Jacaranda Maths Quest 12 Further Mathematics VCE U3&4 6E eBookPLUS & Print + StudyOn VCE Further Mathematics Units 3&4 2E (Book Code)

About this resource ix

About eBookPLUS and studyON xii

Acknowledgements xiii

1 Investigating data distributions 1

1.1 Overview 1

1.2 Types of data 3

1.3 Stem plots 6

1.4 Dot plots, frequency tables and histograms, and bar charts 14

1.5 Describing the shape of stem plots and histograms 29

1.6 The median, the interquartile range, the range and the mode 35

1.7 Boxplots 44

1.8 The mean of a sample 53

1.9 Standard deviation of a sample 57

1.10 Populations and simple random samples 64

1.11 The 68–95–99.7% rule and z-scores 68

1.12 Review: exam practice 78

Answers 89

2 Investigating associations between two variables 99

2.1 Overview 99

2.2 Response and explanatory variables 101

2.3 Two-way (contingency) frequency tables and segmented bar charts 103

2.4 Back-to-back stem plots 110

2.5 Parallel boxplots and dot plots 115

2.6 Scatterplots 120

2.7 Pearson’s product–moment correlation coefficient 128

2.8 Calculating r and the coefficient of determination, r² 133

2.9 Correlation and causation 139

2.10 Review: exam practice 142

Answers 148

3 Investigating and modelling linear associations 157

3.1 Overview 157

3.2 Fitting a straight line — least-squares regression 159

3.3 Interpretation, interpolation and extrapolation 166

3.4 Residual analysis 172

3.5 Transforming to linearity 179

3.6 Review: exam practice 189

4 Investigating and modelling time series data 200

4.1 Overview 200

4.2 Time series and trend lines 202

4.3 Trend lines and forecasting 208

4.4 Smoothing time series 216

4.5 Smoothing with an even number of points 222

4.6 Median smoothing from a graph 227

4.7 Seasonal adjustment 231

4.8 Review: exam practice 243

Answers 250

Revision Topics 1 to 4 266

5 Depreciation of assets 267

5.1 Overview 267

5.2 Generating the terms of a first-order recurrence relation 269

5.3 Modelling flat rate depreciation with a recurrence relation 272

5.4 Modelling reducing balance depreciation with a recurrence relation 276

5.5 Modelling unit cost depreciation with a recurrence relation 283

5.6 Review: exam practice 290

Answers 293

6 Simple and compound interest — investments and loans 298

6.1 Overview 298

6.2 Simple interest 300

6.3 Compound interest as a geometric recurrence relation 305

6.4 Compound interest rule 309

6.5 Finding rate or time for compound interest 315

6.6 Effective annual interest rate 319

6.7 Review: exam practice 323

Answers 325

7 Reducing balance loans, annuities and perpetuities 327

7.1 Overview 327

7.2 Modelling reducing balance loans with recurrence relations 329

7.3 Solving problems involving reducing balance loans using a Finance Solver 335

7.4 The effect of rate and repayment changes on reducing balance loans 347

7.5 Annuities and perpetuities 357

7.6 Annuity investments 367

7.7 Review: exam practice 375

Answers 378

Revision Topics 5 to 7 382

8 Matrices 383

8.1 Overview 383

8.2 Matrix representation 385

8.3 Addition, subtraction and scalar operations with matrices 393

8.4 Multiplying matrices 403

8.5 Multiplicative inverse and solving matrix equations 416

8.6 Dominance and communication matrices 422

8.7 Application of matrices to simultaneous equations 431

8.8 Transition matrices 439

8.9 Review: exam practice 456

Answers 463

Revision Topic 8 470

9 Undirected graphs and networks 471

9.1 Overview 471

9.2 Basic concepts of a network 473

9.3 Planar graphs and Euler’s formula 481

9.4 Walks, trails, paths, cycles and circuits 488

9.5 Trees and their applications 497

9.6 Review: exam practice 511

Answers 518

10 Directed graphs and networks 523

10.1 Overview 523

10.2 Critical path analysis 524

10.3 Critical path analysis with backward scanning and crashing 535

10.4 Network flow 551

10.5 Assignment problems and bipartite graphs 561

10.6 Review: exam practice 572

Answers 581

Revision Topics 9 to 10 588

11 Geometry and measurement 589

11.1 Overview 589

11.2 Review of properties of angles, triangles and polygons 590

11.3 Review of area and perimeter of composite shapes 597

11.4 Total surface area 607

11.5 Volume of prisms, pyramids and spheres 614

11.6 Similar figures 623

11.7 Similar triangles 629

11.8 Triangulation — similarity 636

11.9 Area and volume scale factors 640

11.10 Review: exam practice 650

Answers 655

12 Geometry and trigonometry 658

12.1 Overview 658

12.2 Two- and three-dimensional Pythagoras’ theorem 659

12.3 Trigonometric ratios 667

12.4 The sine rule 675

12.5 Ambiguous case of the sine rule 683

12.6 The cosine rule 687

12.7 Area of triangles 691

12.8 Angles of elevation and depression 697

12.9 Bearings and specification of location 703

12.10 Triangulation — cosine and sine rules 712

12.11 Review: exam practice 721

Answers 730

13 Spherical geometry 733

13.1 Overview 733

13.2 Circle mensuration 735

13.3 Right-angled triangles within a sphere 740

13.4 The earth as a sphere 744

13.5 Time zones 750

13.6 Review: exam practice 753

Answers 756

Revision Topics 11 to 13 758

14 Construction and interpretation of graphs 759

14.1 Overview 759

14.2 Constructing and interpreting straight-line graphs 760

14.3 Line segments and step functions 771

14.4 Simultaneous equations and break-even point 778

14.5 Interpreting non-linear graphs 785

14.6 Constructing non-linear relations and graphs 792

14.7 Review: exam practice 798

Answers 804

15 Linear programming 813

15.1 Overview 813

15.2 Linear inequalities 815

15.3 Simultaneous linear inequalities 819

15.4 Linear programming 825

15.5 Applications 838

15.6 Review: exam practice 851

Answers 856

Revision Topics 14 to 15 865

Glossary 866

Index 874