About the Book
Year Published: 2014
Page Count: 504
ISBN: 978-1-921972-42-3 (9781921972423)
Online ISBN: 978-1-921972-93-5 (9781921972935)
Discontinued Edition
Stock available from Australian warehouse only.
Year Published: 2014
Page Count: 504
ISBN: 978-1-921972-42-3 (9781921972423)
Online ISBN: 978-1-921972-93-5 (9781921972935)
| 1 | SETS AND VENN DIAGRAMS | 11 | |
| A | Sets | 12 | |
| B | Interval notation | 15 | |
| C | Relations | 17 | |
| D | Complements of sets | 18 | |
| E | Properties of union and intersection | 20 | |
| F | Venn diagrams | 21 | |
| G | Numbers in regions | 26 | |
| H | Problem solving with Venn diagrams | 28 | |
| Review set 1A | 31 | ||
| Review set 1B | 33 | ||
| 2 | FUNCTIONS | 35 | |
| A | Relations and functions | 36 | |
| B | Function notation | 40 | |
| C | Domain and range | 43 | |
| D | The modulus function | 46 | |
| E | Composite functions | 49 | |
| F | Sign diagrams | 51 | |
| G | Inverse functions | 54 | |
| Review set 2A | 60 | ||
| Review set 2B | 61 | ||
| 3 | QUADRATICS | 63 | |
| A | Quadratic equations | 65 | |
| B | Quadratic inequalities | 72 | |
| C | The discriminant of a quadratic | 73 | |
| D | Quadratic functions | 75 | |
| E | Finding a quadratic from its graph | 87 | |
| F | Where functions meet | 91 | |
| G | Problem solving with quadratics | 93 | |
| H | Quadratic optimisation | 95 | |
| Review set 3A | 98 | ||
| Review set 3B | 99 | ||
| 4 | SURDS, INDICES, AND EXPONENTIALS | 101 | |
| A | Surds | 102 | |
| B | Indices | 107 | |
| C | Index laws | 108 | |
| D | Rational indices | 111 | |
| E | Algebraic expansion and factorisation | 113 | |
| F | Exponential equations | 116 | |
| G | Exponential functions | 118 | |
| H | The natural exponential e^x | 123 | |
| Review set 4A | 125 | ||
| Review set 4B | 127 | ||
| 5 | LOGARITHMS | 129 | |
| A | Logarithms in base 10 | 130 | |
| B | Logarithms in base a | 133 | |
| C | Laws of logarithms | 135 | |
| D | Logarithmic equations | 138 | |
| E | Natural logarithms | 142 | |
| F | Solving exponential equations using logarithms | 145 | |
| G | The change of base rule | 147 | |
| H | Graphs of logarithmic functions | 149 | |
| Review set 5A | 152 | ||
| Review set 5B | 154 | ||
| 6 | POLYNOMIALS | 155 | |
| A | Real polynomials | 156 | |
| B | Zeros, roots, and factors | 162 | |
| C | The Remainder theorem | 167 | |
| D | The Factor theorem | 169 | |
| E | Cubic equations | 171 | |
| Review set 6A | 173 | ||
| Review set 6B | 173 | ||
| 7 | STRAIGHT LINE GRAPHS | 175 | |
| A | Equations of straight lines | 177 | |
| B | Intersection of straight lines | 183 | |
| C | Intersection of a straight line and a curve | 186 | |
| D | Transforming relationships to straight line form | 187 | |
| E | Finding relationships from data | 192 | |
| Review set 7A | 197 | ||
| Review set 7B | 199 | ||
| 8 | THE UNIT CIRCLE AND RADIAN MEASURE | 201 | |
| A | Radian measure | 202 | |
| B | Arc length and sector area | 205 | |
| C | The unit circle and the trigonometric ratios | 208 | |
| D | Applications of the unit circle | 213 | |
| E | Multiples of π/6 and π/4 | 217 | |
| F | Reciprocal trigonometric ratios | 221 | |
| Review set 8A | 221 | ||
| Review set 8B | 222 | ||
| 9 | TRIGONOMETRIC FUNCTIONS | 225 | |
| A | Periodic behaviour | 226 | |
| B | The sine function | 230 | |
| C | The cosine function | 236 | |
| D | The tangent function | 238 | |
| E | Trigonometric equations | 240 | |
| F | Trigonometric relationships | 246 | |
| G | Trigonometric equations in quadratic form | 250 | |
| Review set 9A | 251 | ||
| Review set 9B | 252 | ||
| 10 | COUNTING AND THE BINOMIAL EXPANSION | 255 | |
| A | The product principle | 256 | |
| B | Counting paths | 258 | |
| C | Factorial notation | 259 | |
| D | Permutations | 262 | |
| E | Combinations | 267 | |
| F | Binomial expansions | 270 | |
| G | The Binomial Theorem | 273 | |
| Review set 10A | 277 | ||
| Review set 10B | 278 | ||
| 11 | VECTORS | 279 | |
| A | Vectors and scalars | 280 | |
| B | The magnitude of a vector | 284 | |
| C | Operations with plane vectors | 285 | |
| D | The vector between two points | 289 | |
| E | Parallelism | 292 | |
| F | Problems involving vector operations | 294 | |
| G | Lines | 296 | |
| H | Constant velocity problems | 298 | |
| Review set 11A | 302 | ||
| Review set 11B | 303 | ||
| 12 | MATRICES | 305 | |
| A | Matrix structure | 307 | |
| B | Matrix operations and definitions | 309 | |
| C | Matrix multiplication | 315 | |
| D | The inverse of a 2 × 2 matrix | 323 | |
| E | Simultaneous linear equations | 328 | |
| Review set 12A | 330 | ||
| Review set 12B | 331 | ||
| 13 | INTRODUCTION TO DIFFERENTIAL CALCULUS | 333 | |
| A | Limits | 335 | |
| B | Rates of change | 336 | |
| C | The derivative function | 340 | |
| D | Differentiation from first principles | 342 | |
| E | Simple rules of differentiation | 344 | |
| F | The chain rule | 348 | |
| G | The product rule | 351 | |
| H | The quotient rule | 353 | |
| I | Derivatives of exponential functions | 355 | |
| J | Derivatives of logarithmic functions | 359 | |
| K | Derivatives of trigonometric functions | 361 | |
| L | Second derivatives | 363 | |
| Review set 13A | 365 | ||
| Review set 13B | 366 | ||
| 14 | APPLICATIONS OF DIFFERENTIAL CALCULUS | 367 | |
| A | Tangents and normals | 369 | |
| B | Stationary points | 375 | |
| C | Kinematics | 380 | |
| D | Rates of change | 388 | |
| E | Optimisation | 393 | |
| F | Related rates | 399 | |
| Review set 14A | 402 | ||
| Review set 14B | 405 | ||
| 15 | INTEGRATION | 409 | |
| A | The area under a curve | 410 | |
| B | Antidifferentiation | 415 | |
| C | The fundamental theorem of calculus | 417 | |
| D | Integration | 422 | |
| E | Rules for integration | 424 | |
| F | Integrating f(ax+b) | 428 | |
| G | Definite integrals | 431 | |
| Review set 15A | 434 | ||
| Review set 15B | 435 | ||
| 16 | APPLICATIONS OF INTEGRATION | 437 | |
| A | The area under a curve | 438 | |
| B | The area between two functions | 440 | |
| C | Kinematics | 444 | |
| Review set 16A | 449 | ||
| Review set 16B | 450 | ||
| ANSWERS | 453 | ||
| INDEX | 503 | ||
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.
Chris completed a BA in Mathematics at the University of Oxford, and an MSc and PhD in Mathematics at the University of Bath. He spent thirteen years in the Mathematics Department at the University of Birmingham, and from 2000-2011 was seconded half time to the UK Higher Education Academy “Maths Stats and OR Network“ to promote learning and teaching of university mathematics. He was awarded a National Teaching Fellowship in 2006. Chris Sangwin joined the University of Edinburgh in 2015 as Professor of Technology Enhanced Science Education.
What are your learning and teaching interests in mathematics?
I teach mathematics at university but am particularly interested in core pure mathematics which starts in school and continues to be taught at university. Solving mathematical problems is at the heart of mathematics, and I enjoy teaching problem solving at university.
What interests you outside mathematics?
I really enjoy hill walking and mountaineering, particularly spending time with friends in the hills.
Why do you choose to collaborate with a small publisher on the other side of the world?
There is a unique team spirit in Haese which other publishers don't have. This makes authorship much more collaborative than my previous experiences, which is really enjoyable and I'm sure leads to much better quality books for students which are, after all, the whole point.
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 Casio fx-CG50, TI-84 Plus CE, TI-nspire, and HP Prime
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.
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.
Graphics calculator instructions for Casio fx-CG50, TI-84 Plus CE, TI-nspire, and HP Prime 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.
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