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  • Maths Quest 12 Further Mathematics 5E VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Further Mathematics Units 3 and 4 2E

Maths Quest 12 Further Mathematics 5E VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Further Mathematics Units 3 and 4 2E

Maths Quest 12 Further Mathematics 5E VCE Units 3 and 4 & eBookPLUS + StudyOn VCE Further Mathematics Units 3 and 4 2E
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Author/s
Barnes
ISBN13 9780730321736
Pub date November 2015
Pages 808
RRP $89.95
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Introduction viii

About eBookPLUS and studyON xi

Acknowledgements xii

topic 1 Univariate data 2

1.1 Kick off with CAS 3

1.2 Types of data 4

1.3 Stem plots 7

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

1.5 Describing the shape of stem plots and histograms 25

1.6 The median, the interquartile range, the range and the mode 31

1.7 Boxplots 38

1.8 The mean of a sample 46

1.9 Standard deviation of a sample 54

1.10 Populations and simple random samples 59

1.11 The 68–95–99.7% rule and z-scores 63

1.12 Review 73

Answers 74

topic 2 Comparing data sets 82

2.1 Kick off with CAS 83

2.2 Back-to-back stem plots 84

2.3 Parallel boxplots and dot plots 89

2.4 Two-way (contingency) frequency tables and segmented bar charts 93

2.5 Review 101

Answers 102

topic 3 Introduction to regression 108

3.1 Kick off with CAS 109

3.2 Response (dependent) and explanatory (independent) variables 110

3.3 Scatterplots 112

3.4 Pearson’s product–moment correlation coefficient 120

3.5 Calculating r and the coefficient of determination 123

3.6 Fitting a straight line — least-squares regression 131

3.7 Interpretation, interpolation and extrapolation 137

3.8 Residual analysis 143

3.9 Transforming to linearity 149

3.10 Review 157

Answers 158

topic 4 Time series 168

4.1 Kick off with CAS 169

4.2 Time series and trend lines 170

4.3 Trend lines and forecasting 174

4.4 Smoothing time series 182

4.5 Smoothing with an even number of points 188

4.6 Median smoothing from a graph 192

4.7 Seasonal adjustment 196

4.8 Review 207

Answers 208

topic 5 Recurrence relations 220

5.1 Kick off with CAS 221

5.2 Generating the terms of a first-order recurrence relation 222

5.3 First-order linear recurrence relations 226

5.4 Graphs of first-order recurrence relations 231

5.5 Review 240

Answers 241

topic 6 Interest and depreciation 244

6.1 Kick off with CAS 245

6.2 Simple interest 246

6.3 Compound interest tables 252

6.4 Compound interest formula 256

6.5 Finding rate or time for compound interest 262

6.6 Flat rate depreciation 266

6.7 Reducing balance depreciation 271

6.8 Unit cost depreciation 278

6.9 Review 285

Answers 286

topic 7 Loans, investments and asset values 292

7.1 Kick off with CAS 293

7.2 Reducing balance loans I 294

7.3 Reducing balance loans II 302

7.4 Reducing balance loans III 310

7.5 Reducing balance and flat rate loan comparisons 323

7.6 Effective annual interest rate 328

7.7 Perpetuities 331

7.8 Annuity investments 338

7.9 Review 352

Answers 353

topic 8 Matrices 358

8.1 Kick off with CAS 359

8.2 Matrix representation 360

8.3 Addition, subtraction and scalar operations with matrices 367

8.4 Multiplying matrices 377

8.5 Multiplicative inverse and solving matrix equations 390

8.6 Dominance and communication matrices 396

8.7 Application of matrices to simultaneous equations 405

8.8 Transition matrices 412

8.9 Review 429

Answers 430

topic 9 Undirected graphs and networks 438

9.1 Kick off with CAS 439

9.2 Basic concepts of a network 440

9.3 Planar graphs and Euler’s formula 448

9.4 Walks, trails, paths, cycles and circuits 454

9.5 Trees and their applications 462

9.6 Review 475

Answers 476

topic 10 Directed graphs and networks 480

10.1 Kick off with CAS 481

10.2 Critical path analysis 482

10.3 Critical path analysis with backward scanning and crashing 492

10.4 Network flow 507

10.5 Assignment problems and bipartite graphs 516

10.6 Review 526

Answers 527

topic 11 Geometry: similarity and mensuration 534

11.1 Kick off with CAS 535

11.2 Properties of angles, triangles and polygons 536

11.3 Area and perimeter I 542

11.4 Area and perimeter II 548

11.5 Great circles 557

11.6 Total surface area 560

11.7 Volume of prisms, pyramids and spheres 567

11.8 Similar figures 576

11.9 Similar triangles 581

11.10 Triangulation — similarity 588

11.11 Area and volume scale factors 593

11.12 Time zones 602

11.13 Review 605

Answers 606

topic 12 Trigonometry 610

12.1 Kick off with CAS 611

12.2 Trigonometry 612

12.3 Pythagorean triads 617

12.4 Three-dimensional Pythagoras’ theorem 620

12.5 Trigonometric ratios 624

12.6 The sine rule 632

12.7 Ambiguous case of the sine rule 638

12.8 The cosine rule 642

12.9 Special triangles 646

12.10 Area of triangles 649

12.11 Review 655

Answers 656

topic 13 Applications of geometry and trigonometry 660

13.1 Kick off with CAS 661

13.2 Angles 662

13.3 Angles of elevation and depression 666

13.4 Bearings 671

13.5 Navigation and specification of locations 677

13.6 Triangulation — cosine and sine rules 686

13.7 Review 694

Answers 695

topic 14 Construction and interpretation of graphs 698

14.1 Kick off with CAS 699

14.2 Constructing and interpreting straight-line graphs 700

14.3 Line segments and step functions 710

14.4 Simultaneous equations and break-even point 717

14.5 Interpreting non-linear graphs 723

14.6 Constructing non-linear relations and graphs 729

14.7 Review 735

Answers 736

topic 15 Linear inequalities and linear programming 744

15.1 Kick off with CAS 745

15.2 Linear inequalities 746

15.3 Simultaneous linear inequalities 749

15.4 Linear programming 754

15.5 Applications 766

15.6 Review 780

Answers 781

Index 788