Mathematics for Australia 12 Essential Mathematics

Mathematics for Australia 12 Essential Mathematics

1 GEOMETRY 9
A 2-dimensional shapes 11
B 3-dimensional solids 18
C Sketching solids 23
D Views of solids 27
E Nets of solids 29
Review set 1A 32
Review set 1B 33
2 LENGTH AND AREA 35
A Metric length 36
B Imperial length 39
C Perimeter 42
D Area 46
E Area formulae 48
F Areas of irregular shapes 54
Review set 2A 60
Review set 2B 61
3 SCALE DIAGRAMS 63
A Scale factor 65
B Scale diagrams 66
C Problems involving bearings 73
Review set 3A 76
Review set 3B 77
4 PYTHAGORAS’ THEOREM 79
A Solving x² = k 80
B Pythagoras’ theorem 82
C The converse of Pythagoras’ theorem 87
D Problem solving 89
Review set 4A 94
Review set 4B 95
5 FURTHER MEASUREMENT 97
A Surface area 98
B Volume 104
C Capacity 110
D Mass 113
E Density 117
Review set 5A 120
Review set 5B 121
6 RIGHT ANGLED TRIANGLE TRIGONOMETRY 123
A Labelling right angled triangles 124
B The trigonometric ratios 125
C Finding sides and angles 128
D Problem solving using trigonometry 132
Review set 6A 137
Review set 6B 138
7 NON-RIGHT ANGLED TRIANGLE TRIGONOMETRY 139
A Trigonometric ratios of obtuse angles 140
B The cosine rule 142
C The sine rule 145
D Problem solving 148
Review set 7A 150
Review set 7B 151
8 BUSINESS APPLICATIONS 153
A Planning business premises 154
B Costing calculations 159
C Depreciation 166
D Insurance 171
E Cost of goods sold 175
F Profit and loss statements 176
G Break-even analysis 180
H Business structures and taxation 185
Review set 8A 188
Review set 8B 190
9 LINE GRAPHS 193
A The Cartesian plane 194
B Graphing linear relationships 196
C Graphing lines from equations 200
D Line graphs 203
E The intersection of line graphs 209
Review set 9A 211
Review set 9B 212
10 PROBABILITY 215
A Probability 216
B Experimental probability 218
C Sample space 223
D Theoretical probability 225
E Compound events 229
F Tree diagrams 234
G Simulations 236
Review set 10A 241
Review set 10B 243
11 STATISTICS 245
A Sampling 246
B Displaying data 255
C Measuring the centre of data 257
D Measuring the spread of data 262
E Back-to-back stem plots 268
F Parallel box plots 271
Review set 11A 275
Review set 11B 278
12 LINEAR CORRELATION 281
A Correlation 282
B Measuring correlation 286
C Line of best fit by eye 294
D Least squares regression line 298
Review set 12A 302
Review set 12B 304
13 INVESTMENTS 307
A Simple interest 308
B Compound interest 311
C Future value annuities 320
D Tax and inflation 326
E Superannuation 331
Review set 13A 335
Review set 13B 336
14 LOANS 339
A Reducing balance loans 340
B Home loans 344
C Strategies to minimise interest 347
D Comparing loans 354
Review set 14A 357
Review set 14B 358
15 EARTH GEOMETRY AND TIME ZONES 361
A Latitude and longitude 362
B Distance on the Earth’s surface 366
C Time zones 370
Review set 15A 375
Review set 15B 376
ANSWERS 377