# Jacaranda Maths Quest 10 Stage 5 NSW Syllabus 3E LearnON & Print

 Author(s): Langsford-willi ISBN: 9780730386414 Pub date: October 2023 RRP: \$75

Jacaranda MathsQuest 10 Stage 5 NSW Syllabus (for the NSW Syllabus)
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Acknowledgements xvi

1 Financial Mathematics 1

1.1 Overview 2

1.2 Simple interest 4

1.4 Compound interest 13

1.5 Depreciation 21

1.6 Review 25

2 Indices and Surds 33

2.1 Overview 34

2.2 Rational and irrational numbers (Path) 36

2.3 Surds (Path) 41

2.4 Operations with surds (Path) 45

2.5 Review of index laws 57

2.6 Negative indices (Path) 63

2.7 Fractional indices (Path) 69

2.8 Combining index laws (Path) 74

2.9 Review 81

3 Algebraic Techniques (Path) 97

3.1 Overview 98

3.2 Special binomial products 100

3.3 Further expansions 105

3.4 Factorising by grouping in pairs 108

3.5 Factorising special products 111

3.7 Adding and subtracting algebraic fractions 119

3.8 Multiplying and dividing algebraic fractions 124

3.9 Applications of binomial products 131

3.10 Review 138

4 Linear Equations and Inequalities 151

4.1 Overview 152

4.2 Solving linear equations review 154

4.3 Solving multi-step equations, including fractions (Path) 159

4.4 Literal equations (Path) 164

4.5 Solving linear inequalities (Path) 167

4.6 Review 174

5 Simultaneous Linear Equations (Path) 183

5.1 Overview 184

5.2 Solving simultaneous linear equations graphically 186

5.3 Solving simultaneous linear equations using substitution 195

5.4 Solving simultaneous linear equations using elimination 200

5.5 Applications of simultaneous linear equations 206

5.6 Review 212

6.1 Overview 224

6.2 Solving quadratic equations algebraically 226

6.4 Solving quadratic equations graphically 240

6.5 The discriminant 248

6.6 Review 255

7 Linear Relationships 267

7.1 Overview 268

7.2 Sketching linear graphs 271

7.3 Determining the equation of a straight line 281

7.4 Parallel and perpendicular lines 291

7.5 The distance between two points formula (Path) 297

7.6 The midpoint of a line segment formula (Path) 301

7.7 Applications to solving problems (Path) 306

7.8 Graphing linear inequalities (Path) 312

7.9 Review 320

8 Non-linear Relationships 343

8.1 Overview 344

8.2 The graph of a parabola 347

8.3 Parabolas and transformations 356

8.4 Parabolas in vertex form (Path) 365

8.5 Parabolas in general form (Path) 374

8.6 Exponential graphs (Path) 379

8.7 The hyperbola (Path) 387

8.8 The circle (Path) 393

8.9 Simultaneous linear and non-linear equations (Path) 398

8.10 Review 406

Semester review 1 436

9 Trigonometry I 439

9.1 Overview 440

9.2 Pythagoras’ theorem 443

9.3 Pythagoras’ theorem in three dimensions (Path) 451

9.4 Trigonometric ratios 457

9.5 Using trigonometry to calculate side lengths 463

9.6 Using trigonometry to calculate angle size 468

9.7 Angles of elevation and depression 473

9.8 Bearings 478

9.9 Applications of trigonometry 485

9.10 Review 490

10 Trigonometry II (Path) 503

10.1 Overview 504

10.2 The sine rule 507

10.3 The cosine rule 515

10.4 Area of triangles 520

10.5 The unit circle 527

10.6 Trigonometric functions 536

10.7 Solving trigonometric equations 543

10.8 Review 548

11 Measurement 563

11.1 Overview 564

11.2 Area 568

11.3 Total surface area 577

11.4 Volume 588

11.5 Review 603

12 Properties of Geometrical Figures (Path) 613

12.1 Overview 614

12.2 Angles, triangles and congruence 617

12.3 Similar triangles 629

12.5 Polygons 650

12.6 Review 658

13 Data Analysis 669

13.1 Overview 670

13.2 Bivariate data 674

13.3 Lines of best fit by eye 684

13.4 Evaluating statistical reports (Path) 696

13.5 Statistical investigations (Path) 708

13.6 Selecting a sample size (Path) 713

13.7 Review 720

14 Probability 737

14.1 Overview 738

14.2 Review of probability and simulations 741

14.3 Tree diagrams and multistage chance experiments 750

14.4 Independent and dependent events 757

14.5 Venn diagrams, 2-way tables and mutually exclusive events (Path) 764

14.6 Conditional probability (Path) 779

14.7 Review 785

15 Polynomials (Path) 799

15.1 Overview 800

15.2 Polynomials 802

15.3 Adding, subtracting and multiplying polynomials 806

15.4 Long division of polynomials 808

15.5 Polynomial values 814

15.6 The remainder and factor theorems 817

15.7 Factorising polynomials 821

15.8 Solving polynomial equations 827

15.9 Review 830

16 Logarithms (Path) 841

16.1 Overview 842

16.2 Logarithms 844

16.3 Logarithm laws 850

16.4 Solving equations 858

16.5 Graphing logarithmic and exponential functions 865

16.6 Review 872

17 Functions and Other Graphs (Path) 883

17.1 Overview 884

17.2 Functions and relations 890

17.3 Graphing cubic functions 901

17.4 Graphing quartic functions 907

17.5 Transformations 912

17.6 Review 924

18 Circle Geometry (Path) 939

18.1 Overview 940

18.2 Angles in a circle 944

18.3 Intersecting chords, secants and tangents 952

18.5 Tangents, secants and chords 965

18.6 Review 972

19 Introduction to Networks (Path) 981

19.1 Overview 982

19.2 Properties of networks 986

19.3 Planar graphs 999

19.4 Connected graphs 1007

19.5 Review 1017