About this resource ix
Acknowledgements xvi
1 Financial Mathematics 1
1.1 Overview 2
1.2 Simple interest 4
1.3 Buying on terms 8
1.4 Compound interest 13
1.5 Depreciation 21
1.6 Review 25
Answers 30
2 Indices and Surds 33
2.1 Overview 34
2.2 Rational and irrational numbers (Path) 36
2.3 Surds (Path) 41
2.4 Operations with surds (Path) 45
2.5 Review of index laws 57
2.6 Negative indices (Path) 63
2.7 Fractional indices (Path) 69
2.8 Combining index laws (Path) 74
2.9 Review 81
Answers 90
3 Algebraic Techniques (Path) 97
3.1 Overview 98
3.2 Special binomial products 100
3.3 Further expansions 105
3.4 Factorising by grouping in pairs 108
3.5 Factorising special products 111
3.6 Factorising non-monic quadratics 116
3.7 Adding and subtracting algebraic fractions 119
3.8 Multiplying and dividing algebraic fractions 124
3.9 Applications of binomial products 131
3.10 Review 138
Answers 144
4 Linear Equations and Inequalities 151
4.1 Overview 152
4.2 Solving linear equations review 154
4.3 Solving multi-step equations, including fractions (Path) 159
4.4 Literal equations (Path) 164
4.5 Solving linear inequalities (Path) 167
4.6 Review 174
Answers 178
5 Simultaneous Linear Equations (Path) 183
5.1 Overview 184
5.2 Solving simultaneous linear equations graphically 186
5.3 Solving simultaneous linear equations using substitution 195
5.4 Solving simultaneous linear equations using elimination 200
5.5 Applications of simultaneous linear equations 206
5.6 Review 212
Answers 219
6 Quadratic Equations (Path) 223
6.1 Overview 224
6.2 Solving quadratic equations algebraically 226
6.3 The quadratic formula 236
6.4 Solving quadratic equations graphically 240
6.5 The discriminant 248
6.6 Review 255
Answers 262
7 Linear Relationships 267
7.1 Overview 268
7.2 Sketching linear graphs 271
7.3 Determining the equation of a straight line 281
7.4 Parallel and perpendicular lines 291
7.5 The distance between two points formula (Path) 297
7.6 The midpoint of a line segment formula (Path) 301
7.7 Applications to solving problems (Path) 306
7.8 Graphing linear inequalities (Path) 312
7.9 Review 320
Answers 328
8 Non-linear Relationships 343
8.1 Overview 344
8.2 The graph of a parabola 347
8.3 Parabolas and transformations 356
8.4 Parabolas in vertex form (Path) 365
8.5 Parabolas in general form (Path) 374
8.6 Exponential graphs (Path) 379
8.7 The hyperbola (Path) 387
8.8 The circle (Path) 393
8.9 Simultaneous linear and non-linear equations (Path) 398
8.10 Review 406
Answers 413
Semester review 1 436
9 Trigonometry I 439
9.1 Overview 440
9.2 Pythagoras’ theorem 443
9.3 Pythagoras’ theorem in three dimensions (Path) 451
9.4 Trigonometric ratios 457
9.5 Using trigonometry to calculate side lengths 463
9.6 Using trigonometry to calculate angle size 468
9.7 Angles of elevation and depression 473
9.8 Bearings 478
9.9 Applications of trigonometry 485
9.10 Review 490
Answers 497
10 Trigonometry II (Path) 503
10.1 Overview 504
10.2 The sine rule 507
10.3 The cosine rule 515
10.4 Area of triangles 520
10.5 The unit circle 527
10.6 Trigonometric functions 536
10.7 Solving trigonometric equations 543
10.8 Review 548
Answers 555
11 Measurement 563
11.1 Overview 564
11.2 Area 568
11.3 Total surface area 577
11.4 Volume 588
11.5 Review 603
Answers 609
12 Properties of Geometrical Figures (Path) 613
12.1 Overview 614
12.2 Angles, triangles and congruence 617
12.3 Similar triangles 629
12.4 Quadrilaterals 638
12.5 Polygons 650
12.6 Review 658
Answers 665
13 Data Analysis 669
13.1 Overview 670
13.2 Bivariate data 674
13.3 Lines of best fit by eye 684
13.4 Evaluating statistical reports (Path) 696
13.5 Statistical investigations (Path) 708
13.6 Selecting a sample size (Path) 713
13.7 Review 720
Answers 728
14 Probability 737
14.1 Overview 738
14.2 Review of probability and simulations 741
14.3 Tree diagrams and multistage chance experiments 750
14.4 Independent and dependent events 757
14.5 Venn diagrams, 2-way tables and mutually exclusive events (Path) 764
14.6 Conditional probability (Path) 779
14.7 Review 785
Answers 791
15 Polynomials (Path) 799
15.1 Overview 800
15.2 Polynomials 802
15.3 Adding, subtracting and multiplying polynomials 806
15.4 Long division of polynomials 808
15.5 Polynomial values 814
15.6 The remainder and factor theorems 817
15.7 Factorising polynomials 821
15.8 Solving polynomial equations 827
15.9 Review 830
Answers 835
16 Logarithms (Path) 841
16.1 Overview 842
16.2 Logarithms 844
16.3 Logarithm laws 850
16.4 Solving equations 858
16.5 Graphing logarithmic and exponential functions 865
16.6 Review 872
Answers 877
17 Functions and Other Graphs (Path) 883
17.1 Overview 884
17.2 Functions and relations 890
17.3 Graphing cubic functions 901
17.4 Graphing quartic functions 907
17.5 Transformations 912
17.6 Review 924
Answers 929
18 Circle Geometry (Path) 939
18.1 Overview 940
18.2 Angles in a circle 944
18.3 Intersecting chords, secants and tangents 952
18.4 Cyclic quadrilaterals 960
18.5 Tangents, secants and chords 965
18.6 Review 972
Answers 978
19 Introduction to Networks (Path) 981
19.1 Overview 982
19.2 Properties of networks 986
19.3 Planar graphs 999
19.4 Connected graphs 1007
19.5 Review 1017
Answers 1022
Semester review 2 1028
Glossary 1031
Index 1043
