Jacaranda Maths Quest 8 Victorian Curriculum

Contents

Naplan Practice vii

About This Resource viii

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 30

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 68

3 Real numbers 73

3.1 Overview 74

3.2 The real number system 76

3.3 Adding and subtracting fractions 82

3.4 Multiplying and dividing fractions 89

3.5 Terminating and recurring decimals 94

3.6 Adding and subtracting decimals 99

3.7 Multiplying and dividing decimals 104

3.8 Estimation 109

3.9 Review 116

Answers 124

4 Applications of percentages 129

4.1 Overview 130

4.2 Percentages 132

4.3 Finding percentages of an amount 138

4.4 Discount 144

4.5 Profit and loss 150

4.6 Goods and Services Tax (GST) 157

4.7 Review 162

Answers 169

5 Ratios and rates 173

5.1 Overview 174

5.2 Introduction to ratios 176

5.3 Simplifying ratios 183

5.4 Proportion 191

5.5 Comparing ratios 197

5.6 Dividing in a given ratio 200

5.7 Rates 206

5.8 Interpreting graphs 210

5.9 Review 219

Answers 226

6 Congruence 233

6.1 Overview 234

6.2 Transformations and tessellations 238

6.3 Congruent figures 256

6.4 Triangle constructions 263

6.5 Congruent triangles 268

6.6 Quadrilaterals 276

6.7 Review 283

Answers 291

Semester review 1 302

7 Algebra 305

7.1 Overview 306

7.2 Using pronumerals 308

7.3 Substitution 313

7.4 Substituting positive and negative numbers 318

7.5 Number laws 321

7.6 Adding and subtracting terms 327

7.7 Multiplying and dividing terms 331

7.8 Expanding brackets 338

7.9 Factorising 343

7.10 Review 347

Answers 354

8 Measurement 359

8.1 Overview 360

8.2 Length and perimeter 363

8.3 Circumference 371

8.4 Areas of rectangles, triangles, parallelograms, rhombuses and kites 380

8.5 Areas of circles 391

8.6 Areas of trapeziums 397

8.7 Volumes of prisms and other solids 402

8.8 Time 408

8.9 24-hour clocks and time zones 414

8.10 Review 423

Answers 433

9 Linear equations 439

9.1 Overview 440

9.2 Backtracking and inverse operations 442

9.3 Keeping equations balanced 447

9.4 Solving linear equations 451

9.5 Equations with the unknown on both sides 460

9.6 Review 466

Answers 473

10 Representing and interpreting data 477

10.1 Overview 478

10.2 Samples and populations 481

10.3 Primary and secondary data 490

10.4 Organising and displaying data 499

10.5 Measures of centre and spread 509

10.6 Analysing data 524

10.7 Review 532

Answers 539

11 Probability 547

11.1 Overview 548

11.2 Experimental probability 551

11.3 Probability scale 559

11.4 Sample spaces and theoretical probability 563

11.5 Complementary events 571

11.6 Venn diagrams and two-way tables 576

11.7 Tree diagrams (extending) 589

11.8 Review 596

Answers 603

12 Coordinates and linear graphs 611

12.1 Overview 612

12.2 The Cartesian plane 615

12.3 Linear patterns 622

12.4 Plotting linear graphs 628

12.5 Determining the rule for a linear relationship 635

12.6 Sketching linear graphs (extending) 649

12.7 Solving equations graphically 654

12.8 Non-linear graphs 661

12.9 Review 669

Answers 677

13 Pythagoras’ theorem 697

13.1 Overview 698

13.2 Pythagoras’ theorem 701

13.3 Calculating shorter side lengths 708

13.4 Applying Pythagoras’ theorem 712

13.5 Pythagorean triads 718

13.6 Review 722

Answers 728

Semester review 2 730

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 732

Index 737