to 2007?2 The Retail Price Index in 1990 was 126.1. The Retail Price Index in 2005 was 192.0.

a What was the percentage increase in prices from 1990 to 2005?

b A family’s usual weekly shop cost £64 in 1990. What would you expect it to cost in 2005?

Igcse Revision

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