Jacaranda Maths Quest 10 Stage 5 NSW Australian curriculum 2e learnON & print: (Maths Quest for New South Wales Junior Series)

Table of Contents:
Overview x Acknowledgments xii 1 Financial mathematics [5.1 and 5.2] 1 1.1 Overview 1 ACMNA211 1.2 [Stage 5.1] Simple interest 2 ACMNA211 1.3 [Stage 5.1] Buying on terms 6 ACMNA229 1.4 [Stage 5.2] Compound interest 11 ACMNA229 1.5 [Stage 5.2] Depreciation 18 1.6 Review 22 Answers 26 2 Indices [5.1, 5.2 and 5.3] 29 2.1 Overview 29 ACMNA212 2.2 [Stage 5.1] Review of index laws 30 ACMNA231 2.3 [Stage 5.2] Negative indices 35 ACMNA264 2.4 [Stage 5.3] Fractional indices 39 ACMNA264 2.5 [Stage 5.3] Combining index laws 44 2.6 Review 49 Answers 54 3 Right-angled triangles (trigonometry) [5.2 and 5.3] 59 3.1 Overview 59 ACMMG222 3.2 [Stage 4] Pythagoras’ theorem 60 ACMMG276 3.3 [Stage 5.3] Pythagoras’ theorem in three dimensions 67 ACMMG223 3.4 [Stage 5.2] Trigonometric ratios 72 ACMMG224 3.5 [Stage 5.2] Using trigonometry to calculate side lengths 77 ACMMG224 3.6 [Stage 5.2] Using trigonometry to calculate angle size 81 ACMMG245 3.7 [Stage 5.2] Angles of elevation and depression 86 ACMMG245 3.8 [Stage 5.2] Bearings 91 ACMMG245 3.9 [Stages 5.2 and 5.3] Applications 97 3.10 Review 102 Answers 108 4 Probability [5.1 and 5.2] 113 4.1 Overview 113 ACMSP226 4.2 [Stage 5.1] Calculating relative frequencies 114 ACMSP245 | ACMSP246 4.3 [Stage 5.2] Two- and three-step chance experiments 127 ACMSP246 4.4 [Stage 5.2] Independent and dependent events 133 ACMSP247 4.5 [Stage 5.2] Conditional probability 139 4.6 Review 143 Answers 148 5 Single variable data analysis [5.1, 5.2 and 5.3] 159 5.1 Overview 159 ACMSP283 5.2 [Stage 5.1] Comparing data displays using mean, median and range 160 ACMSP248 5.3 [Stage 5.2] Quartiles and interquartile range 169 ACMSP249 | ACMSP250 5.4 [Stage 5.2] Constructing, interpreting and comparing boxplots 173 ACMSP278 5.5 [Stage 5.3] The standard deviation 183 ACMSP278 5.6 [Stage 5.3] Comparing data sets 192 5.7 Review 197 Answers 203 6 Statistics in the media [5.1, 5.2 and 5.3] 211 6.1 Overview 211 ACMSP253 6.2 [Stage 5.1] How is data collected? 212 ACMSP253 6.3 [Stages 5.1 and 5.2] Evaluating statistical reports 222 ACMSP253 6.4 [Stages 5.2 and 5.3] Statistical investigations 236 ACMSP227 6.5 [Stages 5.2 and 5.3] Estimating population means and medians 244 6.6 Review 249 Answers 256 7 Algebraic fractions and equations [5.2 and 5.3] 263 7.1 Overview 263 ACMNA234 7.2 [Stage 5.2] Substitution 264 ACMNA232 7.3 [Stages 5.2 and 5.3] Adding and subtracting algebraic fractions 269 ACMNA232 7.4 [Stages 5.2 and 5.3] Multiplying and dividing algebraic fractions 273 ACMNA215 | ACMNA240 7.5 [Stage 5.2] Solving simple equations 276 NSW 7.6 [Stage 5.3] Solving complex linear equations 282 NSW | ACMNA235 7.7 [Stage 5.3] Rearranging literal equations 286 7.8 Review 290 Answers 294 8 Linear relationships [5.2 and 5.3] 299 8.1 Overview 299 ACMNA214 8.2 [Stages 5.2 and 5.3] The distance between two points 300 ACMNA215 8.3 [Stages 5.2 and 5.3] Sketching linear graphs 304 ACMNA294 8.4 [Stages 5.2 and 5.3] Standard forms of the equation of a straight line 310 ACMNA294 8.5 [Stages 5.2 and 5.3] The midpoint of a line segment 316 ACMNA238 8.6 [Stages 5.2 and 5.3] Parallel and perpendicular lines 319 8.7 Review 329 Answers 334 9 Simultaneous linear equations and inequalities [5.2 and 5.3] 345 9.1 Overview 345 ACMNA237 9.2 [Stage 5.2] Graphical solution of simultaneous linear equations 346 ACMNA237 9.3 [Stage 5.2] Solving simultaneous linear equations using substitution 353 ACMNA237 9.4 [Stage 5.2] Solving simultaneous linear equations using elimination 356 ACMNA237 9.5 [Stage 5.2] Applications of simultaneous linear equations 361 NSW 9.6 [Stage 5.3] Solving simultaneous linear and non-linear equations 365 ACMNA236 9.7 [Stage 5.2] Solving linear inequalities 372 9.8 Review 377 Answers 382 10 Surface area and volume [5.1, 5.2 and 5.3] 389 10.1 Overview 389 ACMMG216 10.2 [Stage 5.1] Area 390 ACMMG242 | ACMMG271 10.3 [Stages 5.2 and 5.3] Total surface area 399 ACMMG242 | ACMMG271 10.4 [Stages 5.2 and 5.3] Volume 407 10.5 Review 421 Answers 427 11 Quadratic expressions [5.2 and 5.3] 431 11.1 Overview 431 ACMNA213 | ACMNA233 11.2 [Stages 5.2 and 5.3] Expanding algebraic expressions 432 ACMNA233 | ACMNA269 11.3 [Stages 5.2 and 5.3] Factorising expressions with three terms 438 ACMNA269 11.4 [Stage 5.3] Factorising expressions with two or four terms 443 ACMNA269 11.5 [Stage 5.3] Factorising by completing the square 448 ACMNA269 11.6 [Stage 5.3] Mixed factorisation 452 11.7 Review 454 Answers 458 12 Quadratic equations [5.3] 465 12.1 Overview 465 ACMNA269 12.2 [Stage 5.3] Solving quadratic equations algebraically 466 ACMNA269 12.3 [Stage 5.3] The quadratic formula 473 ACMNA269 12.4 [Stage 5.3] Solving quadratic equations graphically 477 ACMNA269 12.5 [Stage 5.3] The discriminant 481 12.6 Review 486 Answers 491 13 Non-linear relationships [5.3] 497 13.1 Overview 497 ACMNA267 13.2 [Stage 5.3] Plotting parabolas 498 ACMNA267 13.3 [Stage 5.3] Sketching parabolas 504 ACMNA267 13.4 [Stage 5.3] Sketching parabolas of the form y = a(x – h)2 + k 510 ACMNA267 13.5 [Stage 5.3] Sketching parabolas of the form y = ax2 + bx + c 517 ACMNA267 13.6 [Stage 5.3] Exponential functions and graphs 521 ACMNA267 13.7 [Stage 5.3] The hyperbola 527 ACMNA267 13.8 [Stage 5.3] The circle 530 13.9 Review 534 Answers 540 14 Properties of geometrical figures [5.2 and 5.3] 563 14.1 Overview 563 ACMMG243 | ACMMG244 14.2 [Stages 5.2 and 5.3] Angles, triangles and congruence 564 ACMMG220 | ACMMG244 14.3 [Stages 5.2 and 5.3] Similar triangles 574 ACMMG243 | ACMMG244 14.4 [Stages 5.2 and 5.3] Quadrilaterals 581 ACMMG244 14.5 [Stages 5.2 and 5.3] Polygons 592 14.6 Review 597 Answers 603 15 Bivariate data analysis [5.2 and 5.3] 607 15.1 Overview 607 ACMSP251 15.2 [Stage 5.2] Bivariate data 608 ACMSP279 15.3 [Stage 5.3] Lines of best fit 616 ACMSP252 | ACMSP279 15.4 [Stages 5.2 and 5.3] Time as the independent variable 627 15.5 Review 636 Answers 641 16 Surds, indices and logarithms [5.3] 651 16.1 Overview 651 ACMNA264 16.2 [Stage 5.3] Rational and irrational numbers 652 ACMNA264 16.3 [Stage 5.3] Surds 657 ACMNA264 16.4 [Stage 5.3] Operations with surds 661 ACMNA264 16.5 [Stage 5.3] Fractional indices 671 ACMNA264 16.6 [Stage 5.3] Negative indices 676 ACMNA265 16.7 [Stage 5.3] Logarithms 678 ACMNA265 16.8 [Stage 5.3] Logarithm laws 682 ACMNA270 16.9 [Stage 5.3] Solving equations 687 16.10 Review 693 Answers 697 17 Polynomials [5.3] 705 17.1 Overview 705 ACMNA266 17.2 [Stage 5.3] Polynomials 706 ACMNA266 17.3 [Stage 5.3] Adding, subtracting and multiplying polynomials 709 ACMNA266 17.4 [Stage 5.3] Long division of polynomials 711 ACMNA266 17.5 [Stage 5.3] Polynomial values 716 ACMNA266 17.6 [Stage 5.3] The remainder and factor theorems 718 ACMNA266 17.7 [Stage 5.3] Factorising polynomials 722 ACMNA266 17.8 [Stage 5.3] Solving polynomial equations 726 17.9 Review 728 Answers 732 18 Functions and relations [5.3] 737 18.1 Overview 737 NSW 18.2 [Stage 5.3] Functions and relations 738 ACMNA267 18.3 [Stage 5.3] Exponential functions 748 ACMNA268 18.4 [Stage 5.3] Cubic functions 756 ACMNA268 18.5 [Stage 5.3] Quartic functions 762 NSW 18.6 [Stage 5.3] Transformations 766 18.7 Review 774 Answers 778 19 Circle geometry [5.3] 787 19.1 Overview 787 ACMMG272 19.2 [Stage 5.3] Angles in a circle 788 ACMMG272 19.3 [Stage 5.3] Intersecting chords, secants and tangents 795 ACMMG272 19.4 [Stage 5.3] Cyclic quadrilaterals 803 NSW 19.5 [Stage 5.3] Tangents, secants and chords 807 19.6 Review 814 Answers 819 20 Trigonometry [5.3] 823 20.1 Overview 823 ACMMG273 20.2 [Stage 5.3] The sine rule 824 ACMMG273 20.3 [Stage 5.3] The cosine rule 832 ACMMG273 20.4 [Stage 5.3] Area of triangles 836 ACMMG274 20.5 [Stage 5.3] The unit circle 841 ACMMG274 20.6 [Stage 5.3] Trigonometric functions 848 ACMMG275 20.7 [Stage 5.3] Solving trigonometric equations 853 20.8 Review 856 Answers 861 Glossary 871 Index 893