Jacaranda MathsQuest 10 Stage 5 NSW Syllabus (for the NSW Syllabus)
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TABLE OF CONTENTS
About This Resource v
Acknowledgements xii
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
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