Lower Secondary Mathematics WORKBOOK 9 Sample

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Cambridge Lower Secondary

Mathematics WORKBOOK 9

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Lynn Byrd, Greg Byrd & Chris Pearce

Second edition

Original material Š Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

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Cambridge Lower Secondary

Mathematics WORKBOOK 9

SA

M

Greg Byrd, Lynn Byrd & Chris Pearce

Original material Š Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

University Printing House, Cambridge CB2 8BS, United Kingdom One Liberty Plaza, 20th Floor, New York, NY 10006, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia 314–321, 3rd Floor, Plot 3, Splendor Forum, Jasola District Centre, New Delhi – 110025, India 79 Anson Road, #06–04/06, Singapore 079906

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It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781108746502 © Cambridge University Press 2021

This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.

First published 2014 Second edition 2021

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Printed in ‘country’ by ‘printer’

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A catalogue record for this publication is available from the British Library ISBN 978-1-108-74650-2 Paperback with Digital Access (1 Year)

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Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

Contents

Contents How to use this book Acknowledgements

5 6

1.1 Irrational numbers 7 1.2 Standard form 9 1.3 Indices 11

2 Expressions and formulae 2.1 2.2 2.3 2.4

Substituting into expressions Constructing expressions Expressions and indices Expanding the product of two linear expressions 2.5 Simplifying algebraic fractions 2.6 Deriving and using formulae

13 16 23 26 29 33

7 Shapes and measurements

7.1 Circumference and area of a circle 7.2 Areas of compound shapes 7.3 Large and small units

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ultiplying and dividing by powers of 10 M Multiplying and dividing decimals Understanding compound percentages Understanding upper and lower bounds

37 41 45 50

81 86 92

8 Fractions

8.1 Fractions and recurring decimals 8.2 Fractions and the correct order of operations 8.3 Multiplying fractions 8.4 Dividing fractions 8.5 Making calculations easier

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3 Decimals, percentages and rounding 3.1 3.2 3.3 3.4

6.1 Data collection and sampling 77 6.2 Bias 78

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1 Number and calculation

6 Statistical investigations

97

100 103 107 111

9 Sequences and functions 9.1 Generating sequences 9.2 Using the nth term 9.3 Representing functions

114 118 122

4 Equations and inequalities

10 Graphs

4.1 Constructing and solving equations 55 4.2 Simultaneous equations 59 4.3 Inequalities 63

10.1 Functions 127 10.2 Plotting graphs 129 10.3 Gradient and intercept 131 10.4 Interpreting graphs 133

5 Angles 5.1 5.2 5.3 5.4 5.5

Calculating angles 66 Interior angles of polygons 68 Exterior angles of polygons 71 Constructions 72 Pythagoras’ theorem 74

11 Ratio and proportion 11.1 Using ratios 11.2 Direct and inverse proportion

137 141

3 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

13 Position and transformation Contents

12 Probability 12.1 Mutually exclusive events 12.2 Independent events 12.3 Combined events 12.4 Chance experiments

146 148 150 153

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13 Position and transformation

13.1 Bearings and scale drawings 156 13.2 Points on a line segment 160 13.3 Transformations 164 13.4 Enlarging shapes 168

14 Volume, surface area and symmetry

14.1 Calculating the volume of prisms 14.2 Calculating the surface area of triangular prisms, pyramids and cylinders 14.3 Symmetry in three-dimensional shapes

174 178 181

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15 Interpreting and discussing results

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15.1 Interpreting and drawing frequency polygons 15.2 Scatter graphs 15.3 Back-to-back stem-and-leaf diagrams 15.4 Calculating statistics for grouped data 15.5 Representing data

184 189 194 199 203

4 Original material Š Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

How to use this book

How to use this book This workbook provides questions for you to practise what you have learned in class. There is a unit to match each unit in your Learner’s Book. Each exercise is divided into three parts: Focus: these questions help you to master the basics

•

Practice: these questions help you to become more confident in using what you have learned

•

Challenge: these questions will make you think very hard.

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•

You will also find these features:

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Words you need to know.

Worked example

FPO

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Step-by-step examples showing how to solve a problem.

These questions help you to practice thinking and working like a mathematician.

5 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

13 Position and transformation

Acknowledgements

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TBC

6 Original material Š Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

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1 Number and calculation 1.1 Irrational numbers Exercise 1.1

Key words

irrational number surd

Focus 1

Copy this table. Tick (3) the correct boxes.

Number

Rational

36

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48

Irrational

64

84 3

100

Look at these numbers:

12.77 −36 27 500 61 − 3 8

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2

3

a

Write the irrational numbers.

b

Write the integers.

Write whether each of these numbers is an integer or a surd. a

d

4

12

3

25

b

125

e

3

25

c

225

f

125 3

225

Is each of these numbers rational or irrational? Give a reason for each answer. a

3+6

b

3+6

c

64 + 3 64

d

3

8 + 3 19

7 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

1 Number and calculation

Practice

6

a

Find 1.52

b

Show that 2.25 is a rational number.

c

Is 20.25 a rational number? Give a reason for your answer.

d

Is 3 1.331 a rational number? Give a reason for your answer.

Without using a calculator, show that a

7

41 < 4

b b

2 and 3

9<

3

800 < 10

c

1.1 < 1.36 < 1.2

c

6 and 7

1.4 and 1.5

Without using a calculator, estimate a b

9

3

Without using a calculator, find an irrational number between a

8

3<

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5

140 to the nearest integer 3

350 to the nearest integer.

Arun says:

My calculator shows = 2.086 419 753 and this does not have a repeating pattern, so 2 7 81 is irrational.

a

Is Arun correct? Give a reason for your answer.

b

Do you think 2 7 is a rational number? Give a reason for 81 your answer.

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27 81

Challenge 10 a

Use a calculator to show that 2 × 32 is a rational number.

b

Find two irrational numbers with a product of

i 6

ii 9

iii 10

Explain why 5 + 2 is an irrational number.

Tips

b

Find two irrational numbers with a sum of 5.

c

Explain why it is impossible to find two rational numbers with a sum of 5.

Write 5 + 2 as a decimal.

d

Is it possible to find two rational numbers with a product of 5?

Give a reason for your answer.

11 a

8 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

1.2 Standard form

12 This Venn diagram shows all the numbers from a number line.

B

A is the set of integers. B is the set of rational numbers.

A

Copy the diagram and put each of these numbers in the correct place.

25 5.5 5 5 25 3 25 19

13 a If n = 20, find the value of n+2

i

b

Sofia says:

ii

n −2

iii

(

n+2

)(

n −2

)

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If n is an integer, then ( n + 2)( n − 2) is also an integer.

Is Sofia correct? Give some evidence to support your answer.

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1.2 Standard form Exercise 1.2

Key words

Focus

standard form

Write these numbers in standard form.

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1

a

2

b

920 000 000

c

462 000

d

20 800 000

c

640 million

d

406 million

d

1.331 × 108

Write these numbers in standard form. a

3

2 600 000 55 000

b

55 million

These numbers are in standard form. Write each number in full. a

5.3 × 104

b

5.38 × 107

c

7.11 × 1011

4

A light year is the distance light travels in one year.

One light year is 9 460 000 000 000 km.

Write this distance in standard form.

9 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

1 Number and calculation

Practice

6

7

Write these numbers in standard form. a

0.000 03

b

0.000 000 666

c

0.000 050 5

d

0.000 000 000 48

These numbers are in standard form. Write each number in full. a

1.5 × 10−3

b

1.234 × 10−5

c

7.9 × 10−8

d

9.003 × 10−4

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5

Write these numbers in full. a

8 × 10−6

c

6.1 × 10−5

b

4.82 × 10−7

d

7.007 × 10−8

8

The wavelength of visible light is between 0.000 000 4 m and 0.000 000 8 m.

Write each of these numbers in standard form.

9

Look at these five numbers.

A = 9.8 × 10−7

B = 1.2 × 10−6

D = 4.81 × 10−6

E = 5.17 × 10−7

Write the numbers in order of size, smallest first.

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Challenge

C = 3.05 × 10−7

10 The mass of Earth is 5.98 × 1024 kg.

When you write this mass in full, how many zeros does it have?

b

1 The mass of Mars is approximately 10 of the mass of Earth.

Write the mass of Mars in standard form.

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a

11 a Copy and complete this sentence: 6.2 × 107 is times larger than 6.2 × 106. b

How many times larger than 8.5 × 10−3 is 8.5 × 103?

12 These numbers are not in standard form. Write each number in standard form. a

45 × 106

b

28 × 108

c

300× 104

d

995 × 107

13 Write each of these numbers in standard form. a

43 × 10−5

b

125 × 10−8

c

0.7 × 10−5

d

0.08 × 10−7

10 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

1.3 Indices

14 Do these additions. Give your answers in standard form. a

8.1 × 105 + 9.4 × 105

b

6.7 × 107 + 6.7 × 107

c

3.6 × 10−5 + 2.9 × 10−5

d

2.86 × 10−5 + 8.6 × 10−5

1.3 Indices

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Exercise 1.3 Focus

2

3

4

Write each number as a fraction. a

7−1

d

3−4

b

7−2

c

5−3

e

15−2

f

20−2

Write these numbers as powers of 4. a

1 4

d

256

b

1 64

c

1

e

1 256

f

16−1

b

25

c

0.04

e

150

Write each number as a power of 5. a

0.2

d

125−1

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1

Find the value of x−3 when x=2

b

c

x=3

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a

x=5

d

x = 10

Practice 5

6

Write the answer to each multiplication as a power of 12. a

123 × 12 −1

b

12 4 × 12 −5

c

12 −1 × 12 −2

d

12 −4 × 127

Write the answer to each multiplication in index form.

4 −1 −6 a 5 × 5 b 4 −3 × 4 −3 c 8 × 8 d

7

155 × 15 −5

e

5 −6 × 5 −6

Write the answer to each division as a power of 7.

3 4 a 75 ÷ 7 2 b 7 ÷ 7 c

7 4 ÷ 7 −2

d

7 −4 ÷ 7 −3

11 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.

1 Number and calculation

8

Write the answer to each division in index form. −5 2 a 123 ÷ 12 −2 b 5 ÷ 5 c

34 ÷ 38

d

25 −3 ÷ 25 −4

Challenge Find the value of x in these equations. a

23 × 2 x = 2 9

b

32 × 3x = 3−2

c

5 −3 × 5x = 5 −5

d

8x × 8−3 = 8

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9

10 Find the value of y in these equations. a

32 ÷ 34 = 3 y

c

14 2 ÷ 14 y = 14 −4

11 y = x 0 + x −1 + x −2

b

106 ÷ 10 y = 10 2

d

8 y ÷ 83 = 84

Find the value of y when a

b

x=1

c

x=2

x=3

12 This table shows powers of 11.

112 121

114 14 641

115 161 051

116 1 771 561

Use the table to work out the following. Do not use a calculator. a

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113 1331

121 × 14 641

b

1 771 561 ÷ 14 641

13 Find the value of x in this equation: 2 × 4 = 2 2

c

121 ÷ 161 051

x

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3

12 Original material © Cambridge University Press 2021. This material is not final and is subject to further changes prior to publication.