About the Book
Year Published: 2011
Page Count: 600
ISBN: 978-1-921500-22-0 (9781921500220)
Online ISBN: 978-1-921972-92-8 (9781921972928)
Discontinued Editions
Year Published: 2011
Page Count: 600
ISBN: 978-1-921500-22-0 (9781921500220)
Online ISBN: 978-1-921972-92-8 (9781921972928)
| SYMBOLS AND NOTATION USED IN THIS BOOK | 6 | ||
| GRAPHICS CALCULATOR INSTRUCTIONS | 11 | ||
| A | Basic calculations | 12 | |
| B | More calculations | 14 | |
| C | Secondary function and alpha keys | 17 | |
| D | Memory | 17 | |
| E | Lists | 19 | |
| F | Statistics | 21 | |
| G | Working with functions | 23 | |
| 1 | NUMBER | 27 | |
| A | Number types | 28 | |
| B | Operations and brackets | 30 | |
| C | HCF and LCM | 33 | |
| D | Fractions | 35 | |
| E | Powers and roots | 39 | |
| F | Ratio and proportion | 40 | |
| G | Number equivalents | 47 | |
| H | Percentage | 48 | |
| I | Rounding numbers | 49 | |
| J | Time | 54 | |
| Review set 1A | 57 | ||
| Review set 1B | 58 | ||
| 2 | SETS | 59 | |
| A | Set notation | 59 | |
| B | Special number sets | 62 | |
| C | Interval notation | 64 | |
| D | Venn diagrams | 65 | |
| E | Union and intersection | 68 | |
| F | Problem solving | 72 | |
| Review set 2A | 74 | ||
| Review set 2B | 75 | ||
| 3 | ALGEBRA (EXPRESSIONS AND EQUATIONS) | 77 | |
| A | Basic problem solving | 77 | |
| B | Introduction to algebra | 78 | |
| C | Evaluating expressions | 80 | |
| D | Algebraic expressions | 80 | |
| E | Linear equations | 84 | |
| F | Equations of the form x² = k | 88 | |
| G | Forming equations | 89 | |
| H | Problem solving using equations | 91 | |
| Review set 3A | 93 | ||
| Review set 3B | 94 | ||
| 4 | LINES, ANGLES, AND POLYGONS | 95 | |
| A | Angles | 96 | |
| B | Lines and line segments | 97 | |
| C | Polygons | 98 | |
| D | Symmetry | 101 | |
| E | Congruence | 103 | |
| F | Angle properties | 104 | |
| G | Triangles | 108 | |
| H | Isosceles triangles | 111 | |
| I | The interior angles of a polygon | 114 | |
| J | The exterior angles of a polygon | 117 | |
| Review set 4A | 118 | ||
| Review set 4B | 120 | ||
| 5 | ALGEBRA (EXPANSION AND FACTORISATION) | 123 | |
| A | The distributive law | 123 | |
| B | Equations containing brackets | 125 | |
| C | Equations containing fractions | 126 | |
| D | The product (a + b)(c + d) | 128 | |
| E | Difference of two squares | 130 | |
| F | Algebraic common factors | 132 | |
| G | Factorising with common factors | 134 | |
| Review set 5A | 137 | ||
| Review set 5B | 137 | ||
| Review set 5C | 138 | ||
| 6 | GRAPHS, CHARTS, AND TABLES | 139 | |
| A | Interpreting graphs and tables | 140 | |
| B | Types of graphs | 143 | |
| C | Graphs which compare data | 147 | |
| D | Using technology to graph data | 150 | |
| Review set 6A | 152 | ||
| Review set 6B | 153 | ||
| 7 | EXPONENTS | 155 | |
| A | Exponent or index notation | 155 | |
| B | Exponent or index laws | 158 | |
| C | Zero and negative indices | 161 | |
| D | Standard form | 162 | |
| Review set 7A | 166 | ||
| Review set 7B | 167 | ||
| 8 | FORMULAE AND INEQUALITIES | 169 | |
| A | Formula substitution | 169 | |
| B | Formula rearrangement | 172 | |
| C | Formula derivation | 175 | |
| D | Interpreting linear inequalities | 177 | |
| E | Solving linear inequalities | 179 | |
| Review set 8A | 181 | ||
| Review set 8B | 182 | ||
| 9 | SIMULTANEOUS EQUATIONS | 183 | |
| A | Equating values of y | 185 | |
| B | Solution by substitution | 186 | |
| C | Solution by elimination | 187 | |
| D | Problem solving | 190 | |
| Review set 9A | 192 | ||
| Review set 9B | 193 | ||
| 10 | THE THEOREM OF PYTHAGORAS | 195 | |
| A | Pythagoras' theorem | 196 | |
| B | Problem solving | 202 | |
| C | Circle problems | 206 | |
| Review set 10A | 209 | ||
| Review set 10B | 210 | ||
| 11 | MENSURATION (LENGTH AND AREA) | 213 | |
| A | Length | 214 | |
| B | Perimeter | 216 | |
| C | Area | 218 | |
| D | Circles and sectors | 223 | |
| Review set 11A | 227 | ||
| Review set 11B | 228 | ||
| 12 | TOPICS IN ARITHMETIC | 231 | |
| A | Percentage | 231 | |
| B | Profit and loss | 233 | |
| C | Simple interest | 236 | |
| D | Multipliers and chain percentage | 239 | |
| E | Compound growth | 243 | |
| F | Speed, distance and time | 245 | |
| G | Travel graphs | 247 | |
| Review set 12A | 249 | ||
| Review set 12B | 250 | ||
| 13 | MENSURATION (SOLIDS AND CONTAINERS) | 251 | |
| A | Surface area | 251 | |
| B | Volume | 259 | |
| C | Capacity | 265 | |
| D | Mass | 268 | |
| E | Compound solids | 270 | |
| Review set 13A | 273 | ||
| Review set 13B | 275 | ||
| 14 | COORDINATE GEOMETRY | 277 | |
| A | Plotting points | 278 | |
| B | Distance between two points | 280 | |
| C | Midpoint of a line segment | 282 | |
| D | Gradient of a line segment | 284 | |
| E | Parallel lines | 289 | |
| F | Using coordinate geometry | 291 | |
| Review set 14A | 293 | ||
| Review set 14B | 294 | ||
| 15 | ANALYSIS OF DISCRETE DATA | 295 | |
| A | Variables used in statistics | 297 | |
| B | Organising and describing discrete data | 298 | |
| C | The centre of a discrete data set | 302 | |
| D | Measuring the spread of discrete data | 305 | |
| E | Data in frequency tables | 308 | |
| F | Grouped discrete data | 310 | |
| G | Statistics from technology | 312 | |
| Review set 15A | 313 | ||
| Review set 15B | 315 | ||
| 16 | STRAIGHT LINES | 317 | |
| A | Vertical and horizontal lines | 318 | |
| B | Graphing from a table of values | 319 | |
| C | Equations of lines | 321 | |
| D | Graphing lines from equations | 325 | |
| E | Lines of symmetry | 326 | |
| Review set 16A | 328 | ||
| Review set 16B | 328 | ||
| 17 | TRIGONOMETRY | 331 | |
| A | Labelling sides of a right angled triangle | 332 | |
| B | The trigonometric ratios | 333 | |
| C | Problem solving | 340 | |
| D | True bearings | 345 | |
| Review set 17A | 347 | ||
| Review set 17B | 348 | ||
| 18 | ALGEBRAIC FRACTIONS | 351 | |
| A | Simplifying algebraic fractions | 351 | |
| B | Multiplying and dividing algebraic fractions | 355 | |
| C | Adding and subtracting algebraic fractions | 357 | |
| Review set 18A | 359 | ||
| Review set 18B | 360 | ||
| 19 | CONTINUOUS DATA | 361 | |
| A | The mean of continuous data | 362 | |
| B | Cumulative frequency | 364 | |
| Review set 19A | 369 | ||
| Review set 19B | 370 | ||
| 20 | SIMILARITY | 373 | |
| A | Similarity | 373 | |
| B | Similar triangles | 376 | |
| C | Problem solving | 380 | |
| Review set 20A | 383 | ||
| Review set 20B | 384 | ||
| 21 | INTRODUCTION TO FUNCTIONS | 387 | |
| A | Mapping diagrams | 387 | |
| B | Functions | 390 | |
| C | Function notation | 394 | |
| D | Reciprocal functions | 398 | |
| Review set 21A | 400 | ||
| Review set 21B | 401 | ||
| 22 | TRANSFORMATION GEOMETRY | 403 | |
| A | Directed line segments | 404 | |
| B | Component form | 406 | |
| C | Translations | 408 | |
| D | Rotations | 410 | |
| E | Reflections | 411 | |
| F | Enlargements and reductions | 413 | |
| G | Transforming functions | 416 | |
| H | Miscellaneous transformations | 420 | |
| Review set 22A | 422 | ||
| Review set 22B | 423 | ||
| 23 | TWO VARIABLE ANALYSIS | 425 | |
| A | Correlation | 426 | |
| B | Line of best fit by eye | 429 | |
| Review set 23A | 434 | ||
| Review set 23B | 435 | ||
| 24 | FURTHER FUNCTIONS | 437 | |
| A | Unfamiliar functions | 438 | |
| B | Solving equations graphically | 441 | |
| C | Problem solving | 445 | |
| Review set 24A | 447 | ||
| Review set 24B | 447 | ||
| 25 | PROBABILITY | 449 | |
| A | Introduction to probability | 450 | |
| B | Estimating probability | 451 | |
| C | Probabilities from two-way tables | 454 | |
| D | Expectation | 456 | |
| E | Representing combined events | 457 | |
| F | Theoretical probability | 459 | |
| G | Compound events | 463 | |
| H | Using tree diagrams | 467 | |
| I | Sampling with and without replacement | 469 | |
| J | Mutually exclusive and non-mutually exclusive events | 471 | |
| K | Miscellaneous probability questions | 472 | |
| Review set 25A | 474 | ||
| Review set 25B | 475 | ||
| 26 | SEQUENCES | 477 | |
| A | Number sequences | 478 | |
| B | Algebraic rules for sequences | 480 | |
| C | The difference method for sequences | 482 | |
| Review set 26A | 486 | ||
| Review set 26B | 487 | ||
| 27 | CIRCLE GEOMETRY | 489 | |
| A | Circle theorems | 489 | |
| B | Miscellaneous right angle problems | 494 | |
| Review set 27A | 496 | ||
| Review set 27B | 498 | ||
| 28 | MULTI-TOPIC QUESTIONS | 501 | |
| 29 | INVESTIGATION QUESTIONS | 517 | |
| ANSWERS | 542 | ||
| INDEX | 600 | ||
Michael completed a Bachelor of Science at the University of Adelaide, majoring in Infection and Immunity, and Applied Mathematics. He studied laminar heat flow as part of his Honours in Applied Mathematics, and finished a PhD in high speed fluid flows in 2001. He has been the principal editor for Haese Mathematics since 2008.
What motivates you to write mathematics books?
My passion is for education as a whole, rather than just mathematics. In Australia I think it is too easy to take education for granted, because it is seen as a right but with too little appreciation for the responsibility that goes with it. But the more I travel to places where access to education is limited, the more I see children who treat it as a privilege, and the greater the difference it makes in their lives. But as far as mathematics goes, I grew up with mathematics textbooks in pieces on the kitchen table, and so I guess it continues a tradition.
What do you aim to achieve in writing?
I think a few things:
What interests you outside mathematics?
Lots of things! Horses, show jumping and course design, alpacas, badminton, running, art, history, faith, reading, hiking, photography ....
Sandra completed a Bachelor of Science at the University of Adelaide, majoring in Pure Mathematics and Statistics. She taught at Underdale High School and Westminster School before founding Haese and Harris Publications (now Haese Mathematics), together with husband Robert (Bob) and colleague Kim Harris.
What drew you to the field of mathematics?
I always found mathematics the easiest subject at school. I’m not sure why. I intended to study Chemistry at university, but found I didn’t enjoy it as much as I thought I would – so I came back to mathematics, and have been involved with it ever since.
What motivated you to switch from teaching to writing mathematics books?
Bob used to write notes for his class. Other teachers at the school used the notes, then teachers at other schools started asking for them. Eventually Bob said, “Well, I might as well start writing textbooks!”
Initially, I was proofreading. As the workload increased, I began editing as well as proofreading. It just gradually became a full-time job, between writing material, editing and proofreading it, and then distributing the books. These days, Michael does the editing and I do proofreading and audio.
How has the field of textbook publishing changed in the years since you started?
When we started, text was typed and worked solutions were handwritten. Bob would draw any graphics by hand.
We moved to typesetting, but writing a mathematics textbook with the printing tools available presented its own difficulties. For example, symbols had to be copied, cut and pasted by hand onto the original pages, which was very tedious and time-consuming! Fractions were also problematic: we would type a line containing all the numerators, and then a line underneath for all the denominators.
Now it’s all done by computers, which is very much easier, and quicker!
What interests you outside mathematics?
I own a few alpacas. I enjoy my garden - I don’t do much in it, but I enjoy it! I like listening to music; mainly classical, but I enjoy other genres as well.
I really love to travel. The scenery, the history of a place, its architecture, its art – all of those things fascinate me. As a result I also enjoy photography; I like taking pictures of the things I’ve seen and places I’ve experienced.
Student CD/Snowflake (27 months)
A complete electronic copy of the textbook, with interactive, animated, and/or printable extras.
Animated worked examples with step-by-step, voiced explanations.
Graphics Calculator Instructions
For TI-84 Plus and Casio fx-9860G
This book offers SELF TUTOR for every worked example. On the electronic copy of the textbook, access SELF TUTOR by clicking anywhere on a worked example to hear a step-by-step explanation by a teacher. This is ideal for catch-up and revision, or for motivated students who want to do some independent study outside school hours.
Graphics calculator instructions for TI-84 Plus and Casio fx-9860G are included with this textbook. The textbook will either have comprehensive instructions at the start of the book, specific instructions available from icons located throughout, or both. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.
Early prints of this textbook came with a Student CD. Recent prints of this book include 27 months of access for electronic devices through our Snowflake learning platform.
Where relevant, Snowflake or the Student CD include a complete electronic copy of the book with interactive geometry, graphing, and statistics software, demonstrations, games, spreadsheets, and a range of printable worksheets, tables, and diagrams. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.
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