About this resource vi

About eBookPLUS  viii

Acknowledgements ix

Unit 3 Measurement, Scales and Data 1

1 Calculations 1

1.1 Overview 1

1.2 Number operations 2

1.3 Order of operations 4

1.4 Rounding 9

1.5 Estimation and approximation strategies 12

1.6 Decimal fractions 15

1.7 Review: exam practice 23

Answers 27

2 Geometry 29

2.1 Overview 29

2.2 Review of angles 30

2.3 Two-dimensional geometric shapes 39

2.4 Three-dimensional objects 52

2.5 Two-dimensional representations of three-dimensional objects 55

2.6 Review: exam practice 61

Answers 69

3 Linear and area measure 73

3.1 Overview 73

3.2 Units of length and estimation 74

3.3 Perimeters of familiar and composite shapes 78

3.4 Units of area and estimation 87

3.5 Areas of regular shapes 92

3.6 Areas of composite figures 100

3.7 Surface areas of familiar prisms 105

3.8 Surface areas of familiar pyramids and irregular solids 111

3.9 Review: exam practice 117

Answers 126

4 Volume, capacity and mass 128

4.1 Overview 128

4.2 Units of volume and capacity 129

4.3 Volume and capacity of prisms and cylinders 134

4.4 Volume and capacity of pyramids and spheres 141

4.5 Problems involving mass 145

4.6 Review: exam practice 150

Answers 156

5 Scales, plans and models 158

5.1 Overview 158

5.2 Reading and interpreting scale drawings 159

5.3 Calculating measurements from scale drawings 163

5.4 Creating scale drawings 173

5.5 Review: exam practice 182

Answers 187

6 Right-angled triangles 189

6.1 Overview 189

6.2 Pythagoras’ theorem 190

6.3 Trigonometric ratios: sine, cosine and tangent 195

6.4 Calculating unknown side lengths of right-angled triangles 201

6.5 Calculating unknown angles in right-angled triangles 207

6.6 Angles of elevation and depression 212

6.7 Review: exam practice 217

Answers 223

7 Summarising and interpreting data 225

7.1 Overview 225

7.2 Measures of central tendency and mode 226

7.3 Measures of spread 238

7.4 Outliers 251

7.5 Applications of measures of centre and spread 256

7.6 Review: exam practice 261

Answers 267

8 Comparing data sets 270

8.1 Overview 270

8.2 Constructing box plots 271

8.3 Comparing parallel box plots 277

8.4 Comparing back-to-back stem plots 281

8.5 Comparing histograms 288

8.6 Review: exam practice 295

Answers 304

Practice Assessment 1

Essential Mathematics: Problem solving and modelling task 314

Practice Assessment 2

Essential Mathematics: Unit 3 examination 317

Unit 4 Graphs, Chance and Loans 324

9 Cartesian plane 324

9.1 Overview 324

9.2 Plotting points on a Cartesian plane 325

9.3 Generating tables of values for linear functions 328

9.4 Graphing linear functions 335

9.5 Review: exam practice 347

Answers 350

10 Scatterplots and lines of best fit 357

10.1 Overview 357

10.2 Interpreting scatterplots 358

10.3 The line of best fit 368

10.4 Making predictions using a line of best fit 378

10.5 Causality and correlation 387

10.6 Review: exam practice 393

Answers 401

11 Simulations and simple probability 407

11.1 Overview 407

11.2 Theoretical probability and sample spaces 408

11.3 Multi-stage experiments (arrays and tree diagrams) 414

11.4 Relative frequency and simulations 421

11.5 Review: exam practice 431

Answers 435

12 Loans and compound interest 441

12.1 Overview 441

12.2 Simple interest 442

12.3 Simple interest as a recurrence relation 449

12.4 Compound interest 454

12.5 Comparing simple and compound interest 462

12.6 Review: exam practice 476

Answers 481

13 Reducing balance loans 486

13.1 Overview 486

13.2 Modelling reducing balance loans with technology 487

13.3 The effect of interest rate and repayment amount on reducing balance loans 496

13.4 Review: exam practice 503

Answers 507

Practice Assessment 3

Essential Mathematics: Problem solving and modelling task 508

Practice Assessment 4

Essential Mathematics: Unit 4 examination 512

Appendix Maths Skills Workbook 519

Key skill 1 Fractions 520

Key skill 2 Equivalent fractions 521

Key skill 3 Multiplying fractions 522

Key skill 4 Percentage skills 524

Key skill 5 Percentages 525

Key skill 6 Fractions into percentages 526

Key skill 7 Ratios 527

Key skill 8 Using ratios 528

Key skill 9 Simplifying ratios 529

Investigation Crash statistics 530

Answers 532

Glossary 534

Index 539