About the Book
Year Published: 2011
Page Count: 447
ISBN: 978-1-921972-02-7 (9781921972027)
Online ISBN: 978-1-921972-87-4 (9781921972874)
Discontinued Edition
Year Published: 2011
Page Count: 447
ISBN: 978-1-921972-02-7 (9781921972027)
Online ISBN: 978-1-921972-87-4 (9781921972874)
| 1 | NUMBER | 9 | |
| A | Natural numbers | 10 | |
| B | Integers | 13 | |
| C | Index notation | 15 | |
| D | Order of operations | 16 | |
| E | Primes and composites | 19 | |
| F | Square numbers and square roots | 22 | |
| Review set 1 | 24 | ||
| Practice test 1A: Multiple choice | CD | ||
| Practice test 1B: Short response | 25 | ||
| Practice test 1C: Extended response | 25 | ||
| 2 | SETS AND VENN DIAGRAMS | 27 | |
| A | Sets | 28 | |
| B | Complement of a set | 30 | |
| C | Intersection and union | 32 | |
| D | Venn diagrams | 34 | |
| E | Problem solving with Venn diagrams | 38 | |
| Review set 2 | 41 | ||
| Practice test 2A: Multiple choice | CD | ||
| Practice test 2B: Short response | 42 | ||
| Practice test 2C: Extended response | 43 | ||
| 3 | REAL NUMBERS | 45 | |
| A | Fractions | 46 | |
| B | Operations with fractions | 50 | |
| C | Decimal numbers | 54 | |
| D | Operations with decimal numbers | 56 | |
| E | Rational numbers | 59 | |
| F | Irrational numbers | 63 | |
| Review set 3 | 65 | ||
| Practice test 3A: Multiple choice | CD | ||
| Practice test 3B: Short response | 66 | ||
| Practice test 3C: Extended response | 67 | ||
| 4 | ALGEBRAIC OPERATIONS | 69 | |
| A | Algebraic notation | 70 | |
| B | The language of mathematics | 72 | |
| C | Collecting like terms | 74 | |
| D | Product and quotient simplification | 75 | |
| E | Generalising arithmetic | 77 | |
| F | Algebraic substitution | 79 | |
| Review set 4 | 82 | ||
| Practice test 4A: Multiple choice | CD | ||
| Practice test 4B: Short response | 83 | ||
| Practice test 4C: Extended response | 83 | ||
| 5 | PERCENTAGE | 85 | |
| A | Percentage | 86 | |
| B | Expressing one quantity as a percentage of another | 89 | |
| C | Finding a percentage of a quantity | 91 | |
| D | Percentage increase or decrease | 92 | |
| E | Finding a percentage change | 94 | |
| F | Business applications | 96 | |
| Review set 5 | 101 | ||
| Practice test 5A: Multiple choice | CD | ||
| Practice test 5B: Short response | 102 | ||
| Practice test 5C: Extended response | 103 | ||
| 6 | LAWS OF ALGEBRA | 105 | |
| A | Index laws | 106 | |
| B | Expansion laws | 109 | |
| C | The zero index law | 112 | |
| D | The distributive law | 113 | |
| E | Simplifying algebraic expressions | 116 | |
| F | Brackets with negative coefficients | 117 | |
| G | Factorisation of algebraic expressions | 119 | |
| Review set 6 | 121 | ||
| Practice test 6A: Multiple choice | 122 | ||
| Practice test 6B: Short response | 123 | ||
| Practice test 6C: Extended response | 123 | ||
| 7 | EQUATIONS | 125 | |
| A | Solutions of an equation | 127 | |
| B | Linear equations | 128 | |
| C | Maintaining balance | 129 | |
| D | Inverse operations | 131 | |
| E | Algebraic flowcharts | 133 | |
| F | Solving equations | 135 | |
| G | Equations with a repeated unknown | 138 | |
| Review set 7 | 142 | ||
| Practice test 7A: Multiple choice | CD | ||
| Practice test 8B: Short response | 143 | ||
| Practice test 8C: Extended response | 143 | ||
| 8 | THE GEOMETRY OF POLYGONS | 145 | |
| A | Review of geometrical facts | 146 | |
| B | Triangles | 151 | |
| C | Isosceles triangles | 155 | |
| D | Quadrilaterals | 158 | |
| Review set 8 | 164 | ||
| Practice test 8A: Multiple choice | CD | ||
| Practice test 8B: Short response | 166 | ||
| Practice test 8C: Extended response | 167 | ||
| 9 | MEASUREMENT: LENGTH AND AREA | 169 | |
| A | Length | 171 | |
| B | Perimeter | 174 | |
| C | Circumference | 178 | |
| D | Area | 182 | |
| E | Areas of polygons | 185 | |
| F | The area of a circle | 194 | |
| Review set 9 | 196 | ||
| Practice test 9A: Multiple choice | CD | ||
| Practice test 9B: Short response | 197 | ||
| Practice test 9C: Extended response | 199 | ||
| 10 | ALGEBRA: PATTERNS AND FORMULAE | 201 | |
| A | Geometric patterns | 202 | |
| B | Number crunching machines | 205 | |
| C | Substituting into formulae | 209 | |
| D | Using patterns | 210 | |
| E | Practical problems | 213 | |
| Review set 10 | 215 | ||
| Practice test 10A: Multiple choice | CD | ||
| Practice test 10B: Short response | 216 | ||
| Practice test 10C: Extended response | 217 | ||
| 11 | FURTHER MEASUREMENT | 219 | |
| A | Volume | 220 | |
| B | Volume formulae | 222 | |
| C | Capacity | 228 | |
| D | Connecting volume and capacity | 230 | |
| E | Mass | 232 | |
| F | The relationship between units | 234 | |
| G | Time | 235 | |
| H | Time calculations | 236 | |
| I | 24-hour time | 240 | |
| Review set 11 | 241 | ||
| Practice test 11A: Multiple choice | CD | ||
| Practice test 11B: Short response | 243 | ||
| Practice test 11C: Extended response | 243 | ||
| 12 | COORDINATE GEOMETRY | 245 | |
| A | The Cartesian plane | 247 | |
| B | Plotting points from a table of values | 250 | |
| C | Linear relationships | 251 | |
| D | Plotting graphs of linear equations | 254 | |
| E | Horizontal and vertical lines | 256 | |
| F | Points on lines | 258 | |
| G | Using graphs to solve equations | 259 | |
| Review set 12 | 263 | ||
| Practice test 12A: Multiple choice | CD | ||
| Practice test 12B: Short response | 265 | ||
| Practice test 12C: Extended response | 265 | ||
| 13 | RATIO AND PROPORTION | 267 | |
| A | Ratio | 268 | |
| B | Equal ratios | 270 | |
| C | Proportions | 273 | |
| D | Using ratios to divide quantities | 276 | |
| E | Scale diagrams | 279 | |
| Review set 13 | 286 | ||
| Practice test 13A: Multiple choice | CD | ||
| Practice test 13B: Short response | 287 | ||
| Practice test 13C: Extended response | 288 | ||
| 14 | RATES | 289 | |
| A | Rates | 290 | |
| B | Speed | 293 | |
| C | Line graphs | 295 | |
| D | Density | 297 | |
| E | Converting rates | 300 | |
| Review set 14 | 302 | ||
| Practice test 14A: Multiple choice | CD | ||
| Practice test 14B: Short response | 302 | ||
| Practice test 14C: Extended response | 303 | ||
| 15 | PROBABILITY | 305 | |
| A | Probability | 307 | |
| B | Sample space | 308 | |
| C | Theoretical probability | 310 | |
| D | Complementary events | 313 | |
| E | Experimental probability | 315 | |
| F | Probabilities from tabled data | 319 | |
| G | Probabilities from Venn diagrams | 323 | |
| Review set 15 | 326 | ||
| Practice test 15A: Multiple choice | CD | ||
| Practice test 15B: Short response | 328 | ||
| Practice test 15C: Extended response | 329 | ||
| 16 | PROBLEM SOLVING | 331 | |
| A | Writing problems as equations | 332 | |
| B | Problem solving with algebra | 333 | |
| C | Measurement problems | 336 | |
| D | Problem solving by search | 338 | |
| E | Problem solving by working backwards | 340 | |
| F | Miscellaneous problems | 342 | |
| Review set 16 | 347 | ||
| Practice test 16A: Multiple choice | CD | ||
| Practice test 16B: Short response | 348 | ||
| Practice test 16C: Extended response | 349 | ||
| 17 | CONGRUENCE AND TRANSFORMATIONS | 351 | |
| A | Transformations | 352 | |
| B | Congruent figures | 361 | |
| C | Congruent triangles | 366 | |
| D | Proof using congruence | 372 | |
| Review set 17 | 373 | ||
| Practice test 17A: Multiple choice | CD | ||
| Practice test 17B: Short response | 376 | ||
| Practice test 17C: Extended response | 377 | ||
| 18 | STATISTICS | 379 | |
| A | Categorical data | 380 | |
| B | Numerical data | 384 | |
| C | Grouped data | 387 | |
| D | Measuring the centre and spread | 391 | |
| E | Data collection | 398 | |
| Review set 18 | 402 | ||
| Practice test 18A: Multiple choice | CD | ||
| Practice test 18B: Short response | 404 | ||
| Practice test 18C: Extended response | 405 | ||
| ANSWERS | 407 | ||
| INDEX | 446 | ||
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.
Mark has a Bachelor of Science (Honours), majoring in Pure Mathematics, and a Bachelor of Economics, both of which were completed at the University of Adelaide. He studied public key cryptography for his Honours in Pure Mathematics. He started with the company in 2006, and is currently the writing manager for Haese Mathematics.
What got you interested in mathematics? How did that lead to working at Haese Mathematics?
I have always enjoyed the structure and style of mathematics. It has a precision that I enjoy. I spend an inordinate amount of my leisure time reading about mathematics, in fact! To be fair, I tend to do more reading about the history of mathematics and how various mathematical and logic puzzles work, so it is somewhat different from what I do at work.
How did I end up at Haese Mathematics?
I was undertaking a PhD, and I realised that what I really wanted to do was put my knowledge to use. I wanted to pass on to others all this interesting stuff about mathematics. I emailed Haese Mathematics (Haese and Harris Publications as they were known back then), stating that I was interested in working for them. As it happened, their success with the first series of International Baccalaureate books meant that they were looking to hire more people at the time. I consider myself quite lucky!
What are some interesting things that you get to do at work?
On an everyday basis, it’s a challenge (but a fun one!) to devise interesting questions for the books. I want students to have questions that pique their curiosity and get them thinking about mathematics in a different way. I prefer to write questions that require students to demonstrate that they understand a concept, rather than relying on rote memorisation.
When a new or revised syllabus is released for a curriculum that we write for, a lot of work goes into devising a structure for the book that addresses the syllabus. The process of identifying what concepts need to be taught, organising those concepts into an order that makes sense from a teaching standpoint, and finally sourcing and writing the material that addresses those concepts is very involved – but so rewarding when you hold the finished product in your hands, straight from the printer.
What interests you outside mathematics?
Apart from the aforementioned recreational mathematics activities, I play a little guitar, and I enjoy playing badminton and basketball on a social level.
Student CD/Snowflake (15 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 Casio fx-9860G Plus, TI-84 Plus, and TI-nspire
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 Casio fx-9860G Plus, TI-84 Plus, and TI-nspire 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 15 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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