# Maths Quest 10+10a for the Australian Curriculum 2E & eBookPLUS

Author/s |
Boucher |
---|---|

ISBN13 | 9780730317890 |

Pub date | November 2014 |

Pages | 918 |

RRP | $69.95 |

*has been updated based on*

**Maths Quest 10+10A for the Australian Curriculum Second Edition****in-depth research and feedback**from practising teachers of Mathematics.

**KEY FEATURES**

•

**Worked solutions**available to students and teachers for every problem solving and reasoning question.

• An enhanced emphasis on both

**problem solving & reasoning**, creating greater understanding of both

**mathematical concepts and skills**.

• Assessment material incorporating the

**Australian Curriculum Achievement Standards.**

• Improvements to student engagement, with enhanced

**Individual Pathway activities**,

**new interactivities**and

**new videos**telling the

**Story of Mathematics**.

• Teacher support:

**eGuidePLUS**provides online access to the student textbook, teacher notes on each lesson, a range of activities to engage students and end of top assessment items.

* Maths Quest 10+10A for Australian Curriculum 2E and eBookPLUS* is a hard-copy student text accompanied by

**eBookPLUS.**

>

**eBookPLUS**resources include:

• Access from any

**digital device**PC/MAC/iPad/Android Tablet.

• W

**orksheets**- Word documents designed for easy customisation and editing.

•

**Interactivities and games**to reinforce and enhance student learning.

•

**eLessons**- engaging video clips and supporting material.

•

**Weblinks**to

**relevant support material**on the internet.

•

**ProjectsPLUS**- unique

**ICT-based projects**that provide opportunities for students to demonstrate creativity, thinking skills and teamwork.

About eBookPLUS ix

Overview x

Acknowledgements xii

NUMBER AND ALGEBRA

Topic 1 Indices 2

1.1 Overview 2

1.2 Review of index laws 4

Exercise 1.2 6

1.3 Negative indices 9

Exercise 1.3 11

1.4 Fractional indices 14

Exercise 1.4 15

1.5 Combining index laws 18

Exercise 1.5 20

1.6 Review ONLINE ONLY 25

eBookPLUS activities 29

Answers 30

NUMBER AND ALGEBRA

Topic 2 Algebra and equations 34

2.1 Overview 34

2.2 Substitution 36

Exercise 2.2 38

2.3 Adding and subtracting algebraic fractions 41

Exercise 2.3 44

2.4 Multiplying and dividing algebraic fractions 45

Exercise 2.4 47

2.5 Solving simple equations 49

Exercise 2.5 52

2.6 Solving multi-step equations 55

Exercise 2.6 58

2.7 Literal equations 60

Exercise 2.7 61

2.8 Review ONLINE ONLY 63

eBookPLUS activities 67

Answers 68

NUMBER AND ALGEBRA

Topic 3 Coordinate geometry 72

3.1 Overview 72

3.2 Sketching linear graphs 74

Exercise 3.2 78

3.3 Determining linear equations 80

Exercise 3.3 84

3.4 The distance between two points 87

Exercise 3.4 89

3.5 The midpoint of a line segment 91

Exercise 3.5 93

3.6 Parallel and perpendicular lines 94

Exercise 3.6 99

3.7 Review ONLINE ONLY 105

eBookPLUS activities 109

Answers 110

NUMBER AND ALGEBRA

Topic 4 Simultaneous linear

equations and inequalities 116

4.1 Overview 116

4.2 Graphical solution of simultaneous

linear equations 118

Exercise 4.2 122

4.3 Solving simultaneous linear equations

using substitution 124

Exercise 4.3 126

4.4 Solving simultaneous linear equations

using elimination 128

Exercise 4.4 130

4.5 Applications of simultaneous linear equations 133

Exercise 4.5 135

4.6 Solving simultaneous linear and non-linear

equations 137

Exercise 4.6 142

4.7 Solving linear inequalities 144

Exercise 4.7 147

4.8 Inequalities on the Cartesian plane 149

Exercise 4.8 153

4.9 Solving simultaneous linear inequalities 155

Exercise 4.9 157

4.10 Review ONLINE ONLY 160

eBookPLUS activities 165

Answers 166

MEASUREMENT AND GEOMETRY

Topic 5 Trigonometry I 172

5.1 Overview 172

5.2 Pythagoras’ theorem 174

Exercise 5.2 178

5.3 Pythagoras’ theorem in three dimensions 181

Exercise 5.3 184

5.4 Trigonometric ratios 186

Exercise 5.4 189

5.5 Using trigonometry to calculate side

lengths 192

Exercise 5.5 194

5.6 Using trigonometry to calculate angle size 197

Exercise 5.6 199

5.7 Angles of elevation and depression 202

Exercise 5.7 203

5.8 Bearings 207

Exercise 5.8 211

5.9 Applications 213

Exercise 5.9 214

5.10 Review ONLINE ONLY 219

eBookPLUS activities 223

Answers 224

MEASUREMENT AND GEOMETRY

Topic 6 Surface area and

volume 228

6.1 Overview 228

6.2 Area 230

Exercise 6.2 234

6.3 Total surface area 239

Exercise 6.3 244

6.4 Volume 248

Exercise 6.4 254

6.5 Review ONLINE ONLY 261

eBookPLUS activities 265

Answers 266

NUMBER AND ALGEBRA

Topic 7 Quadratic

expressions 268

7.1 Overview 268

7.2 Expanding algebraic expressions 270

Exercise 7.2 273

7.3 Factorising expressions with three terms 276

Exercise 7.3 279

7.4 Factorising expressions with two or

four terms 281

Exercise 7.4 283

7.5 Factorising by completing the square 287

Exercise 7.5 290

7.6 Mixed factorisation 291

Exercise 7.6 292

7.7 Review ONLINE ONLY 295

eBookPLUS activities 299

Answers 300

NUMBER AND ALGEBRA

Topic 8 Quadratic equations 304

8.1 Overview 304

8.2 Solving quadratic equations algebraically 306

Exercise 8.2 310

8.3 The quadratic formula 313

Exercise 8.3 315

8.4 Solving quadratic equations graphically 318

Exercise 8.4 320

8.5 The discriminant 323

Exercise 8.5 326

8.6 Review ONLINE ONLY 329

eBookPLUS activities 333

Answers 334

NUMBER AND ALGEBRA

Topic 9 Non-linear

relationships 336

9.1 Overview 336

9.2 Plotting parabolas 338

Exercise 9.2 342

9.3 Sketching parabolas 345

Exercise 9.3 349

9.4 Sketching parabolas in turning point form 351

Exercise 9.4 355

9.5 Sketching parabolas of the form

y = ax2 + bx + c 358

Exercise 9.5 361

9.6 Exponential functions and graphs 362

Exercise 9.6 365

9.7 The hyperbola 368

Exercise 9.7 370

9.8 The circle 372

Exercise 9.8 374

9.9 Review ONLINE ONLY 377

eBookPLUS activities 381

Answers 382

MEASUREMENT AND GEOMETRY

Topic 10 Deductive geometry 394

10.1 Overview 394

10.2 Angles, triangles and congruence 396

Exercise 10.2 401

10.3 Similar triangles 406

Exercise 10.3 408

10.4 Quadrilaterals 412

Exercise 10.4 418

10.5 Polygons 423

Exercise 10.5 424

10.6 Review ONLINE ONLY 429

eBookPLUS activities 433

Answers 434

ProjectsPLUS ICT ACTIVITY

Getting the budget in order pro-0087 436

STATISTICS AND PROBABILITY

Topic 11 Probability 438

11.1 Overview 438

11.2 Review of probability 440

Exercise 11.2 452

11.3 Tree diagrams 456

Exercise 11.3 459

11.4 Independent and dependent events 462

Exercise 11.4 465

11.5 Conditional probability 469

Exercise 11.5 471

11.6 Subjective probability 473

Exercise 11.6 474

11.7 Review ONLINE ONLY 477

eBookPLUS activities 481

Answers 482

STATISTICS AND PROBABILITY

Topic 12 Univariate data 488

12.1 Overview 488

12.2 Measures of central tendency 490

Exercise 12.2 495

12.3 Measures of spread 501

Exercise 12.3 503

12.4 Box-and-whisker plots 506

Exercise 12.4 512

12.5 The standard deviation 516

Exercise 12.5 523

12.6 Comparing data sets 525

Exercise 12.6 527

12.7 Review ONLINE ONLY 533

eBookPLUS activities 537

Answers 538

STATISTICS AND PROBABILITY

Topic 13 Bivariate data 544

13.1 Overview 544

13.2 Bivariate data 546

Exercise 13.2 549

13.3 Lines of best fi t 554

Exercise 13.3 561

13.4 Time series 567

Exercise 13.4 572

13.5 Review ONLINE ONLY 577

eBookPLUS activities 581

Answers 582

STATISTICS AND PROBABILITY

Topic 14 Statistics in the media 586

14.1 Overview 586

14.2 Populations and samples 588

Exercise 14.2 591

14.3 Primary and secondary data 594

Exercise 14.3 599

14.4 Evaluating inquiry methods and

statistical reports 603

Exercise 14.4 611

14.5 Statistical investigations 616

Exercise 14.5 620

14.6 Review ONLINE ONLY 623

eBookPLUS activities 627

Answers 628

ProjectsPLUS ICT ACTIVITY

Climate change pro-0100 632

NUMBER AND ALGEBRA

Topic 15 Financial mathematics 634

15.1 Overview 634

15.2 Purchasing goods 636

Exercise 15.2 637

15.3 Buying on terms 640

Exercise 15.3 641

15.4 Successive discounts 645

Exercise 15.4 647

15.5 Compound interest 649

Exercise 15.5 653

15.6 Depreciation 656

Exercise 15.6 657

15.7 Loan repayments 660

Exercise 15.7 661

15.8 Review ONLINE ONLY 663

eBookPLUS activities 667

Answers 668

NUMBER AND ALGEBRA

Topic 16 Real numbers 670

16.1 Overview 670

16.2 Number classification review 672

Exercise 16.2 675

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16.3 Surds 677

Exercise 16.3 679

16.4 Operations with surds 680

Exercise 16.4 688

16.5 Fractional indices 691

Exercise 16.5 693

16.6 Negative indices 696

Exercise 16.6 697

16.7 Logarithms 698

Exercise 16.7 700

16.8 Logarithm laws 701

Exercise 16.8 704

16.9 Solving equations 706

Exercise 16.9 709

16.10 Review ONLINE ONLY 713

eBookPLUS activities 717

Answers 718

NUMBER AND ALGEBRA

Topic 17 Polynomials 722

17.1 Overview 722

17.2 Polynomials 724

Exercise 17.2 725

17.3 Adding, subtracting and multiplying

polynomials 726

Exercise 17.3 727

17.4 Long division of polynomials 729

Exercise 17.4 732

17.5 Polynomial values 734

Exercise 17.5 735

17.6 The remainder and factor theorems 736

Exercise 17.6 738

17.7 Factorising polynomials 739

Exercise 17.7 742

17.8 Solving polynomial equations 744

Exercise 17.8 745

17.9 Review ONLINE ONLY 747

eBookPLUS activities 751

Answers 752

NUMBER AND ALGEBRA

Topic 18 Functions and

relations 756

18.1 Overview 756

18.2 Functions and relations 758

Exercise 18.2 766

18.3 Exponential functions 769

Exercise 18.3 773

18.4 Cubic functions 778

Exercise 18.4 781

18.5 Quartic functions 783

Exercise 18.5 785

18.6 Transformations 787

Exercise 18.6 793

18.7 Review ONLINE ONLY 795

eBookPLUS activities 799

Answers 800

MEASUREMENT AND GEOMETRY

Topic 19 Circle geometry 804

19.1 Overview 804

19.2 Angles in a circle 806

Exercise 19.2 811

19.3 Intersecting chords, secants and

tangents 814

Exercise 19.3 818

19.4 Cyclic quadrilaterals 821

Exercise 19.4 822

19.5 Tangents, secants and chords 825

Exercise 19.5 827

19.6 Review ONLINE ONLY 831

eBookPLUS activities 835

Answers 836

MEASUREMENT AND GEOMETRY

Topic 20 Trigonometry II 838

20.1 Overview 838

20.2 The sine rule 840

Exercise 20.2 847

20.3 The cosine rule 849

Exercise 20.3 852

20.4 Area of triangles 854

Exercise 20.4 856

20.5 The unit circle 860

Exercise 20.5 863

20.6 Trigonometric functions 866

Exercise 20.6 868

20.7 Solving trigonometric equations 871

Exercise 20.7 872

20.8 Review ONLINE ONLY 875

eBookPLUS activities 879

Answers 880

Glossary 885

Index 893