Table of Contents

About this resource vii

Acknowledgements xiv

1 Indices, surds and logarithms 1

1.1 Overview 2

1.2 Number classification review 4

1.3 Surds (Optional) 10

1.4 Operations with surds (Optional) 14

1.5 Review of index laws 28

1.6 Negative indices 36

1.7 Fractional indices (Optional) 42

1.8 Combining index laws 48

1.9 Logarithms 54

1.10 Logarithm laws (Optional) 62

1.11 Solving equations (Optional) 69

1.12 Review 75

Answers 86

2 Algebra and equations 95

2.1 Overview 96

2.2 Substitution 98

2.3 Adding and subtracting algebraic fractions 105

2.4 Multiplying and dividing algebraic fractions 111

2.5 Solving simple equations 116

2.6 Solving multi-step equations 123

2.7 Literal equations 130

2.8 Review 136

Answers 141

3 Networks 147

3.1 Overview 148

3.2 Properties of networks 153

3.3 Planar graphs 166

3.4 Connected graphs 174

3.5 Trees and their applications (Extending) 185

3.6 Review 194

Answers 202

4 Linear relationships 209

4.1 Overview 210

4.2 Sketching linear graphs 214

4.3 Determining linear equations 225

4.4 Graphical solution of simultaneous linear equations 240

4.5 Solving simultaneous linear equations using substitution 249

4.6 Solving simultaneous linear equations using elimination 254

4.7 Applications of simultaneous linear equations 260

4.8 Solving simultaneous linear and non-linear equations 268

4.9 Solving linear inequalities 278

4.10 Inequalities on the Cartesian plane 287

4.11 Solving simultaneous linear inequalities 296

4.12 Review 303

Answers 312

5 Trigonometry I 331

5.1 Overview 332

5.2 Pythagoras’ theorem 335

5.3 Pythagoras’ theorem in three dimensions (Optional) 344

5.4 Trigonometric ratios 350

5.5 Using trigonometry to calculate side lengths 357

5.6 Using trigonometry to calculate angle size 363

5.7 Angles of elevation and depression 370

5.8 Bearings 375

5.9 Applications 382

5.10 Review 390

Answers 398

6 Surface area and volume 403

6.1 Overview 404

6.2 Area 408

6.3 Total surface area 418

6.4 Volume 429

6.5 Review 443

Answers 451

7 Quadratic expressions 455

7.1 Overview 456

7.2 Expanding algebraic expressions 458

7.3 Factorising expressions with three terms 466

7.4 Factorising expressions with two or four terms 472

7.5 Factorising by completing the square 477

7.6 Mixed factorisation 483

7.7 Review 487

Answers 493

8 Quadratic equations and graphs 499

8.1 Overview 500

8.2 Solving quadratic equations algebraically 502

8.3 The quadratic formula 511

8.4 Solving quadratic equations graphically 517

8.5 The discriminant 526

8.6 Plotting parabolas from a table of values 533

8.7 Sketching parabolas using transformations 542

8.8 Sketching parabolas using turning point form 552

8.9 Sketching parabolas in expanded form 561

8.10 Review 569

Answers 580

Semester review 1 598

9 Functions, relations and modelling 601

9.1 Overview 602

9.2 Functions and relations 607

9.3 Exponential functions 620

9.4 Exponential graphs 630

9.5 Application of exponentials: Compound interest 640

9.6 Cubic functions 648

9.7 Quartic functions 656

9.8 Sketching the circle 661

9.9 Transformations 667

9.10 Mathematical modelling 674

9.11 Review 679

Answers 688

10 Deductive geometry 705

10.1 Overview 706

10.2 Angles, triangles and congruence 709

10.3 Scale factor and similar triangles 722

10.4 Calculating measurements from scale drawings 731

10.5 Creating scale drawings 742

10.6 Quadrilaterals 751

10.7 Polygons 764

10.8 Review 771

Answers 780

11 Probability 785

11.1 Overview 786

11.2 Review of probability 789

11.3 Tree diagrams 806

11.4 Independent and dependent events 814

11.5 Conditional probability 820

11.6 Counting principles and factorial notation (Optional) 826

11.7 Review 842

Answers 849

12 Univariate data 859

12.1 Overview 860

12.2 Measures of central tendency 865

12.3 Measures of spread 879

12.4 Box plots 886

12.5 The standard deviation (Optional) 897

12.6 Comparing data sets 910

12.7 Populations and samples 918

12.8 Evaluating inquiry methods and statistical reports 926

12.9 Review 940

Answers 952

13 Bivariate data 963

13.1 Overview 964

13.2 Bivariate data 968

13.3 Two-way frequency tables and Likert scales 980

13.4 Lines of best fit by eye 991

13.5 Linear regression and technology (Optional) 1003

13.6 Time series 1011

13.7 Review 1019

Answers 1028

14 Circle geometry (Optional) 1039

14.1 Overview 1040

14.2 Angles in a circle 1044

14.3 Intersecting chords, secants and tangents 1052

14.4 Cyclic quadrilaterals 1060

14.5 Tangents, secants and chords 1065

14.6 Review 1072

Answers 1079

15 Trigonometry II (Optional) 1083

15.1 Overview 1084

15.2 The sine rule 1087

15.3 The cosine rule 1097

15.4 Area of triangles 1103

15.5 The unit circle 1109

15.6 Trigonometric functions 1116

15.7 Solving trigonometric equations 1124

15.8 Review 1130

Answers 1138

Semester review 2 1146

16 Algorithmic thinking

16.1 Overview

16.2 Programs

16.3 Data structures

16.4 Algorithms

16.5 Matrices

16.6 Graphics

16.7 Simulations

16.8 Review

Answers

Algorithms and pseudocode (Optional) 1148

Glossary 1171

Index 1183