# Maths Quest: Preliminary Mathematics General & eBookPLUS, 4th Edition

# Maths Quest: Preliminary Mathematics General & eBookPLUS, 4th Edition

ISBN: 978-1-118-51176-3

Feb 2013, Jacaranda

504 pages

## Description

**Maths Quest Preliminary Mathematics General Fourth Edition** is written for the NEW Mathematics General Stage 6 Syllabus.

This text provides comprehensive coverage of the five strands: Financial Mathematics, Data and Statistics, Measurement, Probability, and Algebra and Modelling. It also covers the two Focus Studies: Mathematics and Communication, and Mathematics and Driving.

The Preliminary Mathematics General course is structured to prepare students for pathways to both the HSC Mathematics General 1 course and the HSC Mathematics General 2 course.

In this text, students are encouraged to understand and experience the application of mathematics in the world, to appreciate the beauty and wonder of mathematics, and to realise the possibilities for their own lives and careers that the study of mathematics can give them.

This text strives to ignite the potential in each student.

**This resource contains the following award-winning features:**

• Two major collaborative, online projects with an emphasis on the themes of the Focus Studies, delivered through ProjectsPLUS.

• Interactivities that bring concepts to life.

• Easy-to-follow worked examples in the Think–Write format.

• Carefully graded exercises that conclude with further development questions designed to extend and challenge students.

• Investigations to stimulate students’ interest and engagement.

• Comprehensive chapter reviews.

• A glossary of mathematical terms that define the terminology introduced in each topic.

• eBookPLUS references throughout to direct students and teachers to relevant online material.

** **This title features eBookPLUS: an electronic version of the textbook and a complimentary set of targeted digital resources. These flexible and engaging ICT activities are available at the

Your eBookPLUS resources include:

• the entire textbook in electronic format

• WorkSHEETS – Word documents to assist with revision and practice

• Spreadsheets

• ProjectsPLUS – two major online, collaborative projects

Click here to view

**JacarandaPLUS website.**Your eBookPLUS resources include:

• the entire textbook in electronic format

• WorkSHEETS – Word documents to assist with revision and practice

• Spreadsheets

• ProjectsPLUS – two major online, collaborative projects

Click here to view

**Maths Quest Preliminary Mathematics General Fourth Edition eBookPLUS**.Introduction vi

About eBookPLUS viii

Acknowledgements ix

Chapter 1. Earning money 1

1A Calculating salary payments 1

Exercise 1A 2

1B Calculating wages 3

Exercise 1B 5

1C Commission and royalties 8

Exercise 1C 9

1D Payment by piece 12

Exercise 1D 13

1E Working overtime 14

Exercise 1E 16

1F Government allowances 19

Exercise 1F 20

1G Additions to and deductions from

gross pay 22

Exercise 1G 23

1H Budgeting 27

Exercise 1H 29

Summary 35

Chapter review 36

ICT activities 39

Answers 40

Chapter 2. Investing money 43

2A Calculation of simple interest 43

Exercise 2A 46

2B Graphing simple interest

functions 48

Exercise 2B 50

2C Calculation of compound interest 53

Exercise 2C 55

2D Calculating compound interest from a table

of compounded values 57

Exercise 2D 60

2E Share dividends 62

Exercise 2E 62

2F Graphing share performance 64

Exercise 2F 66

2G Infl ation and appreciation 68

Exercise 2G 69

Summary 72

Chapter review 73

ICT activities 76

Answers 77

Chapter 3. Taxation 81

3A Calculating allowable deductions 81

Exercise 3A 83

3B Taxable income 85

Exercise 3B 87

3C Medicare levy 90

Exercise 3C 90

3D Calculating tax 91

Exercise 3D 94

3E Calculating GST and VAT 97

Exercise 3E 98

3F Graphing tax functions 101

Exercise 3F 101

Summary 103

Chapter review 104

ICT activities 106

Answers 107

Chapter 4. Statistics and society, data collection and sampling 109

4A Statistical processes 109

Exercise 4A 112

4B Target populations and sampling 114

Exercise 4B 116

4C Population characteristics 118

Exercise 4C 120

4D Types of data 122

Exercise 4D 123

4E Bias 125

Exercise 4E 128

Summary 132

Chapter review 133

ICT activities 136

Answers 137

Chapter 5. Displaying single data sets 141

5A Types of graphs and stem-and-leaf

plots 141

Exercise 5A 144

5B Frequency tables and cumulative frequency 146

Exercise 5B 149

5C Range and interquartile range, deciles and

percentiles 154

Exercise 5C 158

5D Five-number summaries 164

Exercise 5D 166

5E Appropriate graphs and misuse of graphs 169

Exercise 5E 173

Summary 177

Chapter review 178

ICT activities 182

Answers 183

Chapter 6. Summary statistics 189

6A Calculating the mean 189

Exercise 6A 193

6B Median and mode 198

Exercise 6B 201

6C Standard deviation 205

Exercise 6C 208

6D Best summary statistics 212

Exercise 6D 214

Summary 220

Chapter review 221

ICT activities 226

Answers 227

Chapter 7. Measurement 231

7A Measurements as approximations 231

Exercise 7A 233

7B Units of measurement and scientific

notation 234

Exercise 7B 237

7C Ratios 239

Exercise 7C 240

7D Rates 242

Exercise 7D 245

7E Percentage change 247

Exercise 7E 248

Summary 250

Chapter review 251

ICT activities 253

Answers 254

Chapter 8. Perimeter, area and volume 257

8A Perimeter of plane shapes 257

Exercise 8A 259

8B Area of plane shapes 262

Exercise 8B 264

8C Field diagrams 268

Exercise 8C 270

8D Applications of area 271

Exercise 8D 271

8E Volume of prisms 273

Exercise 8E 275

Summary 279

Chapter review 280

ICT activities 282

Answers 283

Chapter 9. Similar figures and trigonometry 285

9A Similar f igures and scale factors 285

Exercise 9A 287

9B Solving problems using similar f igures 291

Exercise 9B 293

9C Calculating trigonometric ratios 297

Exercise 9C 301

9D Finding an unknown side 302

Exercise 9D 305

9E Finding angles 308

Exercise 9E 309

9F Applications of right-angled triangles 312

Exercise 9F 315

Proportional diagrams 316

Summary 317

Chapter review 318

ICT activities 321

Answers 322

Chapter 10. Probability 325

10A Multi-stage events 325

Exercise 10A 327

10B The fundamental counting principle 329

Exercise 10B 331

10C Probability statements 333

Exercise 10C 335

10D Relative frequency 336

Exercise 10D 338

10E Equally likely outcomes 341

Exercise 10E 342

10F The probability formula 343

Exercise 10F 345

10G Writing probabilities as decimals and

percentages 348

Exercise 10G 349

10H Range of probabilities 351

Exercise 10H 353

10I Complementary events 356

Exercise 10I 357

Summary 360

Chapter review 361

ICT activities 364

Answers 365

Chapter 11. Algebraic manipulation 369

11A Operations with algebraic expressions 369

Exercise 11A 371

11B Further multiplication and division 372

Exercise 11B 373

11C Expanding and simplifying algebraic expressions 374

Exercise 11C 375

11d Substitution 376

Exercise 11D 377

11E Solving linear equations 379

Exercise 11E 381

Summary 384

Chapter review 385

ICT activities 387

Answers 388

Chapter 12. Modelling linear relationships 391

12A Graphing linear functions 391

Exercise 12A 393

12B Gradient and y-intercept 395

Exercise 12B 398

12C Drawing graphs using gradient and intercept 400

Exercise 12C 403

12D Simultaneous equations 404

Exercise 12D 407

12E Practical applications of linear functions 409

Exercise 12E 411

Summary 414

Chapter review 415

ICT activities 418

Answers 419

Chapter 13. Focus study: Mathematics and communication 425

Section 1 — Mobile phone bills 425

13A Calculating costs 425

Exercise 13A 427

13B Reading a mobile phone bill 430

Exercise 13B 431

13C Phone usage 432

Exercise 13C 433

13D Choosing the best mobile phone plan for your needs 435

Exercise 13D 435

Section 2 — Digital download and file storage 436

13E Units of storage 436

Exercise 13E 438

13F Digital transfer rates 439

Exercise 13F 439

13G Random selection 440

Exercise 13G 441

Summary 442

Chapter review 443

ICT activities 445

Answers 446

ICT activities — Projectsplus

pro-0135 The cost of piracy 448

Chapter 14. Focus study: Mathematics and driving 451

Section 1 — Costs of purchase and insurance 451

14A Depreciation of new cars 452

Exercise 14A 453

14B Insurance and stamp duty 454

Exercise 14B 456

14C Financing your vehicle 457

Exercise 14C 460

Section 2 — Running costs and depreciation 462

14D Fuel costs 462

Exercise 14D 463

14E Straight line depreciation 465

Exercise 14E 466

14F Declining balance method of depreciation 467

Exercise 14F 468

Section 3 — Road safety 470

14G Speed and stopping distances 470

Exercise 14G 473

14H Blood alcohol concentration (BAC) 474

Exercise 14H 476

Summary 478

Chapter review 479

ICT activities 482

Answers 483

ICT activities — Projectsplus

pro-0136 Causes of accidents 486

Glossary 489

Index 492