KS3 Maths Now Support and Practice Workbook Look Inside

• Build understanding with clear objectives, step-by-step worked examples and practice questions • Strengthen and practise mental maths with warm-ups and fact pages • Use alongside KS3 Maths Now Learn and Practice Book with topics covered in the same order

Support and Practice Workbook

Download a free PDF version for printing and copying (available in colour or black and white): www.collins.co.uk/KS3MathsNow/downloads

KS3 Maths Now

Support pupils to access KS3 Maths with tailored and scaffolded practice.

Support and Practice Workbook

ISBN 978-0-00-837833-2

KS3 Maths Now Learn and Practice Book 978-0-00-836286-7

KS3 Maths Now Teacher Handbook 978-0-00-836285-0

9 780008 378332

Boost confidence with worked examples and practice questions

Contents How to use this book

5

Correlation 179

Factors and multiples

6

Congruence and scaling

183

Sequences 10

Manipulating algebraic expressions 186

Perimeter and area

23

Working with fractions

Negative numbers

35

Circles 191

187

Averages 40

Finding probabilities

193

Equivalent fractions

60

Equations and formulae

202

Algebraic expressions

65

Proportion 204

Angles 80

Applications of graphs

213

Decimals 90

Comparing sets of data

216

Linear graphs

Percentage changes

219

106

Percentages 117

Polygons 222

3D shapes

122

Prisms and cylinders

224

Introduction to probability

132

Compound units

227

Ratio 135

Solving equations graphically

230

Symmetry 143

Pythagoras’ theorem

236

Using data

157

Manipulating brackets

240

Pencil and paper calculations

160

Review sheet

242

Transformations 169

Mental warm-ups

243

Working with numbers

175

Maths Facts

253

Percentage changes

177

Answers 258

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How to use this book Work through each topic step by step Clear learning objectives Worked examples to show you how to answer the questions Practice questions to help you consolidate what you have learned.

Be in charge of your learning You, your teacher or tutor can note down how you feel each topic went and write down any comments.

Practise your mental maths

Remember the key maths facts

Check your own answers

Remind yourself of the key maths facts at any point.

Answers are provided at the end of the Workbook.

Try the mental maths questions at the end of the Workbook to see what you have learned.

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Sequences 1 I can

• recognise patterns in sequences of numbers

Example Here is a sequence of numbers:

9

13

17

21

25

Work out the next two numbers.

Solution The numbers increase by 4 each time.

The next number is 25 + 4 = 29.

The number after 29 is 29 + 4 = 33.

Practice questions 1

Write the next two numbers in each of these number sequences using the rule shown. a The rule is add on 2 each time.

22

24

26

28

b The rule is add on 5 each time.

7

12

17

22

c The rule is subtract 3 each time.

30

27

24

21

d The rule is subtract 10 each time.

95

85

75

65

e The rule is double each time.

1

10

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2

4

8

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2

3

Write the next two numbers in each of these number sequences. a 3

5

7

9

b 42

44

46

48

c 30

35

40

45

d 1

7

13

19

e 40

37

34

31

f 50

44

38

32

g 10

21

32

43

h 120

116

112

108

Write in the missing numbers in each of these number sequences. a 12

16

b 17

22

27

c 99

96

93

d 46

42

24

28

32

40 42

87

47

52

62

81 78 26

72 22

69

18

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Sequences 2 I can

• recognise and describe number patterns

Example 9

Here is a sequence of numbers:

13

17

21

Work out the next two numbers in the sequence.

Solution Look at the differences between the numbers.

They increase by 4 each time. ‘Add 4’ is the term-to-term rule.

The next two numbers are 21 + 4 = 25 and 25 + 4 = 29.

Practice questions 1

12

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Write down the next two terms in these sequences. a 1

2

3

4

5

b 1

3

5

7

9

c 3

6

9

12

15

d 10

9

8

7

6

e 20

18

16

14

12

f 100

95

90

85

80

g 4

14

24

34

44

h 50

48

46

44

42

i 3

2

1

0

–1

j –10

–20

–30

–40

–50

–2

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2

3

4

Work out the next four terms in these sequences using the term-to-term rule shown. a Rule: add 4

3

b Rule: subtract 2

19

c Rule: add 5

8

d Rule: subtract 6

50

e Rule: add 7

10

f Rule: subtract 10

83

g Rule: subtract 4

27

h Rule: add 1

–4

Work out the next two terms in these sequences using the rule shown. a Rule: multiply by 2

1

2

b Rule: divide by 2

40

20

c Rule: multiply by 3

1

3

d Rule: divide by 4

64

16

4

9

Work out the next two numbers in these sequences. a 1

2

4

8

16

b 3

6

12

24

48

c 64

32

16

8

4

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Sequences 3 I can • recognise number patterns

Example Here is a sequence of numbers.

1

2

4

7

11

16

Work out the next two numbers in the sequence.

Solution Look at the differences between the numbers.

1

2 +1

4 +2

7 +3

11 +4

16 +5

+6

+7

The differences increase by one each time.

The next number is 16 + 6 = 22.

Then the one after that is 22 + 7 = 29.

Practice questions 1

Work out the next two numbers in each of these sequences. a 17

20

23

26

29

32

3

4

6

9

13

18

c 10

12

16

22

30

40

1

2

5

10

17

e 80

76

72

68

f 50

49

47

44

40

b

d

14

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g

3

4

7

12

19

28

h

9

9.5

11

13.5

17

21.5

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2

Here is a sequence of patterns.

1+2=3

1+2+3=6

1 + 2 + 3 + 4 = 10

Work out the next two sums in the sequence.

3

Here is a different sequence of patterns.

1+3=4

1+3+5=9

1 + 3 + 5 + 7 = 16

Work out the next two sums in the sequence.

4

Fill in the missing numbers in these sequences. a

9

14

19

b

40

37

34

31

c

4

5

7

10

19

d

1

2

5

10

26

29

44 19 32 37

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65

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Sequences 4 I can

• recognise sequences and find further terms

Example Work out the next two terms in each sequence. a 3 6 12 24 48 __ __ b 2 8 18 32 __ __ c 2 5 7 12 19 31 __ __ Solution a You have already met arithmetic sequences, where the difference between terms is constant.

This is not an arithmetic sequence.

In this sequence each term is double the previous one.

The next two terms are 48 × 2 = 96 and 96 × 2 = 192. b Look at the differences.

2 8 18 32 ____

6 10 14

The next differences will be 18 and 22.

The next two terms are 32 + 18 = 50 and 50 + 22 = 72.

You might also notice that each term is double a square number: 2 × 1 = 2, 2 × 4 = 8, and so on.

The next two will be 2 × 25 = 50 and 2 × 36 = 72 as before. c This is an example of a Fibonacci sequence. Each term is the sum of the previous two.

2 + 5 = 7, 5 + 7 = 12 and so on.

The next two are 19 + 31 = 50 and 31 + 50 = 81.

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Practice questions 1

Work out the next term in each sequence. a 10

16

4

34

____

4

8

16

32

____

c 1

3

9

27

81

____

60

30

15

____

Work out the next term in each sequence. a 3

3

28

b 2

d 120

2

22

12

27

48

75

3

____

b 24

12

6

c 0.5

2

4.5

d 640

160

8

____

12.5

40

10

____

____

Work out the missing terms in each sequence. a 3

____

11

15

19

____

b 5

____

20

40

80

____

6

3

c ____

24

d ____

600

12

300

150

27

____ ____

37.5

a Work out the number of dots in each of the next two patterns.

1

3

6

10

_____

_____

b Work out the next two numbers in each sequence. (Hint: Use the sequence in part a.) i 3

5

8

12

____

____

ii 3

9

18

30

____

____

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5

6

7

Work out the next two terms in each sequence. a 1

1

2

3

b 1

5

6

11

5

8

17

13 28

____ ____

____ ____

Work out the next two fractions in each sequence. a

2 3

3 5

4 7

5 9

b

1 2

3 4

5 8

7 16

6 11

9 32

Work out the number of dots in each of the next two patterns. a

2

6

12

20

_____

_____

_____

_____

b

1

18

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7

19

37

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8

Here is a sequence of growing patterns.

1

2

3

4

There is one small triangle in pattern 1 and four small triangles in pattern 2.

9

a How many small triangles are there in patterns 3 and 4?

________ and ________

b Work out the number of small triangles in pattern 10.

____________________

Here is a sequence of rectangles.

Rectangle 1

Rectangle 2

4 6

Rectangle 3

5 7

Rectangle 4

6 8

Work out the area of the next rectangle in the pattern.

7

9

____________________

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Sequences 5 I can

• use a term-to-term definition to find the terms of a sequence • use a position-to-term definition to find the terms of a sequence • write an expression for the nth term of an arithmetic sequence

Example a This is the start of an arithmetic sequence.

20 24 28 32 …

Work out the 10th term. b The nth term of a sequence is given by the formula n(n + 1).

Work out the 10th term. c This is the start of an arithmetic sequence.

7 16 25 34 …

Find a formula for the nth term.

Solution a In an arithmetic sequence the difference between successive terms is always the same.

In this case the term-to-term rule is ‘add 4’.

To find the 10th term, add 4 nine times to the first term.

The 10th term is 20 + 4 × 9 = 20 + 36 = 56. b To find the 10th term, replace n in the formula with 10.

The 10th term is 10 × (10 + 1) = 10 × 11 = 110. c The term-to-term rule is ‘add 9’. Compare the sequence with the 9 times table.

7 16 25 34 …

9 18 27 36 …

The nth term of the lower sequence is 9n.

So the nth term of the upper sequence is 9n − 2.

20

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Practice questions 1

Find the term-to-term rule for each of these arithmetic sequences. a 5

8

c 53

2

73

14 93

…

____________

113

…

____________

10

b 15 c 6

e 7

14

20 16

d 13

25 26

19 9

18 30 36

25

11

22 35 46

31

13

…

…

37

15

…

… …

26

37

48

…

____________

d 50

46

42

38

…

____________

10th term = ___________________ 12th term = ___________________ 15th term = ___________________ 11th term = ___________________ 50th term = ___________________

…

f 40

37

34

31

28

…

…

10th term = ___________________

g 72

77

82

87

92

…

…

20th term = ___________________

h 72

66

60

54

48

…

…

11th term = ___________________

The nth term of a sequence is 5n − 3. Work out: b the 3rd term ________

c the 12th term ________

The nth term of a sequence is 10n + 8. Work out: b the 8th term ________

c the 15th term ________

The nth term of a sequence is 100 − 2n. Work out: a the 5th term _________

6

…

…

a the 1st term _________

5

…

…

a the 1st term _________

4

b 15

Work out the given term for each sequence. a 6

3

11

b the 10th term ________

c the 24th term ________

The nth term of a sequence is n2 + 4.

Work out the first five terms.

_______________________

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7

The nth term of a sequence is 100 − 2n.

Work out the first five terms.

8

_______________________

The nth term of a sequence is n2 − 1. Work out: a the 1st term _________

9

b the 5th term ________

The nth term of a sequence is n(n + 3). Work out: a the 1st term _________

10

11

a 5

10

15

20

25

30

…

nth term = ___________

b 8

13

18

23

28

33

…

nth term = ___________

c 1

6

c the 7th term ________

11

16

21

26

nth term = ___________

…

Work out a formula for the nth term for each of these arithmetic sequences. nth term = ___________

a 7

9

b 8

14

20

26

32

…

nth term = ___________

c 6

13

20

27

34

…

nth term = ___________

e 7 f 12

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b the 3rd term ________

Work out a formula for the nth term for each of these arithmetic sequences.

d 14

22

c the 9th term ________

11

17 16 14

13

20 25 16

15

23 34 18

…

26 43 20

… … …

nth term = ___________ nth term = ___________ nth term = ___________

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Mental warm-up 1: Number

Mental warm-up 2: Number

1 Round 4719 to the nearest hundred.

2 48 × 9 = 432. What is 432 ÷ 9?

3 Work out 299 + 399.

4 Work out 35 ÷ 4.

5 Tables seat five people. How many ­tables are needed for 27 people?

6 What is the hundreds digit in 3456?

7 The temperature is 2 °C. It falls by five degrees. What is the new temperature?

8W hat fraction of this shape is filled?

Write your answer as simply as possible.

1 Round 18.4 to the nearest 10.

2 13 × 15 = 195. What is 195 ÷ 13?

3 Work out 97 – 79.

4 Work out 73 ÷ 10.

5 Work out 43 + 69.

6 Write in figures six hundred and six.

7 What fraction of this shape is filled?

3 18 4 7 remainder 3 3 7 10 8 Down 4 degrees 11 2000 12 14:15

Answers to Mental warm-up 2: Number

Write down the next number in the ­sequence.

11 What units should you use to measure the mass of a pen?

12 How many minutes is 212 hours?

13 Write 6.45 am in the 24-hour clock.

1 20 2 15 5 112 6 606 9 £30.05 10 101

9 Write 83 mm in centimetres.

10 Here is a sequence of numbers: 30 27 24 21 18

8 The temperature changes from –6 °C to –10 °C. Has it gone up or down? How many degrees?

9 Write thirty pounds and five pence in figures.

10 Write down the next odd number after 99.

11 A bottle holds 2 litres of water. How many millilitres is that?

12 The time now is 13:45. Write down the time 30 minutes later.

1 4800 5 6 10 15

2 48 3 698 6 4 7 –3 °C 11 grams

4 8 remainder 3 1 8 4 9 8.3 cm 12 150 13 06:45

Answers to Mental warm-up 1: Number

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Maths Facts

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