Mathematics Textbook for grade 9Full description...

Author:
Humaira Kaleem

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29/5/08

18:33

Page i

Year Y ear 9, Pupil Book 3

NEW MATHS FRAMEWORKING Matches the revised KS3 Framework

Kevin Evans, Keith Gordon, Trevor Senior, Brian Speed

Maths Frameworking PB 9.3 Chs 1–9

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Contents

Introduction

CHAPTER

CHAPTER

CHAPTER

ii

1

2

3

vi

Algebra 1 & 2 Sequences

1

Quadratic sequences

4

Functions

6

Graphs

8

Limits of sequences

11

National Test questions

12

Functional Maths – Mobile phone tariffs

14

Number 1 The four rules governing fractions

16

Percentages and compound interest

19

Reverse percentages and percentage change

22

Direct and inverse proportion

25

Ratio in area and volume

28

Numbers between 0 and 1

32

Reciprocal of a number

34

Rounding and estimation

35

National Test questions

37

Functional Maths – The London Olympics 2012

40

Algebra

3

Equations, formulae and identities

42

Simultaneous equations

45

Solving by substitution

47

Equations involving fractions

48

Inequalities

50

Graphs showing direct proportion

52

Solving simultaneous equations by graphs

55

National Test questions

57

Maths Frameworking PB 9.3 Chs 1–9

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Page ii

Contents

Introduction

CHAPTER

CHAPTER

CHAPTER

ii

1

2

3

vi

Algebra 1 & 2 Sequences

1

Quadratic sequences

4

Functions

6

Graphs

8

Limits of sequences

11

National Test questions

12

Functional Maths – Mobile phone tariffs

14

Number 1 The four rules governing fractions

16

Percentages and compound interest

19

Reverse percentages and percentage change

22

Direct and inverse proportion

25

Ratio in area and volume

28

Numbers between 0 and 1

32

Reciprocal of a number

34

Rounding and estimation

35

National Test questions

37

Functional Maths – The London Olympics 2012

40

Algebra

3

Equations, formulae and identities

42

Simultaneous equations

45

Solving by substitution

47

Equations involving fractions

48

Inequalities

50

Graphs showing direct proportion

52

Solving simultaneous equations by graphs

55

National Test questions

57

Maths Frameworking PB 9.3 Chs 1–9

CHAPTER

CHAPTER

CHAPTER

CHAPTER

4

5

6

7

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Geometry and Measures 1 Pythagoras’ theorem

58

Solving problems using Pythagoras’ theorem

62

Loci

64

Congruent triangles

68

Circle theorems

70

Tessellations and regular polygons

73

Practical Pythagoras

75

National Test questions

77

Functional Maths – Garden design

80

Statistics

1

Scatter graphs and correlation

82

Scatter graphs and lines of best fit

85

Time series graphs

88

Two-way tables

91

Cumulative frequency diagrams

93

Estimation of a mean from grouped data

95

Statistical investigations

98

National Test questions

101

Functional Maths – Rainforest deforestation

106

Geometry and Measures 2 Similar triangles

108

Metric units for area and volume

112

Length of an arc and area of a sector

114

Volume of a cylinder

116

Rate of change

118

National Test questions

122

Functional Maths – Athletics stadium

124

Number

2

Standard form

126

Multiplying with numbers in standard form

128

Dividing with numbers in standard form

130

Upper and lower bounds 1

132

Upper and lower bounds 2

134

Recurring decimals

136

Efficient use of calculators

139

National Test questions

141

Functional Maths – Paper

144

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Maths Frameworking PB 9.3 Chs 1–9

CHAPTER

8

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Algebra 4 Index notation with algebra – negative powers

146

Square roots, cube roots and other fractional powers 148

CHAPTER

CHAPTER

CHAPTER

CHAPTER

iv

9

Quadratic graphs

151

Cubic graphs

153

National Test questions

155

Functional Maths – Packages

156

Statistics 2 Probability statements

158

Mutually exclusive events and exhaustive events

160

Combining probabilities and tree diagrams

163

Estimates of probability

165

National Test questions

169

Functional Maths – Class test

172

10 Geometry and Measures 3 Fractional enlargements

174

Trigonometry – The tangent of an angle

178

Trigonometry – The sine and cosine of an angle

183

Solving problems using trigonometry

187

National Test questions

189

Functional Maths – Map reading

192

11 Algebra 5 Expansion

194

Factorisation

197

Quadratic expansion

199

Quadratic factorisation

201

Change of subject

202

Graphs from equations in the form A y ± B x = C

205

National Test questions

206

Functional Maths – Trip to Rome

208

12 Solving Problems and Revision Number 1 – Fractions, percentages and decimals

210

Number 2 – The first four rules, ratios and standard form

213

Algebra 1 – Rules of algebra and solving equations

215

Algebra 2 – Graphs

216

Geometry and measures

219

Statistics

222

Maths Frameworking PB 9.3 Chs 1–9

CHAPTER

CHAPTER

CHAPTER

CHAPTER

CHAPTER

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13 Statistics 3 and Revision Statistical techniques

225

A handling data project

231

14 Geometry and Measures 4 and Revision Geometry and measures revision

234

Geometry and measures investigations

236

Symmetry revision

237

Symmetry investigations

239

15 Statistics 4 and Revision Revision of probability

241

A probability investigation

246

16 GCSE Preparation Solving quadratic equations

249

Quadratic equations of the form a x 2 + b x + c

250

Quadratic equations

251

The quadratic formula

252

Completing the square

253

The difference of two squares

255

GCSE past-paper questions

256

17 Functional Maths Practice The Eden Project

260

Road safety

262

Squirrels

264

Mobile shop

266

Index

268

Garden design activity worksheet

271

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Maths Frameworking PB 9.3 Chs 1–9

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Introduction

Learning objectives

See what you are going to cover and what you should already know at the start of each chapter. The purple and blue boxes set the topic in context and provide a handy checklist.

National Curriculum levels

Know what level you are working at so you can easily track your progress with the colour-coded levels at the side of the page.

Worked examples

Understand the topic before you start the exercises by reading the examples in blue boxes. These take you through how to answer a question step-by-step.

Functional Maths

Practise your Functional Maths skills to see how people use Maths in everyday life. Look out for the Functional Maths icon on the page.

Extension activities

Stretch your thinking and investigative skills by working through the extension activities. By tackling these you are working at a higher level.

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Maths Frameworking PB 9.3 Chs 1–9

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Level booster

Progress to the next level by checking the Level boosters at the end of each chapter. These clearly show you what you need to know at each level and how to improve. National Test questions

Practise the past paper Test questions to feel confident and prepared for your KS3 National Curriculum Tests. The questions are levelled so you can check what level you are working at. Extra interactive National Test practice

Watch and listen to the audio/visual National Test questions on the separate Interactive Book CD-ROM to help you revise as a class on a whiteboard. Look out for the computer mouse icon on the page and on the screen. Functional Maths activities

Put Maths into context with these colourful pages showing real-world situations involving Maths. You are practising your Functional Maths skills by analysing data to solve problems. Extra interactive Functional Maths questions and video clips

Extend your Functional Maths skills by taking part in the interactive questions on the separate Interactive Book CD-ROM. Your teacher can put these on the whiteboard so the class can answer the questions on the board.

N E W

Hone your Functional Maths skills further by doing the four exciting tasks given in the new chapter – Functional Maths Practice.

See Maths in action by watching the video clips and doing the related Worksheets on the Interactive Book CD-ROM. The videos bring the Functional Maths activities to life and help you see how Maths is used in the real world. Look out for the computer mouse icon on the page and on the screen.

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