Jacaranda Maths Quest 12 Foundation Mathematics VCE Units 3&4 (learnON & Print)

Part of the series Maths Quest VCE.

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Jacaranda Maths Quest 12 Foundation Mathematics VCE Units 3 and 4

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The best Mathematics series for the new VCE Study Design. Developed by expert Victorian teachers for VCE students.

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Table of Contents

About This Resource vii

Acknowledgements xiv

1 Calculations 1

1.1 Overview 2

1.2 Number operations 3

1.3 Order of operations 6

1.4 Rounding 11

1.5 Estimation and approximation strategies 15

1.6 Decimals and fractions 18

1.7 Rational and irrational numbers 26

1.8 Review 37

Answers 39

2 Ratios, proportion and variation 43

2.1 Overview 44

2.2 Direct variation (proportion) 45

2.3 Direct variation (proportion) and ratios 48

2.4 Partial variation (proportion) 52

2.5 Inverse variation (proportion) 55

2.6 Ratios 59

2.7 Ratio and proportion 65

2.8 Dividing in a given ratio 69

2.9 Review 73

Answers 76

3 Percentages 81

3.1 Overview 82

3.2 Converting percentages 83

3.3 Percentage quantities and percentage error 87

3.4 Application of percentages 90

3.5 Profit and loss 95

3.6 Review 99

Answers 101

4 Linear and simultaneous equations 103

4.1 Overview 104

4.2 Algebraic substitution and transposition 105

4.3 Linear equations 111

4.4 Linear modelling 116

4.5 Solving simultaneous equations graphically 121

4.6 Solving simultaneous equations by substitution 127

4.7 Solving simultaneous equations by elimination 130

4.8 Review 136

Answers 139

5 Data collection and organisation 145

5.1 Overview 146

5.2 Types of data 147

5.3 Collecting, organising and displaying data 150

5.4 Histograms and frequency polygons 161

5.5 Contemporary representation of data 167

5.6 Stem-and-leaf plots 178

5.7 Five-number summary and boxplots 184

5.8 Graphical methods of misrepresenting data 188

5.9 Review 196

Answers 201

6 Measures of central tendency and spread 211

6.1 Overview 212

6.2 Measures of central tendency 213

6.3 Measures of spread 224

6.4 Outliers 238

6.5 Applications of measures of central tendency 244

6.6 Review 249

Answers 254

7 Comparing data sets and long-term prediction 257

7.1 Overview 258

7.2 Constructing boxplots 259

7.3 Comparing parallel boxplots 265

7.4 Comparing back-to-back stem plots 270

7.5 Comparing histograms 276

7.6 The line of best fit 284

7.7 Making predictions using a line of best fit 296

7.8 Review 306

Answers 314

8 Simulations and simple probability 327

8.1 Overview 328

8.2 Theoretical probability and sample spaces 329

8.3 Multi-stage experiments 336

8.4 Relative frequency, simulations and long-term data 343

8.5 Review 355

Answers 359

9 Interest and loans 365

9.1 Overview 366

9.2 Simple interest 367

9.3 Compound interest 375

9.4 Comparing simple and compound interest 382

9.5 Comparing interest, rental and loan costs 392

9.6 Review 399

Answers 402

10 Financial and consumer mathematics 407

10.1 Overview 408

10.2 Taxation and superannuation 409

10.3 Business income and expenditure 418

10.4 Financial products 428

10.5 Financial and economic data 440

10.6 Review 447

Answers 451

11 Scales, plans and models 455

11.1 Overview 456

11.2 Reading and interpreting scale drawings 457

11.3 Calculating measurements from scale drawings 462

11.4 Creating scale drawings 472

11.5 Review 482

Answers 486

12 Right-angled triangles 489

12.1 Overview 490

12.2 Pythagoras’ theorem 491

12.3 Trigonometric ratios - sine, cosine and tangent 496

12.4 Calculating unknown side lengths of right-angled triangles 502

12.5 Calculating unknown angles in right-angled triangles 509

12.6 Angles of elevation and depression 514

12.7 Review 520

Answers 524

13 Measurement 527

13.1 Overview 528

13.2 Units of measurement 529

13.3 Areas of composite figures 537

13.4 Surface areas of pyramids and irregular solids 545

13.5 Limits of accuracy 552

13.6 Scientific notation and significant figures 559

13.7 Review 566

Answers 570

14 Volume 573

14.1 Overview 574

14.2 Review of volume of prisms, units of volume and capacity 575

14.3 Volume of cylinders and spheres 582

14.4 Volume of composite shapes 586

14.5 Review 591

Answers 595

15 Shapes 597

15.1 Overview 598

15.2 Polygons 599

15.3 Transformations 602

15.4 Similarity 614

15.5 Symmetry 617

15.6 Review 624

Answers 630

Glossary 639

Index 645