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
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
B
Mathematics
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
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
C
Mathematics
Answers to exam questions
ii
Unit A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .
Unit B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
11
Unit C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
18
Contents
1
1 Integers
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]
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.
b a multiple of 5.
c a prime number.
d two consecutive numbers.
e a factor of 30.
[1]
[1]
[1]
[1]
[1]
… and its solution
a
b
c
d
e
Any two of 9, 11, 15 and 27
15
3 × 5 = 15
11
8 and 9 or 14 and 15
30 ÷ 6 = 5 and 30 ÷ 15 = 2
6 or 15
Noon
6 p.m.
–3 ºC
2 ºC
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.
Now try these exam questions
1 a Write 478 correct to the nearest 10. bWrite 4290 correct to the nearest 1000. 2 Look at these numbers.
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
From this list choose
a an even number. ba multiple of 7. c a factor of 24. da prime number. e a square number. 3 Write these numbers in order, smallest first.
a 2164, 3025, 4047, 1987, 2146, 3332, 1084 b−3, 6, −8, 4, −2, 1, 0, −4 4 At a weather station, the temperature is
recorded every six hours.
… and its solution
[1]
[1]
Trial
Working out
Result
Too small
6
[1]
[1]
[1]
[1]
[1]
[1]
[1]
6 ÷ 1.5 = 4
42 = 16
Too large

12
2 A magazine advert costs £20, plus 50 pence
per word. Graham paid £48 for an advert.
How many words did it have? 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]
[3]
[3]
Midnight
a How many degrees has the temperature risen
between noon and 6 p.m.?
[1]
bThe 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
3 Data
collection
Here is an exam question …
Simplify these.
a k + k + k + k b 8n − 5n c 4 × f × g [1]
[1]
[1]
… and its solution
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.
a 4k
b 3n
c 4f g
Shoe size
Number of pairs
3–5
3
6–8
4
9–11
8
12 and over
5
Now try these exam questions
1 a Write as simply as possible
[1]
p+p+p+p
bWrite down, in terms of x, the perimeter of this
rectangle as simply as possible.
[3]
... and its solution
9
2x
8
[1]
3x
2 Simplify these.
a 5m + 3m − 4m [1]
[1]
b6k − 3k + 2k [1]
c 4d + 3d − 5d + 2d 3 a Sam has 4 dogs, x cats and y rabbits.
Write an expression for the total number of
pets he has.
[1]
bLee 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]
[2]
b7x + 3y − 2x + 5y
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.
Frequency
7
6
5
4
3
2
1
0
0 3 to 5
6 to 8
9 to 11
Shoe size
12 and
over
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?
bWould you like to see more salads and more
burgers?
3x
2y
2
2y
3x
Revision Notes
[4]
© Hodder Education 2011
2 The table shows the number of passengers travelling
on bus number 38B into town during one day.
a Anil chose these groups: 0−10, 10−20, 20−30,
30−40, 40−50, 50−60.
Explain why these groups are unsuitable.
[1]
bBen 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.
Number of
passengers on bus
Number of buses
(frequency)
Less than 10
5
10−19
24
20−29
19
Absences
30−39
12
0−9
40–49
7
10−19
50–59
3
20−29
Tally marks
Frequency
30−39
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.
Cat
24
17
Girls
Total
Other
Total
62
45
a Copy and complete the table.
[3]
bHow 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]
bDraw 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.
© Hodder Education 2011
[2]
c On the grid below draw a bar chart to show the
distribution of number of absences.
27
38
50−59
Frequency
Boys
Dog
40−49
13
12
11
10
9
8
7
6
5
4
3
2
1
0
Number of absences
[3]
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
Unit A
3
Exam questions: Unit A
Now try these exam questions
Here is another exam question …
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]
bA 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
0.1
0.2
0.25
0.5
0.52
[4]
5 Formulae
… and its solution
a
b
4
K=5×3−8
=7
L=3×4+2×5
= 12 + 10
= 22
Revision Notes
g
g
f
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
[1]
a x = 2. [1]
b x = 5. 3 If P = 8a + 3b, find P when
[2]
a a = 5 and b = 4 [2]
b a = 4 and b = 2.5 4 P and k are connected by the formula P = 20 + 4k.
Find the value of P when
[2]
a k = 2. [2]
b k = 5.5. More exam practice
Here is an exam question …
a K = 5p − 8. Find K when p = 3. b L = 3q + 2r. Find L when q = 4 and r = 5. The diagram shows an isosceles triangle whose base is f
and whose other two sides are g.
[2]
[2]
1 For the formula G = 21 x − 3, work out the value
of G when
a x = 12. b x = 4. 2 For the formula K = 25 − 7g , work out the value
of K when
a g = 3. b g = −2. 3 For the formula H = 0.5a, work out the value of
H when
a a = 12. b a = 4. 4 If Q = 7xy, find Q when
a x = 5 and y = 2. b x = 6 and y = 1.5. [1]
[1]
[1]
[1]
[1]
[1]
[1]
[1]
© Hodder Education 2011
6 Equations 1
7 Coordinates
Here is an exam question …
Here is an exam question …
a Find the values of a and b.
15
5
31
a Plot the following points on the grid. a
4
Solve the following equations.
i 6x = 30 ii x + 5 = 3 iii x = 5 4
b
b
y
8
[2]
7
6
5
[1]
[1]
4
3
[1]
2
1
… and its solution
a
b
0
a = 5, b = 9
i x = 30 ÷ 6
= 5
ii x = 3 − 5
= − 2
iii x = 5 × 4
= 20
b
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
[3]
i 10
ii 19
[1]
a y
8
7
G
C
6
D
5
4
3
E
B
2
1
A
F
1 2 3 4 5 6 7 8
x
2
[4]
2 Solve the following equations.
[1]
a 8x = 32 [1]
b x − 6 = 9 x
[1]
c = 7 5
3 Given that x = 9 and y = 7, calculate the value
of x2 − 5y. [2]
v –u
may be used to find the
4 The formula t =
a
time taken for a car to accelerate from a speed u
to speed v with acceleration a.
[3]
Find t when v = 11.9, u = 5.1 and a = 1.7. 5 The cost, C pence, of printing n party invitations is
given by C = 120 + 4n.
[2]
Find a formula for n in terms of C. © Hodder Education 2011
x
A(3, 1), B(7, 3), C(5, 7), D(3, 5),
E(2, 3), F(5, 1), G(2, 7)
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. 0
5
1 2 3 4 5 6 7 8
… and its solution
Chief Examiner says
b
[3]
b (1, 5)
Unit A
5
Exam questions: Unit A
Now try these exam questions
1
y
5
4
3
2
1
543210
1
2
3
4
5
a Write down the coordinates of A, B, C and D. [4]
bWrite down the equations of the lines passing
through the following points.
i A and B
ii B and C
[2]
5 y
A
5
4
3
2
1
1 2 3 4 5 x
a State the coordinates of point A.
bPlot 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]
bside AB. [2]
3 A is the point (2, 4).
y
7
6
5
4
3
2
1
A
1 2 3 4 5 6 7 x
7 6543210
1
C
2
3
4
5
6
7
A
y
3
2
1
3210
1
2
3
D
4
6
B
1 2 3 4 5 x
b
a Write down the equation of line a. bWrite down the equation of line b. c On the grid draw and label the line x = −3. dOn the grid draw and label the line y = 0. [1]
[1]
[1]
[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]
B
a Write down the coordinates of i B ii C.
bPoint D is such that ABCD is a square. Plot
point D on the grid.
4 ABCD is a trapezium.
543210
1
2
3
4
5
a
[2]
[1]
… and its solution
a Mode = 4
b Median = 5
The value that occurs most often.
There are two middle values, 5
and 5, so the median must be 5.
1 2 3 4 x
Revision Notes
C
© 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
6 The table below shows the number of letters
per word in the first paragraph of two books.
Frequency
Number of letters (n)
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]
1−3
2 The weights, in kilograms, of a rowing crew are as
follows.
80 83 83 86 89 91 93 99
Calculate
a the mean. [3]
bthe 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]
bCalculate the mean number of people per day. [4]
c Find the mode. [1]
4 The data below shows the time taken, in minutes,
by each of 30 students to solve a puzzle.
3 6 14 18 20 14 6 16
13 7 15 8 15 10 14 10
15 5
4
9 16 9 15 12
14 10 6 13 15 12
What is the modal class? [1]
5 A school has to select one student to take part in
a general knowledge quiz.
Kim and Pat took part in six trial quizzes. The
following table shows their scores.
Kim
28
24
21
27
24
26
Pat
33
19
16
32
34
16
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
b
i
ii
i
ii
c 27
the rule is + 7
37
23 + 7 + 7 = 37
5
The rule is −4 and
17 − 4 − 4 − 4 = 5
2 × 4 − 1 = 7, 7 × 4 − 1 = 27
a Calculate Pat’s mean score and range. [2]
bWhich 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
1 For each of these sequences, the numbers are the
number of lines in each picture.
a
7
4
9
7
10
13
c
8
15
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]
bThere 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]
[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, …
b18, 15, 12, 9, …
c 1, 3, 9, 27, …
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
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 (cm2)
Now try these exam questions
1 aPat weighs 106 pounds. Estimate her weight in
kilograms.
bPat is 5 feet tall. How tall is this in metres? [4]
2 Write down the temperature shown on these scales.
a 40
50
90
Temp
°C
80
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]
bFind the term-to-term rule for each of these
sequences.
i 2 5
8
11 …
[2]
ii 30 23 16 9 …
[2]
Here is an exam question …
70
3n
10 Measures
60
3, 4, 5, 6, 7
Revision Notes
22
29
8
30
5
20
3
10
b
c Find the term-to-term rule for the number of
squares in this sequence of patterns.
0
Exam questions: Unit A
Now try these exam questions
© Hodder Education 2011
… and its solution
b
a N
50
60
70
Temp °C
80
B
C
Diagram shown
half size.
c
0
100
Temp °C
200
A
[3]
3 Write these measurements in order of size,
smallest first.
1234 ml 2.59 l 0.375 l 4.68 l 579 ml
[2]
4 a Jim travelled 20 miles home from work.
Approximately how many kilometres is this? [2]
bOn 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]
bEstimate the length of a family car. [1]
Scale 1 cm to 50 m
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.
N
N
C
20 m
8m
A
15 m
B
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
11 Constructions 1
Here is an exam question …
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.
Simon went orienteering. This is a sketch he made of
part of the course.
C
N
B
125°
47°
200 m
Scale 1 cm to 2 m
C
N
300 m
A
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]
© Hodder Education 2011
A
B
Note: the diagram above is not to scale.
Now use your protractor, with the zero line along
the North line, to measure the bearing. It should be
between 069º and 070º.
Unit A
9
Exam questions: Unit A
Now try these exam questions
1 This is a sketch of triangle ABC.
C
9.1 cm
148°
B
5.3 cm
A
a Make an accurate drawing of the triangle.
bMeasure the length of CB and the size of angle BAC.
2 a Draw angles of the following sizes.
i 63°
ii 109°
iii 256°
bMeasure these angles.
i
ii
[4]
[2]
[3]
iii
3 Measure these angles.
a b
10
Revision Notes
[3]
[2]
© 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.
bFind the distance between P and Q.
c Find the bearing of P from Q. 5 The diagram shows a triangle ABC.
The bisector of the angle at A meets line BC at X.
[5]
C
X
8 cm
A
120°
12 cm
B
a Construct the triangle and the bisector of angle A.
bMeasure the distance AX. [5]
Now try these exam questions
12 Using a
calculator
Give your answers to 2 decimal places where
appropriate.
1 Work out these.
283 – 103
a
360
1
b3.2 5.2 −
1.6
1
c
4.5 + 6.8
2 Work out these.
(
Here is an exam question …
Work out the following. Give your answers to 2 decimal
places.
a 4.24 [1]
3.92 + 0.53
b
[2]
3.9 × 0.53
c 350 × 1.00512 [1]
2
.
2
xy
4
=
3
.
9
x2
+
÷
0
.
5
3
)
(
3
.
9
×
0
.
5
3
)
=
7.614 900 ...
c 371.59
[2]
[2]
[2]
2
[2]
4 a Work out of £4.56. bA travel firm offers a discount of 12% on a
holiday costing £490.
How much is the discount? c Three tins of dog food cost £1.38.
What will eight tins of the same dog food
cost? 5 Work out these.
4.6 – 3.9
a
2.5
14
b
2.5 + 7.3
Key in
(
[2]
2
3
311.1696
b 7.61
[2]
b 14.3 – 9.4 Key in
4
)
a 52 of 65 g b35% of £720 3 Work out these.
a 1.6 − 2.8 × 0.15 … and its solution
a 311.17
[1]
Key in
3
5
0
×
1
.
0
0
= 371.587 234 ...
© Hodder Education 2011
5
xy
1
2
6 c 13.69
A recipe for 4 people uses 360 g of flour and
60 g of butter.
How much flour and butter is needed for 6
people? [2]
[2]
[2]
[1]
[2]
[1]
[2]
Unit A
11
a 72 of £19.60 b12.5% of £980 8 Work out these.
[2]
[2]
a 14.6 + 12.44 b14.52 − 12.62 9To fly to America, Bernard bought a ticket for
£748. He had to pay a surcharge of 2.5%.
How much was the surcharge? 10 Work out these.
a 4.7 × 3.9 − 2.6 b(14.6 − 8.6) × 3.5 4.05 15.12
+
c
1.5
6.3
[2]
[2]
[2]
a
3
5
of 200 g b 234 − 154 [2]
[1]
[1]
[2]
12
Revision Notes
8
6
4
2
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
[1]
400–499
0
[2]
500–599
0
[1]
[1]
[1]
c of £26.60 [1]
4 Work out these, giving your answers to 2 decimal
places where appropriate.
a 730 × 1.0115 [1]
b 14 840 × 1.03
c
840 + 1.03
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.
0
4
7
1
3
Here is an exam question …
[1]
[1]
More exam practice
1 Work out these, giving the answers to 2 decimal
places.
a 3.45 b (5.1 + 3.7) × 4.2 5.1 × 2.6
c
14.2 – 6.3
2 Work out the reciprocal of each of these.
Give your answers to 2 decimal places where
appropriate.
a 50 b 0.75 c 32 3 Work out these.
13 Statistical
diagrams 1
Frequency
Exam questions: Unit A
7 Work out these.
[1]
[2]
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).
© 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
Here is an exam question …
a Find the HCF and LCM of 12 and 16. b Work out these, writing each answer as a whole
number.
i 56 ÷ 54 ii 23 × 25 ÷ 27 iii 62 × 52 ÷ 22 [4]
[1]
[1]
[2]
… and its solution
Other
Liberal
Democrats
14 Integers,
powers and
roots
Conservative
Labour
a The Liberal Democrats had 4534 councillors.
Approximately
how many councillors were ‘Others’? [1]
bMeasure 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]
a
b
12 = 2 × 2 × 3
16 = 2 × 2 × 2 × 2
HCF = 2 × 2
Two 2s are common to both.
=4
LCM = 2 × 2 × 2 × 2 × 3
Four 2s and one 3 are in at
= 48
least one of the numbers.
i 56 ÷ 54 = 52
6−4=2
= 25
ii 23 × 25 ÷ 27 = 21
3+5−7=1
=2
iii 62 × 52 ÷ 22 = 36 × 25 ÷ 4
= 225
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 26 b53 c 45 × 42 ÷ 43 2 a Write 30 as the product of its primes. bWrite down the prime factor of 30 that is
also a prime factor of 21. 3 Find the HCF and LCM of 10, 12 and 20. 4 Find the value of (−5)2 + 4 × (−3). 5 a The area of a square is 49 cm2. Work out the
length of one side of the square. bWork out 43. c If the reciprocal of a number is 2.5, what is
the number?
© Hodder Education 2011
[1]
[1]
[2]
[2]
[1]
[5]
[2]
[1]
[1]
[1]
Unit A
13
Exam questions: Unit A
15 Algebra 2
Here is an exam question …
a Expand the brackets and write this expression as
simply as possible.
2(3x − 4) − 5(x + 3) b Factorise this expression completely.
3a2 + 6ab 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
2
d Simplify 2a × 4a . [4]
4 a Multiply out 2(3x + 1). bFactorise completely 12p2 − 15p. 5 Factorise completely 3a2 + 6ab. 6 For the formula S = at + bt2, work out the value
of S when
a a = 3, b = 2, t = 5. b a = 2, b = 3, t = −4. [2]
[2]
[2]
[2]
[2]
[2]
[4]
[2]
… and its solution
16 Statistical
diagrams 2
a 6x − 8 − 5x − 15 = x − 23
Here is an exam question ...
Take care with the signs. −5 × +3 = −15
b 3a(a + 2b)
3a is common to both terms.
c i
ii
d 8a6
H = 17 − 6
= 11
H = 17 − −2
= 19
Multiply the numbers and add the indices.
Now try these exam questions
1 aWrite down the perimeter of this rectangle in
terms of x, as simply as possible.
The numbers below list the ages of the members of a
tennis club.
a Construct a stem-and-leaf diagram with these
ages. [3]
Use it to find out the following.
b How many members the club has
[1]
c The modal age of the members [1]
d Their median age [1]
e The range in their ages [1]
f The fraction of members who are veterans
(over or equal to 40)
[1]
71
39
40
16
57
12
63
34
41
45
17
52
27
16
59
40
60
14
22
48
43
38
65
16
35
23
25
52
36
38
26
31
27
2x
3x
2
b P = ab + b . Work out the value of P when
a and b take these values.
i a = 2 and b = 3 ii a = 4 and b = −5 2 a Simplify 2a + 3b + 3a − 3b. bMultiply out 3(x + 2y). c Factorise completely 3a + 6ab. 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 14
Revision Notes
[1]
[2]
[2]
[2]
[2]
[2]
[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
4
0
0
8
1
3
5
5
9
2
7
2
6
0
3
5
7
1
8
Then put each row into order.
© Hodder Education 2011
1
2
4
6
6
6
7
2
2
3
5
6
7
7
3
1
4
5
6
8
8
4
0
0
1
3
5
8
5
2
2
7
9
6
0
3
5
7
1
Finally add a key.
6
3 = 63
33
The modal age (age with the highest frequency) is 16.
The median age is 38.
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.
b
c
d
e
9
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.
Number of journeys
(frequency)
50
40
30
20
10
0
10
20
30
40
Mileage (m miles)
50
The mileages for Mr Ahmed’s journeys are summarised in this table.
Mileage (m miles)
Frequency
0 < m  10
10 < m  20
20 < m  30
30 < m  40
38
44
10
8
a Draw, on the same grid, the frequency polygon for the mileages of Mr Ahmed’s journeys.
bMake two comparisons between the mileages of Mrs Taylor’s and Mr Ahmed’s journeys.
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.
bFind the median mark.
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
6
21
15
33
25
Number of shoppers
Draw a frequency diagram to represent this information.
© Hodder Education 2011
[2]
[2]
[3]
[1]
[4]
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
4
0
6
9
Key 1  9 means 1.9 cm
a Write down the range and the median diameter of Bob’s pebbles. 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
[2]
bDraw a stem-and-leaf diagram for Eddie’s pebbles and find the range and median. c Compare the two distributions. 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. bWhat was the range of the scores? c What was the modal score? 17 Equations 2
Here is an exam question …
Solve the following equations.
a 2(3 − x) = 1 b 5x + 8 = 6 3
c 4(x + 7) = 3(2x − 4) … and its solution
a 2(3 − x) = 1
6 − 2x = 1
−2x = −5
16
x = 221
Revision Notes
[3]
[3]
[4]
[2 + 2 + 1]
[2]
[3]
[1]
[1]
b 5x + 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 b3p − 4 = p + 8 [2]
[3]
c 3m = 9 4
2 Solve 3(p − 4) = 36. 3 Solve 4(x − 1) = 2x + 3. [2]
[3]
[3]
© 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.
[2]
a Write down an equation in x. [2]
bSolve your equation to find x. c Find the area of the rectangle. [1]
5 Solve these equations.
[2]
a 3x2 = 27
[3]
b4x + 1 = 7 − 2x
18 Ratio and
proportion
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?
bHow many cars?
[2]
4 Adrian, Penelope and Gladys shared a lottery win
in the ratio 2 : 5 : 8.
They won £7000.
How much did each receive, correct to the nearest
penny? [3]
5 The table shows the prices of different packs of
chocolate bars.
Pack
Size
Price
Standard
500 g
£1.15
Family
750 g
£1.59
Special
1.2 kg
£2.49
Find which pack is the best value for money. You
must show clearly how you decide. [4]
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]
bAnother 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]
© Hodder Education 2011
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
Unit A
17
Exam questions: Unit A
… and its solution
Distance (d miles)
Number of guests (f)
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
Mid-interval values
df
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
3 The frequency table shows the number of weeks’
holiday taken by 90 different families in one year.
[5]
Weeks
Frequency
0
2
1
31
2
37
3
16
4
3
5
1
a Draw a frequency diagram to show this information. bFind the median number of weeks’ holiday. c Calculate the mean number of weeks’ holiday taken by these families. 18
Revision Notes
[2]
[1]
[3]
© 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.
20 Pythagoras’
theorem
b a2 = b2 + c2
= 4.62 + 5.02
= 46.16
Here is an exam question ...
a = 46.16
a = 6.8 cm (to 1 d.p.)
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
side AE is 2 m.
What is the maximum height of the shed?
[5]
5.0 cm
B
4.6 cm
b Calculate the length of the hypotenuse of this
triangle. Give your answer to a sensible degree
of accuracy. [4]
A
C
E
D
[5]
... and its solution
a Area of triangle = 21 base × height
= 21 × 4.6 × 5.0
= 11.5 cm2
© Hodder Education 2011
Unit A
19
Exam questions: Unit A
2
21 Planning and
collecting
A
11 cm
B
Here is an exam question …
5 cm
D
C
8 cm
Calculate
a BD
bAB
[2]
[2]
3 Find the length of the side marked x.
… and its solution
7.8 cm
x
9.1 cm
4 Calculate the length of this ladder.
[3]
4.2 m
1.8 m
[3]
5
12
6
X
10
a Show, by calculation, that angle X is not a
right angle.
[3]
bIs angle X greater than 90° or less than 90°?
Use your calculations from part a to support
your decision.
[2]
20
Revision Notes
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]
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.
bAsk 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.
ADo you agree that it is good idea to exercise
regularly?
Yes
No Don’t know
[2]
BHow many hours each week do you exercise?
more than 8 [2]
2–4 6−8
© Hodder Education 2011
bNow 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]
bWrite 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
b
i
ii
i
ii
−5
7 − 4 − 4 − 4 = −5
−4 each time.
39
3 + 9 × 4 = 39
4n − 1
The difference between terms is 4, giving 4n.
If n = 1, 4n = 4, so you need to subtract 1.
Now try these exam questions
1 aWrite down the term-to-term rule of the
following sequences.
i 7, 13, 19, 25, 31 [1]
ii 32, 25, 18, 11, 4 [1]
bWrite down the first five terms of the following
sequences.
[2]
i n + 7 [2]
ii 5n − 3 2 The first four terms of a sequence are 3, 8, 13, 18
a Find the 20th term. [1]
[2]
bFind the nth term. 3 The first five terms of a sequence are 1, 3, 6, 10, 15
a Find the eighth term. [1]
bIs 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]
bFind the i 25th ii 50th term of the sequence. [2]
5 aWrite down the term-to-term rule for this
sequence of numbers.
25, 19, 13, 7, 1 [1]
bWrite 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.
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.
© Hodder Education 2011
Tree
H
o
u
s
e
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]
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
Here is an exam question …
H
o
u
s
e
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.
A
Hedge 10 m
B
Fence
24 m
Fence
C
House
D
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
24 Rearranging
formulae
Within 4 miles of the store
£10
Between 4 miles and 7 miles from
the store
£25
Over 7 miles from the store
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
P = 20 + 12 × 3
= 20 + 36
= 56p
20 + 12S = 95
12S = 75
S = 75 ÷ 12
S = 6.25 cm
P = 20 + 12S
P − 20 = 12S
S = P – 20
12
a
b
c
Now try these exam questions
1 Rearrange each of the following to give d in terms
of e.
[2]
a e = 5d + 3 [3]
b e = 4(3d − 7) 2 The pressure in a gas is given by the formula
P = kNT
V
Make k the subject of this formula.
3 Rearrange these formulae to make the letter in
the brackets the subject.
a T = 25 + 20n (n) b A = 5(a − b) (a)
c V = πr 2h i (r) ii (h)
[2]
[1]
[1]
[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
326 Australia 425
+ 397
+292
723
717
England had the higher score.
a England
b Difference
723
–717
6
England’s score was higher by 6 runs.
Now try these exam questions
1 aJohn saves 10p each week.
How many weeks will it take him to save £5? [1]
bCalculate 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]
b2 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.
bi 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.
b Work out the size of angle B.
In each case, give reasons for your answer.
© Hodder Education 2011
[1]
[2]
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 51 of the tickets.
Ben sells 38 of the tickets.
Chris sells the rest.
a How many raffle tickets does Chris sell?
b What fraction of the tickets does Chris sell?
Give your answer in its simplest form.
[5]
[2]
… and its solution
a Anna sells 51 × 200
= 40
c
[1 + 1 + 1]
2 aSketch a rhombus and mark everything that is
equal.
bDraw in all the lines of symmetry.
[3]
3 In this trapezium, angle A is a right-angle.
A
B
= 17
40
Chief Examiner says
Divide numerator and
denominator by 5.
Here is another exam question …
)
= 0.375
b = 0.2
0.375 + 0.2
= 0.575
1
5
Now try these exam questions
1 3
5
bShade some more squares so that is now
shaded.
Not to scale
[1]
[1]
2 * + 37°
bWhat type of triangle is this?
[2]
[3]
0.375
a 8 3.06040
a What fraction of this shape is shaded?
*°
Revision Notes
85
= 200
b Fraction
… and its solution
C
a Which angle is obtuse?
bWhich 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]
bWrite down the name of this quadrilateral. [1]
5 a Work out the sizes of the angles in this
triangle. [3]
24
Chris sells
a Convert 38 to a decimal.
b Add 38 and 51, giving your answer as a decimal.
D
37°
× 200
= 75
200 − 40 − 75 = 85
3
8
Ben sells
[1]
a What fraction of the shape is shaded?
bWhat fraction of the shape is not shaded?
[1]
[1]
c Shade some more squares so that 58 of the
shape is shaded.
[1]
© Hodder Education 2011
More exam practice
3
5
1 Ordinary marmalade is sugar.
What mass of sugar is there in a 340 g jar of
marmalade.
[2]
2 In a hockey tournament, the Allstars had 48 corners.
They scored from 58 of them. How many corners did
they score from?
[2]
3 Jane buys a 3 metre piece of wood.
She cuts off 41 of it.
How many centimetres of wood has she cut off? [2]
4 Put these fractions in order of size, smallest first.
56 , 41 , 125 , 38 [2]
2
5 Which of the following fractions are equal to 3 ?
,4,3
106 , 46 , 10
[2]
15 9 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]
bThe 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]
© Hodder Education 2011
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]
Unit B
25
Exam questions: Unit B
5 Angles
3
D
Here is an exam question …
A
62°
x
45°
y
a
b
i Work out the size of angle x.
ii Complete this statement for angle x.
The angles on a straight line …………………… . i Work out the size of angle y.
ii Complete this statement for angle y.
Opposite angles ……..………………………… . [3]
E
y°
z°
x°
136°
C
B
In the diagram ABC is a straight line. AB is parallel
to DE. BD = BA.
Find the value of
a x
[1]
by
[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.
146°
p
[2]
p
98°
… and its solution
a i 180 − (62 + 45) = 73º
b i 45º
ii …add to 180º.
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.
[2]
Find the value of p.
5 Work out the size of the angles x, y and z in these
diagrams. Give reasons for your answers.
x
50°
66°
b
y
z
a
135°
47°
[3]
2 Calculate the angles marked with letters. Explain
your reasoning.
118°
64°
a
125°
112°
c
d
[6]
6 Fractions and
mixed numbers
Here is an exam question …
c
b
e
a Work out 37 of 35 kilograms.
2
3
b Which is the greater, or
26
Revision Notes
[5]
13
20
of an amount?
[2]
[2]
© Hodder Education 2011
7 Circles and
polygons
… and its solution
a 37 of 35 kg = 37 × 35
= 15 kg
13
39
b 32 = 40
60 , 20 = 60
2
3
Change both fractions to the
same denominator.
is the greater.
Here is an exam question …
Now try these exam questions
1 Work out the following, giving your answers as
simply as possible.
a 32 + 54 [2]
×
[2]
2 Put these fractions in order of size, smallest first.
b 35
5
6
34 , 107 , 35 , 58 [2]
3 Work out these, giving your answers as simply as
possible.
[3]
a 2 38 – 121 b 32 ÷ 54 4 A piece of metal is inches long. Stuart cuts
off 167 of an inch. How much is left?
[3]
1 Work out these, giving your answers as fractions, as
simply as possible.
a 141 + 2 35 [3]
b 35 × 49 [2]
2 Work out these.
b
3
10
– 2 21 ÷ 154 [3]
… and its solution
a
b
c
d
More exam practice
a
d)
[2]
2 41
4 163
From the six words below, pick the correct one for each
label on the diagram.
a)
Diameter
Tangent
b)
Arc
Chord
c)
Radius
Circumference
Tangent
Arc
Diameter
Chord
Now try these exam questions
1 A weighing machine has a dial which shows up to
5 kilograms.
5 kg
0
[3]
[2]
3 These are the lengths of four nails in inches.
7
1
1 3
12 , 116 , 14 , 18
Put them in order, smallest first.
4 Work out these.
[2]
a 54 × 59 [2]
b 38 ÷ 6 [2]
© Hodder Education 2011
a Explain how you can work out that the arrow
turns through 72° for 1 kilogram.
[1]
bOn 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?
bA 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
bA radius
c A tangent
[3]
Unit B
27
Exam questions: Unit B
More exam practice
1
... and its solution
a 6x − 8 − 5x − 15 = x − 23
A
a
60°
B
40°
60°
b
Take care with the signs. −5 × +3 = −15
D
b 3a(a + 2b)
60°
C
a Find the size of angle a.
b What type of triangle is ABC?
c Find the size of angle b.
2
3a is common to both terms.
[3]
34°
c
d
i H = 17 − 6
= 11
ii H = 17 − −2
= 19
6
Mulitply the numbers and
8a
add the indices.
Now try these exam questions
y
x
Find the size of x and y. Give reasons for your
answers.
[4]
3 Here is a sketch of a regular pentagon, centre O.
O
B
x
[5]
[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.
3a2 + 6ab
[2]
c For the formula H = 17 − 0.5a, work out the value
of H when a takes each of these values.
i a = 12
ii a = −4
[4]
4
2
d Simplify 2a × 4a .
[2]
28
Revision Notes
[1]
[2]
[2]
3 a Explain how you know that 28 is about 5.3. [1]
A
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.
4 The interior angle of a regular polygon is 168°.
Find the number of sides of the polygon.
1 Which of these are correct?
i p3 = p × 3
ii p3 = p + p + p
iii p3 = p × p × p
iv p3 = p2 + p
2 Simplify these.
a x4y3 × x3y2
b3x2y3 × 2xy2
bEstimate the value of 95
[1]
4 a Work out.
i 173
ii 1225 [1 + 1]
bSimplify.
i 87 ÷ 84
7
5
ii 3 ×6 3 [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
r 5
[1]
bWork out 3 729 [1]
9 Decimals and
fractions
Here is an exam question ...
a Write the following decimals as fractions.
i 0.2 ii 0.375
b Find the sum of your fractions in part a.
Give your answer as a fraction.
[3]
[3]
© Hodder Education 2011
... and its solution
a i
ii
1
5
375
1000
… and its solution
a
Divide numerator and denominator
by 125, that is by 5 and by 5 and
by 5.
600
500
Weight
(T tonnes)
38
b 51 + 38 = 0.2 + 0.375 = 0.575 575
Converting this to a fraction = 1000
= 23
40 Draw a straight line from
(0, 0) to (100, 600).
Divide numerator and
denominator by 25.
400
300
200
100
0
Now try these exam questions
2 a Work out 52 + 31
[2]
bConvert 52 and 31 to decimals and add them. [2]
c What do the answers to parts a and b show? [1]
.
..
. . 1
3 Using 0.1 = 91, 0.01 = 991 , 0.001 = 999
write these decimals as fractions in their simplest
terms.
.
a 0.5
[1]
..
b0.5 6
[1]
. .
c 0.612
[2]
4 Convert these decimals into fractions.
Write your answers in their lowest terms.
a 0.55
[2]
b0.036
[2]
c 0.2246
[2]
5 a Write these numbers in order, smallest first.
3.3
0.303
0.33
3.03
[2]
bWrite down a decimal which is between
0.207 and 0.27.
[1]
10 Real-life
graphs
Here is an exam question …
The weight (T tonnes) of coal and its volume (V cubic
metres) are related.
100 m3 of coal weighs 600 tonnes.
a Draw a conversion graph for volume (V) and
weight (T ).
[3]
b Use your graph to find
i the weight of 25 m3 of coal.
[1]
ii the volume of 200 tonnes of coal.
[1]
c Use this information to estimate the volume of
1000 tonnes of coal.
[1]
© Hodder Education 2011
(ii)
10 20 30 40 50 60 70 80 90 100
If the volume of coal is
zero, weight will be zero.
Volume (V m3)
b i 150 tonnes
ii About 33 m3
c About 167 m3
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]
bFind 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$), for amounts up to £100.
250
Australian dollars
(AU$)
1 Write each of the following fractions as a decimal.
b 29 [3]
a 52 (i)
200
150
100
50
0
10 20 30 40 50 60 70 80 90 100
Pounds (£)
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]
bUse the graph to find the number of pounds
equal to
i AU$100.
[1]
iiAU$175.
[1]
3 Gayla records the temperature in the school garden
every hour. Here is a graph showing some of her
results on a particular day. She forgot to take the
temperature at 4 p.m.
20
18
Temperature (°C)
16
14
12
10
8
6
More exam practice
1 The table shows the number of litres of fuel left after
a car has travelled a certain number of kilometres.
Distance travelled (km)
0
50
100
200
Fuel left (litres)
50
45
40
30
a iDraw a pair of axes. Put distance on the
horizontal axis, using a scale of 1 cm to 50 km.
Put fuel left on the vertical axis, using a scale
of 2 cm to 10 litres.
[1]
ii Plot the points from the table and join them
with a straight line.
[1]
b Find the fuel left after travelling 75 km.
[1]
c Find the distance travelled when there is 35 litres
of fuel left.
[1]
d If the car continued travelling at the same rate
until it ran out of fuel, how far would it have
travelled?
[1]
2 This conversion graph is for pounds (£) to Hong
Kong dollars (HK$), for amounts up to £50.
4
2
9 10 11 12 1 2 3 4
a.m.
p.m.
noon
Time
5
600
Distance from start (km)
a At what time was the highest temperature
recorded?
[1]
bEstimate 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.
10
9
8
7
6
5
4
3
2
1
0
500
400
300
200
D
100
B
C
0
A
1
2
3
4
Time (hours)
5
6
[1]
a How far had Jim walked after 121 hours?
bWhat 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]
dWork out his average speed on the return
journey.
[2]
30
700
6
Hong Kong dollars (HK$)
0
Revision Notes
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]
© 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
Temperature (°C)
30
20
10
0
0200
0400
0600
0800
1000
1200
1400
1600
1800
2000
2200
2400
Time
10
20
Time
2000
2200
2400
Temperature (°C)
18
3
−8
a Plot the three points from the table and complete the graph.
b i What was the highest temperature recorded?
ii What was the lowest temperature recorded?
c Work out the difference between the highest and lowest recorded temperatures.
d Estimate the temperature at 0700 on the day that these temperatures were taken.
e Estimate for how long the temperature was above 30°C on that day.
5 This graph is used for converting degrees Celsius (°C) to degrees Fahrenheit (°F).
°F
[1]
[1]
[1]
[2]
[1]
[1]
150
100
50
0
20
40
60 °C
Use the graph to change
a 30 °C to °F
b 115 °F to °C.
© Hodder Education 2011
[2]
Unit B
31
200
150
Kilometres
Exam questions: Unit B
6 This graph can be used to convert distances in miles
to distances in kilometres.
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.
100
50
11 Reflection
0
20
40
60
Miles
80
100
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.
A
543210
1
2
3
4
5
50
Cost (£)
40
20
10
D
1 2 3 4 5 x
E
[4]
[1]
… and its solution
2
4
6
8 10 12 14 16 18 20
Distance (miles)
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.
32
B
C
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.
b Explain why A does not map on to E using the
transformation in part iv.
30
0
y
5
4
3
2
1
Revision Notes
a i
Reflection in y = 3
iii Reflection in y = −21
b E is closer to the line.
ii Reflection in x = −1
iv Reflection in y = x
Now try these exam questions
1 Draw the image of shape A after reflection in the
mirror line.
Mirror line
A
[2]
© Hodder Education 2011
2
b
y
7
6
5
4
A
3
Copy the diagram above and then draw on it all
the lines of reflection symmetry. [1]
2
1
0
–7 –6 –5 –4 –3 –2 –1
–1
1 2 3 4 5 6 7 x
–2
12 Percentages
–3
–4
–5
–6
–7
Here is an exam question …
a Reflect triangle A in the y axis. Label your
triangle B.
[2]
bReflect triangle A in the line y = 1. Label your
triangle C.
[2]
3
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% =
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.
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]
[4]
5 a
Shade 1 more square to give the shape 2 lines of
reflection symmetry.
[1]
© Hodder Education 2011
bWrite 60%
i as a decimal.
ii as a fraction.
[2]
2 List the following numbers in order, starting with
the smallest.
66%, 35 , 0.62, 0.59, 55%
[3]
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]
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.
y
4
More exam practice
2
3
4
5
6
7
T
2
1 Write each of these as a percentage.
a 0.06
[1]
2
5 b
[1]
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]
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]
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]
Mobina cut 90 cm off a piece of wood 2.5 m long.
What percentage of the wood was left?
[3]
Sarah earns £34 720 a year. After deductions she
receives £26 734.40. What percentage was
deducted from her pay?
[3]
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]
0
2
4
4 x
2
2
4
[3]
… and its solution
a and b
y
4
T
2
2
4
R
0
2
4 x
2
S
4
c Reflection in the x-axis.
Now try these exam questions
1 Which two of these shapes are congruent?
13 Rotation
A
B
C
D
E
F
G
H
Rotation symmetry
Try this exam question
For each of these shapes, state
a how many lines of symmetry it has.
bits order of rotational symmetry.
[4]
34
Revision Notes
[1]
© Hodder Education 2011
2 The diagram shows shapes A and B.
y
3
2
1
3 2 1 0
1
2
3
A
1 2 3 x
B
Describe fully the single transformation that maps
shape A on to shape B.
3
y
5
4
3
2
A
1
C
0
54321
1
2
3
4
5
B
x
1 2 3 4 5
a Describe fully the single transformation that
maps triangle A on to triangle B.
[2]
bRotate 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.
[2]
a 0.382 × 18.6 = 26.8584 b24.608 ÷ 1.2 = 25.5296 [2]
84
.
456
c
[2]
= 16.8 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
b 152 ÷ 34 = 1201
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]
bone 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
15 Enlargement
Here is an exam question ...
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.
© Hodder Education 2011
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
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).
3 For this diagram, describe fully the single
transformation that maps trapezium Q on to
trapezium R.
y
4
3
2
1
y
14
12
21 0
1
2
10
8
[3]
Q
R
x
1 2 3 4 5 6
6
4
y
4
4
2
0
2
2 4 6 8 10 12 14 16 18 x
Now try these exam questions
2
5
A
1 2 3 x
3 2 1 0
1
2
3
A
0
2
B
4
6
x
Find the centre and scale factor of the enlargement
that maps shape A on to shape B.
[3]
1 The diagram shows shape A.
y
3
2
1
y
10
9
8
B
7
6
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
[3]
and a y-axis from −5 to 8.
2 The diagram shows the shapes A and B and the
line L.
L
y
7
6
5 B
4
3
A
2
1
4 321 0
1
2
1 2 3 4 5
Revision Notes
4
3
2
A
1
0
–4 –3 –2 –1
–1
1 2 3 4 5 6 7 8 9 10 11 x
–2
–3
–4
x
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.
bDraw 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]
36
5
Rectangle B is an enlargement of rectangle A.
Complete these statements.
a The scale factor of the enlargement is
………………
[1]
b The centre of the enlargement is
…………………… c The area of rectangle B is ……….. times the
area of rectangle A.
[2]
[2]
dThe perimeter of rectangle B is ……….. times
the perimeter of rectangle A. [2]
© 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
Bikes hired out
a
b
c
d
6
1
7
8
10
2
9
4
9
5
25
5
26
7
35
10
22
14
30
18
Draw a scatter diagram to show this information.
Describe the correlation shown in the scatter diagram.
Draw a line of best fit on your diagram.
Use your line of best fit to estimate how many bikes would be hired when there were 3 hours of sunshine.
[2]
[1]
[1]
[1]
... and its solution
a and c
Number of bikes hired
40
35
30
25
20
15
10
5
0
2
4
6
8
Hours of sunshine
10
12
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
Iron produced (million tons)
a Plot these data on a scatter graph.
[3]
9
8
7
6
5
4
3
6
8
10
12
14
Coal used (million tons)
16
bDraw a line of best fit.
c i How much iron would you expect to be produced using 15 million tons of coal?
iiWhy would it be unwise to use the graph to predict values for 1947?
2 The table shows data about cinemas in 10 towns, all approximately the same size.
38
[1]
[1]
[1]
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
Revision Notes
© Hodder Education 2011
a Complete the scatter diagram. (The first 5 points have been plotted for you.)
[2]
Weekly admissions (thousands)
13
12
11
10
9
8
7
10
12
14
16
18
Number of screens
20
22
bDescribe the correlation shown in the scatter diagram
c Draw a line of best fit.
dA new cinema is to be built in another town. It is to have 17 screens.
Estimate the weekly audience.
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
[1]
[1]
[1]
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’.
bComment on the general trend and the daily variation.
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
[3]
[2]
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.
bComment briefly on the relationship between the height of the trees and the number of apples on
the trees.
c Add a line of best fit to your scatter graph.
dExplain 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.
© Hodder Education 2011
[4]
[1]
[1]
[1]
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.
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.
y
5
4
3
2
1
210
1
1 2 3 4 5 x
[2]
… and its solution
a i
y
2
y 2x 3
1
0
x 2y 4
1
1
2
3
ii x = 2 and y = 1 (the coordinates of the point
where the lines meet).
b Gradient = 34
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]
bside AB.
[2]
2 Write down the gradient of the line with
[1]
equation y = 2x − 4.
More exam practice
1 a Draw the graph of y = 3x − 1.
b i Write down the gradient of the line.
ii Write down the equation of a line parallel
to y = 3x − 1.
2 Work out the gradient of this line.
(4, 5)
4 x
[3]
y
5
4
3
2
1
0
1
[2]
[1]
[1]
[2]
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]
2
3
40
Revision Notes
© Hodder Education 2011
Graphical solution of simultaneous
equations
Now try this exam question
1 Solve these simultaneous equations graphically.
x + y = 2
[4]
y = 3x + 4
18 Congruence
and
transformations
Here is an exam question …
Inequalities
y
4
Here is an exam question …
a Describe the inequality shown on these number
lines.
i
0 1 2 3 4 5 6
[1]
ii
3 2 1 0
1
2
3
4
b Solve the inequality 5x  3x + 8.
[1]
[2]
… and its solution
a
b
i 1  x  6
5x  3x + 8
2x  8
x4
ii −2  x  3
Now try these exam questions
1 a Solve these inequalities.
[1]
i 2x  x + 7
[2]
ii 5x  2x − 6
bShow the answers to part a on number
lines.
[1 + 2]
2 Solve these inequalities.
[2]
a 8x + 5  25
[2]
b2x + 9  4x
[3]
3 Solve the inequality −6  5x − 1  9.
4 Find all the integers that satisfy 5  2x + 1  15.[3]
© Hodder Education 2011
2
0
2
A
2
4
6
8
10
x
2
a
b
Reflect shape A in the y-axis.
Label the image B.
Reflect shape B in the line x = 3.
Label the image C.
[4]
… and its solution
y
4
B
2
2
0
A
2
x3
4
C
6
8
10 x
2
Unit B
41
Exam questions: Unit B
Now try these exam questions
3 Which two of the triangles A, B, C and D are
congruent to triangle X?
Explain why you chose these triangles.
1 Which of these pairs of triangles are congruent?
A
B
67°
43°
C
D
X
2.5 cm
2.5 cm
43°
E
F
67°
2.5 cm
H
70°
2.5 cm
2.5 cm
[3]
y
7
6
5
4
3
2
A
1
0
–7 –6 –5 –4 –3 –2 –1
–1
1 2 3 4 5 6 7 x
4
70°
D
C
2 The grid shows the position of shape A.
B
A
43°
G
70°
63°
67°
NOT TO SCALE
[4]
y
5
4
3
2
1
0
54321
1
2
3
4
5
A
1 2 3 4 5
x
–2
–3
[2]
–6
a Reflect triangle A in the line x = 3.
Label the image B.
 3
bTranslate triangle A by  
 –4 
–7
Label the image C.
[2]
–4
–5
a Reflect shape A in the y-axis. Label the
image B.
bRotate shape A 180° clockwise about the
origin. Label the image C.
c Describe the single transformation that
maps shape B on to shape C.
42
Revision Notes
[1]
[2]
[1]
© 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.
7.4 cm
bHow 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
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
1 cm
2 cm
3 cm
3 cm
44
Revision Notes
© Hodder Education 2011
More exam practice
… and its solution
1 The diagram shows the net of a box.
a i 91
ii 0
8 cm
2 cm 2 cm
2 cm 2 cm
8 cm
3 cm
3 cm
2 cm 2 cm
2 cm 2 cm
8 cm
8 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.
iii
2
9
b
1, 2, 3
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
3, 2, 1
i
ii
4 and 8 are both multiples of 4.
There are six ways of playing the
three tracks.
5
6
Now try these exam questions
1 Here is a fair spinner
used in a game.
6
4
8
7
5
6
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]
© Hodder Education 2011
4
4
The score is the number where the arrow stops.
Helen spins the spinner once.
a What score is she most likely to get?
[1]
bMark 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
bOne 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]
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
Filling
B
C
B
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.
60
=
a Experimental probability of a silver car 200
28
=
b Experimental probability of a blue car 200
Now try these exam questions
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.
btails.
[2]
2 On an aircraft the number of passengers in each
class is shown in this table.
Class
Number of
passengers
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
[2]
3
10 .
7
50 .
First
Business
Economy
15
65
420
Estimate the probability that one of the passengers
chosen at random travelled in
a first class.
bbusiness class.
[3]
[1]
c Peter says the probability that the first
customer will buy a brown bread and cheese
sandwich is 51. If he is correct, what is the
probability that first customer will not buy a
brown bread and cheese sandwich.
[1]
46
Revision Notes
© Hodder Education 2011
Now try these exam questions
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
35
72
Cheese
& onion
Other
38
a How many people chose cheese & onion
flavour crisps?
bEstimate 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]
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]
bThe area of the rectangle
[2]
2 a On centimetre squared paper, draw two
different rectangles which each have an area
[2]
of 12 cm2.
bWork 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
b
Here is an exam question ...
a Find the perimeter of this rectangle.
b Find the area of this rectangle.
[2]
[2]
7 cm
4 cm
... and its solution
a 7 + 4 + 7 + 4 = 22 cm
b 7 × 4 = 28 cm2
© Hodder Education 2011
[4]
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.
... and its solution
a Volume of cuboid = length × width × height
= 40 × 20 × 30
= 24 000 cm3
b Surface area = 2 × top + 2 × side + 2 × front
= 2(20 × 40) + 2 (40 × 30) + 2(20 × 40)
= 1600 + 2400 + 1200
= 5200 cm2
Now try these exam questions
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.
1 Calculate the volume of this cuboid.
[2]
1.5 m
4.6 m
5.2 m
2 The volume of water in this fish tank is 10 000 cm3.
All the sides and base of the tank are rectangles.
41.2 m
79.6 m
d
Work out the area of the field.
[2]
5 Mr Chan has drawn this plan of his lounge floor.
2
2
1
50 cm
20 cm
1
Calculate the depth of water in the tank.
[3]
4
4 Measures
6
What is the perimeter and area of his lounge floor?
All lengths are in metres.
[4]
Here is an exam question ...
5m
The volume of a cuboid
3m
Here is an exam question ...
a Find the volume of this cuboid.
b Find the total surface area of this cuboid.
30 cm
40 cm
20 cm
48
Revision Notes
[2]
[2]
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]
© 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
ii in m2.
i in cm2.
bThe dimensions were measured to the nearest
centimetre.
Write down the bounds between which the
dimensions must lie.
[5]
2 A block of wood is a cuboid measuring 6.5 cm
by 8.2 cm by 12.0 cm.
a Calculate the volume of the cuboid.
The density of the wood is 1.5 g/cm3.
bCalculate 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?
bCalculate Peter’s speed, in kilometres per hour.[5]
4 The population of Denmark is 5.45 million. The
land area of Denmark is 42 400 km2. Calculate the
population density of Denmark. Give your answer
to a sensible degree of accuracy.
[3]
5 The dimensions of this rectangle are given to the
nearest cm.
Calculate upper and lower bounds for the
perimeter.
[4]
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 = 21 × 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
4.6 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]
bFind the average speed, in mph, for the whole
journey.
[3]
bCalculate 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
5 cm
0.7 cm
6 cm
© Hodder Education 2011
Unit C
49
Exam questions: Unit C
6 Probability 2
3 The area of this triangle is 18.9 cm².
The height, AD, = 4.5 cm.
Calculate the base, BC, of the triangle.
Here is an exam question …
A
a Complete the table.
Outcome
Square
Triangle
0.2
0.35
Probability
B
4
D
Star
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]
C
5.2 cm
3 cm E
… and its solution
6 cm
a P(Circle) = 1 − (0.2 + 0.35 + 0.3)
= 1 − 0.85
= 0.15
b 3 parts blue, 1 part red.
P(red) = 41
B
ABCD is a parallelogram.
AE = 3 cm, EB = 6 cm and DE = 5.2 cm.
Calculate the following.
a The area of the parallelogram
bThe perimeter of the parallelogram
5
5 cm
8 cm
4 cm
Circle
C
D
A
[2]
Now try these exam questions
[2]
[4]
3 cm
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
bThe total surface area of the shape
6 This triangle and this parallelogram have the
same area.
[2]
[4]
1 The probability of getting a 2 with a spinner is 35 .
What is the probability of not getting a 2?
[1]
2 Coloured sweets are packed in bags of 20. There are
five different colours of sweet. The probabilities of
four colours are given in the table.
Colour
Orange
Probability
0.05
White
Yellow Green
Red
0.2
0.35
0.25
a Find the probability of picking a white sweet. [2]
bFind 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.
Vehicle
5.6 cm
Frequency
8.5 cm
Revision Notes
Motorcycle
Lorries
72
15
28
Vans
Buses
33
12
4.8 cm
Calculate the height of the parallelogram.
50
Cars
[4]
Vehicle
Frequency
© Hodder Education 2011
2
3
4
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]
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]
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]
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 × 102 = 714.2 cm2 (to 1 d.p.)
Perimeter of shape = two semicircles + two sides of
square
= circumference of whole circle +
40cm
= π × 20 + 40
= 102.8 cm (to 1 d.p.)
Here is another exam question …
Find the volume of this greenhouse.
The ends are semi-circles.
Area of end = 21 × πr2
= 21 × π × 2.52
Volume = area of end × length
= (21 × π × 2.52) × 11
= 108 m3 (to 3 s.f.)
Now try these exam questions
1 Work out the area of the lawn in this diagram. [4]
© Hodder Education 2011
Lawn
2 The circumference of a circle is 26 cm. Calculate
the radius of this circle.
[2]
3
3m
2.5 m
A heart shape is made from a square and two
semi-circles. Find the area and perimeter of the
heart shape.
20 cm
Patio
28 m
Here is an exam question …
11 m
solution
24 m
7 Perimeter, area
and volume 2
5m
… and its
[3]
[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]
bFind the area of the path.
[4]
Unit C
51
Exam questions: Unit C
4 All the lengths in this question are in centimetres.
6
7 This sweet box is in the shape of a prism. The base is
an isosceles right-angled triangle.
2
4
2
10
NOT TO
SCALE
2
7.4 cm
4
5.2 cm
a Calculate the perimeter of the shape.
bCalculate the area of the shape. 5
[1]
[3]
8 cm
4 cm
Find the volume of the box.
8
2 cm
1 cm
1 cm
3 cm
2 cm
3 cm
10 cm
3 cm
a Find the area of this shape.
bFind the perimeter of this shape.
6
2m
0.5 m
2
[3]
1.5 m
0.8 m
1
[3]
[3]
Calculate the volume of this prism.
9 This is a triangular prism.
1.5 m
3
1.5 m
3 cm
5 cm
0.2 m
4.5 m
The diagram shows a games presentation rostrum.
Find the volume of the rostrum.
[3]
7 cm
[2]
4 cm
a Find its volume.
bFind its surface area.
10 Find the volume of coffee in this cylindrical
tin.
[6]
[3]
7.5 cm
14 cm
52
Revision Notes
© Hodder Education 2011
8 Using a
calculator
Now try these exam questions
Here is an exam question …
Work out the following, giving your answers to 2
decimal places.
a 5.62
b 167 24 + 16
c 2.72 + 8.32
d 3 + 5 × 7 [1]
[2]
[2]
[1]
… and its solution
a
b
c
d
31.36
4.18
76.18
6.16
Here is another exam question …
Work out the following. Give your answers correct to 3
significant figures.
a 4.24
[1]
2
3
.
9
+
0
.
53
b
[2]
3.9 × 0.53
c 350 × 1.00512
[1]
Key in
4
.
2
xy
4
311.1696
b 7.61
Key in
(
3
.
9
x2
+
0
.
5
3
)
÷
(
3
.
9
×
0
.
5
3
)
=
5
xy
7.614 900 ...
c 372
Key in
3
5
0
×
1
.
0
0
1
2
[2]
[2]
c 4.752 – 1.242 [2]
b 9.63 c 7.9 − 3.6 × 1.25
d 37 of £164
=
[5]
b 52 + 122 3 Work out these.
a 43% of £640
b 52 of 47.5 m
c 84.6 − 23.9
4 Work out these.
a 1.83 – 0.93 3.75
b4.6 × 5.2 − 17.1
c 3.7 + 2.1
4.8
5 Work out these.
a 4.312 − 1.92
b 8.2 – 12.7 16.3
6 Work out these.
a 4.12
… and its solution
a 311
Give your answers to 3 significant figures where
appropriate.
1 Round these numbers to the number of
significant figures shown in the brackets.
a 5678 (2)
b230 421 (3)
c 0.005 69 (1)
d0.006 073 8 (4)
e 0.898 (2)
2 Work out these.
a 4.2 – 12.7 1.25
[1]
[2]
[2]
[2]
[1]
[1]
[1]
[2]
[1]
[1]
[2]
[2]
7 £1627 is shared equally between five friends.
How much does each one get?
[2]
8 aA shopkeeper makes a special offer on
fertilizer priced at £3.68. He reduces it by 83p.
What is the new price?
[2]
bAt 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
using a calculator and his
10 John worked out
2+3
answer was 5. Explain what he did wrong.
[1]
=
371.587 234 ...
© Hodder Education 2011
Unit C
53
Exam questions: Unit C
4 Work out these, giving the answers to 2 decimal
places.
More exam practice
1 Work out these.
a 432 + 234 b 274 – 132 c 35 × 37 2 Work out these.
a 56
[2]
[2]
[2]
[1]
b 31 (Give the answer 2 d.p.)
[1 + 1]
3
.
84
c
[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]
a 3.23 + 2.55
[1]
1
4
b 37.2 c
[1]
[1 + 1]
1.67−3
5 Work out these, giving the answers to 3 significant
figures.
a 3 + 5 + 7 [2]
1
1
1
b
[2]
+
+ 5
7
3
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
−
7 Work out these.
1.43
[1 + 1]
0.84
a 231 – 134 b
c
2
7 of £434
194
485 , as a fraction
[2]
[1]
in lowest terms
[1]
9 Trial and improvement
Here is an exam question …
A solution of the equation x3 + 4x2 = 8 lies between −3 and −3.5. Find this solution by trial and improvement.
Give your answer correct to 2 decimal places.
[4]
… and its solution
x = −3
–33 + 4 × −32 = 9
x = −3.5
−3.53 + 4 × −3.52 = 6.125
x = −3.3
−3.33 + 4 × −3.32 = 7.623
x = −3.2
−3.23 + 4 × −3.22 = 8.192
x = −3.25
−3.253 + 4 × −3.252 = 7.921 875
x = −3.23
−3.233 + 4 × −3.232 = 8.033 333
x = −3.24
−3.243 + 4 × −3.242 = 7.978 176
To 2 decimal places, either x = −3.23 or x = −3.24.
x = −3.235 − 3.2353 + 4 × −3.2352 = 8.005 897
So the answer is between −3.235 and −3.24
x = −3.24 (to 2 d.p.)
54
Revision Notes
Too big.
Too small. Try between −3.5 and −3.
Too small. Try between −3.3 and −3.
Too big. Try between −3.3 and −3.2.
Too small. Try between −3.25 and −3.2.
Too big. Try between −3.23 and −3.25.
Too small.
Try halfway between to check.
Too big.
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.
© Hodder Education 2011
10 Enlargement
Now try these exam questions
1 The volume of this cuboid is 200 cm3.
Here is an exam question ...
x1
A
x
4x
5 cm
[2]
a Explain why x3 + x2 = 50.
3
2
bFind the solution of x + x = 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]
3 cm
D
6 cm
B
C
E
12 cm
Triangles ABC and ADE are similar.
Calculate a CE
b BC.
[5]
... and its solution
First draw the triangles separately.
More exam practice
1 The equation x3 − 15x + 3 = 0 has a solution
between 3 and 4. Use trial and improvement to
find this solution. Give your answer to 1 decimal
place. Show clearly the outcomes of your trials. [3]
2 Use trial and improvement to calculate, correct
to 2 decimal places, the solution of the equation
x3 − 5x − 2 = 0 which lies between 2 and 3. Show
all your trials and their outcomes.
[3]
A
3 a Show that the equation x3 − 8x + 5 = 0 has a
root between x = 2 and x = 3.
[3]
b Use trial and improvement
5 cmto find this root 6 cm
correct to 1 decimal place. Show all your trials
and their outcomes.
[3]
B
3
4 The volume, V cm , of this cuboid is given by
V = x3 + 6x2.
A
A
8 cm
5 cm
6 cm
B
C
D
12 cm
A
8 cm
C
D
12 cm
E
Scale factor = 58 = 1.6
AE = 6 × 1.6 = 9.6, so CE = 9.6 − 6 = 3.6 cm
x
BC = 112.6 x
= 7.5 cm
x6
a Complete the table of values of x from 1 to 6. [2]
x
1
2
3
4
5
6
V
b Use trial and improvement to find the
dimensions of the cuboid if its volume is 200 cm3.
Give your answer correct to 1 decimal place.
Show all your trials.
[3]
© Hodder Education 2011
Unit C
55
Exam questions: Unit C
Now try these exam questions
Q Triangle EDC is similar to triangle ABC.
3
1 PQRS is an enlargement of ABCD.
A
P
B
7 cm
A
9 cm
8 cm
D
C
10 cm
S
P
C
S
R
15 cm
Calculate the following.
a PQ
bBC
2 The triangles ABC and PQR are similar.
[3]
P [2]
7 cm
C
8 cm
Q
P
7 cm
C
7.5
6
C
3
O
[3]
[2]
B
5
D
9.1 cm
Q
Calculate the lengths of the following.
a QR
bAC
Revision Notes
12 cm
AO = 3 cm, DO = 5 cm, AB = 7.5 cm and CO = 6 cm.
9.1
Calculate
the lengths of the following.
cm
a CD
[3]
bBO
[2]
R
5 These shapes
are similar.
The radius of the small circle is 5 cm. The radius
of the large circle is 8 cm.
5 cm
B
C
D
A
A
56
B
6 cm
a Calculate the length of BD.
bCalculate the value of this fraction in its
simplest form: Area of ∆ EDC
Area of ∆ ABC
4 Triangles AOB and DOC are similar.
9 cm
m
R
15 cm
Q
B
cm
E
R
[3]
[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]
bCalculate the values of these fractions.
i Circumference of small circle
Circumference of large ciircle
ii Area of small circle [4]
Area of large circle
© Hodder Education 2011
11 Graphs
a
b
c
d
Distance–time and other real-life
graphs
… and its solution
a
b
c
d
Here is an exam question …
Distance from home
in kilometres
The graph shows Philip’s cycle journey between his
home and the sports centre.
y
8
7
6
B
5
4
3
2
1
A
0
20
C
Explain what happened between C and D.
[1]
Explain what happened at B.
[1]
Explain what happened at E.
[1]
Work out the total distance that Philip travelled. [2]
Philip was at the sports centre.
Philip’s speed changed, perhaps due to a steep hill.
Philip arrived home.
12 km
6 km there and 6 km back.
D
E
40 60 80 100 120
Time in minutes
Now try these exam questions
Height in metres above sea level
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.
80
70
60
50
40
30
20
10
0
5
10
15
20
Time in seconds
25
30
a How high is the rocket above sea level after 10 seconds.
bHow long does it take before the rocket lands in the sea?
c Write down the time when the rocket is at the same height as it started.
dWrite down the times when the rocket is 10 m above the cliff.
© Hodder Education 2011
[1]
[1]
[1]
[2]
Unit C
57
200
4.3 m
150
Cost (£)
Exam questions: Unit C
2 Katy needs new carpet for her kitchen. She measures
the floor and draws a plan.
2m
100
50
1.5 m
1.6 m
0
a Calculate the total area of the floor. State the
units of your answer.
[4]
bThis 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]
5
10
Area (m2)
15
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.
120
110
90
Overweight
80
Distance from school (km)
Weight (kg)
100
70
OK
60
50
40
140
58
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.
Underweight
150
Revision Notes
160
170
Height (cm)
180
190
8
6
4
2
0
8.20 a.m.
8.30 a.m.
8.40 a.m.
Time
8.50 a.m.
© 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
y x2 x 3
8
7
6
5
4
3
y2
2
1
2
0
1
1
1
2
3
4
x
2
3
Speed
Now try these exam questions
1 a Complete the table of values and draw the
graph of y = x2 − 2x + 1 for values of x from
−1 to 3.
Time
Quadratic graphs
x
–1
0
y
Here is an exam question …
a Make a table of values and draw the graph of
y = x2 − x − 3 for values of x from −2 to 4.
b Use your graph to solve the equation
x2 − x − 3 = 2.
[4]
[2]
a
−2
−1
0
1
2
3
4
x2
4
1
0
1
4
9
16
−x
2
1
0
−1
−2
−3
−4
−3
−3
−3
−3
−3
−3
−3
−3
y
3
−1
−3
−3
−1
3
9
3
1
−1
0
y
x
2
4
bUse the graph to find the value of x when
y = 3.
[2]
2 a Complete the table for y = 4x − x2 and draw
the graph.
[4]
x
… and its solution
1
[2]
1
2
3
4
3
5
0
bUse your graph to find
i the value of x when 4x − x2 is as large as
possible.
ii between which values of x the value of
4x − x2 − 2 is larger than 0.
[1]
[2]
More exam practice
1 a Complete the table and draw the graph of
y = x2 − 4 for values of x from −3 to 3.
x
−3
y
5
−2
−1
0
−3
−4
1
2
3
0
b Use your graph to find the solutions of the
equation x2 − 4 = 0.
© Hodder Education 2011
[4]
[2]
Unit C
59
Exam questions: Unit C
2 a Draw the graph of y = x2 − 3x − 5 for values
of x from −2 to 5.
b Use your graph to find the solutions of the
equation x2 − 3x − 5 = 0.
3 a Draw the graph of x2 + 4x − 4 for values of x
from −6 to 2.
b Use your graph to find the solutions of the
equation x2 + 4x − 4 = 0.
c On the graph, draw the line y = −5 and use
this to find the solutions of the equation
x2 + 4x − 4 = −5.
4 z
D
C
y
A
2
G
O
7
3
[2]
[4]
[2]
[3]
K
L
1
F
B
H
[4]
J
3
E
x
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]
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]
60
Revision Notes
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]
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?
b A washing machine cost £265 in 1998.
What would you expect it to cost in 2008?
[2]
[2]
... and its solution
51.9
× 100 = 31.86%
162.9
b 265 × 1.3186 = £349.43 (approx £350)
a Increase = 51.9 % increase =
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?
bA family’s usual weekly shop cost £64 in 1990.
What would you expect it to cost in 2005?
© Hodder Education 2011