Jacaranda Maths Quest 9 Victorian Curriculum, 3e learnON and Print

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 Number skills and exponent laws 1

1.1 Overview 2

1.2 Real numbers 4

1.3 Rounding numbers and significant figures 11

1.4 Review of exponent laws 16

1.5 Raising powers 24

1.6 Negative exponents 28

1.7 Scientific notation 34

1.8 Square roots and cube roots 41

1.9 Surds (extending) 44

1.10 Review 56

Answers 64

2 Algebra 71

2.1 Overview 72

2.2 Using variables 74

2.3 Algebra in worded problems 83

2.4 Simplification of algebraic expressions 88

2.5 Expanding brackets 95

2.6 Difference of two squares and perfect squares 104

2.7 Further expansions 109

2.8 The highest common factor 112

2.9 The highest common binomial factor 118

2.10 Solving worded problems 122

2.11 Review 131

Answers 138

3 Linear equations 147

3.1 Overview 148

3.2 Solving linear equations and inequations 150

3.3 Solving linear equations with brackets 161

3.4 Solving linear equations with variables on both sides 165

3.5 Solving problems with linear equations 169

3.6 Rearranging formulas 175

3.7 Review 181

Answers 187

4 Congruence and similarity 191

4.1 Overview 192

4.2 Ratio and scale 195

4.3 Congruent figures 204

4.4 Nets, polyhedra and Euler’s formula 212

4.5 Similar figures 217

4.6 Area and volume of similar figures 229

4.7 Review 238

Answers 247

5 Pythagoras and trigonometry 253

5.1 Overview 254

5.2 Pythagoras’ theorem 258

5.3 Applications of Pythagoras’ theorem 267

5.4 Trigonometric ratios 274

5.5 Calculating unknown side lengths 282

5.6 Calculating unknown angles 291

5.7 Angles of elevation and depression 299

5.8 Review 305

Answers 315

6 Linear and non-linear graphs 321

6.1 Overview 322

6.2 Plotting linear graphs 325

6.3 Features of linear graphs 331

6.4 The equation of a straight line 339

6.5 Sketching linear graphs 348

6.6 Technology and linear graphs 356

6.7 Practical applications of linear graphs 360

6.8 Midpoint of a line segment and distance between two points 365

6.9 Non-linear relations 371

6.10 Review 385

Answers 393

Semester review 1 410

7 Proportion and rates 413

7.1 Overview 414

7.2 Direct linear proportion 416

7.3 Proportionality 421

7.4 Introduction to rates 426

7.5 Constant and variable rates 429

7.6 Review 436

Answers 444

8 Financial mathematics (extending) 447

8.1 Overview 448

8.2 Salaries and wages 451

8.3 Penalty rates 455

8.4 Simple interest 461

8.5 Compound interest 469

8.6 Review 478

Answers 483

9 Measurement 487

9.1 Overview 488

9.2 Absolute, relative and percentage error 492

9.3 Perimeter and circumference 498

9.4 Area 508

9.5 Area and perimeter of a sector 518

9.6 Surface area of rectangular and triangular prisms 525

9.7 Surface area of a cylinder 531

9.8 Volume of prisms and cylinders 536

9.9 Review 549

Answers 559

10 Probability 565

10.1 Overview 566

10.2 Theoretical probability 572

10.3 Experimental probability 579

10.4 Venn diagrams and two-way tables 588

10.5 Compound events 605

10.6 Review 618

Answers 625

11 Statistics 633

11.1 Overview 634

11.2 Collecting data 638

11.3 Organising data 647

11.4 Displaying data 657

11.5 Measures of centre 672

11.6 Measures of spread 688

11.7 Review 697

Answers 703

12 Quadratic equations and graphs 715

12.1 Overview 716

12.2 Quadratic equations 718

12.3 The Null Factor Law 723

12.4 Solving quadratic equations with two terms 727

12.5 Factorising and solving monic quadratic equations 731

12.6 Graphs of quadratic functions 737

12.7 Sketching parabolas of the form y = ax2 746

12.8 Sketching parabolas of the form y = (x - h)2 + k 752

12.9 Sketching parabolas of the form y = (x + a)(x + b) 764

12.10 Applications 768

12.11 Review 774

Answers 783

Semester review 2 808

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

Algorithms and pseudocode (Optional) 810

Glossary 833

Index 840