About This Resource v

Acknowledgements xii

NAPLAN practice

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Set B Non-calculator

Set C Calculator allowed

Set D Non-calculator

Set E Calculator allowed

Set F Non-calculator

1 Financial mathematics 1

1.1 Overview 2

1.2 Salaries and wages 5

1.3 Special rates 9

1.4 Piecework 15

1.5 Commissions and royalties 18

1.6 Loadings and bonuses 22

1.7 Taxation and net earnings 26

1.8 Simple interest 31

1.9 Introduction to compound interest 39

1.10 Review 47

Answers 52

2 Indices and surds 57

2.1 Overview 58

2.2 Applying the index laws to variables 60

2.3 Simplify algebraic products and quotients using index laws 69

2.4 Applying index laws to numerical and algebraic expressions involving negative-integer indices 73

2.5 Surds (Path) 80

2.6 Introduction to fractional indices (Path) 90

2.7 Review 95

Answers 101

3 Numbers of any magnitude 107

3.1 Overview 108

3.2 Very small and very large measurements 110

3.3 Absolute and percentage error 119

3.4 Estimating and rounding numbers to a specified degree of accuracy 126

3.5 Scientific notation 132

3.6 Review 139

Answers 146

4 Algebraic techniques 151

4.1 Overview 152

4.2 Simplifying algebraic expressions 154

4.3 Simplifying algebraic fractions 160

4.4 Expanding algebraic expressions and collecting like terms 166

4.5 Expanding binomial products 171

4.6 Difference of two squares and perfect squares (Path) 175

4.7 Further expansions (Path) 180

4.8 The highest common factor 183

4.9 The highest common binomial factor (Path) 188

4.10 Factorising monic quadratic expressions (Path) 192

4.11 Review 197

Answers 202

5 Linear equations 209

5.1 Overview 210

5.2 Solving linear equations 212

5.3 Solving linear equations with brackets 220

5.4 Solving linear equations with pronumerals on both sides 223

5.5 Solving worded problems and substituting into formulas 227

5.6 Review 235

Answers 241

6 Quadratic equations (Path) 245

6.1 Overview 246

6.2 Quadratic equations and cubic equations of the form ax³ = k 248

6.3 The Null Factor Law 254

6.4 Solving quadratic equations with two terms 257

6.5 Solving monic quadratic equations 261

6.6 Applications of quadratic equations 265

6.7 Review 269

Answers 273

7 Linear relationships 277

7.1 Overview 278

7.2 Plotting linear graphs 281

7.3 Features of linear graphs 286

7.4 The equation of a straight line, y = mx + c 295

7.5 Sketching linear graphs 303

7.6 Technology and linear graphs 311

7.7 Practical applications of linear graphs 315

7.8 Midpoint of a line segment and distance between two points 320

7.9 Review 327

Answers 334

Semester review 1 348

8 Non-linear relationships 351

8.1 Overview 352

8.2 Quadratic relationships and graphs 354

8.3 Quadratic equations of the form y = kx² 364

8.4 Quadratic equations of the form y = kx² + c 369

8.5 Exponential relationships and graphs 375

8.6 Applications of linear and non-linear relationships 380

8.7 Review 387

Answers 394

9 Variation and rates of change (Path) 409

9.1 Overview 410

9.2 Direct linear proportion 412

9.3 Direct proportion and ratio 417

9.4 Inverse proportion 422

9.5 Introduction to rates 427

9.6 Constant and variable rates 430

9.7 Review 441

Answers 449

10 Trigonometry 455

10.1 Overview 456

10.2 Trigonometric ratios and right-angled triangles 460

10.3 Calculating unknown side lengths 468

10.4 Calculating unknown angles 476

10.5 Angles of elevation and depression 483

10.6 Review 489

Answers 495

11 Measurement 499

11.1 Overview 500

11.2 Length and perimeter 504

11.3 Area 511

11.4 Area and perimeter of a sector 521

11.5 Surface area of rectangular and triangular prisms 528

11.6 Surface area of a cylinder 539

11.7 Volume of prisms and cylinders 543

11.8 Review 555

Answers 564

12 Properties of geometrical figures 569

12.1 Overview 570

12.2 Ratio and scale 573

12.3 Similar figures 586

12.4 Area and volume of similar figures (Path) 596

12.5 Review 605

Answers 612

13 Data analysis 615

13.1 Overview 616

13.2 Measures of central tendency 620

13.3 Measures of spread: Range and interquartile range 633

13.4 Measures of spread: Standard deviation 640

13.5 Box plots 647

13.6 Describing and comparing data sets 655

13.7 Review 666

Answers 676

14 Probability 685

14.1 Overview 686

14.2 Theoretical probability 691

14.3 Observed probability and simulations 698

14.4 Tree diagrams and two-step experiments 707

14.5 Exploring Venn diagrams and 2-way tables (Path) 718

14.6 Venn diagrams and 2-way tables using set notation (Path) 732

14.7 Mutually and non-mutually exclusive events (Path) 748

14.8 Review 758

Answers 764

Semester review 2 774

Glossary 776

Index 782