About the Book
Year Published: 2009
Page Count: 752
ISBN: 978-1-921500-04-6 (9781921500046)
Online ISBN: 978-1-921972-91-1 (9781921972911)
Discontinued Editions
Year Published: 2009
Page Count: 752
ISBN: 978-1-921500-04-6 (9781921500046)
Online ISBN: 978-1-921972-91-1 (9781921972911)
| Symbols and notation used in this book | 6 | ||
| Graphics calculator instructions | 11 | ||
| A | Basic calculations | 12 | |
| B | Basic functions | 13 | |
| C | Secondary function and alpha keys | 17 | |
| D | Memory | 17 | |
| E | Lists | 19 | |
| F | Statistical graphs | 21 | |
| G | Working with functions | 22 | |
| H | Two variable analysis | 26 | |
| Assumed Knowledge (Number) | 29 | ||
| A | Number types | CD | |
| B | Operations and brackets | CD | |
| C | HCF and LCM | CD | |
| D | Fractions | CD | |
| E | Powers and roots | CD | |
| F | Ratio and proportion | CD | |
| G | Number equivalents | CD | |
| H | Rounding numbers | CD | |
| I | Time | CD | |
| Assumed Knowledge (Geometry and Graphs) | 30 | ||
| A | Angles | CD | |
| B | Lines and line segments | CD | |
| C | Polygons | CD | |
| D | Symmetry | CD | |
| E | Constructing triangles | CD | |
| F | Congruence | CD | |
| G | Interpreting graphs and tables | CD | |
| 1 | Algebra (expansion and factorisation) | 31 | |
| A | The distributive law | 32 | |
| B | The product (a+b)(c+d) | 33 | |
| C | Difference of two squares | 35 | |
| D | Perfect squares expansion | 37 | |
| E | Further expansion | 39 | |
| F | Algebraic common factors | 40 | |
| G | Factorising with common factors | 42 | |
| H | Difference of two squares factorisation | 45 | |
| I | Perfect squares factorisation | 47 | |
| J | Expressions with four terms | 48 | |
| K | Factorising x²+bx+c | 49 | |
| L | Splitting the middle term | 51 | |
| M | Miscellaneous factorisation | 54 | |
| Review set 1A | 55 | ||
| Review set 1B | 56 | ||
| 2 | Sets | 57 | |
| A | Set notation | 57 | |
| B | Special number sets | 60 | |
| C | Interval notation | 61 | |
| D | Venn diagrams | 63 | |
| E | Union and intersection | 65 | |
| F | Problem solving | 69 | |
| Review set 2A | 72 | ||
| Review set 2B | 73 | ||
| 3 | Algebra (equations and inequalities) | 75 | |
| A | Solving linear equations | 75 | |
| B | Solving equations with fractions | 80 | |
| C | Forming equations | 83 | |
| D | Problem solving using equations | 85 | |
| E | Power equations | 87 | |
| F | Interpreting linear inequalities | 88 | |
| G | Solving linear inequalities | 89 | |
| Review set 3A | 91 | ||
| Review set 3B | 92 | ||
| 4 | Lines, angles and polygons | 93 | |
| A | Angle properties | 93 | |
| B | Triangles | 98 | |
| C | Isosceles triangles | 100 | |
| D | The interior angles of a polygon | 103 | |
| E | The exterior angles of a polygon | 106 | |
| Review set 4A | 107 | ||
| Review set 4B | 109 | ||
| 5 | Graphs, charts and tables | 111 | |
| A | Statistical graphs | 112 | |
| B | Graphs which compare data | 116 | |
| C | Using technology to graph data | 119 | |
| Review set 5A | 120 | ||
| Review set 5B | 122 | ||
| 6 | Exponents and surds | 123 | |
| A | Exponent or index notation | 123 | |
| B | Exponent or index laws | 126 | |
| C | Zero and negative indices | 129 | |
| D | Standard form | 131 | |
| E | Surds | 134 | |
| F | Properties of surds | 137 | |
| G | Multiplication of surds | 139 | |
| H | Division by surds | 142 | |
| Review set 6A | 143 | ||
| Review set 6B | 145 | ||
| 7 | Formulae and simultaneous equations | 147 | |
| A | Formula substitution | 148 | |
| B | Formula rearrangement | 150 | |
| C | Formula derivation | 153 | |
| D | More difficult rearrangements | 155 | |
| E | Simultaneous equations | 158 | |
| F | Problem solving | 164 | |
| Review set 7A | 166 | ||
| Review set 7B | 167 | ||
| 8 | The theorem of Pythagoras | 169 | |
| A | Pythagoras' theorem | 170 | |
| B | The converse of Pythagoras' theorem | 176 | |
| C | Problem solving | 177 | |
| D | Circle problems | 181 | |
| E | Three-dimensional problems | 185 | |
| Review set 8A | 187 | ||
| Review set 8B | 188 | ||
| 9 | Mensuration (length and area) | 191 | |
| A | Length | 192 | |
| B | Perimeter | 194 | |
| C | Area | 196 | |
| D | Circles and sectors | 201 | |
| Review set 9A | 206 | ||
| Review set 9B | 207 | ||
| 10 | Topics in arithmetic | 209 | |
| A | Percentage | 209 | |
| B | Profit and loss | 211 | |
| C | Simple interest | 214 | |
| D | Reverse percentage problems | 217 | |
| E | Multipliers and chain percentage | 218 | |
| F | Compound growth | 222 | |
| G | Speed, distance and time | 224 | |
| H | Travel graphs | 226 | |
| Review set 10A | 228 | ||
| Review set 10B | 229 | ||
| 11 | Mensuration (solids and containers) | 231 | |
| A | Surface area | 231 | |
| B | Volume | 239 | |
| C | Capacity | 245 | |
| D | Mass | 248 | |
| E | Compound solids | 249 | |
| Review set 11A | 253 | ||
| Review set 11B | 254 | ||
| 12 | Coordinate geometry | 255 | |
| A | Plotting points | 256 | |
| B | Distance between two points | 258 | |
| C | Midpoint of a line segment | 261 | |
| D | Gradient of a line segment | 263 | |
| E | Gradient of parallel and perpendicular lines | 267 | |
| F | Using coordinate geometry | 270 | |
| Review set 12A | 272 | ||
| Review set 12B | 273 | ||
| 13 | Analysis of discrete data | 275 | |
| A | Variables used in statistics | 277 | |
| B | Organising and describing discrete data | 278 | |
| C | The centre of a discrete data set | 282 | |
| D | Measuring the spread of discrete data | 285 | |
| E | Data in frequency tables | 288 | |
| F | Grouped discrete data | 290 | |
| G | Statistics from technology | 292 | |
| Review set 13A | 293 | ||
| Review set 13B | 295 | ||
| 14 | Straight lines | 297 | |
| A | Vertical and horizontal lines | 297 | |
| B | Graphing from a table of values | 299 | |
| C | Equations of lines (gradient-intercept form) | 301 | |
| D | Equations of lines (general form) | 304 | |
| E | Graphing lines from equations | 307 | |
| F | Lines of symmetry | 308 | |
| Review set 14A | 310 | ||
| Review set 14B | 311 | ||
| 15 | Trigonometry | 313 | |
| A | Labelling sides of a right angled triangle | 314 | |
| B | The trigonometric ratios | 316 | |
| C | Problem solving | 322 | |
| D | The first quadrant of the unit circle | 327 | |
| E | True bearings | 330 | |
| F | 3-dimensional problem solving | 331 | |
| Review set 15A | 336 | ||
| Review set 15B | 337 | ||
| 16 | Algebraic fractions | 339 | |
| A | Simplifying algebraic fractions | 339 | |
| B | Multiplying and dividing algebraic fractions | 344 | |
| C | Adding and subtracting algebraic fractions | 346 | |
| D | More complicated fractions | 348 | |
| Review set 16A | 351 | ||
| Review set 16B | 352 | ||
| 17 | Continuous data | 353 | |
| A | The mean of continuous data | 354 | |
| B | Histograms | 355 | |
| C | Cumulative frequency | 359 | |
| Review set 17A | 364 | ||
| Review set 17B | 365 | ||
| 18 | Similarity | 367 | |
| A | Similarity | 367 | |
| B | Similar triangles | 370 | |
| C | Problem solving | 373 | |
| D | Area and volume of similar shapes | 376 | |
| Review set 18A | 380 | ||
| Review set 18B | 381 | ||
| 19 | Introduction to functions | 383 | |
| A | Mapping diagrams | 383 | |
| B | Functions | 385 | |
| C | Function notation | 389 | |
| D | Composite functions | 391 | |
| E | Reciprocal functions | 393 | |
| F | The absolute value function | 395 | |
| Review set 19A | 398 | ||
| Review set 19B | 399 | ||
| 20 | Transformation geometry | 401 | |
| A | Translations | 402 | |
| B | Rotations | 404 | |
| C | Reflections | 406 | |
| D | Enlargements and reductions | 408 | |
| E | Stretches | 410 | |
| F | Transforming functions | 413 | |
| G | The inverse of a transformation | 416 | |
| H | Combinations of transformations | 417 | |
| Review set 20A | 419 | ||
| Review set 20B | 420 | ||
| 21 | Quadratic equations and functions | 421 | |
| A | Quadratic equations | 422 | |
| B | The Null Factor law | 423 | |
| C | The quadratic formula | 427 | |
| D | Quadratic functions | 429 | |
| E | Graphs of quadratic functions | 431 | |
| F | Axes intercepts | 438 | |
| G | Line of symmetry and vertex | 441 | |
| H | Finding a quadratic function | 445 | |
| I | Using technology | 446 | |
| J | Problem solving | 447 | |
| Review set 21A | 451 | ||
| Review set 21B | 453 | ||
| 22 | Two variable analysis | 455 | |
| A | Correlation | 456 | |
| B | Line of best fit by eye | 459 | |
| C | Linear regression | 461 | |
| Review set 22A | 466 | ||
| Review set 22B | 467 | ||
| 23 | Further functions | 469 | |
| A | Cubic functions | 469 | |
| B | Inverse functions | 473 | |
| C | Using technology | 475 | |
| D | Tangents to curves | 480 | |
| Review set 23A | 481 | ||
| Review set 23B | 481 | ||
| 24 | Vectors | 483 | |
| A | Directed line segment representation | 484 | |
| B | Vector equality | 485 | |
| C | Vector addition | 486 | |
| D | Vector subtraction | 489 | |
| E | Vectors in component form | 491 | |
| F | Scalar multiplication | 496 | |
| G | Parallel vectors | 497 | |
| H | Vectors in geometry | 499 | |
| Review set 24A | 501 | ||
| Review set 24B | 503 | ||
| 25 | Probability | 505 | |
| A | Introduction to probability | 506 | |
| B | Estimating probability | 507 | |
| C | Probabilities from two-way tables | 510 | |
| D | Expectation | 512 | |
| E | Representing combined events | 513 | |
| F | Theoretical probability | 515 | |
| G | Compound events | 519 | |
| H | Using tree diagrams | 522 | |
| I | Sampling with and without replacement | 524 | |
| J | Mutually exclusive and non-mutually exclusive events | 527 | |
| K | Miscellaneous probability questions | 528 | |
| Review set 25A | 530 | ||
| Review set 25B | 531 | ||
| 26 | Sequences | 533 | |
| A | Number sequences | 534 | |
| B | Algebraic rules for sequences | 535 | |
| C | Geometric sequences | 537 | |
| D | The difference method for sequences | 539 | |
| Review set 26A | 544 | ||
| Review set 26B | 545 | ||
| 27 | Circle geometry | 547 | |
| A | Circle theorems | 547 | |
| B | Cyclic quadrilaterals | 556 | |
| Review set 27A | 561 | ||
| Review set 27B | 562 | ||
| 28 | Exponential functions and equations | 565 | |
| A | Rational exponents | 566 | |
| B | Exponential functions | 568 | |
| C | Exponential equations | 570 | |
| D | Problem solving with exponential functions | 573 | |
| E | Exponential modelling | 576 | |
| Review set 28A | 577 | ||
| Review set 28B | 578 | ||
| 29 | Further trigonometry | 579 | |
| A | The unit circle | 579 | |
| B | Area of a triangle using sine | 583 | |
| C | The sine rule | 585 | |
| D | The cosine rule | 588 | |
| E | Problem solving with the sine and cosine rules | 591 | |
| F | Trigonometry with compound shapes | 593 | |
| G | Trigonometric graphs | 595 | |
| H | Graphs of y=asin(bx) and y=acos(bx) | 599 | |
| Review set 29A | 601 | ||
| Review set 29B | 602 | ||
| 30 | Variation and power modelling | 605 | |
| A | Direct variation | 606 | |
| B | Inverse variation | 612 | |
| C | Variation modelling | 615 | |
| D | Power modelling | 619 | |
| Review set 30A | 622 | ||
| Review set 30B | 623 | ||
| 31 | Logarithms | 625 | |
| A | Logarithms in base a | 625 | |
| B | The logarithmic function | 627 | |
| C | Rules for logarithms | 629 | |
| D | Logarithms in base 10 | 630 | |
| E | Exponential and logarithmic equations | 634 | |
| Review set 31A | 636 | ||
| Review set 31B | 637 | ||
| 32 | Inequalities | 639 | |
| A | Solving one variable inequalities with technology | 639 | |
| B | Linear inequality regions | 641 | |
| C | Integer points in regions | 644 | |
| D | Problem solving (Extension) | 645 | |
| Review set 32A | 647 | ||
| Review set 32B | 648 | ||
| 33 | Multi-Topic Questions | 649 | |
| 34 | Investigation and modelling questions | 661 | |
| A | Investigation questions | 661 | |
| B | Modelling questions | 669 | |
| Answers | 673 | ||
| Index | 752 | ||
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 (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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