Cambridge Mathematics Applications Units 1&2 for Western Australia

Introduction viii
Overview ix
Acknowledgements xiii
1 Computation and practical arithmetic 1
1A Order of operations . . . . . . . . . . . . . . . . . . . . . 2
1B Directed numbers . . . . . . . . . . . . . . . . . . . . . . 3
1C Powers and roots . . . . . . . . . . . . . . . . . . . . . . 5
1D Approximations, decimal places and significant figures . . . 6
1E Currency exchange rates . . . . . . . . . . . . . . . . . . 13
1F Percentages . . . . . . . . . . . . . . . . . . . . . . . . . 18
1G Percentage increase and decrease . . . . . . . . . . . . . 22
1H Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1I Expressing ratios in their simplest form . . . . . . . . . . . 29
1J Unit cost method . . . . . . . . . . . . . . . . . . . . . . 32
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Key ideas and chapter summary . . . . . . . . . . . . . . 34
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 35
Short-answer questions . . . . . . . . . . . . . . . . . 35
Extended-response questions . . . . . . . . . . . . . . . 37
2 Consumer arithmetic 40
2A Percentages and applications . . . . . . . . . . . . . . . . 41
2B Simple interest . . . . . . . . . . . . . . . . . . . . . . . 47
2C Rearranging the simple interest formula . . . . . . . . . . 58
2D Compound interest . . . . . . . . . . . . . . . . . . . . . 62
2E Time payment agreements . . . . . . . . . . . . . . . . . . 71
2F Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
2G Calculating income and preparing personal budgets . . . . . 80
2H Government allowances and pensions . . . . . . . . . . . . 90
2I Shares and dividends . . . . . . . . . . . . . . . . . . . . 94
2J Financial investigation: buying a car . . . . . . . . . . . . . 98
2K Using spreadsheets . . . . . . . . . . . . . . . . . . . . . 98
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Key ideas and chapter summary . . . . . . . . . . . . . . 103
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 104
Short-answer questions . . . . . . . . . . . . . . . . . 105
Extended-response questions . . . . . . . . . . . . . . . 107
3 Shape and measurement 109
3A Pythagoras’ theorem . . . . . . . . . . . . . . . . . . . . 110
3B Pythagoras’ theorem in three dimensions . . . . . . . . . . 114
3C Mensuration: perimeter and area . . . . . . . . . . . . . . 121
3D Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3E Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
3F Volume of a cone . . . . . . . . . . . . . . . . . . . . . . 140
3G Volume of a pyramid . . . . . . . . . . . . . . . . . . . . . 143
3H Volume of a sphere . . . . . . . . . . . . . . . . . . . . . 146
3I Surface area . . . . . . . . . . . . . . . . . . . . . . . . 147
3J Similar figures . . . . . . . . . . . . . . . . . . . . . . . 153
3K Similar triangles . . . . . . . . . . . . . . . . . . . . . . 160
3L Similar solids . . . . . . . . . . . . . . . . . . . . . . . . 164
3M Problem solving and modelling . . . . . . . . . . . . . . . 167
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
Key ideas and chapter summary . . . . . . . . . . . . . . 169
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 170
Short-answer questions . . . . . . . . . . . . . . . . . 171
Extended-response questions . . . . . . . . . . . . . . . 173
4 Linear and non-linear expressions 176
4A Substitution of values into a formula . . . . . . . . . . . . . 177
4B Using formulas . . . . . . . . . . . . . . . . . . . . . . . 183
4C Constructing a table of values . . . . . . . . . . . . . . . . 186
4D Solving linear equations with one unknown . . . . . . . . . 192
4E Developing a formula: setting up linear equations in
one unknown . . . . . . . . . . . . . . . . . . . . . . . . 196
4F Developing a formula: setting up linear equations in
two unknowns . . . . . . . . . . . . . . . . . . . . . . . . 200
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Key ideas and chapter summary . . . . . . . . . . . . . . 203
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 203
Short-answer questions . . . . . . . . . . . . . . . . . 203
Extended-response questions . . . . . . . . . . . . . . . 205
5 Matrices 207
5A The basics of a matrix . . . . . . . . . . . . . . . . . . . . 208
5B Using matrices to model (represent) practical situations . . . 215
5C Adding and subtracting matrices . . . . . . . . . . . . . . 217
5D Scalar multiplication . . . . . . . . . . . . . . . . . . . . 220
5E Matrix multiplication . . . . . . . . . . . . . . . . . . . . 225
5F Applications of matrices . . . . . . . . . . . . . . . . . . . 232
5G Communications and connections . . . . . . . . . . . . . . 236
5H Identity matrices . . . . . . . . . . . . . . . . . . . . . . 240
5I Extended application and problem-solving tasks . . . . . . . 244
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Key ideas and chapter summary . . . . . . . . . . . . . . 245
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 246
Short-answer questions . . . . . . . . . . . . . . . . . 246
Extended-response questions . . . . . . . . . . . . . . . 248
6 Investigating and comparing data distributions 250
6A Types of data . . . . . . . . . . . . . . . . . . . . . . . . 251
6B Displaying and describing categorical data distributions . . . 254
6C Interpreting and describing frequency tables
and bar charts . . . . . . . . . . . . . . . . . . . . . . . 258
6D Displaying and describing numerical data . . . . . . . . . . 262
6E Characteristics of distributions of numerical data:
shape, location and spread . . . . . . . . . . . . . . . . . 273
6F Dot plots and stem-and-leaf plots . . . . . . . . . . . . . . 275
6G Summarising data . . . . . . . . . . . . . . . . . . . . . . 280
6H Boxplots . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
6I Comparing the distribution of a numerical variable across two
or more groups . . . . . . . . . . . . . . . . . . . . . . . 300
6J Statistical investigation . . . . . . . . . . . . . . . . . . . 306
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
Key ideas and chapter summary . . . . . . . . . . . . . . 307
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 308
Short-answer questions . . . . . . . . . . . . . . . . . 309
Extended-response questions . . . . . . . . . . . . . . . 313
7 The normal distribution 315
7A The normal distribution and the 68–95–99.7% rule . . . . . . 316
7B Determination of other percentages using a CAS . . . . . . 320
7C Quantiles . . . . . . . . . . . . . . . . . . . . . . . . . . 326
7D Standard scores . . . . . . . . . . . . . . . . . . . . . . 332
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Key ideas and chapter summary . . . . . . . . . . . . . . 337
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 337
Short-answer questions . . . . . . . . . . . . . . . . . 337
Extended-response questions . . . . . . . . . . . . . . . 339
8 Right-angled trigonometry 340
8A Trigonometry basics . . . . . . . . . . . . . . . . . . . . . 341
8B Finding an unknown side in a right-angled triangle . . . . . . 345
8C Finding an angle in a right-angled triangle . . . . . . . . . . 348
8D Applications of right-angled triangles . . . . . . . . . . . . 353
8E Angles of elevation and depression . . . . . . . . . . . . . 356
8F Bearings and navigation . . . . . . . . . . . . . . . . . . . 361
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Key ideas and chapter summary . . . . . . . . . . . . . . 366
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 367
Short-answer questions . . . . . . . . . . . . . . . . . 367
Extended-response questions . . . . . . . . . . . . . . . 371
9 Non-right-angled trigonometry 372
9A The area of a triangle . . . . . . . . . . . . . . . . . . . . 373
9B The sine rule . . . . . . . . . . . . . . . . . . . . . . . . 379
9C The cosine rule . . . . . . . . . . . . . . . . . . . . . . . 389
9D Extended application and problem-solving task . . . . . . . 396
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
Key ideas and chapter summary . . . . . . . . . . . . . . 398
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 399
Short-answer questions . . . . . . . . . . . . . . . . . 399
Extended-response questions . . . . . . . . . . . . . . . 402
10 Linear graphs and models 404
10A Drawing straight-line graphs . . . . . . . . . . . . . . . . 405
10B Determining the slope of a straight line . . . . . . . . . . . 410
10C The intercept–slope form of the equation of a straight line . 415
10D Finding the equation of a straight-line graph from its intercept
and slope . . . . . . . . . . . . . . . . . . . . . . . . . . 418
10E Finding the equation of a straight-line graph using two points
on the graph . . . . . . . . . . . . . . . . . . . . . . . . 420
10F Finding the equation of a straight-line graph from two points
using a CAS calculator . . . . . . . . . . . . . . . . . . . 421
10G Linear modelling . . . . . . . . . . . . . . . . . . . . . . 425
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 436
Key ideas and chapter summary . . . . . . . . . . . . . . 436
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 437
Short-answer questions . . . . . . . . . . . . . . . . . 437
Extended-response questions . . . . . . . . . . . . . . . 441
11 Simultaneous linear equations 443
11A Finding the point of intersection of two linear graphs . . . . 444
11B Solving simultaneous linear equations algebraically . . . . . 448
11C Solving simultaneous linear equations using CAS . . . . . . 453
11D Practical applications of simultaneous equations . . . . . . 455
11E Problem solving and modelling . . . . . . . . . . . . . . . 460
Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
Key ideas and chapter summary . . . . . . . . . . . . . . 462
Skills check . . . . . . . . . . . . . . . . . . . . . . . . 462
Short-answer questions . . . . . . . . . . . . . . . . . 462
Extended-response questions . . . . . . . . . . . . . . . 464
Glossary 466
Answers 473