# Jacaranda Shop

# 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)**

NSW's most supportive Maths resource

Developed by expert teachers, every lesson is carefully designed to support learning online, offline, in class, and at home.

**Supporting students **Whether students need a challenge or a helping hand, they have the tools to help them take the next step, in class and at home:

- concepts brought to life with rich multi-media
- easy navigation
- differentiated pathways
- immediate corrective feedback
- Worked solutions for every question
- personalised pathways that also allow for social learning
- opportunities for remediation, extension, acceleration
- tracking progress and growth

**Supporting teachers **Teachers are empowered to teach their class, their way with flexible resources perfect for teaching and learning:

- 100’s of ready-made and customisable lessons
- comprehensive Syllabus coverage and planning documentation
- a variety of learning activities
- assessment for, as and of learning
- marking, tracking, monitoring and reporting capabilities
- ability to add own materials

**Supporting schools **Schools are set up for success with our unmatched customer service, training and solutions tailored to you:

- Learning Management System (LMS) integration
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- dedicated customer specialists
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About this resource ix

Acknowledgements xvi

**1 Financial Mathematics 1**

1.1 Overview 2

1.2 Simple interest 4

1.3 Buying on terms 8

1.4 Compound interest 13

1.5 Depreciation 21

1.6 Review 25

Answers 30

**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

Answers 90

**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

3.6 Factorising non-monic quadratics 116

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

Answers 144

**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

Answers 178

**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

Answers 219

**6 Quadratic Equations (Path) 223**

6.1 Overview 224

6.2 Solving quadratic equations algebraically 226

6.3 The quadratic formula 236

6.4 Solving quadratic equations graphically 240

6.5 The discriminant 248

6.6 Review 255

Answers 262

**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

Answers 328

**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

Answers 413

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

Answers 497

**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

Answers 555

**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

Answers 609

**12 Properties of Geometrical Figures (Path) 613**

12.1 Overview 614

12.2 Angles, triangles and congruence 617

12.3 Similar triangles 629

12.4 Quadrilaterals 638

12.5 Polygons 650

12.6 Review 658

Answers 665

**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

Answers 728

**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

Answers 791

**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

Answers 835

**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

Answers 877

**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

Answers 929

**18 Circle Geometry (Path) 939**

18.1 Overview 940

18.2 Angles in a circle 944

18.3 Intersecting chords, secants and tangents 952

18.4 Cyclic quadrilaterals 960

18.5 Tangents, secants and chords 965

18.6 Review 972

Answers 978

**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

Answers 1022

Semester review 2 1028

Glossary 1031

Index 1043