JACARANDA MATHS
STAGE 4 NSW SYLLABUS | THIRD EDITION SYLLABUS 2024 LANGSFORD WILLING | SMITH
QUEST 8
Contents Aboutthisresource vii Acknowledgements xiv NAPLANpractice SetA Calculatorallowed SetB Non-calculator SetC Calculatorallowed SetD Non-calculator SetE Calculatorallowed SetF Non-calculator 1 Integers 1 1.1 Overview 2 1.2 Addingandsubtractingintegers 4 1.3 Multiplyingintegers 11 1.4 Dividingintegers 15 1.5 Orderofoperationswithintegers 19 1.6 Review 23 Answers 29 2 Indexlaws 33 2.1 Overview 34 2.2 Reviewofindexform 36 2.3 Multiplyingpowers 41 2.4 Dividingpowers 45 2.5 Thezeroindex 50 2.6 Raisingpowers 54 2.7 Review 60 Answers 66 3 Realnumbers 71 3.1 Overview 72 3.2 Therealnumbersystem 74 3.3 Addingandsubtractingfractions 80 3.4 Multiplyinganddividingfractions 88 3.5 Terminatingandrecurringdecimals 93 3.6 Addingandsubtractingdecimals 97 3.7 Multiplyinganddividingdecimals 102 3.8 Estimation 107 3.9 Review 114 Answers 120 4 Percentages 125 4.1 Overview 126 4.2 Percentages 128 4.3 Findingpercentagesofanamount 133 4.4 Discount 139 4.5 Profitandloss 145 4.6 GoodsandServicesTax(GST) 152 4.7 Review 157 Answers 162 5 Ratiosandrates 173 5.1 Overview 174 5.2 Ratios 176 5.3 Simplifyingratios 183 5.4 Proportion 191 5.5 Comparingratios 197 5.6 Dividinginagivenratio 201 5.7 Rates 207 5.8 Interpretinggraphs 212 5.9 Review 221 Answers 227 6 Algebraictechniques 231 6.1 Overview 232 6.2 Usingpronumerals 236 6.3 Substitution 254 6.4 Substitutingpositiveandnegative numbers 262 6.5 Numberlaws 270 6.6 Addingandsubtractingterms 287 6.7 Multiplyinganddividingterms 295 6.8 Expandingbrackets 302 6.9 Factorising 303 6.10 Review 305 Answers 306 Semesterreview1 307 7 Equations 309 7.1 Overview 313 7.2 Backtrackingandinverseoperations 318 7.3 Keepingequationsbalanced 321 7.4 Solvinglinearequationsandsimple quadraticequations 327 7.5 Equationswithunknownsonbothsides 331 7.6 Review 338 Answers 343 8 Length,areaandvolume359 8.1 Overview 360 8.2 Lengthandperimeter 363 8.3 Circumference 371 8.4 Areasofrectangles,triangles, parallelograms,rhombusesandkites 380 8.5 Areasofcircles 393 8.6 Areasoftrapeziums 399 CONTENTS v UNCORRECTEDPAGE PROOFS
8.7 Volumesofprismsandothersolids 404 8.8 Time 411 8.9 24-hourclocksandtimezones (extending) 417 8.10 Review 426 Answers 435 9 Linearrelationships 439 9.1 Overview 440 9.2 TheCartesianplane 442 9.3 Linearpatterns 447 9.4 Lineargraphs 451 9.5 Graphingwithtechnology 461 9.6 Solvingequationsgraphically 468 9.7 Review 469 Answers 473 10 Data 477 10.1 Overview 478 10.2 Datacollectionmethods 481 10.3 Primaryandsecondarydata(extending) 492 10.4 Organisinganddisplayingdata 501 10.5 Measuresofcentreandspread 534 10.6 Analysingdata 536 10.7 Review 538 Answers 540 11 Probability 547 11.1 Overview 548 11.2 Experimentalprobability 551 11.3 Probabilityscale 559 11.4 Samplespacesandtheoreticalprobability 563 11.5 Complementaryevents 571 11.6 Review 598 Answers 604 12 Right-angledtriangles (Pythagoras’theorem) 697 12.1 Overview 698 12.2 Pythagoras’theorem 701 12.3 Calculatingshortersidelengths 708 12.4 ApplyingPythagoras’theorem 712 12.5 Pythagoreantriads 718 12.6 Review 722 Answers 727 Semesterreview2 729 Glossary 732 Index 737 vi CONTENTS UNCORRECTEDPAGE PROOFS