Maths Quest 10
Table of Contents
Introduction vii About eBookPLUS ix Acknowledgements x Chapter 1 Number and algebra, patterns and algebra Indices 1 Are you ready? 2 1A Review of index laws 3 Exercise 1A 5 1B Negative indices 7 Exercise 1B 10 1C Fractional indices 12 Exercise 1C 14 1D Combining index laws 17 Exercise 1D 20 Summary 23 Chapter review 24 eBookPLUS activities 26 Chapter 2 Number and algebra, patterns and algebra Linear algebra 27 Are you ready? 28 2A Substitution 29 Exercise 2A 31 2B Adding and subtracting algebraic fractions 33 Exercise 2B 36 2C Multiplying and dividing algebraic fractions 37 Exercise 2C 39 2D Solving linear equations 40 Exercise 2D 43 2E Solving equations with algebraic fractions and multiple brackets 45 Exercise 2E 48 Summary 50 Chapter review 52 eBookPLUS activities 54 Chapter 3 Number and algebra, linear and non-linear relationships Coordinate geometry 55 Are you ready? 56 3A Sketching linear graphs 57 Exercise 3A 62 3B Determining linear equations 64 Exercise 3B 67 3C The distance between two points on a straight line 68 Exercise 3C 70 3D The midpoint of a line segment 71 Exercise 3D 73 3E Parallel and perpendicular lines 74 Exercise 3E 79 Summary 83 Chapter review 85 eBookPLUS activities 88 Chapter 4 Number and algebra, linear and non-linear relationships Simultaneous linear equations and inequations 89 Are you ready? 90 4A Graphical solution of simultaneous linear equations 91 Exercise 4A 94 4B Solving simultaneous linear equations using substitution 96 Exercise 4B 98 4C Solving simultaneous linear equations using elimination 99 Exercise 4C 101 4D Problem solving using simultaneous linear equations 103 Exercise 4D 105 4E Solving linear inequations 106 Exercise 4E 108 4F Sketching linear inequations 110 Exercise 4F 113 4G Solving simultaneous linear inequations 116 Exercise 4G 118 Summary 123 Chapter review 125 eBookPLUS activities 130 Chapter 5 measurement and geometry,pythagoras and trigonometry Trigonometry I 131 Are you ready? 132 5A Pythagoras? theorem 133 Exercise 5A 137 5B Pythagoras? theorem in three dimensions 140 Exercise 5B 143 5C Trigonometric ratios 145 Exercise 5C 149 5D Using trigonometry to calculate side lengths 151 Exercise 5D 154 5E Using trigonometry to calculate angle size 156 Exercise 5E 158 5F Angles of elevation and depression 161 Exercise 5F 163 5G Bearings and compass directions 165 Exercise 5G 169 5H Applications 172 Exercise 5H 173 Summary 177 Chapter review 179 eBookPLUS activities 182 Chapter 6 measurement and geometry using units of measurement Surface area and volume 183 Are you ready? 184 6A Area 185 Exercise 6A 189 6B Total surface area 193 Exercise 6B 199 6C Volume 203 Exercise 6C 208 Summary 213 Chapter review 214 eBookPLUS activities 218 Chapter 7 Number and algebra patterns and algebra Quadratic expressions 219 Are you ready? 220 7A Expanding algebraic expressions 221 Exercise 7A 225 7B Factorising expressions with three terms 227 Exercise 7B 229 7C Factorising expressions with two or four terms 231 Exercise 7C 234 7D Factorising by completing the square 236 Exercise 7D 239 7E Mixed factorisation 240 Exercise 7E 240 Summary 242 Chapter review 244 eBookPLUS activities 246 Chapter 8 Number and algebra linear and non-linear relationships Quadratic equations 247 Are you ready? 248 8A Solving quadratic equations 249 Exercise 8A 253 8B The quadratic formula 255 Exercise 8B 257 8C Solving quadratic equations by inspecting graphs 258 Exercise 8C 261 8D Finding solutions to quadratic equations by interpolation and using the discriminant 263 Exercise 8D 267 8E Solving a quadratic equation and a linear equation simultaneously 269 Exercise 8E 272 Summary 274 Chapter review 276 eBookPLUS activities 278 Chapter 9 Number and algebra linear and non-linear relationships Functions 279 Are you ready? 280 9A Plotting parabolas 281 Exercise 9A 284 9B Sketching parabolas using the basic graph of y = x2 287 Exercise 9B 291 9C Sketching parabolas in turning point form 292 Exercise 9C 296 9D Sketching parabolas of the form y = ax2 + bx + c 298 Exercise 9D 302 9E Exponential functions and their graphs 306 Exercise 9E 309 9F The hyperbola 312 Exercise 9F 314 9G The circle 315 Exercise 9G 317 Summary 319 Chapter review 321 eBookPLUS activities 324 Chapter 10 measurement and geometry geometric reasoning Deductive geometry 325 Are you ready? 326 10A Congruence review 327 Exercise 10A 329 10B Similarity review 332 Exercise 10B 335 10C Congruence and proof 336 Exercise 10C 338 10D Quadrilaterals: definitions and properties 340 Exercise 10D 341 10E Quadrilaterals and proof 344 Exercise 10E 345 Summary 347 Chapter review 349 eBookPLUS activities 351 projects plus ict activity pro-0099 Backyard flood 352 Chapter 11 problem solving Problem solving I 355 Chapter 12 statistics and probability Chance Probability 379 Are you ready? 380 12A Review of probability 381 Exercise 12A 392 12B Complementary and mutually exclusive events 396 Exercise 12B 400 12C Two-way tables and tree diagrams 403 Exercise 12C 410 12D Independent and dependent events 413 Exercise 12D 415 12E Conditional probability 417 Exercise 12E 419 12F Subjective probability 420 Exercise 12F 421 Summary 423 Chapter review 425 eBookPLUS activities 428 Chapter 13 statistics and probability data representation and interpretation Univariate data 429 Are you ready? 430 13A Measures of central tendency 431 Exercise 13A 435 13B Measures of spread 439 Exercise 13B 442 13C Box-and-whisker plots 444 Exercise 13C 447 13D The standard deviation 449 Exercise 13D 451 13E Comparing data sets 454 Exercise 13E 455 13F Skewness 459 Exercise 13F 461 Summary 464 Chapter review 466 eBookPLUS activities 470 Chapter 14 statistics and probability data representation and interpretation Bivariate data 471 Are you ready? 472 14A Identifying related pairs of variables 474 Exercise 14A 476 14B Graphing bivariate data 477 Exercise 14B 481 14C Scatterplots 483 Exercise 14C 488 Summary 491 Chapter review 492 eBookPLUS activities 496 Chapter 15 statistics and probability data representation and interpretation Statistics in the media 497 Are you ready? 498 15A Populations and samples 499 Exercise 15A 502 15B Primary and secondary data 503 Exercise 15B 508 15C Evaluating inquiry methods and statistical reports 511 Exercise 15C 518 15D Statistical investigations 521 Exercise 15D 525 Summary 527 Chapter review 529 eBookPLUS activities 533 projects plus ict activity pro-0100 Climate change 534 Chapter 16 Number and algebra money and financial mathematics Financial maths 537 Are you ready? 538 16A Purchasing goods 539 Exercise 16A 540 16B Buying on terms 542 Exercise 16B 543 16C Successive discounts 546 Exercise 16C 547 16D Compound interest 549 Exercise 16D 551 16E Depreciation 553 Exercise 16E 554 16F Loan repayments 556 Exercise 16F 558 Summary 560 Chapter review 562 eBookPLUS activities 564 Chapter 17 problem solving Problem solving II 565 Answers 589 Glossary 660 Index 672
