Jacaranda Maths Quest 9 Australian Curriculum, 4e learnON and Print

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 Number skills and index laws 1

1.1 Overview 2

1.2 Real numbers 4

1.3 Rounding numbers and significant figures 10

1.4 Review of index laws 15

1.5 Raising powers 22

1.6 Negative indices 27

1.7 Scientific notation 32

1.8 Square roots and cube roots 38

1.9 Surds (extending) 41

1.10 Review 52

Answers 61

2 Algebra 67

2.1 Overview 68

2.2 Using pronumerals 70

2.3 Algebra in worded problems 79

2.4 Simplification of algebraic expressions 84

2.5 Expanding brackets 90

2.6 Difference of two squares and perfect squares 99

2.7 Further expansions 104

2.8 The highest common factor 107

2.9 The highest common binomial factor 113

2.10 Solving worded problems 117

2.11 Review 126

Answers 134

3 Linear equations 143

3.1 Overview 144

3.2 Solving linear equations 146

3.3 Solving linear equations with brackets 155

3.4 Solving linear equations with pronumerals on both sides 158

3.5 Solving problems with linear equations 162

3.6 Rearranging formulas 168

3.7 Review 173

Answers 180

4 Congruence and similarity 185

4.1 Overview 186

4.2 Ratio and scale 189

4.3 Congruent figures 198

4.4 Nets, polyhedra and Euler’s formula 206

4.5 Similar figures 211

4.6 Area and volume of similar figures 220

4.7 Review 229

Answers 239

5 Pythagoras and trigonometry 245

5.1 Overview 246

5.2 Pythagoras’ theorem 250

5.3 Applications of Pythagoras’ theorem 258

5.4 Trigonometric ratios 265

5.5 Calculating unknown side lengths 273

5.6 Calculating unknown angles 282

5.7 Angles of elevation and depression 289

5.8 Review 295

Answers 305

6 Linear and non-linear graphs 311

6.1 Overview 312

6.2 Plotting linear graphs 314

6.3 Features of linear graphs 320

6.4 The equation of a straight line 328

6.5 Sketching linear graphs 336

6.6 Technology and linear graphs 344

6.7 Practical applications of linear graphs 348

6.8 Midpoint of a line segment and distance between two points 353

6.9 Non-linear relations (parabolas, hyperbolas, circles) 359

6.10 Review 370

Answers 379

Semester review 1 394

7 Proportion and rates 397

7.1 Overview 398

7.2 Direct linear proportion 400

7.3 Proportionality 405

7.4 Introduction to rates 409

7.5 Constant and variable rates 412

7.6 Review 419

Answers 428

8 Financial mathematics 431

8.1 Overview 432

8.2 Salaries and wages 435

8.3 Penalty rates 439

8.4 Simple interest 445

8.5 Compound interest 453

8.6 Review 462

Answers 468

9 Measurement 471

9.1 Overview 472

9.2 Measurement 476

9.3 Area 485

9.4 Area and perimeter of a sector 495

9.5 Surface area of rectangular and triangular prisms 501

9.6 Surface area of a cylinder 508

9.7 Volume of prisms and cylinders 512

9.8 Review 523

Answers 533

10 Probability 537

10.1 Overview 538

10.2 Theoretical probability 544

10.3 Experimental probability 551

10.4 Venn diagrams and two-way tables 559

10.5 Two-step experiments 576

10.6 Review 588

Answers 596

11 Statistics 603

11.1 Overview 604

11.2 Sampling 608

11.3 Collecting data 616

11.4 Displaying data 626

11.5 Measures of centre 639

11.6 Measures of spread 650

11.7 Review 661

Answers 668

12 Quadratic equations and graphs 681

12.1 Overview 682

12.2 Quadratic equations 684

12.3 The Null Factor Law 689

12.4 Solving quadratic equations with two terms 693

12.5 Factorising and solving monic quadratic equations 697

12.6 Graphs of quadratic functions 703

12.7 Sketching parabolas of the form y = ax ² 712

12.8 Sketching parabolas of the form y =(x − h) ² + k 718

12.9 Sketching parabolas of the form y =(x + a)(x + b) 730

12.10 Applications 735

12.11 Review 740

Answers 750

Semester review 2 776

13 Algorithmic thinking

13.1 Overview

13.2 Programs

13.3 Arrays

13.4 Loops

13.5 Set structures

13.6 Sorting algorithms

13.7 The Monte Carlo method

13.8 Review

Answers

Glossary 778

Index 784