# Jacaranda Maths Quest 10 Stage 5 NSW Australian Curriculum 2E LearnON & Print

 Author(s): Elms ISBN: 9780730347170 Pub date: November 2017 RRP: \$69.95
Jacaranda Maths Quest 10 Stage 5 NSW Australian curriculum, 2nd Edition learnON & Print

This combined print and digital title provides 100% coverage of the NSW Australian curriculum for Mathematics. The textbook comes with a complimentary activation code for learnON, the powerful digital learning platform making learning personalised and visible for both students and teachers.

The latest editions of Jacaranda Maths Quest NSW Australian curriculum series include these key features:

• Worked examples featuring the familiar THINK/WRITE columns providing exemplary solutions and explanations
• Carefully graded questions in each exercise and individual pathway interactivities providing questions for learners at three levels
• Worked solutions for every question providing immediate feedback and help resolve misconceptions at the point of learning
• Features a new exercise structure based on Working Mathematically, with two exercise sets per sub-topic to test knowledge and put theory into practice
• The reading content contains embedded videos addressing the 50 common maths misconceptions and hundreds of interactivities at the point of learning
• Completely new curriculum grids, work programs and even a poster for schools show complete coverage of every dot point in the curriculum

For teachers, learnON includes additional teacher resources such as quarantined questions and answers, curriculum grids and work programs.

To complement the Maths Quest series, assessON Maths Quest is available for Years 7–10.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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