About this resource viii
About eBookPLUS and studyON xi
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
Answers 37
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
Answers 78
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
Answers 125
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
Answers 167
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
Answers 199
Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry
TOPIC 3 Growth and decay in sequences 202
Practice 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
Answers 229
Revision Unit 3 Bivariate Data, Sequences and Change, and Earth Geometry
TOPIC 4 Earth geometry and time zones 231
Practice 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
Answers 264
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
Answers 290
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
Answers 323
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
Answers 377
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
Answers 437
Revision Unit 4 Investing and Networking
TOPIC 3 Networks and decision mathematics 444
Practice Assessment 3
Unit 4 Examination 445
Practice Assessment 4
Units 3 & 4 Examination 456
Glossary 482
Index 486
