This book presents an alternative course for Year 10 students. The particular aim of the book is to show the everyday applications of mathematics in the context of the world around us.
There are 19 ’core’ chapters. These chapters cover the basic skills of mathematics appropriate for Year 10 students who may go on to complete a Mathematical Applications or a Foundation Mathematics course at Year 11.
In addition, there are four ’option’ chapters which are entirely focused on particular themes. Throughout these chapters, the emphasis is on relating the theory and application of mathematics to real-life:
The authors hope that by presenting a course of mathematics in this way, students may understand the relevance and importance of mathematics in everyday life.
By clicking on the CD-link icon, students can access a range of interactive features, including:
The CD is ideal for independent study. Students can revisit concepts taught in class and also discover new ideas for themselves. It is fantastic for demonstrations and simulations. The CD also contains the text of the book – students can leave the textbook at school and keep the CD at home to save carrying a heavy textbook to and from school each day.
| 1 | MONEY | 9 | |
| A | Spending | 10 | |
| B | Methods of payment | 12 | |
| C | Credit cards | 17 | |
| D | Banking | 19 | |
| E | Budgeting | 21 | |
| Review of Chapter 1 | 23 | ||
| 2 | WHOLE NUMBERS AND FRACTIONS | 25 | |
| A | Rounding numbers | 26 | |
| B | Estimation and approximation | 28 | |
| C | Problem solving | 31 | |
| D | Fractions | 32 | |
| Review of Chapter 2 | 37 | ||
| 3 | DECIMALS AND PERCENTAGES | 39 | |
| A | Decimals | 40 | |
| B | Fraction and decimal conversions | 43 | |
| C | Percentage | 44 | |
| D | Working with percentage | 46 | |
| E | Standard form | 48 | |
| Review of Chapter 3 | 51 | ||
| 4 | MEASUREMENT | 53 | |
| A | Reading instruments and meters | 54 | |
| B | Converting length measurements | 56 | |
| C | Perimeter and length | 58 | |
| D | Time | 62 | |
| E | Rates of change | 64 | |
| Review of Chapter 4 | 67 | ||
| 5 | INTERPRETING GRAPHS | 69 | |
| A | Graphical interpretation | 70 | |
| B | Interpreting line graphs | 72 | |
| C | Finding speed from graphs | 74 | |
| D | Conversion graphs | 76 | |
| E | Travel graphs | 77 | |
| F | Time series data | 79 | |
| G | Step graphs | 81 | |
| Review of Chapter 5 | 83 | ||
| 6 | ALEGBRA (EQUATIONS AND FORMULAE) | 85 | |
| A | Simplifyng in algebra | 86 | |
| B | Solutions of equations | 86 | |
| C | Inverse operations | 87 | |
| D | Solving equations | 88 | |
| E | Problem solving with equations | 90 | |
| F | Substitution into formulae | 92 | |
| G | Solving within a formula | 93 | |
| H | Inequalities | 94 | |
| Review of Chapter 6 | 95 | ||
| 7 | PERCENTAGE CHANGE | 97 | |
| A | Using a multiplier | 98 | |
| B | Chain percentage problems | 100 | |
| C | Appreciation | 101 | |
| D | Interest calculations | 102 | |
| E | Depreciation | 109 | |
| Review of Chapter 7 | 111 | ||
| 8 | BUSINESS MATHEMATICS | 113 | |
| A | Profit and loss | 114 | |
| B | Discount | 117 | |
| C | Goods and services tax (GST) | 118 | |
| D | Deductions from earnings | 121 | |
| E | Income tax | 122 | |
| F | Loan repayments | 123 | |
| Review of Chapter 8 | 125 | ||
| 9 | AREA, VOLUME AND MASS | 127 | |
| A | Area | 128 | |
| B | Area formulae | 130 | |
| C | Surface area | 133 | |
| D | Volume | 137 | |
| E | Capacity | 140 | |
| F | Possible project | 143 | |
| G | Mass and density | 143 | |
| H | Accuracy of measurements | 145 | |
| Review of Chapter 9 | 147 | ||
| 10 | TRANSFORMATIONS | 149 | |
| A | Translations | 151 | |
| B | Rotations | 152 | |
| C | Reflections | 155 | |
| D | Enlargements and reductions | 159 | |
| E | Tesselations | 161 | |
| Review of Chapter 10 | 164 | ||
| 11 | RATIO, SCALE DIAGRAMS AND MAPS | 165 | |
| A | Ratios | 166 | |
| B | Scale diagrams | 169 | |
| C | Using scale diagrams | 171 | |
| D | Bearings and directions | 172 | |
| Review of Chapter 11 | 177 | ||
| 12 | ANGLES AND POLYGONS | 179 | |
| A | Classifying angles by size | 180 | |
| B | Angle pairs on parallel lines | 181 | |
| C | Angles at a point and on a line | 184 | |
| D | Triangles | 185 | |
| E | Angles of a quadrilateral | 188 | |
| F | Polygons | 192 | |
| Review of Chapter 12 | 194 | ||
| 13 | PYTHAGORAS’ RULE | 197 | |
| A | The rule of Pythagoras (review) | 199 | |
| B | Further problem solving | 204 | |
| C | Testing for right angles | 208 | |
| D | True bearings and navigation | 209 | |
| Review of Chapter 13 | 211 | ||
| 14 | GEOMETRICAL CONSTRUCTION | 213 | |
| A | Constructing a triangle given its sides | 215 | |
| B | Bisecting angles | 216 | |
| C | Constructing perpendiculars | 217 | |
| D | Angle construction | 221 | |
| E | Finding a circle’s centre | 222 | |
| F | Constructing parallel lines | 223 | |
| G | Regular polygon construction | 226 | |
| Review of Chapter 14 | 227 | ||
| 15 | STATISTICS | 229 | |
| A | Types of data | 231 | |
| B | Organising data | 232 | |
| C | Displaying data | 234 | |
| D | Continuous numerical data | 237 | |
| E | Measuring the middle | 240 | |
| F | Measuring the spread of data | 246 | |
| G | Box-and-whisker plots | 249 | |
| H | Parallel boxplots | 251 | |
| I | Statistics using technology | 253 | |
| Review of Chapter 15 | 255 | ||
| 16 | TRIGONOMETRY | 257 | |
| A | Labelling sides of a right angled triangle | 258 | |
| B | Trigonometric ratios | 261 | |
| C | Using the sine ratio | 262 | |
| D | Using the cosine ratio | 264 | |
| E | Using the tangent ratio | 265 | |
| F | Problem solving with trigonometry | 267 | |
| Review of Chapter 16 | 271 | ||
| 17 | LINEAR GRAPHS | 273 | |
| A | Plotting points | 274 | |
| B | The slope of lines | 276 | |
| C | Plotting graphs from rules | 280 | |
| D | Straight lines (y = mx + c) | 281 | |
| E | Finding equations of lines | 282 | |
| F | The line of best fit | 284 | |
| Review of Chapter 17 | 285 | ||
| 18 | SOLIDS | 287 | |
| A | Solids | 288 | |
| B | Nets of solids | 291 | |
| C | Projections | 292 | |
| D | Perspective drawings | 294 | |
| E | Views | 296 | |
| Review of Chapter 18 | 299 | ||
| 19 | SIMULATIONS AND PROBABILITY | 301 | |
| A | Experimental probability | 303 | |
| B | Estimating probabilities from data | 305 | |
| C | Chance investigations | 307 | |
| D | Probability calculation | 310 | |
| E | Using tree diagrams | 312 | |
| F | Using life tables | 315 | |
| Review of Chapter 19 | 317 | ||
| 20 | THE SHARE MARKET | 319 | |
| A | Introduction | 320 | |
| B | Newspaper share listings | 320 | |
| C | Buying shares | 321 | |
| D | Selling shares | 323 | |
| E | Breakeven price | 325 | |
| F | Capital gain on shares | 327 | |
| G | Dividends on shares | 329 | |
| H | Yield on shares | 330 | |
| I | The all ordinaries index | 333 | |
| Review of Chapter 20 | 334 | ||
| 21 | BUILDING, CONSTRUCTION AND MANUFACTURING | 337 | |
| A | The building sequence | 340 | |
| B | The site and the floor | 340 | |
| C | Building the walls and the roof | 342 | |
| D | The doors | 344 | |
| E | The wall cladding and roof covering | 345 | |
| F | Other jobs | 345 | |
| 22 | MATHEMATICS AND FOOD | 347 | |
| A | Measuring in cooking | 348 | |
| B | Nutritional value | 351 | |
| C | Cooking times | 352 | |
| D | Wastage | 353 | |
| E | Catering | 355 | |
| F | Food production and consumption | 357 | |
| Review of Chapter 22 | 359 | ||
| 23 | BUYING AND RUNNING A CAR | 361 | |
| A | Buying a car | 362 | |
| B | Paying for the car | 363 | |
| C | On-road costs | 367 | |
| D | Additional costs | 369 | |
| E | Travelling | 371 | |
| F | Running costs | 372 | |
| Review of Chapter 23 | 375 | ||
| ANSWERS | 377 | ||
| INDEX | 413 | ||
We have written this book to provide an alternative course for Year 10 students. Our particular aim was to show the everyday applications of mathematics in the context of the real world.
We have deliberately presented the content in short chapters and because mastery of the basic skills is so important, nineteen chapters cover the core skills that we feel are appropriate for Year 10 students who may go on to complete a Mathematical Applications or a Foundation Mathematics course at Year 11.
In addition, there are four ‘option’ chapters which are entirely focused on particular themes:
In these chapters, the emphasis is on relating the theory and application of mathematics to real life.
Throughout the book, there are worked examples, exercises and activities and with the support of the interactive Student CD, students are given the structure and content for independent practice and revision.
We hope that by presenting a course of mathematics in this way, students may understand the relevance and importance of mathematics in everyday life, but we also caution that no single book should be the sole resource for any classroom teacher.
We welcome your feedback.
Email: info@haeseandharris.com.au
Web: www.haeseandharris.com.au
