About the Book
Year Published: 2023
Page Count: 744
ISBN: 978-1-925489-63-7 (9781925489637)
Online ISBN: 978-1-925489-64-4 (9781925489644)
Discontinued Editions
Year Published: 2023
Page Count: 744
ISBN: 978-1-925489-63-7 (9781925489637)
Online ISBN: 978-1-925489-64-4 (9781925489644)
| 1 | INDICES | 11 | |
| A | Index laws | 12 | |
| B | Expansion laws | 15 | |
| C | The zero index law | 18 | |
| D | The negative index law | 19 | |
| E | Rational indices | 22 | |
| F | Standard form | 27 | |
| Review sets | 32 | ||
| 2 | ALGEBRA: EXPANSION | 33 | |
| A | The distributive law | 34 | |
| B | The product $(a + b)(c + d)$ | 37 | |
| C | The difference between two squares | 39 | |
| D | The perfect squares expansion | 41 | |
| E | Further expansion | 44 | |
| Review sets | 46 | ||
| 3 | LINEAR EQUATIONS | 47 | |
| A | Linear equations | 48 | |
| B | Equations with a repeated unknown | 51 | |
| C | Problem solving | 53 | |
| Review sets | 54 | ||
| 4 | PLANE GEOMETRY | 55 | |
| A | Angle properties | 56 | |
| B | Angle pairs on parallel lines | 58 | |
| C | Triangles | 61 | |
| D | Isosceles triangles | 66 | |
| E | Quadrilaterals | 69 | |
| F | Angle sum of a quadrilateral | 72 | |
| G | Angle sum of an $n$-sided polygon | 74 | |
| H | Circles | 77 | |
| I | Geometric construction | 78 | |
| Review sets | 84 | ||
| 5 | SETS AND VENN DIAGRAMS | 85 | |
| A | Sets | 86 | |
| B | Complement of a set | 88 | |
| C | Intersection and union | 90 | |
| D | Special number sets | 92 | |
| E | Interval notation | 95 | |
| F | Venn diagrams | 98 | |
| G | Venn diagram regions | 101 | |
| H | Numbers in regions | 103 | |
| I | Problem solving with Venn diagrams | 105 | |
| Review sets | 108 | ||
| 6 | ALGEBRA: FACTORISATION | 109 | |
| A | Algebraic common factors | 110 | |
| B | Factorising with common factors | 112 | |
| C | Difference between two squares factorisation | 114 | |
| D | Perfect squares factorisation | 117 | |
| E | Factorising $x^2 + bx + c$ | 119 | |
| F | Expressions with four terms | 121 | |
| G | Factorising $ax^2 + bx + c$, $a \neq 1$ | 122 | |
| H | Miscellaneous factorisation | 125 | |
| Review sets | 126 | ||
| 7 | SURDS AND OTHER RADICALS | 127 | |
| A | Radicals | 128 | |
| B | Properties of radicals | 130 | |
| C | Simplest surd form | 132 | |
| D | Power equations | 133 | |
| E | Operations with radicals | 136 | |
| F | Division with surds | 139 | |
| Review sets | 142 | ||
| 8 | PYTHAGORAS' THEOREM | 143 | |
| A | Pythagoras' theorem | 144 | |
| B | Pythagorean triples | 149 | |
| C | Problem solving | 150 | |
| D | The converse of Pythagoras' theorem | 155 | |
| Review sets | 156 | ||
| 9 | ALGEBRAIC FRACTIONS | 157 | |
| A | Evaluating algebraic fractions | 158 | |
| B | Simplifying algebraic fractions | 159 | |
| C | Multiplying algebraic fractions | 164 | |
| D | Dividing algebraic fractions | 165 | |
| E | Adding and subtracting algebraic fractions | 166 | |
| F | Equations with algebraic fractions | 171 | |
| Review sets | 174 | ||
| 10 | FORMULAE | 175 | |
| A | Formula construction | 176 | |
| B | Substituting into formulae | 177 | |
| C | Rearranging formulae | 179 | |
| D | Rearrangement and substitution | 182 | |
| E | Predicting formulae | 185 | |
| Review sets | 188 | ||
| 11 | APPLICATIONS OF PERCENTAGES | 189 | |
| A | Percentage increase or decrease | 190 | |
| B | Finding a percentage change | 192 | |
| C | Finding the original amount | 195 | |
| D | Business calculations | 196 | |
| E | Appreciation and depreciation | 199 | |
| F | Simple interest | 201 | |
| G | Compound interest | 204 | |
| Review sets | 206 | ||
| 12 | MEASUREMENT: LENGTH | 207 | |
| A | Units of length | 208 | |
| B | Perimeter | 210 | |
| C | Scale diagrams | 215 | |
| D | Errors in measuring length | 219 | |
| Review sets | 220 | ||
| 13 | MEASUREMENT: AREA | 221 | |
| A | Units of area | 222 | |
| B | Area of polygons | 224 | |
| C | Area of circles and sectors | 229 | |
| D | Surface area of a solid with planar faces | 233 | |
| E | Surface area of a cylinder | 236 | |
| F | Surface area of a cone | 237 | |
| G | Surface area of a sphere | 239 | |
| Review sets | 242 | ||
| 14 | MEASUREMENT: VOLUME AND CAPACITY | 243 | |
| A | Units of volume | 244 | |
| B | Volume of a solid of uniform cross-section | 245 | |
| C | Volume of a tapered solid | 248 | |
| D | Volume of a sphere | 251 | |
| E | Capacity | 253 | |
| F | Connecting volume and capacity | 254 | |
| Review sets | 256 | ||
| 15 | COORDINATE GEOMETRY | 257 | |
| A | The Cartesian plane | 258 | |
| B | The distance between two points | 261 | |
| C | Midpoints | 264 | |
| D | Gradient | 267 | |
| E | Parallel and perpendicular lines | 271 | |
| F | Using coordinate geometry | 275 | |
| Review sets | 278 | ||
| 16 | STRAIGHT LINES | 279 | |
| A | Vertical and horizontal lines | 280 | |
| B | Points on a line | 281 | |
| C | Axes intercepts | 282 | |
| D | Graphing from a table of values | 283 | |
| E | Gradient-intercept form | 284 | |
| F | General form | 286 | |
| G | Finding the equation of a line | 287 | |
| H | Perpendicular bisectors | 293 | |
| Review sets | 294 | ||
| 17 | SIMULTANEOUS EQUATIONS | 295 | |
| A | Graphical solution | 296 | |
| B | Solution by equating values of $y$ | 297 | |
| C | Solution by substitution | 298 | |
| D | Solution by elimination | 299 | |
| E | Problem solving | 302 | |
| Review sets | 306 | ||
| 18 | RATES | 307 | |
| A | Rates | 308 | |
| B | Speed | 310 | |
| C | Density | 312 | |
| D | Pressure | 314 | |
| E | Unit cost | 315 | |
| F | Exchange rates | 317 | |
| G | Converting rates | 318 | |
| Review sets | 320 | ||
| 19 | LINE GRAPHS | 321 | |
| A | Line graphs | 322 | |
| B | Constant rates of change | 324 | |
| C | Average rates of change | 326 | |
| D | Instantaneous rates of change | 328 | |
| E | Finding a quantity from its rate of change | 331 | |
| Review sets | 334 | ||
| 20 | TRANSFORMATIONS | 335 | |
| A | Translations | 336 | |
| B | Reflections | 339 | |
| C | Line symmetry | 342 | |
| D | Rotations | 345 | |
| E | Rotational symmetry | 349 | |
| F | Enlargements and reductions | 351 | |
| G | Invariant points | 358 | |
| Review sets | 360 | ||
| 21 | CONGRUENCE AND SIMILARITY | 361 | |
| A | Congruence | 362 | |
| B | Congruent triangles | 363 | |
| C | Proof using congruence | 368 | |
| D | Similarity | 372 | |
| E | Similar triangles | 375 | |
| F | Problem solving | 378 | |
| G | Areas of similar figures | 382 | |
| H | Volumes of similar solids | 384 | |
| Review sets | 386 | ||
| 22 | TRIGONOMETRY | 387 | |
| A | Scale diagrams in geometry | 388 | |
| B | Labelling right angled triangles | 389 | |
| C | The trigonometric ratios | 390 | |
| D | Finding side lengths | 393 | |
| E | Finding angles | 395 | |
| F | Problem solving | 396 | |
| G | Bearings | 403 | |
| Review sets | 406 | ||
| 23 | QUADRATIC EQUATIONS | 407 | |
| A | Quadratic equations | 408 | |
| B | Equations of the form $x^2 = k$ | 409 | |
| C | The null factor law | 410 | |
| D | Solving by factorisation | 411 | |
| E | Completing the square | 416 | |
| F | The quadratic formula | 418 | |
| G | Problem solving | 420 | |
| H | Non-linear simultaneous equations | 425 | |
| Review sets | 426 | ||
| 24 | FUNCTIONS | 427 | |
| A | Functions | 428 | |
| B | Graphs | 429 | |
| C | Function notation | 431 | |
| D | Composite functions | 433 | |
| E | Transformations of graphs | 434 | |
| F | Reciprocal functions | 438 | |
| G | Inverse functions | 440 | |
| Review sets | 444 | ||
| 25 | PROPORTION | 445 | |
| A | Direct proportion | 446 | |
| B | Powers in direct proportion | 449 | |
| C | Inverse proportion | 452 | |
| D | Powers in inverse proportion | 455 | |
| Review sets | 456 | ||
| 26 | QUADRATIC FUNCTIONS | 457 | |
| A | Quadratic functions | 458 | |
| B | Graphs of quadratic functions | 460 | |
| C | Using transformations to graph quadratics | 462 | |
| D | Axes intercepts | 467 | |
| E | Using axes intercepts to graph quadratics | 469 | |
| F | Axis of symmetry | 471 | |
| G | Vertex | 473 | |
| H | Problem solving | 475 | |
| Review sets | 476 | ||
| 27 | INEQUALITIES | 477 | |
| A | Linear inequalities | 478 | |
| B | Solving linear inequalities | 479 | |
| C | Double linear inequalities | 483 | |
| D | Regions of the Cartesian plane | 485 | |
| E | Sign diagrams | 489 | |
| F | Quadratic inequalities | 493 | |
| Review sets | 494 | ||
| 28 | FURTHER FUNCTIONS | 495 | |
| A | Cubic functions | 496 | |
| B | Exponential functions | 498 | |
| C | Modelling with functions | 501 | |
| Review sets | 502 | ||
| 29 | NUMBER SEQUENCES | 503 | |
| A | Number sequences | 504 | |
| B | Arithmetic sequences | 507 | |
| C | Geometric sequences | 510 | |
| D | Fibonacci-type sequences | 513 | |
| E | The difference method for quadratic sequences | 515 | |
| Review sets | 518 | ||
| 30 | NUMERICAL METHODS | 519 | |
| A | Change of sign methods | 520 | |
| B | Iterative formulae | 523 | |
| Review sets | 524 | ||
| 31 | CIRCLE GEOMETRY | 525 | |
| A | Angle in a semi-circle theorem | 526 | |
| B | Chords of a circle theorem | 528 | |
| C | Radius-tangent theorem | 530 | |
| D | Tangents from an external point theorem | 533 | |
| E | Alternate segment theorem | 535 | |
| F | Angle at the centre theorem | 537 | |
| G | Angles subtended by the same arc theorem | 539 | |
| H | Cyclic quadrilaterals | 541 | |
| I | The equation of a circle | 544 | |
| Review sets | 546 | ||
| 32 | ADVANCED TRIGONOMETRY | 547 | |
| A | The unit circle | 548 | |
| B | Multiples of $30$° and $45$° | 553 | |
| C | The area of a triangle | 556 | |
| D | The sine rule | 558 | |
| E | The cosine rule | 561 | |
| F | Problem solving | 564 | |
| G | Trigonometric functions | 566 | |
| Review sets | 570 | ||
| 33 | COUNTING AND PROBABILITY | 571 | |
| A | Sample space and events | 573 | |
| B | The product rule for counting | 575 | |
| C | The sum rule for counting | 577 | |
| D | Theoretical probability | 578 | |
| E | The addition law of probability | 583 | |
| F | Independent events | 585 | |
| G | Dependent events | 588 | |
| H | Experimental probability | 591 | |
| I | Probabilities from tabled data | 593 | |
| J | Frequency trees | 596 | |
| K | Expectation | 597 | |
| L | Conditional probability | 598 | |
| Review sets | 602 | ||
| 34 | STATISTICS: NUMERICAL DATA | 603 | |
| A | Numerical variables | 604 | |
| B | Discrete numerical data | 606 | |
| C | Continuous numerical data | 608 | |
| D | Describing the distribution of a data set | 612 | |
| E | Measures of centre | 615 | |
| F | Measures of spread | 623 | |
| G | Box plots | 626 | |
| H | Cumulative frequency graphs | 628 | |
| Review sets | 632 | ||
| 35 | BIVARIATE STATISTICS | 633 | |
| A | Scatter graphs | 634 | |
| B | Correlation | 636 | |
| C | Causality | 639 | |
| D | Line of best fit by eye | 640 | |
| Review sets | 643 | ||
| 36 | VECTORS | 645 | |
| A | Vectors and scalars | 646 | |
| B | Geometric vector addition | 648 | |
| C | Geometric vector subtraction | 651 | |
| D | Geometric scalar multiplication | 654 | |
| E | Vectors in component form | 656 | |
| F | Position vectors | 658 | |
| G | The magnitude of a vector | 659 | |
| H | Operations with vectors | 660 | |
| I | Parallel vectors | 664 | |
| Review sets | 667 | ||
| ANSWERS | 668 | ||
| INDEX | 742 | ||
Ngoc Vo completed a Bachelor of Mathematical Sciences at the University of Adelaide, majoring in Statistics and Applied Mathematics. Her Mathematical interests include regression analysis, Bayesian statistics, and statistical computing. Ngoc has been working at Haese Mathematics as a proof reader and writer since 2016.
What drew you to the field of mathematics?
Originally, I planned to study engineering at university, but after a few weeks I quickly realised that it wasn't for me. So I switched to a mathematics degree at the first available opportunity. I didn't really have a plan to major in statistics, but as I continued my studies I found myself growing more fond of the discipline. The mathematical rigor in proving distributional results and how they link to real-world data -- it all just seemed to click.
What are some interesting things that you get to do at work?
As the resident statistician here at Haese Mathematics, I get the pleasure of writing new statistics chapters and related material. Statistics has always been a challenging subject to both teach and learn, however it doesn't always have to be that way. To bridge that gap, I like to try and include as many historical notes, activities, and investigations as I can to make it as engaging as possible. The reasons why we do things, and the people behind them are often important things we forget to talk about. Statistics, and of course mathematics, doesn't just exist within the pages of your textbook or even the syllabus. There's so much breadth and depth to these disciplines, most of the time we just barely scratch the surface.
What interests you outside mathematics?
In my free time I like studying good typography and brushing up on my TeX skills to become the next TeXpert. On the less technical side of things, I also enjoy scrapbooking, painting, and making the occasional card.
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.
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.
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 ....
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-991EX, TI-84 Plus CE, Casio fx-CG50, 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.
Graphics calculator instructions for Casio fx-991EX, TI-84 Plus CE, Casio fx-CG50, 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.
This book is available on electronic devices through our Snowflake learning platform. This book includes 24 months of Snowflake access, featuring a complete electronic copy of the textbook.
Where relevant, Snowflake features include 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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