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 terms439
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
