Table of Contents

About This Resource vii Acknowledgements xiv 1 Calculations 1 1.1 Overview 2 1.2 Number operations 3 1.3 Order of operations 6 1.4 Rounding 11 1.5 Estimation and approximation strategies 15 1.6 Decimals and fractions 18 1.7 Rational and irrational numbers 26 1.8 Review 37 Answers 39 2 Ratios, proportion and variation 43 2.1 Overview 44 2.2 Direct variation (proportion) 45 2.3 Direct variation (proportion) and ratios 48 2.4 Partial variation (proportion) 52 2.5 Inverse variation (proportion) 55 2.6 Ratios 59 2.7 Ratio and proportion 65 2.8 Dividing in a given ratio 69 2.9 Review 73 Answers 76 3 Percentages 81 3.1 Overview 82 3.2 Converting percentages 83 3.3 Percentage quantities and percentage error 87 3.4 Application of percentages 90 3.5 Profit and loss 95 3.6 Review 99 Answers 101 4 Linear and simultaneous equations 103 4.1 Overview 104 4.2 Algebraic substitution and transposition 105 4.3 Linear equations 111 4.4 Linear modelling 116 4.5 Solving simultaneous equations graphically 121 4.6 Solving simultaneous equations by substitution 127 4.7 Solving simultaneous equations by elimination 130 4.8 Review 136 Answers 139 5 Data collection and organisation 145 5.1 Overview 146 5.2 Types of data 147 5.3 Collecting, organising and displaying data 150 5.4 Histograms and frequency polygons 161 5.5 Contemporary representation of data 167 5.6 Stem-and-leaf plots 178 5.7 Five-number summary and boxplots 184 5.8 Graphical methods of misrepresenting data 188 5.9 Review 196 Answers 201 6 Measures of central tendency and spread 211 6.1 Overview 212 6.2 Measures of central tendency 213 6.3 Measures of spread 224 6.4 Outliers 238 6.5 Applications of measures of central tendency 244 6.6 Review 249 Answers 254 7 Comparing data sets and long-term prediction 257 7.1 Overview 258 7.2 Constructing boxplots 259 7.3 Comparing parallel boxplots 265 7.4 Comparing back-to-back stem plots 270 7.5 Comparing histograms 276 7.6 The line of best fit 284 7.7 Making predictions using a line of best fit 296 7.8 Review 306 Answers 314 8 Simulations and simple probability 327 8.1 Overview 328 8.2 Theoretical probability and sample spaces 329 8.3 Multi-stage experiments 336 8.4 Relative frequency, simulations and long-term data 343 8.5 Review 355 Answers 359 9 Interest and loans 365 9.1 Overview 366 9.2 Simple interest 367 9.3 Compound interest 375 9.4 Comparing simple and compound interest 382 9.5 Comparing interest, rental and loan costs 392 9.6 Review 399 Answers 402 10 Financial and consumer mathematics 407 10.1 Overview 408 10.2 Taxation and superannuation 409 10.3 Business income and expenditure 418 10.4 Financial products 428 10.5 Financial and economic data 440 10.6 Review 447 Answers 451 11 Scales, plans and models 455 11.1 Overview 456 11.2 Reading and interpreting scale drawings 457 11.3 Calculating measurements from scale drawings 462 11.4 Creating scale drawings 472 11.5 Review 482 Answers 486 12 Right-angled triangles 489 12.1 Overview 490 12.2 Pythagoras' theorem 491 12.3 Trigonometric ratios — sine, cosine and tangent 496 12.4 Calculating unknown side lengths of right-angled triangles 502 12.5 Calculating unknown angles in right-angled triangles 509 12.6 Angles of elevation and depression 514 12.7 Review 520 Answers 524 13 Measurement 527 13.1 Overview 528 13.2 Units of measurement 529 13.3 Areas of composite figures 537 13.4 Surface areas of pyramids and irregular solids 545 13.5 Limits of accuracy 552 13.6 Scientific notation and significant figures 559 13.7 Review 566 Answers 570 14 Volume 573 14.1 Overview 574 14.2 Review of volume of prisms, units of volume and capacity 575 14.3 Volume of cylinders and spheres 582 14.4 Volume of composite shapes 586 14.5 Review 591 Answers 595 15 Shapes 597 15.1 Overview 598 15.2 Polygons 599 15.3 Transformations 602 15.4 Similarity 614 15.5 Symmetry 617 15.6 Review 624 Answers 630 Glossary 639 Index 645

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