Maths Frameworking - Pupil Book 3.3 [Third Edition]

by Kevin Evans, Keith Gordon (Illustrator)

Overview

Ensure progress at the right pace with Pupil Book 3.3, the higher tier for the third year of teaching KS3. With fluency, mathematical reasoning and problem solving integrated throughout you can be confident you’re covering the main aims of the new curriculum and preparing students for revised GCSEs ahead.

Product Details

ISBN-13:	9780007537792
Publisher:	HarperCollins UK
Publication date:	09/01/2014
Series:	Maths Frameworking
Edition description:	Third Edition, Third edition
Pages:	360
Product dimensions:	7.40(w) x 10.30(h) x 0.50(d)
Age Range:	14 Years

Table of Contents

Introduction 4

1 Percentages 6

1.1 Simple interest 7

1.2 Percentage increases and decreases 10

1.3 Calculating the original value 14

1.4 Repeated percentage changes 17

Ready to progress? 20

Review questions 20

Challenge: Exponential growth 22

2 Equations and formulae 24

2.1 Multiplying out brackets 25

2.2 Factorising algebraic expressions 26

2.3 Expressions with several variables 28

2.4 Equations with fractions 31

Ready to progress? 34

Review questions 34

Investigation: Body mass index 36

3 Polygons 38

3.1 Properties of polygons 39

3.2 Interior and exterior angles of regular polygons 44

3.3 Tessellations and regular polygons 46

Ready to progress? 48

Review questions 48

Mathematical reasoning: Semi-regular tessellations 50

4 Using data 52

4.1 Scatter graphs and correlation 53

4.2 Two-way tables 59

4.3 Estimation of a mean from grouped data 62

4.4 Cumulative frequency diagrams 65

4.5 Statistical investigations 70

Ready to progress? 72

Review questions 72

Challenge: Census 74

5 Applications of graphs 76

5.1 Step graphs 77

5.2 Time graphs 82

5.3 Exponential growth graphs 87

Ready to progress? 92

Review questions 92

Problem solving: Mobile phone tariffs 94

6 Pythagoras' theorem 96

6.1 Introducing Pythagoras' theorem 97

6.2 Using Pythagoras' theorem to solve problems 101

6.3 The converse of Pythagoras' theorem 104

Ready to progress? 106

Review questions 106

Activity: Practical Pythagoras 108

7 Fractions 110

7.1 Adding and subtracting fractions 111

7.2 Multiplying fractions and mixed numbers 113

7.3 Dividing fractions and mixed numbers 115

7.4 Algebraic fractions 118

Ready to progress? 120

Review questions 120

Investigation: Fractions, from one to six 122

8 Algebra 124

8.1 Expanding the product of two brackets 125

8.2 Expanding expressions with more than two brackets 128

8.3 Factorising quadratic expressions with positive coefficients 130

8.4 Factorising quadratic expressions with negative coefficients 132

8.5 The difference of two squares 134

Ready to progress? 136

Review questions 136

Challenge: Graphs from expressions 138

9 Decimal numbers 140

9.1 Powers of 10 141

9.2 Standard form 143

9.3 Multiplying with numbers in standard form 147

9.4 Dividing with numbers in standard form 149

9.5 Upper and lower bounds 151

Ready to progress? 154

Review questions 154

Mathematical reasoning: To the stars and back 156

10 Surface area and volume of cylinders 158

10.1 Volume of a cylinder 159

10.2 Surface area of a cylinder 162

10.3 Composite shapes 166

Ready to progress? 170

Review questions 170

Problem solving: Packaging soup 172

11 Solving equations graphically 174

11.1 Graphs from equations in the form ay ± bx = c 175

11.2 Solving simultaneous equations by drawing graphs 177

11.3 Solving quadratic equations by drawing graphs 179

11.4 Solving cubic equations by drawing graphs 181

Ready to progress? 184

Review questions 184

Challenge: Maximum packages 186

12 Compound units 188

12.1 Speed 189

12.2 More compound units 193

12.3 Unit costs 196

Ready to progress? 200

Review questions 200

Challenge: Population density 202

13 Right-angled triangles 204

13.1 Introduction to trigonometric ratios 205

13.2 How to find trigonometric ratios of angles 207

13.3 Using trigonometric ratios to find angles 210

13.4 Using trigonometric ratios to find lengths 215

Ready to progress? 218

Review questions 218

Investigation: Barnes Wallis and the bouncing bomb 220

14 Revision and GCSE preparation 222

14.1 Practice 223

14.2 Revision 232

GCSE-type questions 239

Glossary 242

Index 245