About the Book
Year Published: 2018
Page Count: 720
ISBN: 978-1-925489-61-3 (9781925489613)
Online ISBN: 978-1-925489-62-0 (9781925489620)
Discontinued Editions - Pre-order now
Year Published: 2018
Page Count: 720
ISBN: 978-1-925489-61-3 (9781925489613)
Online ISBN: 978-1-925489-62-0 (9781925489620)
| 1 | NUMBER | 11 | |
| A | The number line | 12 | |
| B | Adding and subtracting negatives | 15 | |
| C | Multiplying negative numbers | 18 | |
| D | Dividing negative numbers | 19 | |
| E | Index notation | 20 | |
| F | Square numbers and square roots | 23 | |
| G | Order of operations | 24 | |
| H | Factors and multiples | 27 | |
| I | Primes and composites | 28 | |
| J | Highest common factor | 29 | |
| K | Lowest common multiple | 30 | |
| Review set 1A | 32 | ||
| Review set 1B | 33 | ||
| 2 | REAL NUMBERS | 35 | |
| A | Fractions | 36 | |
| B | Operations with fractions | 40 | |
| C | Decimal numbers | 44 | |
| D | Operations with decimal numbers | 46 | |
| E | Percentage | 49 | |
| Review set 2A | 54 | ||
| Review set 2B | 55 | ||
| 3 | UNITS | 57 | |
| A | Units of length | 60 | |
| B | Units of area | 63 | |
| C | Units of volume | 65 | |
| D | Units of capacity | 65 | |
| E | Units of mass | 67 | |
| F | Time | 67 | |
| Review set 3A | 72 | ||
| Review set 3B | 73 | ||
| 4 | APPROXIMATION AND ESTIMATION | 75 | |
| A | Rounding numbers | 76 | |
| B | Errors from rounding | 80 | |
| C | Estimation | 82 | |
| Review set 4A | 84 | ||
| Review set 4B | 85 | ||
| 5 | ALGEBRA | 87 | |
| A | Algebraic notation | 88 | |
| B | The language of mathematics | 90 | |
| C | Collecting like terms | 92 | |
| D | Writing expressions | 94 | |
| E | Generalising arithmetic | 96 | |
| Review set 5A | 97 | ||
| Review set 5B | 98 | ||
| 6 | RATIO | 99 | |
| A | Ratio | 100 | |
| B | Writing ratios as fractions | 102 | |
| C | Equal ratios | 103 | |
| D | Proportions | 105 | |
| E | Using ratios to divide quantities | 107 | |
| F | Scale diagrams | 108 | |
| Review set 6A | 113 | ||
| Review set 6B | 114 | ||
| 7 | INDICES | 117 | |
| A | Index laws | 118 | |
| B | Expansion laws | 121 | |
| C | The zero index law | 123 | |
| D | The negative index law | 124 | |
| E | Standard form | 127 | |
| Review set 7A | 132 | ||
| Review set 7B | 133 | ||
| 8 | ALGEBRA: EXPANSION | 135 | |
| A | The distributive law | 136 | |
| B | The product $(a + b)(c + d)$ | 140 | |
| C | Perfect square expansion | 142 | |
| D | Difference between two squares | 144 | |
| Review set 8A | 145 | ||
| Review set 8B | 146 | ||
| 9 | LINEAR EQUATIONS AND INEQUALITIES | 147 | |
| A | Linear equations | 148 | |
| B | Maintaining balance | 149 | |
| C | Inverse operations | 151 | |
| D | Algebraic flowcharts | 152 | |
| E | Solving linear equations | 154 | |
| F | Equations with a repeated unknown | 157 | |
| G | Rational equations | 160 | |
| H | Problem solving | 163 | |
| I | Linear inequalities | 165 | |
| J | Solving linear inequalities | 167 | |
| Review set 9A | 171 | ||
| Review set 9B | 172 | ||
| 10 | GEOMETRY | 175 | |
| A | Points and lines | 176 | |
| B | Measuring and classifying angles | 179 | |
| C | Angle properties | 182 | |
| D | Angle pairs | 185 | |
| E | Parallel lines | 188 | |
| F | Bearings | 192 | |
| G | Geometric construction | 194 | |
| Review set 10A | 201 | ||
| Review set 10B | 203 | ||
| 11 | SHAPE | 205 | |
| A | Polygons | 206 | |
| B | Triangles | 208 | |
| C | Isosceles triangles | 213 | |
| D | Quadrilaterals | 216 | |
| E | Angles of an $n$-sided polygon | 221 | |
| F | Circles | 223 | |
| Review set 11A | 226 | ||
| Review set 11B | 228 | ||
| 12 | SOLIDS | 231 | |
| A | Solids | 232 | |
| B | Nets of solids | 234 | |
| C | Drawing rectangular solids | 236 | |
| D | Views of solids | 238 | |
| Review set 12A | 244 | ||
| Review set 12B | 245 | ||
| 13 | ALGEBRAIC FACTORISATION | 247 | |
| A | Common factors | 248 | |
| B | Factorising with common factors | 250 | |
| C | Difference between two squares | 253 | |
| D | Perfect square factorisation | 255 | |
| E | Factorising quadratic trinomials | 257 | |
| F | Miscellaneous factorisation | 260 | |
| Review set 13A | 261 | ||
| Review set 13B | 261 | ||
| 14 | TABLES, GRAPHS, AND CHARTS | 263 | |
| A | Interpreting tables | 265 | |
| B | Interpreting graphs | 269 | |
| C | Graphs of categorical data | 273 | |
| D | Comparing categorical data | 277 | |
| E | Time series data | 281 | |
| Review set 14A | 284 | ||
| Review set 14B | 287 | ||
| 15 | PYTHAGORAS’ THEOREM | 291 | |
| A | Solving $x^2 = k$ | 292 | |
| B | Pythagoras’ theorem | 294 | |
| C | The converse of Pythagoras’ theorem | 299 | |
| D | Problem solving | 301 | |
| Review set 15A | 304 | ||
| Review set 15B | 305 | ||
| 16 | MEASUREMENT | 307 | |
| A | Perimeter | 308 | |
| B | Area | 312 | |
| C | Surface area | 319 | |
| D | Volume | 324 | |
| E | Capacity | 331 | |
| Review set 16A | 333 | ||
| Review set 16B | 335 | ||
| 17 | FORMULAE AND FUNCTIONS | 337 | |
| A | Number machines | 338 | |
| B | Formula construction | 341 | |
| C | Substituting into formulae | 345 | |
| D | Rearranging formulae | 347 | |
| E | Rearrangement and substitution | 350 | |
| F | Predicting formulae | 353 | |
| Review set 17A | 354 | ||
| Review set 17B | 356 | ||
| 18 | APPLICATIONS OF PERCENTAGE | 357 | |
| A | Percentage increase and decrease | 358 | |
| B | Business calculations | 362 | |
| C | Chain percentage problems | 366 | |
| D | Appreciation and depreciation | 367 | |
| E | Simple interest | 368 | |
| F | Compound interest | 370 | |
| Review set 18A | 372 | ||
| Review set 18B | 373 | ||
| 19 | RATES | 375 | |
| A | Rates | 376 | |
| B | Speed | 379 | |
| C | Density | 383 | |
| D | Pressure | 386 | |
| E | Unit cost | 387 | |
| F | Exchange rates | 389 | |
| G | Converting rates | 390 | |
| Review set 19A | 392 | ||
| Review set 19B | 393 | ||
| 20 | COORDINATE GEOMETRY | 395 | |
| A | The Cartesian plane | 397 | |
| B | Linear relationships | 399 | |
| C | Gradient | 402 | |
| D | Parallel lines | 407 | |
| E | Axes intercepts | 409 | |
| F | The equation of a line | 410 | |
| G | Graphing lines in the form $y = mx + c$ | 412 | |
| H | Graphing lines in the form $Ax + By = C$ | 416 | |
| I | Vertical and horizontal lines | 417 | |
| J | Finding the equation of a line | 418 | |
| Review set 20A | 421 | ||
| Review set 20B | 423 | ||
| 21 | SIMULTANEOUS EQUATIONS | 425 | |
| A | Trial and error solution | 427 | |
| B | Graphical solution | 428 | |
| C | Solution by equating values of $y$ | 429 | |
| D | Solution by substitution | 430 | |
| E | Solution by elimination | 431 | |
| F | Problem solving with simultaneous equations | 434 | |
| Review set 21A | 437 | ||
| Review set 21B | 438 | ||
| 22 | TRANSFORMATIONS | 439 | |
| A | Translations | 441 | |
| B | Reflections and line symmetry | 445 | |
| C | Rotations and rotational symmetry | 450 | |
| D | Enlargements and reductions | 455 | |
| Review set 22A | 458 | ||
| Review set 22B | 460 | ||
| 23 | SIMILARITY AND CONGRUENCE | 463 | |
| A | Similar figures | 464 | |
| B | Similar triangles | 467 | |
| C | Problem solving | 471 | |
| D | Congruent figures | 473 | |
| E | Congruent triangles | 475 | |
| F | Proof using congruence | 480 | |
| Review set 23A | 481 | ||
| Review set 23B | 483 | ||
| 24 | TRIGONOMETRY | 485 | |
| A | Scale diagrams in geometry | 486 | |
| B | Labelling right angled triangles | 487 | |
| C | The trigonometric ratios | 488 | |
| D | Finding side lengths | 491 | |
| E | Finding angles | 493 | |
| F | Problem solving with trigonometry | 495 | |
| G | The first quadrant of the unit circle | 498 | |
| Review set 24A | 501 | ||
| Review set 24B | 503 | ||
| 25 | QUADRATIC EQUATIONS AND FUNCTIONS | 505 | |
| A | Quadratic equations | 506 | |
| B | The Null Factor law | 507 | |
| C | Solving quadratic equations | 508 | |
| D | Problem solving with quadratic equations | 512 | |
| E | Quadratic functions | 514 | |
| F | Graphs of quadratic functions | 515 | |
| G | Axes intercepts | 516 | |
| H | Axis of symmetry | 520 | |
| I | Vertex | 521 | |
| Review set 25A | 523 | ||
| Review set 25B | 524 | ||
| 26 | PROPORTION | 525 | |
| A | Direct proportion | 526 | |
| B | Inverse proportion | 530 | |
| Review set 26A | 534 | ||
| Review set 26B | 535 | ||
| 27 | FURTHER FUNCTIONS | 537 | |
| A | Reciprocal functions | 538 | |
| B | Cubic functions | 540 | |
| C | Other functions | 543 | |
| Review set 27A | 545 | ||
| Review set 27B | 546 | ||
| 28 | NUMBER SEQUENCES | 547 | |
| A | Number sequences | 548 | |
| B | Arithmetic sequences | 551 | |
| C | Geometric sequences | 554 | |
| D | Fibonacci-type sequences | 555 | |
| Review set 28A | 557 | ||
| Review set 28B | 557 | ||
| 29 | PROBABILITY | 559 | |
| A | Probability | 561 | |
| B | Experimental probability | 563 | |
| C | Sample space | 568 | |
| D | Theoretical probability | 569 | |
| E | Venn diagrams | 571 | |
| F | The addition law of probability | 575 | |
| G | Tables and grids | 577 | |
| H | Independent events | 579 | |
| I | Dependent events | 581 | |
| J | Tree diagrams | 583 | |
| K | Expectation | 586 | |
| Review set 29A | 587 | ||
| Review set 29B | 589 | ||
| 30 | STATISTICS | 591 | |
| A | Populations and samples | 593 | |
| B | Discrete data | 594 | |
| C | Continuous data | 600 | |
| D | Measuring the centre | 602 | |
| E | Measuring the spread | 610 | |
| Review set 30A | 612 | ||
| Review set 30B | 613 | ||
| 31 | BIVARIATE STATISTICS | 615 | |
| A | Scatter graphs | 616 | |
| B | Correlation | 618 | |
| C | Line of best fit | 622 | |
| Review set 31A | 625 | ||
| Review set 31B | 627 | ||
| 32 | VECTORS | 629 | |
| A | Directed line segment representation | 630 | |
| B | Vector equality | 631 | |
| C | Vector addition | 633 | |
| D | Vector subtraction | 635 | |
| E | Vectors in component form | 636 | |
| F | The vector between two points | 641 | |
| G | Scalar multiplication | 642 | |
| Review set 32A | 644 | ||
| Review set 32B | 645 | ||
| ANSWERS | 647 | ||
| INDEX | 719 | ||
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 ....
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.
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.
Textbook includes Snowflake (27 months)
27 months online Snowflake access which features a complete electronic copy of the textbook.
Animated worked examples with step-by-step, voiced explanations.
For Casio fx-CG20 AU, TI-84 Plus CE, and Casio fx-991EX
The textbook is available on electronic devices through our Snowflake learning platform. This book includes 27 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.
Calculator instructions for Casio fx-CG20 AU, TI-84 Plus CE, and Casio fx-991EX 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 calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology.
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.
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