Tableof contents SYMBOLS AND NOTATION USED IN THIS BOOK GRAPHICS CALCULATOR INSTRUCTIONS Casio fx-9860G PLUS Casio fx-CG20 Texas Instruments TI-84 Plus Texas Instruments TI-nspire 10 18 CD CD CD CD 19 20 22 25 29 30 33 35 36 37 38 40 42 45 48 52 58 60 64 70 71 72 73 74 81 83 1 NUMBER PROPERTIES AWords used in mathematics B Exponent notation C Factors of positive integers DMultiples of positive integers E Order of operations F Special number sets Review set 1A Review set 1B 2 MEASUREMENT ATime B Temperature C Scientific notation (standard form) DInternational system (SI) units E Rounding numbers F Rates GAccuracy of measurements HError and percentage error I Currency conversions Review set 2A Review set 2B Review set 2C 3 LAWS OF ALGEBRA ALaws of exponents B The distributive law C The product (a+b)(c+d) DDifference of two squares E Perfect squares expansions F Further expansion Review set 3A Review set 3B 4 EQUATIONS AND FORMULAE AAlgebraic substitution B Linear equations C Equations involving fractions DSolving equations using technology E Problem solving with linear equations F Formula substitution GFormula rearrangement HLinear simultaneous equations I Problem solving with simultaneous equations J Quadratic equations KProblem solving with quadratics Review set 4A Review set 4B Review set 4C 5 SEQUENCES AND SERIES ANumber sequences B The general term of a number sequence C Arithmetic sequences DGeometric sequences E Series F Compound interest GDepreciation Review set 5A Review set 5B Review set 5C 6 DESCRIPTIVE STATISTICS ATypes of data B Simple quantitative discrete data C Grouped quantitative discrete data 84 85 87 89 90 91 92 94 98 99 101 103 105 108 113 115 121 124 125 126 127 128 129 130 135 140 146 152 154 155 156 157 159 161 166 DQuantitative continuous data E Measuring the centre of data F Measuring the spread of data GBox and whisker plots HCumulative frequency graphs I Standard deviation Review set 6A Review set 6B Review set 6C 7 SETS AND VENN DIAGRAMS ASets B Set builder notation C Complements of sets DVenn diagrams E Venn diagram regions F Numbers in regions GProblem solving with Venn diagrams Review set 7A Review set 7B 8 LOGIC APropositions B Compound propositions C Truth tables and logical equivalence DImplication and equivalence E Converse, inverse, and contrapositive F Valid arguments Review set 8A Review set 8B Review set 8C 9 PROBABILITY AExperimental probability B Sample space C Theoretical probability DCompound events E Tree diagrams 167 170 182 186 193 197 206 207 208 211 213 215 216 219 222 223 225 228 229 231 232 235 240 245 247 249 254 255 256 257 259 265 267 272 275 F Sampling with and without replacement GExpectation HProbabilities from Venn diagrams I Laws of probability J Conditional probability KIndependent events Review set 9A Review set 9B Review set 9C 1 THE NORMAL DISTRIBUTION 0 AThe normal distribution B Probabilities using a calculator C Quantiles or k-values Review set 10A Review set 10B Review set 10C 1 TWO VARIABLE STATISTICS 1 ACorrelation B Measuring correlation C Line of best fit by eye DLinear regression E The ² test of independence Review set 11A Review set 11B 1 PYTHAGORAS' THEOREM 2 APythagoras' theorem B Right angles in geometry C The converse of Pythagoras' theorem DProblem solving E Three-dimensional problems Review set 12A Review set 12B Review set 12C 278 281 285 289 290 294 296 296 298 299 300 304 308 312 312 313 315 316 320 328 331 334 345 347 349 350 355 360 362 368 371 372 373 1 COORDINATE GEOMETRY 3 ADistance between two points B Midpoints C Gradient DParallel and perpendicular lines E Applications of gradient F Vertical and horizontal lines GEquations of lines HGraphing lines I Perpendicular bisectors Review set 13A Review set 13B Review set 13C Review set 13D 1 PERIMETER, AREA, AND VOLUME 4 AConversion of units B Perimeter C Area DSurface area E Volume F Capacity GDensity (Extension) HHarder applications Review set 14A Review set 14B Review set 14C 1 TRIGONOMETRY 5 ALabelling right angled triangles B The trigonometric ratios C Using trigonometry in geometric figures DProblem solving using trigonometry E 3-dimensional problem solving F Areas of triangles 375 377 380 384 388 390 393 394 400 404 406 406 407 409 411 413 415 418 424 428 434 438 439 440 441 443 445 446 447 454 458 460 465 GThe cosine rule HThe sine rule I Using the sine and cosine rules J The ambiguous case (Extension) Review set 15A Review set 15B Review set 15C 1 FUNCTIONS 6 ARelations and functions B Function notation C Domain and range DLinear models Review set 16A Review set 16B Review set 16C 1 QUADRATIC FUNCTIONS 7 AQuadratic functions B Graphs from tables of values C Axes intercepts DGraphs of the form y = ax² E Graphs of quadratic functions F Axis of symmetry GVertex HFinding a quadratic from its graph I Where functions meet J Quadratic models Review set 17A Review set 17B Review set 17C 1 EXPONENTIAL FUNCTIONS 8 AEvaluating exponential functions B Graphs of exponential functions C Exponential equations 468 471 474 476 478 479 481 483 484 487 489 492 497 498 499 501 502 505 507 509 511 513 515 517 520 522 526 527 528 529 531 531 536 DGrowth and decay Review set 18A Review set 18B 1 UNFAMILIAR FUNCTIONS 9 AProperties of functions B Asymptotes C Combined power functions DCombined functions E Where functions meet Review set 19A Review set 19B 2 DIFFERENTIAL CALCULUS 0 ARates of change B Instantaneous rates of change C The derivative function DRules of differentiation E Equations of tangents F Normals to curves Review set 20A Review set 20B Review set 20C 2 APPLICATIONS OF DIFFERENTIAL 1 CALCULUS AIncreasing and decreasing functions B Stationary points C Rates of change DOptimisation Review set 21A Review set 21B Review set 21C 2 MISCELLANEOUS PROBLEMS 2 AShort questions 536 541 542 543 544 547 549 553 555 556 557 559 560 563 568 572 576 579 582 583 584 585 586 590 594 598 607 608 609 611 612 B Long questions ANSWERS 637 655