Jacaranda Maths Quest 10+10A Australian Curriculum, learnON and Print

About this resource vi

Acknowledgements xii

1 Indices, surds and logarithms 1

1.1 Overview 2

1.2 Number classification review 4

1.3 Surds (10A) 9

1.4 Operations with surds (10A) 14

1.5 Review of index laws 28

1.6 Negative indices 35

1.7 Fractional indices (10A) 40

1.8 Combining index laws 47

1.9 Application of indices: Compound interest 53

1.10 Logarithms (10A) 60

1.11 Logarithm laws (10A) 66

1.12 Solving equations (10A) 73

1.13 Review 79

Answers 91

2 Algebra and equations 99

2.1 Overview 100

2.2 Substitution 102

2.3 Adding and subtracting algebraic fractions 109

2.4 Multiplying and dividing algebraic fractions 114

2.5 Solving simple equations 119

2.6 Solving multi-step equations 126

2.7 Literal equations 132

2.8 Review 138

Answers 144

3 Coordinate geometry 149

3.1 Overview 150

3.2 Sketching linear graphs 152

3.3 Determining linear equations 163

3.4 Parallel and perpendicular lines 173

3.5 The distance between two points 178

3.6 The midpoint of a line segment 182

3.7 Applications and collinearity 187

3.8 Review 194

Answers 204

4 Simultaneous linear equations and inequalities 215

4.1 Overview 216

4.2 Graphical solution of simultaneous linear equations 220

4.3 Solving simultaneous linear equations using substitution 229

4.4 Solving simultaneous linear equations using elimination 234

4.5 Applications of simultaneous linear equations 240

4.6 Solving simultaneous linear and non-linear equations 246

4.7 Solving linear inequalities 256

4.8 Inequalities on the Cartesian plane 262

4.9 Solving simultaneous linear inequalities 271

4.10 Review 278

Answers 288

5 Trigonometry I 301

5.1 Overview 302

5.2 Pythagoras’ theorem 305

5.3 Pythagoras’ theorem in three dimensions (10A) 314

5.4 Trigonometric ratios 320

5.5 Using trigonometry to calculate side lengths 327

5.6 Using trigonometry to calculate angle size 332

5.7 Angles of elevation and depression 338

5.8 Bearings 343

5.9 Applications 350

5.10 Review 356

Answers 365

6 Surface area and volume 371

6.1 Overview 372

6.2 Area 376

6.3 Total surface area 386

6.4 Volume 397

6.5 Review 411

Answers 420

7 Quadratic expressions 423

7.1 Overview 424

7.2 Expanding algebraic expressions 426

7.3 Factorising expressions with three terms 434

7.4 Factorising expressions with two or four terms 439

7.5 Factorising by completing the square 445

7.6 Mixed factorisation 451

7.7 Review 455

Answers 462

8 Quadratic equations 469

8.1 Overview 470

8.2 Solving quadratic equations algebraically 472

8.3 The quadratic formula 481

8.4 Solving quadratic equations graphically 486

8.5 The discriminant 495

8.6 Review 502

Answers 511

Semester review 1 516

9 Non-linear relationships 519

9.1 Overview 520

9.2 Plotting parabolas from a table of values 524

9.3 Sketching parabolas using transformations 533

9.4 Sketching parabolas using turning point form 544

9.5 Sketching parabolas in expanded form 552

9.6 Exponential graphs 559

9.7 Inverse proportion 567

9.8 Sketching the hyperbola 572

9.9 Sketching the circle 578

9.10 Review 584

Answers 593

10 Deductive geometry 617

10.1 Overview 618

10.2 Angles, triangles and congruence 621

10.3 Similar triangles 633

10.4 Quadrilaterals 641

10.5 Polygons 652

10.6 Review 660

Answers 669

11 Probability 673

11.1 Overview 674

11.2 Review of probability 677

11.3 Tree diagrams 693

11.4 Independent and dependent events 701

11.5 Conditional probability 707

11.6 Review 713

Answers 720

12 Univariate data 727

12.1 Overview 728

12.2 Measures of central tendency 733

12.3 Measures of spread 747

12.4 Box plots 754

12.5 The standard deviation (10A) 765

12.6 Comparing data sets 776

12.7 Populations and samples 784

12.8 Evaluating inquiry methods and statistical reports 792

12.9 Review 806

Answers 819

13 Bivariate data 829

13.1 Overview 830

13.2 Bivariate data 834

13.3 Lines of best fit by eye 844

13.4 Linear regression using technology (10A) 855

13.5 Time series 863

13.6 Review 871

Answers 879

14 Polynomials 887

14.1 Overview 888

14.2 Polynomials 890

14.3 Adding, subtracting and multiplying polynomials 894

14.4 Long division of polynomials 898

14.5 Polynomial values 904

14.6 The remainder and factor theorems 908

14.7 Factorising polynomials 911

14.8 Solving polynomial equations 917

14.9 Review 920

Answers 926

15 Functions and relations 931

15.1 Overview 932

15.2 Functions and relations 938

15.3 Exponential functions 951

15.4 Cubic functions 961

15.5 Quartic functions 969

15.6 Transformations 974

15.7 Review 983

Answers 990

16 Circle geometry 999

16.1 Overview 1000

16.2 Angles in a circle 1004

16.3 Intersecting chords, secants and tangents 1012

16.4 Cyclic quadrilaterals 1020

16.5 Tangents, secants and chords 1025

16.6 Review 1032

Answers 1040

17 Trigonometry II 1043

17.1 Overview 1044

17.2 The sine rule 1047

17.3 The cosine rule 1058

17.4 Area of triangles 1064

17.5 The unit circle 1070

17.6 Trigonometric functions 1076

17.7 Solving trigonometric equations 1083

17.8 Review 1088

Answers 1097

Semester review 2 1104

18 Algorithmic thinking

18.1 Overview

18.2 Programs

18.3 Data structures

18.4 Algorithms

18.5 Matrices

18.6 Graphics

18.7 Simulations

18.8 Review

Answers

Glossary 1106

Index 1117