About this resource x

Acknowledgements xii

Topic 1 Numeracy 1 1

1.1 Overview 1

1.2 Set A 2

1.3 Set B 4

Answers 8

Topic 2 Number skills 9

2.1 Overview 9

2.2 Rational numbers 10

2.3 Surds 14

2.4 Real numbers 24

2.5 Scientific notation 27

2.6 Review 32

Answers 37

Topic 3 Algebra 42

3.1 Overview 42

3.2 Using pronumerals 43

3.3 Algebra in worded problems 49

3.4 Simplifying algebraic expressions 53

3.5 Expanding brackets 58

3.6 Expansion patterns 65

3.7 Further expansions 69

3.8 The highest common factor 71

3.9 The highest common binomial factor 75

3.10 Applications 78

3.11 Review 85

Answers 91

Topic 4 Linear equations 101

4.1 Overview 101

4.2 Solving linear equations 102

4.3 Solving linear equations with brackets 109

4.4 Solving linear equations with pronumerals on both sides 111

4.5 Solving problems with linear equations 115

4.6 Rearranging formulas 119

4.7 Review 122

Answers 128

Topic 5 Congruence and similarity 132

5.1 Overview 132

5.2 Ratio and scale 133

5.3 Congruent figures 140

5.4 Similar figures 147

5.5 Area and volume of similar figures 157

5.6 Review 162

Answers 169

Topic 6 Pythagoras and trigonometry 174

6.1 Overview 174

6.2 Pythagoras’ theorem 175

6.3 Applications of Pythagoras’ theorem 183

6.4 What is trigonometry? 189

6.5 Calculating unknown side lengths 196

6.6 Calculating unknown angles 203

6.7 Angles of elevation and depression 209

6.8 Review 215

Answers 222

Project: Learning or earning? 229

Topic 7 Linear and non-linear graphs 231

7.1 Overview 231

7.2 Plotting linear graphs 232

7.3 The equation of a straight line 236

7.4 Sketching linear graphs 245

7.5 Technology and linear graphs 250

7.6 Determining linear rules 253

7.7 Practical applications of linear graphs 260

7.8 Midpoint of a line segment and distance between two points 264

7.9 Non-linear relations (parabolas, hyperbolas, circles) 269

7.10 Review 276

Answers 282

Topic 8 Proportion and rates 297

8.1 Overview 297

8.2 Direct proportion 298

8.3 Direct proportion and ratio 302

8.4 Inverse proportion 306

8.5 Introduction to rates 310

8.6 Constant and variable rates 312

8.7 Rates of change 318

8.8 Review 323

Answers 329

Topic 9 Numeracy 2 336

9.1 Overview 336

9.2 Set C 337

9.3 Set D 340

Answers 344

Topic 10 Indices 345

10.1 Overview 345

10.2 Review of index laws 346

10.3 Raising a power to another power 352

10.4 Negative indices 356

10.5 Square roots and cube roots 360

10.6 Review 363

Answers 368

Topic 11 Financial mathematics 373

11.1 Overview 373

11.2 Salaries and wages 374

11.3 Special rates 377

11.4 Piecework 382

11.5 Commission and royalties 385

11.6 Loadings and bonuses 388

11.7 Taxation and net earnings 392

11.8 Simple interest 396

11.9 Compound interest 401

11.10 Review 406

Answers 411

Topic 12 Measurement 416

12.1 Overview 416

12.2 Measurement 417

12.3 Area 426

12.4 Area and perimeter of a sector 436

12.5 Surface area of rectangular and triangular prisms 442

12.6 Surface area of a cylinder 447

12.7 Volume of prisms and cylinders 451

12.8 Review 461

Answers 469

Topic 13 Probability 475

13.1 Overview 475

13.2 Theoretical probability 476

13.3 Experimental probability 482

13.4 Venn diagrams and two-way tables 488

13.5 Two-step experiments 498

13.6 Mutually exclusive and independent events 507

13.7 Conditional probability 516

13.8 Review 521

Answers 527

Topic 14 Statistics 537

14.1 Overview 537

14.2 Sampling 538

14.3 Collecting data 548

14.4 Displaying data 557

14.5 Measures of central tendency 568

14.6 Measures of spread 577

14.7 Review 586

Answers 592

Topic 15 Numeracy 3 604

15.1 Overview 604

15.2 Set E 605

15.3 Set F 609

Answers 613

Project: Backyard flood? 614

Topic 16 Quadratic algebra 617

16.1 Overview 617

16.2 Factorisation patterns 618

16.3 Factorising monic quadratics 622

16.4 Factorising non-monic quadratics 625

16.5 Simplifying algebraic fractions 628

16.6 Quadratic equations 634

16.7 The Null Factor Law 637

16.8 Solving the quadratic equation ax² + bx + c = 0 640

16.9 Solving quadratic equations with two terms 644

16.10 Applications 647

16.11 Review 650

Answers 656

Topic 17 Quadratic functions 663

17.1 Overview 663

17.2 Graphs of quadratic functions 664

17.3 Plotting points to graph quadratic functions 669

17.4 Sketching parabolas of the form y = ax² 675

17.5 Sketching parabolas of the form y = ax² + c 679

17.6 Sketching parabolas of the form y = (x – h)² 683

17.7 Sketching parabolas of the form y = (x – h)² + k 687

17.8 Sketching parabolas of the form y = (x + a) (x + b) 691

17.9 Applications 696

17.10 Review 699

Answers 706

Topic 18 Programming

18.1 Overview

18.2 Programs

18.3 Arrays

18.4 Loops

18.5 Set structures

18.6 Sorting algorithms

18.7 The Monte Carlo method

18.8 Review

Answers

Glossary 724

Index 732