# 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