About this resource vii

Acknowledgements xiv

NAPLAN practice

Set A Calculator allowed

Set B Non-calculator

Set C Calculator allowed

Set D Non-calculator

Set E Calculator allowed

Set F Non-calculator

1 Integers 1

1.1 Overview 2

1.2 Adding and subtracting integers 4

1.3 Multiplying integers 11

1.4 Dividing integers 15

1.5 Order of operations with integers 19

1.6 Review 23

Answers 29

2 Index laws 33

2.1 Overview 34

2.2 Review of index form 36

2.3 Multiplying powers 41

2.4 Dividing powers 45

2.5 The zero index 50

2.6 Raising powers 54

2.7 Review 60

Answers 67

3 Real numbers 71

3.1 Overview 72

3.2 The real number system 74

3.3 Adding and subtracting fractions 80

3.4 Multiplying and dividing fractions 88

3.5 Terminating and recurring decimals 93

3.6 Adding and subtracting decimals 97

3.7 Multiplying and dividing decimals 102

3.8 Estimation 107

3.9 Review 114

Answers 121

4 Applications of percentages 127

4.1 Overview 128

4.2 Percentages 130

4.3 Finding percentages of an amount 136

4.4 Discount 142

4.5 Profit and loss 148

4.6 Goods and Services Tax (GST) and Income Tax 155

4.7 Review 162

Answers 168

5 Ratios and rates 171

5.1 Overview 172

5.2 Introduction to ratios 174

5.3 Simplifying ratios 181

5.4 Proportion 189

5.5 Comparing ratios 195

5.6 Dividing in a given ratio 199

5.7 Rates 205

5.8 Interpreting graphs 210

5.9 Review 219

Answers 225

6 Congruence 231

6.1 Overview 232

6.2 Transformations and tessellations 236

6.3 Congruent figures 254

6.4 Triangle constructions and objects in 3D 262

6.5 Congruent triangles and similar shapes 270

6.6 Quadrilaterals 287

6.7 Review 295

Answers 302

Semester review 1 312

7 Algebra 315

7.1 Overview 316

7.2 Using pronumerals 318

7.3 Substitution 323

7.4 Substituting positive and negative numbers 328

7.5 Number laws 331

7.6 Adding and subtracting terms 337

7.7 Multiplying and dividing terms 341

7.8 Expanding brackets 348

7.9 Factorising 353

7.10 Review 357

Answers 363

8 Measurement 369

8.1 Overview 370

8.2 Length and perimeter 373

8.3 Circumference 381

8.4 Areas of rectangles, triangles, parallelograms, rhombuses and kites 390

8.5 Areas of circles 403

8.6 Areas of trapeziums 409

8.7 Volumes of prisms and other solids 414

8.8 Time 421

8.9 24-hour clocks and time zones 427

8.10 Review 436

Answers 445

9 Linear equations 451

9.1 Overview 452

9.2 Backtracking and inverse operations 454

9.3 Keeping equations balanced 459

9.4 Solving linear equations and inequations 463

9.5 Equations with the unknown on both sides 473

9.6 Review 479

Answers 485

10 Representing and interpreting data 489

10.1 Overview 490

10.2 Data collection methods 493

10.3 Primary and secondary data 504

10.4 Organising and displaying data 513

10.5 Measures of centre and spread 523

10.6 Analysing data 538

10.7 Review 546

Answers 552

11 Probability 561

11.1 Overview 562

11.2 Experimental probability 565

11.3 Probability scale 573

11.4 Sample spaces and theoretical probability 577

11.5 Complementary events 585

11.6 Venn diagrams and two-way tables 590

11.7 Tree diagrams 603

11.8 Review 612

Answers 618

12 Coordinates and linear graphs 627

12.1 Overview 628

12.2 The Cartesian plane 631

12.3 Linear patterns 638

12.4 Plotting linear graphs 645

12.5 Determining the rule for a linear relationship 651

12.6 Sketching linear graphs (extending) 666

12.7 Solving equations graphically 671

12.8 Non-linear graphs 680

12.9 Review 687

Answers 694

13 Pythagoras’ theorem 715

13.1 Overview 716

13.2 Pythagoras’ theorem 719

13.3 Calculating shorter side lengths 726

13.4 Applying Pythagoras’ theorem 730

13.5 Pythagorean triads 736

13.6 Review 740

Answers 745

Semester review 2 748

14 Algorithmic thinking

14.1 Overview

14.2 Expressions

14.3 Decisions

14.4 Functions

14.5 Testing

14.6 Debugging

14.7 Review

Answers

Glossary 750

Index 755