Exam style questions - Hodder Plus Home

Contents Exam questions
A
Mathematics
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
B
Mathematics
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
Contents
i

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
C
Mathematics
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
Answers to exam questions
Unit A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Unit B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Unit C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
ii
Contents

1 Integers
Here is an exam question …
Look at these numbers.
6, 8, 9, 11, 14, 15, 18, 27
From 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 solution
a Any two of 9, 11, 15 and 27
b 15
3 × 5 = 15
c 11
d 8 and 9 or 14 and 15
e 6 or 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.
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 solution
3 × 8.99 = 26.97
2 × 1.45 = 2.90
1 × 1.75 = 1.75
2 × 2.49 = 4.98
Total = 36.60
Each paid £36.60 ÷ 3 = £12.20
Now try these exam questions
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
6 6 ÷ 1.5 = 4
4 2 = 16
Too small
Too large
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]
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]
© Hodder Education 2011 Unit A
1

Exam questions: Unit A
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 solution
a 4k
b 3n
c 4fg
Now try these exam questions
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.
3 Data
collection
Here 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
... and its solution
[3]
2x
3x
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.
3x
[1]
Frequency
9
8
7
6
5
4
3
2
1
0
0 3 to 5 6 to 8 9 to 11 12 and
over
Shoe size
Now try these exam questions
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
2y
2y
3x
[4]
2 Revision Notes © Hodder Education 2011

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.
Frequency
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 Tally marks 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.
13
12
11
10
9
8
7
6
5
4
3
2
1
0
4 Decimals
Here 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 solution
Cost = 13.8 × 17.5p
= 241.5p
= £2.42 to nearest penny
Number of absences
[3]
© Hodder Education 2011 Unit A
3

Exam questions: Unit A
Now try these exam questions
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.
5
100
1
4
1
50
1
2
13
25
1
10
4
20
2
5
5 Formulae
Here 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
= 7
b L = 3 × 4 + 2 × 5
= 12 + 10
= 22
0.1
0.2
0.25
0.5
0.52
[4]
Here is another exam question …
The diagram shows an isosceles triangle whose base is f
and whose other two sides are g.
g
f
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 + 2g
b p = 1.7 + 2 × 2.4 = 1.7 + 4.8
= 6.5 m
Now try these exam questions
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 when
a x = 2. [1]
b x = 5. [1]
3 If P = 8a + 3b, find P when
a 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]
More exam practice
1 For the formula G = 1 2 x − 3, work out the value
of G when
a x = 12. [1]
b x = 4. [1]
2 For the formula K = 25 − 7g, work out the value
of K when
a g = 3. [1]
b g = −2. [1]
3 For the formula H = 0.5a, work out the value of
H when
a a = 12. [1]
b a = 4. [1]
4 If Q = 7xy, find Q when
a x = 5 and y = 2. [1]
b x = 6 and y = 1.5. [1]
4 Revision Notes © Hodder Education 2011

6 Equations 1
Here is an exam question …
a Find the values of a and b.
15
31
[2]
b Solve the following equations.
i 6x = 30 [1]
ii x + 5 = 3 [1]
iii
x
4 = 5 [1]
… and its solution
a a = 5, b = 9
b i x = 30 ÷ 6
= 5
ii x = 3 − 5
= − 2
iii x = 5 × 4
= 20
5
4
a
b
7 Coordinates
Here is an exam question …
a Plot the following points on the grid. [3]
y
8
7
6
5
4
3
2
1
0 1 2 3 4 5 6 7 8
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]
x
Chief Examiner says
x
means x ÷ 4 and the inverse of ÷ is ×.
4
Now try these exam questions
1 For the given inputs, find the output from these
number machines.
a i 16
ii 9
6
iii 4
b
i 10
ii 19
5
2
[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 x 2 − 5y. [2]
4 The formula t = v – u may be used to find the
a
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]
[3]
… and its solution
a y
8
7 G C
6
5 D
4
3 E
B
2
1 A F
0 1 2 3 4 5 6 7 8
b (1, 5)
x
© Hodder Education 2011 Unit A
5

Exam questions: Unit A
Now try these exam questions
1
y
5
4
3
2
1
A
543210 1
1 2 3 4 5
2
3
4
5
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 of
a side AC. [2]
b side AB. [2]
3 A is the point (2, 4).
y
7
6
5
4
3
2
1
76543210 1 2 3 4 5 6 7
1
C
2
B
3
4
5
6
7
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.
A
y
3
2
1
B
3210 1 2 3 4
1
C
2
3
D
4
x
A
x
x
5
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]
543210 1
1 2 3 4 5
2
3
4
b
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]
8 Statistical
calculations 1
Here 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 5
5 6 6 7 7 8
a Find the mode of these marks. [1]
b Find the median of these marks. [1]
… and its solution
a Mode = 4
b Median = 5
y
5
4
3
2
1
a
x
The value that occurs most often.
There are two middle values, 5
and 5, so the median must be 5.
6 Revision Notes © Hodder Education 2011

Now try these exam questions
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
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]
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.
9 Sequences 1
Here 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 solution
a i the rule is + 7
ii 37
23 + 7 + 7 = 37
b i 5
ii The rule is −4 and
17 − 4 − 4 − 4 = 5
c 27
2 × 4 − 1 = 7, 7 × 4 − 1 = 27
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]
© Hodder Education 2011 Unit A
7

Exam questions: Unit A
Now try these exam questions
1 For each of these sequences, the numbers are the
number of lines in each picture.
a
b
c
3 5 7 9
4 7 10
13
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, …
8 15 22
29
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
10 Measures
Here 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 solution
a metres (m)
b millilitres (ml)
c square centimetres (cm 2 )
Now try these exam questions
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
20
30
40
50
60
70
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]
10
0
Temp
°C
90
80
8 Revision Notes © Hodder Education 2011

50
60 70 80
Temp °C
… and its solution
a N
B
C
Diagram shown
half size.
c
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]
11 Constructions 1
Here is an exam question …
Simon went orienteering. This is a sketch he made of
part of the course.
N
A
47°
0
300 m
100 200
Temp °C
B
125°
200 m
C
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]
[3]
A
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 solution
a Step 1: Draw the line AB 7.5 cm long.
Step 2: Using compasses, draw an arc 10 cm from A,
and an arc 4 cm from B.
Step 3: 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.
A
A
N
N
15 m
Scale 1 cm to 50 m
20 m
B
Scale 1 cm to 2 m
Note: the diagram above is not to scale.
N
8 m
C
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
© Hodder Education 2011 Unit A
9

Exam questions: Unit A
Now try these exam questions
1 This is a sketch of triangle ABC.
C
148°
B
9.1 cm
5.3 cm
A
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 Measure these angles.
a
b
[3]
[2]
10 Revision Notes © Hodder Education 2011

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.
C
8 cm
A
X
120°
12 cm
B
a Construct the triangle and the bisector of angle A.
b Measure the distance AX. [5]
12 Using a
calculator
Here is an exam question …
Work out the following. Give your answers to 2 decimal
places.
a 4.2 4 [1]
b 3 9 2
. + 0 . 53
[2]
3. 9 × 0.
53
c 350 × 1.005 12 [1]
… and its solution
a 311.17
b 7.61
c 371.59
= 371.587 234 ... people [2]
Now try these exam questions
Give your answers to 2 decimal places where
appropriate.
1 Work out these.
283 – 103
a [1]
360
b 3.2 (
5.2 − 1
1. 6) 1
c
4. 5 + 6.
8
[2]
2 Work out these.
a 2 5
of 65 g [2]
b 35% of £720 [2]
3 Work out these.
a 1.6 − 2.8 × 0.15 [2]
b
2 2
14. 3 – 9. 4
[2]
Key in
4 a Work out 2 3
of £4.56. [2]
4 . 2 x y 4 =
b A travel firm offers a discount of 12% on a
holiday costing £490.
311.1696
How much is the discount [2]
c Three tins of dog food cost £1.38.
Key in
What will eight tins of the same dog food
( 3 . 9 x 2 +
cost [2]
0 . 5 3 ) ÷
5 Work out these.
( 3 . 9 ×
a 4 . 6 – 3 . 9
[1]
2.
5
0 . 5 3 ) =
14
7.614 900 ...
b
2. 5 + 7.
3
[2]
Key in
c 13. 69
[1]
3 5 0 ×
6 A recipe for 4 people uses 360 g of flour and
60 g of butter.
1 . 0 0 5 x y 1 2
How much flour and butter is needed for 6
© Hodder Education 2011 Unit A
11

Exam questions: Unit A
7 Work out these.
a 2 7
of £19.60 [2]
b 12.5% of £980 [2]
8 Work out these.
a 14. 6 + 12.
44
[2]
b 14.5 2 − 12.6 2 [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 . 05 15.
12
+
1.
5 6.
3
[2]
More exam practice
1 Work out these, giving the answers to 2 decimal
places.
a 3.4 5 [1]
b (5.1 + 3.7) × 4.2 [1]
5. 1 × 2.
6
c
[2]
14. 2 – 6.
3
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 3 2 [1]
3 Work out these.
a 3 5
of 200 g [1]
b 2 3 4 − 14 5 [2]
4
c
7
of £26.60 [1]
4 Work out these, giving your answers to 2 decimal
places where appropriate.
a 730 × 1.01 15 [1]
b 14 1 3
840 × 1.
03
c
840 + 1.
03
[1]
[2]
13 Statistical
diagrams 1
Here 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.
Frequency
8
6
4
2
0 100 200 300 400 500 600
Number of people (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 solution
The 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).
12 Revision Notes © Hodder Education 2011

Now try these exam questions
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.
Nationalist
Liberal
Democrats
Other
Labour
Conservative
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]
14 Integers,
powers and
roots
Here 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 5 6 ÷ 5 4 [1]
ii 2 3 × 2 5 ÷ 2 7 [1]
iii 6 2 × 5 2 ÷ 2 2 [2]
… and its solution
a 12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
HCF = 2 × 2
= 4
LCM = 2 × 2 × 2 × 2 × 3
= 48
b i 5 6 ÷ 5 4 = 5 2
= 25
ii 2 3 × 2 5 ÷ 2 7 = 2 1
Two 2s are common to both.
= 2
iii 6 2 × 5 2 ÷ 2 2 = 36 × 25 ÷ 4
= 225
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.
Now try these exam questions
1 Write the following as whole numbers.
a 2 6 [1]
b 5 3 [1]
c 4 5 × 4 2 ÷ 4 3 [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 cm 2 . Work out the
length of one side of the square. [1]
b Work out 4 3 . [1]
c If the reciprocal of a number is 2.5, what is
the number [1]
© Hodder Education 2011 Unit A
13

Exam questions: Unit A
15 Algebra 2
ages. [3]
c i H = 17 − 6
Use it to find out the following.
= 11
b How many members the club has [1]
ii H = 17 − −2
c The modal age of the members [1]
= 19
d Their median age [1]
d 8a 6 Multiply the numbers and add the indices. e The range in their ages [1]
4 a Multiply out 2(3x + 1). [2]
b Factorise completely 12p 2 − 15p. [2]
5 Factorise completely 3a 2 + 6ab. [2]
Here is an exam question …
6 For the formula S = at + bt 2 , work out the value
of S when
a Expand the brackets and write this expression as
a a = 3, b = 2, t = 5. [2]
simply as possible.
b a = 2, b = 3, t = −4. [2]
2(3x − 4) − 5(x + 3) [4]
b Factorise this expression completely.
3a 2 + 6ab [2]
c For the formula H = 17 − 0.5a, work out the
value of H when a takes each of these values.
16 Statistical
i a = 12 ii a = −4 [4]
d Simplify 2a 4 × 4a 2 . [2]
diagrams 2
… and its solution
a 6x − 8 − 5x − 15 = x − 23
Take care with the signs. −5 × +3 = −15
Here is an exam question ...
b 3a(a + 2b)
The numbers below list the ages of the members of a
tennis club.
3a is common to both terms.
a Construct a stem-and-leaf diagram with these
Now try these exam questions
f The fraction of members who are veterans
(over or equal to 40) [1]
1 a Write down the perimeter of this rectangle in
terms of x, as simply as possible.
2x
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
3x
[1]
b P = ab + b 2 . 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 + 32b
ii 3(5a + 2b) = 15a + 6b
iii 3(5a + 2b) = 15a + 2b
iv 3(5a + 2b) = 8a + 5b [1]
... and its solution
a 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.
14 Revision Notes © Hodder Education 2011

1 2 4 6 6 6 7
Finally add a key.
6 3 = 63
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
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.
Now try these exam questions
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.
50
Number of journeys
(frequency)
40
30
20
10
0
10 20 30 40 50
Mileage (m miles)
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]
© Hodder Education 2011 Unit A
15

Exam questions: Unit A
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]
17 Equations 2
Here is an exam question …
Solve the following equations.
a 2(3 − x) = 1 [3]
b 5 x + 8 = 6
[3]
3
c 4(x + 7) = 3(2x − 4) [4]
… and its solution
a 2(3 − x) = 1
6 − 2x = 1
−2x = −5
x = 2 1 2
b 5 x + 8 = 6
3
5x + 8 = 18
5x = 10
x = 2
c 4(x + 7) = 3(2x − 4)
4x + 28 = 6x − 12
40 = 2x
x = 20
Now try these exam questions
1 Solve these.
a 3x = x + 1 [2]
b 3p − 4 = p + 8 [3]
c 3 m = 9
4
[2]
2 Solve 3(p − 4) = 36. [3]
3 Solve 4(x − 1) = 2x + 3. [3]
16 Revision Notes © Hodder Education 2011

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 3x 2 = 27 [2]
b 4x + 1 = 7 − 2x [3]
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
18 Ratio and
proportion
Here 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 solution
Ratio is 5 : 7
Total = 12
One share = 28.8 ÷ 12
= £2.40
John receives 5 × 2.40 = £12
Peter receives 7 × 2.40 = £16.80
Check: £12 + £16.80 = £28.80
Now try these exam questions
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]
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]
19 Statistical
calculations 2
Here 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
© Hodder Education 2011 Unit A
17

Exam questions: Unit A
… and its solution
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 = 3380
120
= 28.2 miles
Now try these exam questions
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]
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
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.
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
[5]
3 The frequency table shows the number of weeks’
holiday taken by 90 different families in one year.
Weeks
Frequency
0 2
1 31
2 37
3 16
4 3
5 1
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]
18 Revision Notes © Hodder Education 2011

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.
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
[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]
20 Pythagoras’
theorem
b a 2 = b 2 + c 2
= 4.6 2 + 5.0 2
= 46.16
a = 46.
16
a = 6.8 cm (to 1 d.p.)
Here is an exam question ...
Now try these exam questions
a Find the area of this triangle.
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
5.0 cm
side AE is 2 m.
What is the maximum height of the shed [5]
4.6 cm
B
b Calculate the length of the hypotenuse of this
triangle. Give your answer to a sensible degree
A
C
of accuracy. [5]
... and its solution
a Area of triangle = 1 2
base × height
= 1 2
× 4.6 × 5.0
= 11.5 cm
E
D
© Hodder Education 2011 Unit A
19

Exam questions: Unit A
2
Calculate
a BD [2]
b AB [2]
3 Find the length of the side marked x.
4 Calculate the length of this ladder.
5
D
4.2 m
6
11 cm
9.1 cm
X
7.8 cm
8 cm
12
10
A
x
1.8 m
[3]
[3]
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]
B
5 cm
C
21 Planning and
collecting
Here 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 solution
a 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
A leading question is one that encourages you to
give a particular answer. Amy’s question encourages
you to say ‘Yes’.
Now try these exam questions
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]
20 Revision Notes © Hodder Education 2011

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 2
Here 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 solution
a i −5
ii −4 each time.
b i 39
ii 4n − 1
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.
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.
Now try these exam questions
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, 18
a Find the 20th term. [1]
b Find the nth term. [2]
3 The first five terms of a sequence are 1, 3, 6, 10, 15
a 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]
23 Constructions 2
Here is an exam question …
This is the plan of a garden drawn on a scale of 1 cm
to 2 m.
Tree
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]
H
o
u
s
e
© Hodder Education 2011 Unit A
21

Exam questions: Unit A
… 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.
Scale 1 cm to 2 m
Tree
Now try these exam questions
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.
H
o
u
s
e
24 Rearranging
formulae
Here 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 solution
a P = 20 + 12 × 3
= 20 + 36
= 56p
b 20 + 12S = 95
12S = 75
S = 75 ÷ 12
S = 6.25 cm
c P = 20 + 12S
P − 20 = 12S
S = P – 20
12
A
Hedge
B
10 m
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
Fence
24 m
Fence
House
Within 4 miles of the store
£10 Between 4 miles and 7 miles from
the store
£25 Over 7 miles from the store
C
D
Now try these exam questions
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
kNT
P =
V
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 = πr 2 h i (r) ii (h) [3]
Draw three separate diagrams to show the three
delivery areas.
Use a scale of 1 cm to represent 2 miles. [6]
22 Revision Notes © Hodder Education 2011

1 Working with
numbers
Here 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 326
+ 397
Australia 425
+ 292
723
717
England had the higher score.
b Difference 723
– 717
6
England’s score was higher by 6 runs.
Now try these exam questions
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 to
a 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, 5.74
a 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]
More exam practice
1 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 to
a 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
quadrilaterals
Here is an exam question …
B
34° A
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.
© Hodder Education 2011 Unit B
23

Exam questions: Unit B
… and its solution
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.
Now try these exam questions
1 Name these shapes.
a
b
3 Fractions
Here is an exam question …
Anna, Ben and Chris have 200 raffle tickets to sell.
Anna sells 1 of the tickets.
5
Ben sells 3 8
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]
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.
D
A
B
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]
C
… and its solution
a Anna sells
1
5 × 200
= 40
Ben sells
3
8 × 200
= 75
Chris sells 200 − 40 − 75 = 85
b Fraction = 85
200
= 17
40
Here is another exam question …
a Convert 3 8 to a decimal. [2]
b Add 3 8 and 1 5
, giving your answer as a decimal. [3]
… and its solution
0.
375
6 4
a 8)
3.
0 0 0
= 0.375
b 1 5 = 0.2
0.375 + 0.2
= 0.575
Chief Examiner says
Divide numerator and
denominator by 5.
Now try these exam questions
1
37°
* + 37°
*°
Not to scale
2
a What fraction of this shape is shaded [1]
b Shade some more squares so that 3 5
is now
shaded. [1]
b What type of triangle is this [1]
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 5 8
of the
shape is shaded. [1]
24 Revision Notes © Hodder Education 2011

More exam practice
1 Ordinary marmalade is 3 5 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 5 8
of them. How many corners did
they score from [2]
3 Jane buys a 3 metre piece of wood.
She cuts off 1 4 of it.
How many centimetres of wood has she cut off [2]
4 Put these fractions in order of size, smallest first.
5 1
6
, 5 3
4
, 12
, 8
[2]
5 Which of the following fractions are equal to 2 3
6 4
10
, 10 4
6
, 3
15
, 9
, 2
[2]
4 Solving
problems
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 solution
3 × 8.99 = 26.97
2 × 1.45 = 2.90
1 × 1.75 = 1.75
2 × 2.49 = 4.98
Total = 36.60
Each paid £36.60 ÷ 3 = £12.20
Now try these exam questions
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]
More exam practice
1 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]
© Hodder Education 2011 Unit B
25

Exam questions: Unit B
5 Angles
Here is an exam question …
62°
y
x
45°
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]
3
A
D
z ° x °
In the diagram ABC is a straight line. AB is parallel
to DE. BD = BA.
Find the value of
a 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.
p
y °
146°
p
98°
136°
B
E
C
… and its solution
a i 180 − (62 + 45) = 73º ii …add to 180º.
b i 45º ii …are equal.
Now try these exam questions
1 Find the size of each of the angles marked a, b, c. In
each case give a reason for your answer.
c
66°
b
a
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.
50° x
z
135°
112° 125°
y
47°
2 Calculate the angles marked with letters. Explain
your reasoning.
a
64°
d
118°
[3]
6 Fractions and
mixed numbers
[6]
c b e
[5]
Here is an exam question …
a Work out 3 7
of 35 kilograms. [2]
b Which is the greater, 2 13
3
or
20
of an amount [2]
26 Revision Notes © Hodder Education 2011

… and its solution
a 3 7 of 35 kg = 3 7 × 35
= 15 kg
b
3
2 2
3
39
= 60
40
=
60
, 13
20
is the greater.
Change both fractions to the
same denominator.
7 Circles and
polygons
Here is an exam question …
Now try these exam questions
From the six words below, pick the correct one for each
1 Work out the following, giving your answers as
label on the diagram.
a)
simply as possible.
Diameter
4 A piece of metal is 2
4 1 inches long. Stuart cuts
off 7
16 of an inch. How much is left [3] … and its solution
a 2 4
3
+
5
b 3 5
5
× 6
[2]
[2]
Tangent
Arc
b)
c)
3
,
7
,
3
,
5
Radius
4 10 5 8
[2]
3 Work out these, giving your answers as simply as
Circumference
2 Put these fractions in order of size, smallest first.
Chord
possible.
d)
3 1
a 2
8
– 12
[3]
b
3
2 ÷
4
5
[2]
[3]
More exam practice
1 Work out these, giving your answers as fractions, as
simply as possible.
a 11
3
+ 2
[3]
4
5
b 3 4
5
×
9
[2]
2 Work out these.
3 1
a 4 – 2
[3]
b
3
10
16
2
÷
4
15
[2]
3 These are the lengths of four nails in inches.
11
7
, 1 , 11
, 1
2
16
4
3
8
Put them in order, smallest first. [2]
4 Work out these.
4 5
a 5
×
9
[2]
b 3 8
÷ 6
[2]
a Tangent
b Arc
c Diameter
d Chord
Now try these exam questions
1 A weighing machine has a dial which shows up to
5 kilograms.
5 kg
0
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 arc
b A radius
c A tangent [3]
© Hodder Education 2011 Unit B
27

Exam questions: Unit B
More exam practice
1
2
B
60°
A
a
40°
b
D
60° 60°
C
a Find the size of angle a.
b What type of triangle is ABC
c Find the size of angle b. [3]
34°
... and its solution
a 6x − 8 − 5x − 15 = x − 23
Take care with the signs. −5 × +3 = −15
b 3a(a + 2b)
3a is common to both terms.
c i H = 17 − 6
= 11
ii H = 17 − −2
= 19
d 8a 6
Mulitply the numbers and
add the indices.
x
y
Find the size of x and y. Give reasons for your
answers. [4]
3 Here is a sketch of a regular pentagon, centre O.
B
x
A
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
indices
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.
3a 2 + 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 2a 4 × 4a 2 . [2]
Now try these exam questions
1 Which of these are correct
i p 3 = p × 3
ii p 3 = p + p + p
iii p 3 = p × p × p
iv p 3 = p 2 + p [1]
2 Simplify these.
a x 4 y 3 × x 3 y 2 [2]
b 3x 2 y 3 × 2xy 2 [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 17 3
ii 1225 [1 + 1]
b Simplify.
i 8 7 ÷ 8 4
ii 3 7 3 5
×
6
[1 + 1]
3
5 a Put a circle round the term which is equal to
r × r × r × r × r
5r r + 5 r 5 r5 [1]
3
b Work out 729
[1]
9 Decimals and
fractions
Here 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]
28 Revision Notes © Hodder Education 2011

... and its solution
a i
b 1 5
1
5
ii
375
1000
3
8
3
8
+ = 0.2 + 0.375 = 0.575
Converting this to a fraction = 575
1000
= 23
40
Divide numerator and denominator
by 125, that is by 5 and by 5 and
by 5.
Divide numerator and
denominator by 25.
Now try these exam questions
1 Write each of the following fractions as a decimal.
a 2 5 b 2 9 [3]
2 a Work out 2 5 + 1 3 [2]
b Convert 2 5 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]
10 Real-life
graphs
… and its solution
a
Weight
(T tonnes)
b i 150 tonnes
ii About 33 m 3
c About 167 m 3
600
500
400
300
200
100
(i)
(ii)
0 10 20 30 40 50 60 70 80 90 100
Volume (V m 3 )
If the volume of coal is
zero, weight will be zero.
Draw a straight line from
(0, 0) to (100, 600).
Now try these exam questions
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$), for amounts up to £100.
250
Here is an exam question …
The weight (T tonnes) of coal and its volume (V cubic
metres) are related.
100 m 3 of coal weighs 600 tonnes.
a Draw a conversion graph for volume (V) and
weight (T ). [3]
b Use your graph to find
i the weight of 25 m 3 of coal. [1]
ii the volume of 200 tonnes of coal. [1]
c Use this information to estimate the volume of
1000 tonnes of coal. [1]
Australian dollars
(AU$)
200
150
100
50
0 10 20 30 40 50 60 70 80 90 100
Pounds (£)
© Hodder Education 2011 Unit B
29

Exam questions: Unit B
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$175. [1]
3 Gayla records the temperature in the school garden
every hour. Here is a graph showing some of her
results on a particular day. She forgot to take the
temperature at 4 p.m.
Temperature (°C)
20
18
16
14
12
10
8
6
4
2
0 9 10 11 12 1 2 3 4 5 6
a.m.
noon
Time
p.m.
a At what time was the highest temperature
recorded [1]
b Estimate when the temperature was first 9 °C. [1]
c The temperature fell steadily between 3 p.m. and
5 p.m. Estimate the temperature at 4 p.m. [1]
4 Jim went out walking.
In the diagram ABCD represents his walk.
Distance from start (km)
10
D
9
8
7
B
6
C
5
4
3
2
1
A
0 1 2 3 4 5 6
Time (hours)
a How far had Jim walked after 1 1 2 hours [1]
b What does the part of the graph BC represent [1]
c After walking 9 km, Jim turned round and walked
straight back to his starting place without
stopping. It took him 2 hours to get back.
Draw a line on a copy of the grid to show this. [2]
d Work out his average speed on the return
journey. [2]
More exam practice
1 The table shows the number of litres of fuel left after
a car has travelled a certain number of kilometres.
Distance travelled (km) 0 50 100 200
Fuel left (litres) 50 45 40 30
a i Draw a pair of axes. Put distance on the
horizontal axis, using a scale of 1 cm to 50 km.
Put fuel left on the vertical axis, using a scale
of 2 cm to 10 litres. [1]
ii Plot the points from the table and join them
with a straight line. [1]
b Find the fuel left after travelling 75 km. [1]
c Find the distance travelled when there is 35 litres
of fuel left. [1]
d If the car continued travelling at the same rate
until it ran out of fuel, how far would it have
travelled [1]
2 This conversion graph is for pounds (£) to Hong
Kong dollars (HK$), for amounts up to £50.
Hong Kong dollars (HK$)
700
600
500
400
300
200
100
0 10 20 30
Pounds (£)
40 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]
30 Revision Notes © Hodder Education 2011

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.
40
30
Temperature (°C)
20
10
0
10
0200 0400 0600 0800 1000 1200 1400 1600 1800 2000 2200 2400
Time
20
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).
°F
150
100
50
0 20 40 60 °C
Use the graph to change
a 30 °C to °F b 115 °F to °C. [2]
© Hodder Education 2011 Unit B
31

Exam questions: Unit B
6 This graph can be used to convert distances in miles
to distances in kilometres.
Kilometres
200
150
100
50
0 20 40 60
Miles
80 100
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 convert
a 5 kilograms to pounds.
b 75 pounds to kilograms.
11 Reflection
Here is an exam question …
Use the graph to change
a 20 miles to kilometres.
b 100 kilometres to miles.
7 This graph can be used to calculate the fare for a
taxi ride.
50
40
A
y
5
4
3
2
1
543210 1
1 2 3 4 5
2
3
E
4
5
C
B
D
x
Cost (£)
30
20
10
0 2 4 6 8 10 12 14 16 18 20
Distance (miles)
a Describe the transformation that maps
i B on to D ii A on to C
iii 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 solution
a i Reflection in y = 3 ii Reflection in x = −1
iii Reflection in y = − 1 2
b E is closer to the line.
iv Reflection in y = x
Use the graph to find
a 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 convert
a 5 gallons to litres.
b 75 litres to gallons.
Now try these exam questions
1 Draw the image of shape A after reflection in the
mirror line.
Mirror line
A
[2]
32 Revision Notes © Hodder Education 2011

2
y
7
6
5
4
3
2
1
A
b
Copy the diagram above and then draw on it all
the lines of reflection symmetry. [1]
3
–7 –6 –5 –4 –3 –2 –1
–1
0 1 2 3 4 5 6 7 x
–2
–3
–4
–5
–6
–7
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]
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.
12 Percentages
Here 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 solution
a 58% are girls
b 42% = 42
100
= 21
50
c 0.12 × 900 = 108
42 + 58 = 100
Cancel by 2.
12 × 900 = 10 800 and there are two figures
after the decimal point, giving 108.00 = 108.
Now try these exam questions
1 a Shade 75% of this shape. [1]
5 a
[4]
Shade 1 more square to give the shape 2 lines of
reflection symmetry. [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%, 3 5 , 0.62, 0.59, 55% [3]
© Hodder Education 2011 Unit B
33

Exam questions: Unit B
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]
More exam practice
1 Write each of these as a percentage.
a 0.06 [1]
b 2 5 [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]
Recognising and describing rotations
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.
… and its solution
a and b
y
4
2
4
c Reflection in the x-axis.
2
4 2 0 2 4
x
y
4
2
4 2 0 2 4
x
R
2
4
Now try these exam questions
T
T
S
[3]
13 Rotation
Rotation symmetry
1 Which two of these shapes are congruent
A
B
C
D
Try this exam question
For each of these shapes, state
a how many lines of symmetry it has.
b its order of rotational symmetry.
E
G
F
H
[4]
[1]
34 Revision Notes © Hodder Education 2011

2 The diagram shows shapes A and B.
3
y
3
2
1
A
3 2 1
1
1 2 3
2 B
3
x
Describe fully the single transformation that maps
shape A on to shape B.
C
y
5
4
3
2
1
A
B
543210 1
1 2
2
3
4
5
x
3 4 5
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]
Now try these exam questions
1 Use estimation techniques to show that these sums
are incorrect.
a 0.38 2 × 18.6 = 26.8584 [2]
b 24.608 ÷ 1.2 = 25.5296 [2]
c
84.
456
= 16.
8
[2]
7. 824 + 4.
6
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
2 3 1
b 15
÷
4
= 120
c −6.3 × −2.4 ÷ −1.5 = 10.08 [3]
3 Estimate the answer to this calculation.
8.
935
0. 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 to
a 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]
14 Estimation
Here is an exam question ...
Use estimation techniques to show that these sums are
incorrect.
a
53. 73 × 0.
097
= 2.
6865
[2]
19.
4
b 23.815 ÷ 0.85 = 20.242 75 [2]
... and its solution
a Rounding each number to 1 sf we get
50 × 0.
1 5
= = 0.
25
20 20
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 Enlargement
Here 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]
y
14
12
10
8
6
4
2
0 2 4 6 8 10 12 14 16 18 x
.
© Hodder Education 2011 Unit B
35

Exam questions: Unit B
.. 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).
y
14
12
10
8
6
4
2
3 For this diagram, describe fully the single
transformation that maps trapezium Q on to
trapezium R. [3]
4
y
4
3
2 R
Q
1
21
1
1 2 3 4 5 6 x
2
y
4
0 2 4 6 8 10 12 14 16 18 x
2
A
B
Now try these exam questions
1 The diagram shows shape A.
y
3
2
1
A
3 2 1
1
1 2 3
2
3
x
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.
y
7
6
L
5
4
B
3 A
2
1
4321
1
1 2 3 4 5 x
2
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
0 2 4
6 x
Find the centre and scale factor of the enlargement
that maps shape A on to shape B. [3]
5
y
10
9
8
7
6
5
4
3
2
1
A
–4 –3 –2 –1
–1
0 1 2 3 4 5 6 7 8 9 10 11 x
–2
–3
–4
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
B
…………………… [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]
36 Revision Notes © Hodder Education 2011

16 Scatter diagrams and
time series
Here 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 solution
a and c
40
Number of bikes hired
35
30
25
20
15
10
5
0
2 4 6 8 10 12
Hours of sunshine
b Positive correlation
d About 12 bikes
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.
© Hodder Education 2011 Unit B
37

Exam questions: Unit B
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]
Iron produced (million tons)
9
8
7
6
5
4
3
6 8 10 12 14 16
Coal used (million tons)
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
38 Revision Notes © Hodder Education 2011

a Complete the scatter diagram. (The first 5 points have been plotted for you.) [2]
13
Weekly admissions (thousands)
12
11
10
9
8
7
10 12 14 16 18 20 22
Number of screens
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]
© Hodder Education 2011 Unit B
39

Exam questions: Unit B
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]
17 Straight lines
and inequalities
Straight-line graphs
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.
… and its solution
a i
y
5
4
3
2
1
(4, 5)
21 1
x
1
0 2 3 4 5
y
2
1
1
2
y 2x 3
x 2y 4
0 1 2 3 4
x
[2]
ii
x = 2 and y = 1 (the coordinates of the point
where the lines meet).
b Gradient = 3 4
Now try these exam questions
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 of
a side AC. [2]
b side AB. [2]
2 Write down the gradient of the line with
equation y = 2x − 4. [1]
More exam practice
1 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]
y
5
4
3
2
1
0
1
1 2 3
x
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]
3
40 Revision Notes © Hodder Education 2011

Graphical solution of simultaneous
equations
Now try this exam question
1 Solve these simultaneous equations graphically.
y = 3x + 4 x + y = 2 [4]
18 Congruence
and
transformations
Inequalities
Here is an exam question …
a Describe the inequality shown on these number
lines.
i
0 1 2 3 4 5 6
[1]
Here is an exam question …
y
4
A
2
2
0 2 4 6 8 10 x
2
ii
3 2 1 0 1 2 3 4
[1]
b Solve the inequality 5x 3x + 8. [2]
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]
… and its solution
a i 1 x 6 ii −2 x 3
b 5x 3x + 8
2x 8
x 4
… and its solution
B
y
4
2
A
x 3
C
Now try these exam questions
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]
2 0 2 4 6 8
2
10
x
© Hodder Education 2011 Unit B
41

Exam questions: Unit B
Now try these exam questions
1 Which of these pairs of triangles are congruent
A
B
C
E
D
F
3 Which two of the triangles A, B, C and D are
congruent to triangle X
Explain why you chose these triangles.
43°
43°
2.5 cm
2.5 cm
A
X
67°
67°
2.5 cm
43°
B
70°
G
2 The grid shows the position of shape A.
y
7
6
5
4
3
2
1
H
[3]
–7 –6 –5 –4 –3 –2 –1
–1
0 1 2 3 4 5 6 7 x
–2
–3
–4
–5
–6
–7
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]
A
4
70°
67°
2.5 cm
C
y
5
4
3
2
1
NOT TO SCALE
A
543210 1
1 2
2
3
4
5
x
3 4 5
2.5 cm
[4]
a Reflect triangle A in the line x = 3.
Label the image B. [2]
⎛ 3⎞
b Translate triangle A by
⎝
⎜
–4⎠
⎟
Label the image C. [2]
D
70°
63°
42 Revision Notes © Hodder Education 2011

1 Two-dimensional representation
of solids
Here is an exam question ...
The diagram represents a toilet roll.
12 cm
6 cm
11 cm
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 solution
a
© Hodder Education 2011 Unit C
43

Exam questions: Unit C
Now try these exam questions
1 This sweet box is in the shape of a prism.
The base is an isosceles right-angled triangle.
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]
P
7.4 cm
S
5.2 cm
Construct the net of the box. [4]
2 a How many faces does this L-shaped prism have
2 cm
1 cm
2 cm
3 cm
1 cm
3 cm
44 Revision Notes © Hodder Education 2011

More exam practice
1 The diagram shows the net of a box.
3 cm
2 cm 2 cm
8 cm
2 cm 2 cm 2 cm 2 cm
8 cm
2 cm
2 cm
8 cm
8 cm
3 cm
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.
… and its solution
a i
1
9
ii 0
iii
2
9
b i 1, 2, 3
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
3, 2, 1
ii
5
6
4 and 8 are both multiples of 4.
There are six ways of playing the
three tracks.
Now try these exam questions
1 Here is a fair spinner
used in a game.
4
6
4
8
7
5
6
4
Make an isometric drawing of the shape. [3]
2 Probability 1
Calculating probabilities
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]
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]
0 1
c Mark with a cross (), on the scale below, the
probability that she gets an even number score.
Explain your answer. [2]
0 1
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]
A
B
C
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]
© Hodder Education 2011 Unit C
45

Exam questions: Unit C
More exam practice
1 Choose the most appropriate word from this list to
describe each of the events below.
Impossible Very unlikely Unlikely Evens
Likely 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 is
a 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.
Bread
B
B
Filling
C
E
Experimental probabilities
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 be
a silver.
b blue.
Give your answers as fractions in their lowest
terms. [3]
... and its solution
The total number of cars = 36 + 44 + 28 + 60
+ 32 = 200.
a Experimental probability of a silver car 60
200
b Experimental probability of a blue car 200
28
Now try these exam questions
= .
3
10
7
50
= .
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 down
a 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
[2]
b Explain why the probability that the first
customer buys a brown bread and cheese
sandwich does not have to be
1
number 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]
Estimate the probability that one of the passengers
chosen at random travelled in
a first class.
b business class. [3]
46 Revision Notes © Hodder Education 2011

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
Number
of
people
Cheese
& onion
Other
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]
Now try these exam questions
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 cm 2 . [2]
b Work out the perimeter of each of your
rectangles. [2]
More exam practice
1 Find the perimeter and area of each of these shapes.
a
3 Perimeter, area
and volume 1
Here is an exam question ...
a Find the perimeter of this rectangle. [2]
b Find the area of this rectangle. [2]
b
7 cm
4 cm
... and its solution
a 7 + 4 + 7 + 4 = 22 cm
b 7 × 4 = 28 cm 2
[4]
© Hodder Education 2011 Unit C
47

Exam questions: Unit C
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.
... and its solution
a Volume of cuboid = length × width × height
= 40 × 20 × 30
= 24 000 cm 3
b Surface area = 2 × top + 2 × side + 2 × front
= 2(20 × 40) + 2 (40 × 30) + 2(20 × 40)
= 1600 + 2400 + 1200
= 5200 cm 2
Now try these exam questions
1 Calculate the volume of this cuboid. [2]
4.6 m
5.2 m
1.5 m
41.2 m
2 The volume of water in this fish tank is 10 000 cm 3 .
All the sides and base of the tank are rectangles.
79.6 m
Work out the area of the field. [2]
5 Mr Chan has drawn this plan of his lounge floor.
2
2
20 cm
50 cm
d
1 1
4
Calculate the depth of water in the tank. [3]
6
4 Measures
What is the perimeter and area of his lounge floor
All lengths are in metres. [4]
The volume of a cuboid
Here is an exam question ...
a Find the volume of this cuboid. [2]
b Find the total surface area of this cuboid. [2]
20 cm
40 cm
30 cm
Here is an exam question ...
3 m
5 m
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]
48 Revision Notes © Hodder Education 2011

... and its solution
a Upper bound 5.5 m Lower bound 4.5 m
b 5.5 × 3.5 = 19.25 m² Upper bound of width = 3.5 m
c 19.25 × 10 000 = 192 500 cm²
Now try these exam questions
1 A rectangle has dimensions 354 cm by 64 cm.
a Work out the area
i in cm 2 . ii in m 2 .
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/cm 3 .
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 km 2 . 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]
5 The area of
triangles and
parallelograms
Here is an exam question …
The area of this triangle is 48 cm².
Calculate the value of h. [3]
h cm
12 cm
… and its solution
Area = 1 2
× 12 × h = 48
So 6h = 48
And h = 8 cm
Now try these exam questions
1 a Find the area of this triangle.
5.0 cm
18 cm
13 cm
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]
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]
Not to scale
4.6 cm
4.6 cm
0.7 cm
5 cm
6 cm
© Hodder Education 2011 Unit C
49

Exam questions: Unit C
3 The area of this triangle is 18.9 cm².
The height, AD, = 4.5 cm.
Calculate the base, BC, of the triangle.
4
B
A
D
D
C
C
6 Probability 2
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]
5
A
5.2 cm
3 cm E 6 cm
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]
8 cm
B
5 cm
… and its solution
a P(Circle) = 1 − (0.2 + 0.35 + 0.3)
= 1 − 0.85
= 0.15
b 3 parts blue, 1 part red.
P(red) = 1 4
Now try these exam questions
1 The probability of getting a 2 with a spinner is 3 5 .
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.
4 cm
3 cm
Colour Orange White Yellow Green Red
Probability 0.05 0.2 0.25 0.35
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.
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]
More exam practice
1 Ahmed is counting vehicles passing a junction
between 8.00 a.m. and 8.30 a.m.
5.6 cm
8.5 cm 4.8 cm
Calculate the height of the parallelogram. [4]
Vehicle Cars Motorcycle Lorries
Frequency 72 15 28
Vehicle Vans Buses
Frequency 33 12
50 Revision Notes © Hodder Education 2011

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]
… and its solution
Shape = square of side 20 cm + one whole circle of
radius 10 cm
Area of shape = 20 × 20 + π × 10 2 = 714.2 cm 2 (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 = 1 2 × πr2
= 1 2 × π × 2.52
Volume = area of end × length
= ( 1 2 × π × 2.52 ) × 11
= 108 m 3 (to 3 s.f.)
5 m
Now try these exam questions
11 m
1 Work out the area of the lawn in this diagram. [4]
7 Perimeter, area
and volume 2
Here 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.
24 m Patio
28 m
2 The circumference of a circle is 26 cm. Calculate
the radius of this circle. [2]
3
3 m
2.5 m
Lawn
20 cm
[6]
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]
© Hodder Education 2011 Unit C
51

Exam questions: Unit C
4 All the lengths in this question are in centimetres.
10
2
6
4
4
2
2
NOT TO
SCALE
7 This sweet box is in the shape of a prism. The base is
an isosceles right-angled triangle.
7.4 cm
5.2 cm
5
a Calculate the perimeter of the shape. [1]
b Calculate the area of the shape. [3]
8 cm
8
Find the volume of the box. [3]
2 cm
1 cm
10 cm
4 cm
3 cm
2 cm
3 cm
1 cm
3 cm
6
a Find the area of this shape. [3]
b Find the perimeter of this shape. [3]
2 m
0.5 m
2
1.5 m
0.8 m
4.5 m
1
1.5 m
3
1.5 m
0.2 m
The diagram shows a games presentation rostrum.
Find the volume of the rostrum. [3]
Calculate the volume of this prism. [2]
9 This is a triangular prism.
7 cm
5 cm
4 cm
3 cm
a Find its volume.
b Find its surface area. [6]
10 Find the volume of coffee in this cylindrical
tin. [3]
7.5 cm
14 cm
52 Revision Notes © Hodder Education 2011

8 Using a
calculator
Here is an exam question …
Work out the following, giving your answers to 2
decimal places.
a 5.6 2 [1]
b
167
24 + 16
[2]
c 2.7 2 + 8.3 2 [2]
d 3 + 5 × 7
[1]
… and its solution
a 31.36
b 4.18
c 76.18
d 6.16
Here is another exam question …
Work out the following. Give your answers correct to 3
significant figures.
a 4.2 4 [1]
b 3 9 2
. + 0 . 53
[2]
3. 9 × 0.
53
c 350 × 1.005 12 [1]
… and its solution
a 311
b 7.61
c 372
Key in
4 . 2 x y 4 =
311.1696
Key in
( 3 . 9 x 2 +
0 . 5 3 )
( 3 . 9 ×
÷
0 . 5 3 ) =
7.614 900 ...
Key in
3 5 0 ×
1 . 0 0 5 x y 1 2
Now try these exam questions
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 . 7
1.
25 2
[2]
2 2
b 5 + 12
[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.
93
3.
75
[2]
b 4.6 × 5.2 − 17.1 [1]
c 3 . 7 + 2 . 1
4.
8
[1]
5 Work out these.
a 4.31 2 − 1.9 2 [1]
b 8 . 2 – 1 . 7
16.
3 2
[2]
c
2 2
4. 75 – 1. 24
[2]
6 Work out these.
a 4.1 2 [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]
4
10 John worked out using a calculator and his
2 + 3
answer was 5. Explain what he did wrong. [1]
=
371.587 234 ...
© Hodder Education 2011 Unit C
53

Exam questions: Unit C
More exam practice
1 Work out these.
a 4 2 3 + 23 4 [2]
b 2 4 7 – 12 3 [2]
3 3
c 5
× 7
[2]
2 Work out these.
a 5 6 [1]
b 31 (Give the answer 2 d.p.) [1 + 1]
c
3.
84
[1]
2. 19 – 1.
59
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 3.2 3 + 2.5 5 [1]
b 37.2 1 4 [1]
c 1.67 −3 [1 + 1]
5 Work out these, giving the answers to 3 significant
figures.
a 3 + 5 + 7
[2]
b
1 1 1
+ + [2]
3 5 7
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 1.4 3 − 0.8 4 [1 + 1]
7 Work out these.
a 2 1 3 – 13 4 [2]
b 2 7
of £434 [1]
194
c
485
, as a fraction in lowest terms [1]
9 Trial and improvement
Here is an exam question …
A solution of the equation x 3 + 4x 2 = 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 solution
x = −3 –3 3 + 4 × −3 2 = 9 Too big.
x = −3.5 −3.5 3 + 4 × −3.5 2 = 6.125 Too small. Try between −3.5 and −3.
x = −3.3 −3.3 3 + 4 × −3.3 2 = 7.623 Too small. Try between −3.3 and −3.
x = −3.2 −3.2 3 + 4 × −3.2 2 = 8.192 Too big. Try between −3.3 and −3.2.
x = −3.25 −3.25 3 + 4 × −3.25 2 = 7.921 875 Too small. Try between −3.25 and −3.2.
x = −3.23 −3.23 3 + 4 × −3.23 2 = 8.033 333 Too big. Try between −3.23 and −3.25.
x = −3.24 −3.24 3 + 4 × −3.24 2 = 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 − 3.235 3 + 4 × −3.235 2 = 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.
54 Revision Notes © Hodder Education 2011

Now try these exam questions
1 The volume of this cuboid is 200 cm 3 .
x 1
10 Enlargement
Here is an exam question ...
4x
x
A
a Explain why x 3 + x 2 = 50. [2]
b Find the solution of x 3 + x 2 = 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]
More exam practice
1 The equation x 3 − 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
x 3 − 5x − 2 = 0 which lies between 2 and 3. Show
all your trials and their outcomes. [3]
3 a Show that the equation x 3 A
− 8x + 5 = 0 has a
root between x = 2 and x = 3. [3]
b Use trial and improvement 5 cmto find this root 6 cm
correct to 1 decimal place. Show all your trials
and their outcomes. [3]
4 The volume, V cm 3 B
, of this cuboid is given by
V = x 3 + 6x 2 .
C
3 cm
D
Triangles ABC and ADE are similar.
Calculate a CE b BC. [5]
... and its solution
First draw the triangles separately.
B
D
B
5 cm 6 cm
A
12 cm
5 cm 6 cm
8 cm
A
12 cm
C
D
C
E
E
8 cm
A
12 cm
x
x
Scale factor = 8 5 = 1.6
AE = 6 × 1.6 = 9.6, so CE = 9.6 − 6 = 3.6 cm
BC = 12
1. 6
= 7.5 cm
x 6
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 cm 3 .
Give your answer correct to 1 decimal place.
Show all your trials. [3]
© Hodder Education 2011 Unit C
55

m
Exam questions: Unit C
B
Now try these exam questions
1 PQRS is an enlargement of ABCD.
3 Q Triangle EDC is similar to triangle ABC.
B
P
7 cm
A
A
9 cm E
8 cm
D C S R 6 cm
10 cm 15 cm
B
C
D
Q
12 cm
P
a Calculate the length of BD. [3]
9 cm
b Calculate the value of this fraction in its
simplest form:
Area of ∆ EDC
[2]
Area of ∆ ABC
C S R
4 Triangles AOB and DOC are similar.
15 cm
A
7.5
B
Calculate the following.
3
a PQ [3]
6 O 5
b BC P[2]
C
D
2 The triangles ABC and PQR are similar.
AO = 3 cm, DO = 5 cm, AB = 7.5 cm and CO = 6 cm.
A
7 cm 9.1 Calculate cm the lengths of the following.
5 cm
a CD [3]
b BO [2]
B
C Q
5 These shapes R are similar.
8 cm
The radius of the small circle is 5 cm. The radius
P
of the large circle is 8 cm.
7 cm 9.1 cm
C
Q
R
Calculate the lengths of the following.
a QR [3]
b AC [2]
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 circle
Circumference of large circle
ii
Area of small circle
[4]
Area of large circle
56 Revision Notes © Hodder Education 2011

11 Graphs
Distance–time and other real-life
graphs
Here is an exam question …
The graph shows Philip’s cycle journey between his
home and the sports centre.
Distance from home
in kilometres
y
8
7
C
D
6
B
5
4
3
2
1
A
E
0 20 40 60 80 100 120
Time in minutes
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 solution
a Philip was at the sports centre.
b Philip’s speed changed, perhaps due to a steep hill.
c Philip arrived home.
d 12 km
6 km there and 6 km back.
Now try these exam questions
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.
Height in metres above sea level
80
70
60
50
40
30
20
10
0 5 10 15 20 25 30
Time in seconds
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]
© Hodder Education 2011 Unit C
57

Exam questions: Unit C
2 Katy needs new carpet for her kitchen. She measures
the floor and draws a plan.
2 m
4.3 m
1.5 m
1.6 m
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]
Cost (£)
200
150
100
50
0 5 10 15
Area (m 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]
More exam practice
1 The graph can be used to divide people into three
groups – underweight, OK and overweight according
to their height.
Weight (kg)
120
110
100
90
80
70
60
50
Overweight
OK
Underweight
40
140 150 160 170 180 190
Height (cm)
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.
Distance from school (km)
8
6
4
2
0
8.20 a.m. 8.30 a.m. 8.40 a.m. 8.50 a.m.
Time
58 Revision Notes © Hodder Education 2011

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]
b x = −1.8 and x = 2.8
y
9
8
y x 2 x 3
7
6
5
4
3
y 2
2 1
2
1
0
x
1 2 3 4
1
2
3
Speed
Time
Now try these exam questions
1 a Complete the table of values and draw the
graph of y = x 2 − 2x + 1 for values of x from
−1 to 3. [2]
Quadratic graphs
Here is an exam question …
a Make a table of values and draw the graph of
y = x 2 − x − 3 for values of x from −2 to 4. [4]
b Use your graph to solve the equation
x 2 − x − 3 = 2. [2]
… and its solution
a
x −2 −1 0 1 2 3 4
x 2 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
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 − x 2 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 − x 2 is as large as
possible. [1]
ii between which values of x the value of
4x − x 2 − 2 is larger than 0. [2]
More exam practice
1 a Complete the table and draw the graph of
y = x 2 − 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 x 2 − 4 = 0. [2]
© Hodder Education 2011 Unit C
59

Exam questions: Unit C
2 a Draw the graph of y = x 2 − 3x − 5 for values
of x from −2 to 5. [4]
b Use your graph to find the solutions of the
equation x 2 − 3x − 5 = 0. [2]
3 a Draw the graph of x 2 + 4x − 4 for values of x
from −6 to 2. [4]
b Use your graph to find the solutions of the
equation x 2 + 4x − 4 = 0. [2]
c On the graph, draw the line y = −5 and use
this to find the solutions of the equation
x 2 + 4x − 4 = −5. [3]
4 z
D
C
A
2
O
G
y
H
B
7
3
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 H
c The midpoint of BC [3]
L
J
E
3
K
1
F
x
More exam practice
1 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 after
a 1 year [2]
b 5 years [2]
12 Percentages
Percentage increase and decrease
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 solution
Total amount = £5500 × (1.04) 5
= £6691.59 (to the nearest penny)
Now try these exam questions
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]
Solving problems
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]
... and its solution
a Increase = 51.9 % increase = 51 . 9 × 100 = 31.86%
162.
9
b 265 × 1.3186 = £349.43 (approx £350)
Now try these exam questions
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
60 Revision Notes © Hodder Education 2011