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How to use this book
Organise your learning The Contents table at the start of the Workbook shows the topics you are going to cover. It can be used by: your teacher or tutor to set a date for you to complete each topic by you can give a tra ffic light colour for each topic to show how you feel it went yYou, your teacher and your parent or carer to write comments.
Work through each topic step by step For each topic, there are: clear learning objectives worked exam ples to show you how to answer the questions practice questions to help you consolidate what you have learnt. A glossary and answers are available on Collins Connect. At the end of each chapter, there’s a comments box for your teacher or tutor to fill in on how you did.
Practise your mental maths Try the mental maths questions at the end of the Workbook to see what you have learned.
Celebrate your progress When you finish the Workbook, your teacher or tutor can fill in the Record of achievement certificate for you to keep.
How to use this book
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Step 4 Contents Strand/topic
Page Hours Due date
Feedback
1 Number 1.1 Adding and subtracting fractions
6
1
1.2 Calculations with fractions
9
1
1.3 Using fractions, decimals and percentages
11
1
2.1 Collecting like terms
15
1
2.2 Expanding brackets
17
1
2.3 Solving equations
18
1
2.4 Sequences
20
1
2.5 Straight-line graphs
23
1
2.6 Real-life graphs
26
1
3.1 Percentage change
29
1
3.2 Ratio
31
1
3.3 Direct proportion
33
1
2 Algebra
3 Ratio, proportion and rates of change
4
Contents
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Strand/topic
Page Hours Due date
Feedback
4 Geometry and measures 4.1 Properties of quadrilaterals
36
1
4.2 Parallel lines
38
1
4.3 Angles of polygons
41
1
4.4 Translations, rotations and reflections
43
1
4.5 Enlargement
47
1
4.6 Three-dimensional objects
50
1
4.7 Constructions with a straight edge and compasses
53
1
4.8 Areas of triangles and parallelograms
57
1
4.9 Volumes of cuboids
60
1
4.10 The circumference and area of a circle
63
1
5.1 Calculating probabilities
65
1
5.2 Sample spaces
68
1
6.1 Constructing charts and diagrams
71
1
6.2 Appropriate graphical representation
74
1
5 Probability
6 Statistics
Mental maths warm-ups Record of achievement certificate Contents
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1
Number
1.1 Adding and subtracting fractions I can • use equivalent fractions to add or subtract two fractions • add or subtract mixed numbers
Example Work these out. a
2 3
+
3 4
b 3 12 − 165
Solution a 3 and 4 are factors of 12 so change the fractions to 12ths. 4 2 3
3
8 12
3 4
4 2 3
+
3 4
9 12 3
= = =
8 9 12 + 12 17 12 5 112
Add the numerators only. 8 + 9 = 17 17 ÷ 12 = 1 remainder 5
b Change the mixed numbers to improper fractions. 3 12 − 165 =
7 11 2 − 6 11 = 21 6 − 6 = 10 6 5 =3 = 132
6
Change
7 2
to sixths.
Subtract the numerators. 21 − 11 = 10 To simplify, divide the numerator and the denominator by 2. Write the answer as a mixed number.
1 Number
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Practice questions 1
Complete these additions and subtractions. Write each answer in its simplest possible form.
2
5 = a 1+ 5 = + 4 12 12 12
b
3 = c 5+ 3 = + 8 16 16 16
5 = d 3− 5 = − 4 12 12 12
= e 1+ 3 = + 3 5 15 15
f
= g 5+ 1= + 8 3 24 24
h 1− 2 = = − 2 9 18 18
4 3 = − = − 5 4 20 20
Work these out. Write your answers as simply as possible. a 1+ 1 = 3 6
e
3
7 1 7 = − = − 10 2 10 10
5 1 + = 12 6
b
1 2 − = 3 9
c
3 1 + = 8 4
d
9 1 − = 16 4
f
11 3 − = 12 4
g
7 1 + = 10 5
h
7 1 − = 16 8
Work these out. Write your answers as simply as possible. a 2+ 1 = 3 4
e
5 1 + = 9 6
b 2−2= 3 5
f
9 3 − = 10 4
c
3 1 + = 8 3
d 7−2= 8 3
g
1 3 + = 4 5
h
3 2 − = 4 5
1.1 Adding and subtracting fractions
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4
Complete these additions and subtractions. Write each answer as simply as possible. a 3 12 + 143 = =
2 4
+ +
b 2 65 + 132 =
4
=
4
=
8 8
− −
7 d 5 12 − 2 12 =
4
=
8
=
5
6
8
+
6
3 6
=
= c 4 83 − 143 =
+
6
2 12
− −
12 12
=
Work out these additions and subtractions. a 143 + 2 12 =
b 2 32 + 161 =
c 2 83 + 143 =
e 4 41 − 183 =
f 5 12 − 161 =
g 2 41 −
5 12
7 d 116 + 2 41 =
=
h 4 91 − 132 =
Work out these additions and subtractions. a 131 + 2 12 =
b 2 32 + 3 12 =
c 3 31 + 135 =
d 132 + 2 41 =
e 3 12 − 131 =
f 3 31 −
g 3 31 − 151 =
h 4 12 − 152 =
1 2
=
1 Number
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1.2 Calculations with fractions I can • calculate a fraction of a quantity • multiply an integer by a fraction • divide an integer by a fraction
Example a
Work out:
5 of £360 8
b 6×
5 8
c 6÷
5 . 8
Solution 1 8
a Divide by 8 to find 5 8
then multiply by 5 to find 85 .
of £360 = 360 ÷ 8 × 5 = 225
With a calculator, just follow the steps shown.
The answer is £225. Notice that you get the same answer if you reverse the order of the operations. 360 × 5 ÷ 8 = 225
You can multiply by 5 first and then divide by 8 if you wish.
b Multiply the numerator by 6 and then divide by the denominator. 6×
5 8
=
6× 5 8
=
c To divide by 6÷
5 8
= 6×
5 8 8 5
30 8
=
15 4
= 3 43
Cancel the fraction if you can.
multiply by the inverse, which is 85 . =
6×8 5
=
48 5
= 9 35
Practice questions 1
Work these out. a
2 of £18 = ________ 3
b 3 of £14 = ________ 4
d
3 of £16 = ________ 5
e
g
7 of £55 = ________ 10
h 2 of £1700 = ________ 5
j
2 of £16.50 = ________ 3
k
2 of 91 kg = ________ 7
3 of £86.40 = ________ 4
c
7 of 200 kg = ________ 8
f
5 of 30 km = ________ 12
i
3 of 5200 kg = ________ 8
l
7 of 30 kg = ________ 12
1.2 Calculations with fractions
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2
Work these out. Write each answer as simply as possible. a 4×
2 = ________ 3
b 6×
3 = ________ 4
c 5×
5 = ________ 8
d 4×
3 = ________ 8
e 3×
5 = ________ 6
f 9×
3 = ________ 5
h 4×
11 = ________ 12
i 10 ×
g 6 × 7 = ________ 10 j 7×
3
3 = ________ 5
3 = ________ 4
b 6÷
3 = ________ 5
c 3÷
d 5÷
1 = ________ 4
e 8÷
2 = ________ 3
f 10 ÷
3 = ________ 4
1 = ________ 6
5 = ________ 6 5 = ________ 8
h 15 ÷
2 = ________ 3
i 2÷
7 = ________ 12
k 11 ÷
5 = ________ 8
l 24 ÷
2 = ________ 3
Work out a 30 ×
2 = ________ 3
b 30 ÷
2 = ________ 3
c 30 ×
3 = ________ 4
d 30 ÷
3 = ________ 4
e 30 ×
2 = ________ 5
f 30 ÷
2 = ________ 5
Decide whether these are multiplications or divisions a 16 _____
10
5 = ________ 12
a 4÷
j 7÷
5
l 8×
Work these out. Write each answer as simply as possible.
g 20 ÷
4
k 12 × 5 = ________ 8
2 = ________ 3
3 4
= 21 31
b 48 _____
2 5
= 19 51
c 31 _____
3 8
= 82 32
1 Number
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1.3 Using fractions, decimals and percentages I can • compare fractions, decimals and percentages • use fractions, decimals or percentages to compare different proportions
Example Write these in order of size, smallest first. 5 2 65% 0.7 8 3 Solution Convert them to decimals. 2 ÷ 3 = 0.666… so
2 3
= 0.667 to 3 d.p.
65 ÷ 100 = 0.65 so 65% = 0.65
0.7 is already a decimal. 5 ÷ 8 = 0.625 so
5 8
= 0.625
The order is 0.625, 0.65, 0.667 and 0.7. That is 85 , 65%,
2 3
and 0.7.
Example There are 32 men and 25 women in a room. a What percentage of the people are men?
b What percentage are women?
Solution a There are 32 + 25 = 57 people. The fraction who are men is
32 . 57
32 ÷ 57 = 0.561 … = 56% b The percentage who are women is
25 57
= 25 ÷ 57 = 0.439 … = 44%.
You could also find this from 100% − 56% = 44%.
1.3 Using fractions, decimals and percentages
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Practice questions 1
Put these sets of numbers in order, smallest first. a
1 3
0.3
2.5%
120%
1.3
d 101%
2
0.28
2 12
b 20% c 141
35%
19 20
_______________________________________
0.225 1.19
0.929
99.5%
_______________________________________ _______________________________________ _______________________________________
There are 185 books and 143 are fiction. What percentage are fiction? ___________________
3
There are 63 cars and 12 vans in a car park. What is the percentage of: a cars ___________________
4
b vans? ___________________
There are 85 teachers in a school. 56 are women. What is the percentage of: a women ___________________
5
There are 45 cats and 17 dogs. What is the percentage of each animal? a cats ___________________
6
b men? ___________________
b dogs ___________________
There are 245 people in a survey of where they went on holiday. Here are the results. Region
UK
Rest of Europe
Rest of the world
Number
153
69
23
Work out the percentage visiting each region. a UK ________
12
b Rest of Europe ________
c Rest of the world ________
1 Number
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7
8
Here are some test marks. Draw a line from the test mark to the corresponding percentage. 14 out of 25
56%
39 out of 60
59%
47 out of 80
63%
75 out of 120
65%
111 out of 160
69%
In an athletics club there are 63 men and 24 women. The percentage of members who are women is approximately: 24%
28%
38%
63%
72%
Circle the correct answer.
9
On Monday 32 people took a driving test and 19 passed. On Tuesday 41 people took a driving test and 29 passed. On which day did a larger percentage pass? Circle the correct answer.
Monday
Tuesday
Justify your answer.
10
______________________________________________________________________________
10
A small box of biscuits has 11 chocolate biscuits and 18 plain biscuits. A large box has 18 chocolate biscuits and 26 plain biscuits. Which box has a larger percentage of chocolate biscuits? Justify your answer.
11
______________________________________________________________________________ 1.3 Using fractions, decimals and percentages
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Comments, next steps, misconceptions
14
1 Number
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