Jacaranda MathsQuest 9 Stage 5 NSW Syllabus (for the NSW Syllabus)
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TABLE OF CONTENTS
About This Resource v
Acknowledgements xii
NAPLAN practice
- Set A Calculator allowed
- Set B Non-calculator
- Set C Calculator allowed
- Set D Non-calculator
- Set E Calculator allowed
- Set F Non-calculator
1 Financial mathematics 1
- 1.1 Overview 2
- 1.2 Salaries and wages 5
- 1.3 Special rates 9
- 1.4 Piecework 15
- 1.5 Commissions and royalties 18
- 1.6 Loadings and bonuses 22
- 1.7 Taxation and net earnings 26
- 1.8 Simple interest 31
- 1.9 Introduction to compound interest 39
- 1.10 Review 47
- Answers 52
2 Indices and surds 57
- 2.1 Overview 58
- 2.2 Applying the index laws to variables 60
- 2.3 Simplify algebraic products and quotients using index laws 69
- 2.4 Applying index laws to numerical and algebraic expressions involving negative-integer indices 73
- 2.5 Surds (Path) 80
- 2.6 Introduction to fractional indices (Path) 90
- 2.7 Review 95
- Answers 101
3 Numbers of any magnitude 107
- 3.1 Overview 108
- 3.2 Very small and very large measurements 110
- 3.3 Absolute and percentage error 119
- 3.4 Estimating and rounding numbers to a specified degree of accuracy 126
- 3.5 Scientific notation 132
- 3.6 Review 139
- Answers 146
4 Algebraic techniques 151
- 4.1 Overview 152
- 4.2 Simplifying algebraic expressions 154
- 4.3 Simplifying algebraic fractions 160
- 4.4 Expanding algebraic expressions and collecting like terms 166
- 4.5 Expanding binomial products 171
- 4.6 Difference of two squares and perfect squares (Path) 175
- 4.7 Further expansions (Path) 180
- 4.8 The highest common factor 183
- 4.9 The highest common binomial factor (Path) 188
- 4.10 Factorising monic quadratic expressions (Path) 192
- 4.11 Review 197
- Answers 202
5 Linear equations 209
- 5.1 Overview 210
- 5.2 Solving linear equations 212
- 5.3 Solving linear equations with brackets 220
- 5.4 Solving linear equations with pronumerals on both sides 223
- 5.5 Solving worded problems and substituting into formulas 227
- 5.6 Review 235
- Answers 241
6 Quadratic equations (Path) 245
- 6.1 Overview 246
- 6.2 Quadratic equations and cubic equations of the form ax3 = k 248
- 6.3 The Null Factor Law 254
- 6.4 Solving quadratic equations with two terms 257
- 6.5 Solving monic quadratic equations 261
- 6.6 Applications of quadratic equations 265
- 6.7 Review 269
- Answers 273
7 Linear relationships 277
- 7.1 Overview 278
- 7.2 Plotting linear graphs 281
- 7.3 Features of linear graphs 286
- 7.4 The equation of a straight line, y = mx + c 295
- 7.5 Sketching linear graphs 303
- 7.6 Technology and linear graphs 311
- 7.7 Practical applications of linear graphs 315
- 7.8 Midpoint of a line segment and distance between two points 320
- 7.9 Review 327
- Answers 334
Semester review 1 348
- 8 Non-linear relationships 351
- 8.1 Overview 352
- 8.2 Quadratic relationships and graphs 354
- 8.3 Quadratic equations of the form y = kx2 364
- 8.4 Quadratic equations of the form y = kx2 + c 369
- 8.5 Exponential relationships and graphs 375
- 8.6 Applications of linear and non-linear relationships 380
- 8.7 Review 387
- Answers 394
9 Variation and rates of change (Path) 409
- 9.1 Overview 410
- 9.2 Direct linear proportion 412
- 9.3 Direct proportion and ratio 417
- 9.4 Inverse proportion 422
- 9.5 Introduction to rates 427
- 9.6 Constant and variable rates 430
- 9.7 Review 441
- Answers 449
10 Trigonometry 455
- 10.1 Overview 456
- 10.2 Trigonometric ratios and right-angled triangles 460
- 10.3 Calculating unknown side lengths 468
- 10.4 Calculating unknown angles 476
- 10.5 Angles of elevation and depression 483
- 10.6 Review 489
- Answers 495
11 Measurement 499
- 11.1 Overview 500
- 11.2 Length and perimeter 504
- 11.3 Area 511
- 11.4 Area and perimeter of a sector 521
- 11.5 Surface area of rectangular and triangular prisms 528
- 11.6 Surface area of a cylinder 539
- 11.7 Volume of prisms and cylinders 543
- 11.8 Review 555
- Answers 564
12 Properties of geometrical figures 569
- 12.1 Overview 570
- 12.2 Ratio and scale 573
- 12.3 Similar figures 586
- 12.4 Area and volume of similar figures (Path) 596
- 12.5 Review 605
- Answers 612
13 Data analysis 615
- 13.1 Overview 616
- 13.2 Measures of central tendency 620
- 13.3 Measures of spread: Range and interquartile range 633
- 13.4 Measures of spread: Standard deviation 640
- 13.5 Box plots 647
- 13.6 Describing and comparing data sets 655
- 13.7 Review 666
- Answers 676
14 Probability 685
- 14.1 Overview 686
- 14.2 Theoretical probability 691
- 14.3 Observed probability and simulations 698
- 14.4 Tree diagrams and two-step experiments 707
- 14.5 Exploring Venn diagrams and 2-way tables (Path) 718
- 14.6 Venn diagrams and 2-way tables using set notation (Path) 732
- 14.7 Mutually and non-mutually exclusive events (Path) 748
- 14.8 Review 758
- Answers 764
Semester review 2 774
Glossary 776
Index 782
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