# Jacaranda Maths Quest 12 General Mathematics Units 3&4 for Queensland eBookPLUS & Print + StudyOn General Mathematics Units 3&4 for Qld (Book Code)

 Author(s): Morris ISBN: 9780730380207 Pub date: August 2019 RRP: \$89.95
Jacaranda Maths Quest 12 General Mathematics Units 3 & 4 for Queensland Print & eBookPLUS + studyON
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Acknowledgements xii

Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry 1

Topic 1 Bivariate Data Analysis

1 Identifying and describing associations between two variables 1

1.1 Overview 1

1.2 Bivariate data 2

1.3 Two-way frequency tables 6

1.4 Scatterplots 15

1.5 Pearson’s correlation coefficient (r) 24

1.6 Review: exam practice 32

2 Fitting a linear model to numerical data 41

2.1 Overview 41

2.2 Review of the general equation of a straight line 42

2.3 Fitting a least-squares line to data 48

2.4 The coefficient of determination and residual plots 58

2.5 Association and causation 67

2.6 Review: exam practice 72

Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry

Topic 1 Bivariate data analysis 86

Topic 2 Time Series Analysis

3 Time series analysis 87

3.1 Overview 87

3.2 Constructing and describing time series plots 88

3.3 Fitting a least-squares line to time series data 92

3.4 Smoothing time series data using simple moving averages 96

3.5 Seasonal indices and deseasonalising data 108

3.6 Review: exam practice 119

Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry

Topic 2 Time series analysis 134

Topic 3 Growth and Decay in Sequences

4 The arithmetic sequence 135

4.1 Overview 135

4.2 Using recursion to generate an arithmetic sequence 136

4.3 Using the rule for the nth term of an arithmetic sequence to make predictions 143

4.4 Simple interest and other applications of arithmetic sequences 148

4.5 Straight-line and unit cost depreciation 156

4.6 Review: exam practice 163

5 The geometric sequence 171

5.1 Overview 171

5.2 Using recursion to generate a geometric sequence 172

5.3 Using the rule for the nth term of a geometric sequence 180

5.4 Compound interest and other applications of geometric sequences 185

5.5 Reducing balance depreciation 190

5.6 Review: exam practice 196

Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry

Topic 3 Growth and decay in sequences 202

Pratice Assessment 1

Problem solving and modelling task 203

Topic 4 Earth Geometry and Time Zones

6 Earth geometry and time zones 207

6.1 Overview 207

6.2 Latitude and longitude 208

6.3 Distances on the Earth’s surface 216

6.4 Time zones 220

6.5 Review: exam practice 224

Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry

Topic 4 Earth geometry and time zones 231

Pratice Assessment 2

Unit 3 Examination 232

Unit 4 Investing and Networking 245

Topic 1 Loans, Investments and Annuities

7 Compound interest loans and investments 245

7.1 Overview 245

7.2 Modelling a compound interest loan or investment using a recurrence relation 246

7.3 Effective annual rate of interest 250

7.4 Compound interest problems: future values and present values 253

7.5 Compound interest problems: interest rates and number of compounding periods 256

7.6 Review: exam practice 261

8 Reducing balance loans 267

8.1 Overview 267

8.2 Modelling a reducing balance loan using a recurrence relation 268

8.3 The effect of the interest rate and repayment amount on the time taken to repay the loan 273

8.4 Solving problems involving reducing balance loans with and without the use of technology 277

8.5 Review: exam practice 286

9 Annuities and perpetuities 293

9.1 Overview 293

9.2 Introduction to annuities 294

9.3 Using recurrence relations to model annuities 299

9.4 Annuity and perpetuity calculations 309

9.5 Review: exam practice 319

Revision Unit 4 Investing and Networking

Topic 1 Loans, investments and annuities 327

Topic 2 Graphs and Networks

10 Graphs and networks 328

10.1 Overview 328

10.2 Graphs, associated terminology and the adjacency matrix 329

10.3 Planar graphs 342

10.4 Connected graphs 350

10.5 Weighted graphs and trees 358

10.6 Review: exam practice 368

Revision Unit 4 Investing and Networking

Topic 2 Graphs and networks 389

Topic 3 Networks and Decision Mathematics

11 Networks and decision mathematics 390

11.1 Overview 390

11.2 Critical paths 391

11.3 Critical path analysis with backward scanning 402

11.4 Network flow 410

11.5 Bipartite graphs and the Hungarian algorithm 423

11.6 Review: exam practice 431

Revision Unit 4 Investing and Networking

Topic 3 Networks and decision mathematics 444

Pratice Assessment 3

Unit 4 Examination 445

Pratice Assessment 4

Units 3 & 4 Examination 456

Glossary 482

Index 486