Jacaranda Maths Quest 12 Mathematics Standard 2

Overview viii

About eBookPLUS and studyON ix

Acknowledgements x

1 Simultaneous linear equations 1

1.1 Overview 1

1.2 Review of linear equations 2

1.3 Graphing linear equations 7

1.4 Simultaneous linear equations 14

1.5 Review 22

Answers 27

2 Non-linear relationships 41

2.1 Overview 41

2.2 Exponential functions 42

2.3 Quadratic functions 52

2.4 Reciprocal functions 70

2.5 Review 83

Answers 90

3 Non-right-angled trigonometry 99

3.1 Overview 99

3.2 Review of trigonometric ratios 100

3.3 The sine rule 108

3.4 The cosine rule 112

3.5 Area of a triangle 118

3.6 Bearings and navigation 124

3.7 Angles of elevation and depression 131

3.8 Applications to practical problems 137

3.9 Radial surveys 141

3.10 Review 146

Answers 152

4 Rates and ratios 156

4.1 Overview 156

4.2 Working with rates 157

4.3 Household appliances 164

4.4 Working with ratios 168

4.5 Building plans and elevation views 173

4.6 Sections of land 181

4.7 Review 193

Answers 201

5 Investments 205

5.1 Overview 205

5.2 Applications of simple interest 206

5.3 Compound interest 211

5.4 Comparing investments and compounding problems 219

5.5 Shares 227

5.6 Review 234

Answers 241

6 Depreciation and loans 247

6.1 Overview 247

6.2 The declining-balance method of depreciation 248

6.3 Reducing balance loans 253

6.4 Credit cards 261

6.5 Review 275

Answers 283

7 Annuities 287

7.1 Overview 287

7.2 Introduction to annuities 288

7.3 Using recurrence relations to model annuities 293

7.4 Annuity calculations 302

7.5 Review 309

Answers 314

8 Bivariate data analysis 318

8.1 Overview 318

8.2 Scatterplots 319

8.3 Lines of best fit 328

8.4 The statistical investigation process 342

8.5 Review 352

Answers 362

9 The normal distribution 372

9.1 Overview 372

9.2 The bell curve 373

9.3 z-scores 380

9.4 Using normal distributions 386

9.5 Review 399

Answers 403

10 Networks and shortest paths 407

10.1 Overview 407

10.2 Solving problems with networks 408

10.3 Weighted networks and shortest paths 422

10.4 Minimum spanning trees 434

10.5 Review 447

Answers 456

11 Critical path analysis 466

11.1 Overview 466

11.2 Critical paths 467

11.3 Critical path analysis with backward scanning 478

11.4 Network flow 486

11.5 Review 499

Answers 507

Glossary 513

Index 521