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
