# Jacaranda Maths Quest 10+10a Australian Curriculum3e LearnON & Print

Author(s): | Boucher |

ISBN: | 9780730346395 |

Pub date: | November 2017 |

RRP: | $79.95 |

*Jacaranda Maths Quest 10 + 10A Australian Curriculum, 3rd Edition learnON & Print*This combined print and digital title provides 100% coverage of the Australian Curriculum for Mathematics. The textbook comes with a complimentary activation code for learnON, the powerful digital learning platform making learning personalised and visible for both students and teachers.

The latest editions of

*Jacaranda Maths Quest Australian Curriculum*series include these key features:

**Videos to address the 50 most commonly held misconceptions about maths**are directly embedded at the point of learning**Worked examples**featuring the familiar THINK/WRITE columns provide exemplary solutions and explanations**Carefully graded questions in each exercise**enables progression and caters to learners of different levels**Fully worked solutions**demonstrate best practice and help prevent misconceptions**Investigations and rich tasks**that provide students with opportunities for open-ended problem solving**Reading content with integrated media**providing a dynamic and uninterrupted learning experience

For teachers, learnON includes additional teacher resources such as quarantined questions and answers, curriculum grids and work programs.

To complement the Maths Quest series,

*assessON Maths Quest*is available for Years 7–10.

About this resource xi

Acknowledgements xiii

**Topic 1 Indices 1**

1.1 Overview 1

1.2 Review of index laws 2

1.3 Negative indices 7

1.4 Fractional indices 11

1.5 Combining index laws 16

1.6 Review 21

Answers 26

**Topic 2 Algebra and equations 31**

2.1 Overview 31

2.2 Substitution 32

2.3 Adding and subtracting algebraic fractions 37

2.4 Multiplying and dividing algebraic fractions 41

2.5 Solving simple equations 45

2.6 Solving multi-step equations 50

2.7 Literal equations 54

2.8 Review 57

Answers 61

**Topic 3 Coordinate geometry 66**

3.1 Overview 66

3.2 Sketching linear graphs 67

3.3 Determining linear equations 75

3.4 The distance between two points 82

3.5 The midpoint of a line segment 85

3.6 Parallel and perpendicular lines 88

3.7 Review 97

Answers 104

**Topic 4 Simultaneous linear equations and inequalities 112**

4.1 Overview 112

4.2 Graphical solution of simultaneous linear equations 113

4.3 Solving simultaneous linear equations using substitution 119

4.4 Solving simultaneous linear equations using elimination 122

4.5 Applications of simultaneous linear equations 127

4.6 Solving simultaneous linear and non-linear equations 131

4.7 Solving linear inequalities 138

4.8 Inequalities on the Cartesian plane 142

4.9 Solving simultaneous linear inequalities 148

4.10 Review 152

Answers 158

**Topic 5 Trigonometry I 167**

5.1 Overview 167

5.2 Pythagoras’ theorem 168

5.3 Pythagoras’ theorem in three dimensions 175

5.4 Trigonometric ratios 180

5.5 Using trigonometry to calculate side lengths 185

5.6 Using trigonometry to calculate angle size 190

5.7 Angles of elevation and depression 196

5.8 Bearings 200

5.9 Applications 207

5.10 Review 212

Answers 218

**Topic 6 Surface area and volume 224**

6.1 Overview 224

6.2 Area 225

6.3 Total surface area 234

6.4 Volume 243

6.5 Review 254

Answers 261

**Topic 7 Quadratic expressions 264**

7.1 Overview 264

7.2 Expanding algebraic expressions 265

7.3 Factorising expressions with three terms 272

7.4 Factorising expressions with two or four terms 277

7.5 Factorising by completing the square 281

7.6 Mixed factorisation 286

7.7 Review 288

Answers 293

**Topic 8 Quadratic equations 298**

8.1 Overview 298

8.2 Solving quadratic equations algebraically 299

8.3 The quadratic formula 306

8.4 Solving quadratic equations graphically 310

8.5 The discriminant 315

8.6 Review 320

Answers 325

**Topic 9 Non-linear relationships 329**

9.1 Overview 329

9.2 Plotting parabolas 330

9.3 Sketching parabolas 337

9.4 Sketching parabolas in turning point form 343

9.5 Sketching parabolas of the form y = ax2 + bx + c 350

9.6 Exponential functions and graphs 353

9.7 The hyperbola 359

9.8 The circle 362

9.9 Review 366

Answers 372

**Topic 10 Deductive geometry 394**

10.1 Overview 394

10.2 Angles, triangles and congruence 395

10.3 Similar triangles 405

10.4 Quadrilaterals 412

10.5 Polygons 422

10.6 Review 426

Answers 433

Project: Getting the budget in order 437

**Topic 11 Probability 439**

11.1 Overview 439

11.2 Review of probability 440

11.3 Tree diagrams 456

11.4 Independent and dependent events 462

11.5 Conditional probability 468

11.6 Subjective probability 472

11.7 Review 475

Answers 481

**Topic 12 Univariate data 491**

12.1 Overview 491

12.2 Measures of central tendency 492

12.3 Measures of spread 503

12.4 Box-and-whisker plots 508

12.5 The standard deviation 517

12.6 Comparing data sets 526

12.7 Review 532

Answers 539

**Topic 13 Bivariate data 549**

13.1 Overview 549

13.2 Bivariate data 550

13.3 Lines of best fit 557

13.4 Time series 569

13.5 Review 578

Answers 583

**Topic 14 Statistics in the media 591**

14.1 Overview 591

14.2 Populations and samples 592

14.3 Primary and secondary data 597

14.4 Evaluating inquiry methods and statistical reports 606

14.5 Statistical investigations 618

14.6 Review 624

Answers 633

Project: Climate change 639

**Topic 15 Financial mathematics 640**

15.1 Overview 640

15.2 Purchasing goods 641

15.3 Buying on terms 645

15.4 Successive discounts 650

15.5 Compound interest 654

15.6 Depreciation 660

15.7 Loan repayments 663

15.8 Review 666

Answers 670

**Topic 16 Real numbers 675**

16.1 Overview 675

16.2 Number classification review 676

16.3 Surds 681

16.4 Operations with surds 684

16.5 Fractional indices 695

16.6 Negative indices 699

16.7 Logarithms 702

16.8 Logarithm laws 706

16.9 Solving equations 711

16.10 Review 716

Answers 722

**Topic 17 Polynomials 728**

17.1 Overview 728

17.2 Polynomials 729

17.3 Adding, subtracting and multiplying polynomials 731

17.4 Long division of polynomials 733

17.5 Polynomial values 738

17.6 The remainder and factor theorems 741

17.7 Factorising polynomials 743

17.8 Solving polynomial equations 747

17.9 Review 750

Answers 754

**Topic 18 Functions and relations 759**

18.1 Overview 759

18.2 Functions and relations 760

18.3 Exponential functions 770

18.4 Cubic functions 779

18.5 Quartic functions 784

18.6 Transformations 787

18.7 Review 795

Answers 800

**Topic 19 Circle geometry 807**

19.1 Overview 807

19.2 Angles in a circle 808

19.3 Intersecting chords, secants and tangents 815

19.4 Cyclic quadrilaterals 823

19.5 Tangents, secants and chords 826

19.6 Review 832

Answers 838

**Topic 20 Trigonometry II 842**

20.1 Overview 842

20.2 The sine rule 843

20.3 The cosine rule 851

20.4 Area of triangles 855

20.5 The unit circle 861

20.6 Trigonometric functions 866

20.7 Solving trigonometric equations 871

20.8 Review 873

Answers 879

**Topic 21 STEM extension: Programming**

21.1 Overview 889

21.2 Programs 890

21.3 Data structures 899

21.4 Algorithms 912

21.5 Matrices 926

21.6 Graphics 932

21.7 Simulations 943

21.8 Review 958

Answers 966

Glossary 887

Index 900