Contents. Introduction x Acknowledgements

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1 Contents Introduction x Acknowledgements xiii CHAPTER 1 Number skills 1 Are you ready? 2 Order of operations 3 Exercise 1A 4 Integers 6 Exercise 1B 7 Investigation Golf scores 9 Estimation and rounding 10 Exercise 1C Quick Questions 1 14 Decimals 14 Exercise 1D 16 Code puzzle 18 Fractions 19 Exercise 1E 22 Percentages 24 Exercise 1F 27 Career profile Greg McIntyre Production manager 29 Investigation Interesting times Quick Questions 2 30 Index notation, square roots and higher order roots 30 Exercise 1G 33 Further estimation and calculator use 34 Exercise 1H 35 Investigation World population 35 Code puzzle 36 Applications 37 Exercise 1I 38 Summary 41 Chapter review 42 CHAPTER 2 Indices 45 Are you ready? 46 What are indices? 47 Exercise 2A 47 Investigation The chessboard problem 48 Powers and bases 49 Exercise 2B 50 Multiplication using indices 51 Exercise 2C 53 Code puzzle 54 Division using indices 55 Exercise 2D 57 Zero index 58 Exercise 2E Quick Questions 1 61 Raising a power to another power 61 Exercise 2F 63 Negative indices 64 Exercise 2G 65 Square roots and cube roots 66 Exercise 2H Quick Questions 2 68 Investigation Experimenting with spreadsheets 68 Scientific notation (standard form) 68 Exercise 2I 72 Investigation Alpha Centauri 73 Summary 74 Chapter review 75 CHAPTER 3 Measurement 77 Are you ready? 78 Introduction 79 Accuracy of measurement 79 Investigation Measuring distance 80 Investigation Judging the winning result 81 Investigation Measuring height 81 Estimation and approximation in measurement 82 Investigation Estimating measurements 82 Exercise 3A 83 Career profile Lyn Butcher Nurse 85 Error 86 Exercise 3B 91 Scale drawing 93 Exercise 3C Quick Questions 1 96 Pythagoras theorem 96 Exercise 3D Quick Questions Investigation Shortest path 102 Working with different units 103 Exercise 3E 104 Code puzzle 107 Time, speed and travel graphs 108 Exercise 3F 111

2 vi Investigation More units of measurement 112 Summary 113 Chapter review 114 CHAPTER 4 Algebraic expressions and relationships 117 Are you ready? 118 Using pronumerals 119 Exercise 4A 121 Generalised arithmetic 122 Exercise 4B 125 Like terms 128 Exercise 4C 130 Investigation Algebra rectangles 131 Code puzzle Quick Questions Multiplication and division 133 Exercise 4D 136 Using grouping symbols 137 Exercise 4E 139 Investigation Oops! Any errors? 140 Investigation The Bagels game 140 Simplifying expressions with grouping symbols 141 Exercise 4F 142 Algebraic fractions 143 Exercise 4G Quick Questions Common factors 147 Exercise 4H 151 Substitution and formulas 153 Exercise 4I 155 Investigation Good health 156 History of mathematics Heron (c. 100 AD) and Brahmagupta ( AD) 157 Summary 158 Chapter review 159 CHAPTER 5 Linear equations and inequalities 161 Are you ready? 162 What is a linear equation? 163 Exercise 5A 165 Career profile Alexander Iampolsky Computer programmer 166 Solving one-step equations 167 Exercise 5B 170 Solving multi-step equations 171 Exercise 5C Quick Questions Solving equations with pronumerals on both sides 178 Exercise 5D 179 Code puzzle 180 Solving linear equations with grouping symbols 181 Exercise 5E 182 Solving problems with linear equations 183 Exercise 5F Quick Questions Solving linear inequalities 188 Exercise 5G 190 Investigation The cost of concrete 191 Rearranging formulas 192 Exercise 5H 194 Investigation Maximum viewing area 195 Summary 196 Chapter review 197 CHAPTER 6 Perimeter, area and volume 199 Are you ready? 200 Metric units of length 201 Exercise 6A 202 Perimeter 204 Exercise 6B 206 Code puzzle 209 Area 210 Exercise 6C 212 Career profile Brenda Galey Forest assessment management officer 216 Area and perimeter of a sector 217 Exercise 6D 218 Investigation Tethered donkey Quick Questions Surface area of rectangular and triangular prisms 222 Exercise 6E 225 Surface area of a cylinder 228 Exercise 6F Quick Questions Volume of prisms and cylinders 232 Exercise 6G 236 Volume of pyramids, cones and composite solids 240

3 vii Investigation Comparing volumes of pyramids and prisms 240 Exercise 6H 242 Investigation Maintaining an Olympic pool 244 Volume of spheres and composite solids 244 Exercise 6I 246 Code puzzle 249 Summary 250 Chapter review 251 CHAPTER 7 Collecting and organising data 255 Are you ready? 256 Dot plots and stem-and-leaf plots 257 Exercise 7A Quick Questions Displaying ungrouped data 262 Exercise 7B 264 Investigation Temperature graph Displaying grouped data 267 Exercise 7C 269 Investigation Temperature graph Career profile Col Hutchinson Historian Quick Questions Cumulative frequency 273 Exercise 7D 276 Investigation Temperature graph Summary 279 Chapter review 280 CHAPTER 8 Rates 283 Are you ready? 284 Introduction 285 Ratios 285 Exercise 8A Quick Questions Simplifying rates 290 Exercise 8B 292 Solving problems using rates 293 Exercise 8C 294 Investigation Cricket run rate Quick Questions Speed 297 Exercise 8D 300 Code puzzle 302 Best buys 303 Exercise 8E 304 Summary 306 Chapter review 307 CHAPTER 9 Geometry 309 Are you ready? 310 Angle review 311 Exercise 9A 315 Angles and parallel lines 317 Exercise 9B 319 Code puzzle 320 Other polygons 321 Investigation Sum of angles in a polygon 321 Investigation Angles in a regular polygon 323 Exercise 9C 324 Investigation Parliamentary question time 325 Constructing and drawing triangles 326 Exercise 9D Quick Questions Further sketching and constructing 331 Exercise 9E Quick Questions Constructing polygons 339 Exercise 9F 345 Summary 346 Chapter review 347 CHAPTER 10 Coordinates and linear graphs 349 Are you ready? 350 Plotting linear graphs 351 History of mathematics René Descartes ( ) 351 Exercise 10A 354 Gradient and y-intercept 356 Exercise 10B Quick Questions Investigation Gradient and y-intercept 362 Finding the rule for linear graphs 363 Exercise 10C 365 Sketching linear graphs 366 Exercise 10D 371 Determining the equation of a straight line 371 Exercise 10E 373

4 viii Code puzzle 374 Using the coordinates of two points to find the gradient 375 Exercise 10F 376 Investigation Predicting a person s height Quick Questions Parallel lines 379 Investigation Investigating linear equations 379 Exercise 10G 380 Distance between two points 381 Exercise 10H 383 Midpoint of a line segment 384 Exercise 10I 385 Investigation A Roman aqueduct 386 Summary 387 Chapter review 388 CHAPTER 11 Consumer arithmetic 391 Are you ready? 392 Wages and salaries 393 Exercise 11A 394 Working overtime 395 Exercise 11B 396 Career profile Jo Mooney Direct care worker 397 Piecework 398 Exercise 11C Quick Questions Commission and royalties 401 Exercise 11D 402 Investigation Earning money 403 Code puzzle 404 Loadings and bonuses 405 Exercise 11E 406 Investigation Earnings and budgeting 408 Net earnings 409 Exercise 11F 410 Simple interest 411 Exercise 11G Quick Questions Compound interest 416 Exercise 11H 419 Summary 420 Chapter review 421 CHAPTER 12 Summary statistics 423 Are you ready? 424 Measures of central tendency 425 Exercise 12A Quick Questions Code puzzle 435 Grouped data mean and modal class 436 Exercise 12B Quick Questions Using cumulative frequency to find the median 440 Exercise 12C 444 Investigation How many use the monorail? 446 Summary 447 Chapter review 448 CHAPTER 13 Probability 451 Are you ready? 452 Introduction to probability 453 Exercise 13A 455 Sample space 457 Exercise 13B 459 Relative frequency 461 Investigation Investigating relative frequency 462 Exercise 13C Quick Questions Experimental probability 466 Exercise 13D 468 Theoretical probability of an event 471 Exercise 13E Quick Questions Code puzzle 475 Estimating probability 476 Investigation Simulating days of the week 478 Exercise 13F 478 Investigation Who s watching? 479 Summary 480 Chapter review 481 CHAPTER 14 Right-angled trigonometry 483 Are you ready? 484 What is trigonometry? 485 Naming the sides of a right-angled triangle 485

5 ix Investigation The cosine and tangent ratios 488 Exercise 14A 490 Trigonometric ratios 494 Exercise 14B 496 Finding trigonometric ratios using a calculator 499 Exercise 14C 500 Finding side lengths 500 Exercise 14D 502 Angles and the calculator 505 Exercise 14E Quick Questions Finding the size of an angle 509 Exercise 14F Quick Questions Code puzzle 515 Applications 516 Exercise 14G 518 Investigation Using an inclinometer to measure inaccessible heights 520 Bearings 521 Exercise 14H 524 History of mathematics George Everest ( ) 526 Summary 527 Chapter review 528 Chapter 15 is included as optional extension material. CHAPTER 15 Surds 531 Are you ready? 532 Rational and irrational numbers 533 Rational numbers 533 Exercise 15A 535 Irrational numbers 536 History of mathematics Richard Dedekind ( ) 538 Exercise 15B 539 Investigation Irrational numbers on the number line 541 Investigation Plotting a graph of y = x Quick Questions Simplifying surds 542 Exercise 15C 545 Investigation Braking distances 547 Addition and subtraction of surds 548 Exercise 15D 549 Code puzzle 551 Multiplication and division of surds 552 Exercise 15E 555 Career profile Peter Richardson Analyst programmer Quick Questions Writing surd fractions with a rational denominator 559 Exercise 15F 560 Summary 562 Chapter review 563 APPENDIX Working mathematically 565 Introduction to working mathematically 566 Questioning skills 568 Strategies for investigation and problem solving 569 Create a table, then look for a pattern or a result 569 Draw a diagram, then look for a pattern or a result 571 Set up equations and find a solution, making use of technology such as a computer spreadsheet 572 Work backwards from the answer 573 Use a process of elimination 575 Look at similar but simpler problems 576 Use trial and error (guess and check), making use of technology such as a computer spreadsheet 577 Communicating, reasoning and reflecting 579 Answers 581 Index 627