Jacaranda Maths Quest 9 Australian curriculum 3e learnON & Print

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About this resource x Acknowledgements xii Topic 1 Numeracy 1 1 1.1 Overview 1 1.2 Set A 2 1.3 Set B 4 Answers 8 Topic 2 Number skills 9 2.1 Overview 9 2.2 Rational numbers 10 2.3 Surds 14 2.4 Real numbers 24 2.5 Scientific notation 27 2.6 Review 32 Answers 37 Topic 3 Algebra 42 3.1 Overview 42 3.2 Using pronumerals 43 3.3 Algebra in worded problems 49 3.4 Simplifying algebraic expressions 53 3.5 Expanding brackets 58 3.6 Expansion patterns 65 3.7 Further expansions 69 3.8 The highest common factor 71 3.9 The highest common binomial factor 75 3.10 Applications 78 3.11 Review 85 Answers 91 Topic 4 Linear equations 101 4.1 Overview 101 4.2 Solving linear equations 102 4.3 Solving linear equations with brackets 109 4.4 Solving linear equations with pronumerals on both sides 111 4.5 Solving problems with linear equations 115 4.6 Rearranging formulas 119 4.7 Review 122 Answers 128 Topic 5 Congruence and similarity 132 5.1 Overview 132 5.2 Ratio and scale 133 5.3 Congruent figures 140 5.4 Similar figures 147 5.5 Area and volume of similar figures 157 5.6 Review 162 Answers 169 Topic 6 Pythagoras and trigonometry 174 6.1 Overview 174 6.2 Pythagoras’ theorem 175 6.3 Applications of Pythagoras’ theorem 183 6.4 What is trigonometry? 189 6.5 Calculating unknown side lengths 196 6.6 Calculating unknown angles 203 6.7 Angles of elevation and depression 209 6.8 Review 215 Answers 222 Project: Learning or earning? 229 Topic 7 Linear and non-linear graphs 231 7.1 Overview 231 7.2 Plotting linear graphs 232 7.3 The equation of a straight line 236 7.4 Sketching linear graphs 245 7.5 Technology and linear graphs 250 7.6 Determining linear rules 253 7.7 Practical applications of linear graphs 260 7.8 Midpoint of a line segment and distance between two points 264 7.9 Non-linear relations (parabolas, hyperbolas, circles) 269 7.10 Review 276 Answers 282 Topic 8 Proportion and rates 297 8.1 Overview 297 8.2 Direct proportion 298 8.3 Direct proportion and ratio 302 8.4 Inverse proportion 306 8.5 Introduction to rates 310 8.6 Constant and variable rates 312 8.7 Rates of change 318 8.8 Review 323 Answers 329 Topic 9 Numeracy 2 336 9.1 Overview 336 9.2 Set C 337 9.3 Set D 340 Answers 344 Topic 10 Indices 345 10.1 Overview 345 10.2 Review of index laws 346 10.3 Raising a power to another power 352 10.4 Negative indices 356 10.5 Square roots and cube roots 360 10.6 Review 363 Answers 368 Topic 11 Financial mathematics 373 11.1 Overview 373 11.2 Salaries and wages 374 11.3 Special rates 377 11.4 Piecework 382 11.5 Commission and royalties 385 11.6 Loadings and bonuses 388 11.7 Taxation and net earnings 392 11.8 Simple interest 396 11.9 Compound interest 401 11.10 Review 406 Answers 411 Topic 12 Measurement 416 12.1 Overview 416 12.2 Measurement 417 12.3 Area 426 12.4 Area and perimeter of a sector 436 12.5 Surface area of rectangular and triangular prisms 442 12.6 Surface area of a cylinder 447 12.7 Volume of prisms and cylinders 451 12.8 Review 461 Answers 469 Topic 13 Probability 475 13.1 Overview 475 13.2 Theoretical probability 476 13.3 Experimental probability 482 13.4 Venn diagrams and two-way tables 488 13.5 Two-step experiments 498 13.6 Mutually exclusive and independent events 507 13.7 Conditional probability 516 13.8 Review 521 Answers 527 Topic 14 Statistics 537 14.1 Overview 537 14.2 Sampling 538 14.3 Collecting data 548 14.4 Displaying data 557 14.5 Measures of central tendency 568 14.6 Measures of spread 577 14.7 Review 586 Answers 592 Topic 15 Numeracy 3 604 15.1 Overview 604 15.2 Set E 605 15.3 Set F 609 Answers 613 Project: Backyard flood? 614 Topic 16 Quadratic algebra 617 16.1 Overview 617 16.2 Factorisation patterns 618 16.3 Factorising monic quadratics 622 16.4 Factorising non-monic quadratics 625 16.5 Simplifying algebraic fractions 628 16.6 Quadratic equations 634 16.7 The Null Factor Law 637 16.8 Solving the quadratic equation ax2 + bx + c = 0 640 16.9 Solving quadratic equations with two terms 644 16.10 Applications 647 16.11 Review 650 Answers 656 Topic 17 Quadratic functions 663 17.1 Overview 663 17.2 Graphs of quadratic functions 664 17.3 Plotting points to graph quadratic functions 669 17.4 Sketching parabolas of the form y = ax2 675 17.5 Sketching parabolas of the form y = ax2 + c 679 17.6 Sketching parabolas of the form y = (x – h)2 683 17.7 Sketching parabolas of the form y = (x – h)2 + k 687 17.8 Sketching parabolas of the form y = (x + a) (x + b) 691 17.9 Applications 696 17.10 Review 699 Answers 706 Topic 18 Programming 18.1 Overview 18.2 Programs 18.3 Arrays 18.4 Loops 18.5 Set structures 18.6 Sorting algorithms 18.7 The Monte Carlo method 18.8 Review Answers Glossary 724 Index 732 Show more