Jacaranda Maths Quest 12 General Mathematics VCE Units 3&4 7E (learnON & Print)

Part of the series Maths Quest VCE.

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Jacaranda Maths Quest 12 General Mathematics VCE Units 3 and 4

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Table of Contents

About This Resource vii

Acknowledgements xiv

1 Investigating data distributions 1

1.1 Overview 2

1.2 Types of data 3

1.3 Stem plots 8

1.4 Dot plots, frequency tables, histograms, bar charts and logarithmic scales 17

1.5 Describing stem plots and histograms 32

1.6 Summary statistics 39

1.7 The five-number summary and boxplots 49

1.8 The mean of a sample 58

1.9 Standard deviation of a sample 65

1.10 The 68-95-99�7% rule and z-scores 73

1.11 Review 84

Answers 97

2 Investigating associations between two variables 109

2.1 Overview 110

2.2 Response and explanatory variables 111

2.3 Contingency (two-way) frequency tables and segmented bar charts 114

2.4 Back-to-back stem plots 123

2.5 Parallel boxplots and dot plots 129

2.6 Scatterplots 135

2.7 Estimating and interpreting Pearson’s product-moment correlation coefficient 145

2.8 Calculating r and the coefficient of determination, r 2 150

2.9 Cause and effect 156

2.10 Review 162

Answers 170

3 Investigating and modelling linear associations 181

3.1 Overview 182

3.2 Least squares line of best fit 183

3.3 Interpretation, interpolation and extrapolation 191

3.4 Residual analysis 199

3.5 Transforming to linearity 208

3.6 Review 220

Answers 229

4 Investigating and modelling time series data 237

4.1 Overview 238

4.2 Time series plots and trends 239

4.3 Fitting the least squares line and forecasting 249

4.4 Smoothing using the moving mean with an odd number of points 258

4.5 Smoothing using the moving mean with an even number of points 264

4.6 Median smoothing from a graph 270

4.7 Seasonal adjustment 276

4.8 Review 289

Answers 299

5 Modelling depreciation of assets using recursion 319

5.1 Overview 320

5.2 A first-order linear recurrence relation 321

5.3 Modelling flat rate depreciation with a recurrence relation 325

5.4 Modelling reducing balance depreciation with a recurrence relation 331

5.5 Modelling unit cost depreciation with a recurrence relation 339

5.6 Review 348

Answers 353

6 Modelling compound interest investments and loans using recursion 359

6.1 Overview 360

6.2 Simple interest 361

6.3 Compound interest as a geometric recurrence relation 367

6.4 Compound interest using a rule 372

6.5 Calculating rate or time for compound interest 378

6.6 Nominal and effective annual interest rate 383

6.7 Review 388

Answers 392

7 Modelling reducing balance loans, annuities and perpetuities using recursion 395

7.1 Overview 396

7.2 Modelling reducing balance loans with recurrence relations 397

7.3 Solving reducing balance loan problems using finance solver 404

7.4 The effect of rate and repayment changes on reducing balance loans 417

7.5 Annuities and perpetuities 430

7.6 Annuity investments 441

7.7 Review 450

Answers 456

8 Matrices 461

8.1 Overview 462

8.2 Matrix representation 463

8.3 Addition, subtraction and scalar operations with matrices 471

8.4 Multiplying matrices 483

8.5 The inverse of a matrix and its determinant 497

8.6 Dominance and communication matrices 505

8.7 Transition matrices and Leslie matrices 516

8.8 Review 537

Answers 547

9 Undirected graphs, networks and trees 555

9.1 Overview 556

9.2 Basic concepts of a network 557

9.3 Planar graphs and Euler’s formula 567

9.4 Walks, trails, paths, cycles and circuits 576

9.5 Trees and their applications 587

9.6 Review 603

Answers 611

10 Directed graphs and network flow 617

10.1 Overview 618

10.2 Precedence tables and activity networks 619

10.3 Critical path analysis with backward scanning and crashing 630

10.4 Flow problems 647

10.5 Bipartite graphs and allocation problems 659

10.6 Review 672

Answers 683

Glossary 691

Index 697