About the Book
Year Published: 2018
Page Count: 736
ISBN: 978-1-925489-65-1 (9781925489651)
Online ISBN: 978-1-925489-66-8 (9781925489668)
Discontinued Editions
Year Published: 2018
Page Count: 736
ISBN: 978-1-925489-65-1 (9781925489651)
Online ISBN: 978-1-925489-66-8 (9781925489668)
1 | EXPONENTS | 13 | |
A | Exponent or index notation | 13 | |
B | The Fundamental Theorem of Arithmetic | 15 | |
C | Exponent or index laws | 16 | |
D | Zero and negative exponents | 20 | |
E | Standard form | 23 | |
Review set 1A | 27 | ||
Review set 1B | 27 | ||
2 | ALGEBRA: EXPANSION | 29 | |
A | The distributive law | 30 | |
B | The product $(a + b)(c + d)$ | 31 | |
C | Difference between two squares | 34 | |
D | Perfect squares expansion | 36 | |
E | Further expansion | 38 | |
Review set 2A | 40 | ||
Review set 2B | 40 | ||
3 | ALGEBRA: FACTORISATION | 41 | |
A | Algebraic common factors | 42 | |
B | Factorising with common factors | 43 | |
C | Difference between two squares factorisation | 46 | |
D | Perfect squares factorisation | 48 | |
E | Expressions with four terms | 50 | |
F | Factorising $x^2 + bx + c$ | 50 | |
G |
Factorising $ax^2 + bx + c$, a ≠ 1 |
53 | |
H | Miscellaneous factorisation | 55 | |
Review set 3A | 56 | ||
Review set 3B | 56 | ||
4 | STATISTICAL GRAPHS | 57 | |
A | Graphs of categorical data | 58 | |
B | Comparing categorical data | 62 | |
C | Line graphs | 66 | |
Review set 4A | 68 | ||
Review set 4B | 70 | ||
5 | ALGEBRA: LINEAR EQUATIONS | 73 | |
A | Maintaining balance | 74 | |
B | Inverse operations | 75 | |
C | Linear equations | 76 | |
D | Equations with a repeated unknown | 79 | |
E | Rational equations | 81 | |
F | Problem solving | 83 | |
Review set 5A | 85 | ||
Review set 5B | 86 | ||
6 | SETS AND VENN DIAGRAMS | 87 | |
A | Set notation | 87 | |
B | Complement of a set | 90 | |
C | Intersection and union | 91 | |
D | Special number sets | 92 | |
E | Interval notation | 94 | |
F | Venn diagrams | 96 | |
G | Venn diagram regions | 99 | |
H | Problem solving with Venn diagrams | 103 | |
Review set 6A | 106 | ||
Review set 6B | 107 | ||
7 | ANGLES AND POLYGONS | 109 | |
A | Angle theorems | 109 | |
B | Parallel lines | 112 | |
C | Triangles | 116 | |
D | Isosceles triangles | 119 | |
E | The interior angles of a polygon | 122 | |
F | The exterior angles of a polygon | 124 | |
Review set 7A | 125 | ||
Review set 7B | 127 | ||
8 | SURDS AND OTHER RADICALS | 129 | |
A | Surds | 130 | |
B | Power equations | 131 | |
C | Properties of radicals | 132 | |
D | Simplest form | 134 | |
E | Operations with radicals | 134 | |
F | Divisions involving surds | 137 | |
Review set 8A | 139 | ||
Review set 8B | 140 | ||
9 | PYTHAGORAS' THEOREM | 141 | |
A | Pythagoras' theorem | 142 | |
B | The converse of Pythagoras' theorem | 146 | |
C | Problem solving | 147 | |
Review set 9A | 152 | ||
Review set 9B | 153 | ||
10 | FORMULAE | 155 | |
A | Formula construction | 156 | |
B | Substituting into formulae | 157 | |
C | Rearranging formulae | 159 | |
D | Rearrangement and substitution | 163 | |
Review set 10A | 165 | ||
Review set 10B | 166 | ||
11 | MEASUREMENT: PERIMETER AND AREA | 167 | |
A | Perimeter | 167 | |
B | Area of polygons | 172 | |
C | Area of a circle | 175 | |
Review set 11A | 180 | ||
Review set 11B | 181 | ||
12 | MEASUREMENT: SOLIDS AND CONTAINERS | 183 | |
A | Surface area | 183 | |
B | V olume | 190 | |
C | Capacity | 197 | |
D | Density | 199 | |
Review set 12A | 201 | ||
Review set 12B | 203 | ||
13 | APPLICATIONS OF PERCENTAGE | 205 | |
A | Finding a percentage of a quantity | 205 | |
B | Percentage increase and decrease | 206 | |
C | Finding the original amount | 209 | |
D | Profit and loss | 210 | |
E | Chain percentage problems | 211 | |
F | Simple interest | 213 | |
G | Compound interest | 215 | |
Review set 13A | 217 | ||
Review set 13B | 218 | ||
14 | COORDINATE GEOMETRY | 219 | |
A | The Cartesian plane | 220 | |
B | The distance between two points | 222 | |
C | Midpoints | 225 | |
D | Gradient | 227 | |
E | Parallel and perpendicular lines | 231 | |
F | Collinear points | 233 | |
G | Using coordinate geometry | 233 | |
Review set 14A | 235 | ||
Review set 14B | 236 | ||
15 | SPEED, DISTANCE, AND TIME | 237 | |
A | Speed, distance, and time | 237 | |
B | Travel graphs | 240 | |
Review set 15A | 243 | ||
Review set 15B | 244 | ||
16 | STRAIGHT LINES | 245 | |
A | Vertical and horizontal lines | 245 | |
B | Properties of a straight line | 246 | |
C | Gradient-intercept form | 249 | |
D | General form | 250 | |
E | Finding the equation of a line | 252 | |
F | Lines of symmetry | 257 | |
Review set 16A | 258 | ||
Review set 16B | 260 | ||
17 | SIMULTANEOUS EQUATIONS | 261 | |
A | Graphical solution | 262 | |
B | Solution by equating values of $y$ | 263 | |
C | Solution by substitution | 264 | |
D | Solution by elimination | 265 | |
E | Problem solving with simultaneous equations | 268 | |
Review set 17A | 270 | ||
Review set 17B | 270 | ||
18 | ONE-VARIABLE STATISTICS | 271 | |
A | Variables used in statistics | 273 | |
B | Organising data | 275 | |
C | Measuring the centre of discrete data | 283 | |
D | Measuring the spread of discrete data | 289 | |
E | Estimating the centre of data in class intervals | 292 | |
F | Cumulative frequency | 295 | |
Review set 18A | 300 | ||
Review set 18B | 302 | ||
19 | TWO-VARIABLE ANALYSIS | 305 | |
A | Correlation | 306 | |
B | Line of best fit by eye | 309 | |
C | Linear regression | 312 | |
Review set 19A | 316 | ||
Review set 19B | 317 | ||
20 | ALGEBRAIC FRACTIONS | 319 | |
A | Evaluating algebraic fractions | 320 | |
B | Simplifying algebraic fractions | 321 | |
C | Multiplying and dividing algebraic fractions | 325 | |
D | Adding and subtracting algebraic fractions | 327 | |
Review set 20A | 330 | ||
Review set 20B | 331 | ||
21 | SIMILARITY | 333 | |
A | Similar figures | 333 | |
B | Similar triangles | 337 | |
C | Problem solving | 340 | |
D | Areas of similar objects | 343 | |
E | V olumes of similar objects | 345 | |
Review set 21A | 347 | ||
Review set 21B | 349 | ||
22 | TRIGONOMETRY | 351 | |
A | Labelling right angled triangles | 352 | |
B | The trigonometric ratios | 354 | |
C | Finding side lengths | 356 | |
D | Finding angles | 358 | |
E | Problem solving | 359 | |
F | True bearings | 366 | |
G | The angle between a line and a plane | 368 | |
H | The angle between two planes | 370 | |
Review set 22A | 372 | ||
Review set 22B | 373 | ||
23 | QUADRATIC EQUATIONS | 375 | |
A | Equations of the form $x^2 = k$ | 376 | |
B | Solving equations by factorisation | 377 | |
C | The quadratic formula | 381 | |
D | Problem solving | 383 | |
Review set 23A | 386 | ||
Review set 23B | 387 | ||
24 | TRANSFORMATION GEOMETRY | 389 | |
A | Translations | 390 | |
B | Reflections | 392 | |
C | Rotations | 395 | |
D | Enlargements and reductions | 397 | |
E | Stretches | 399 | |
F | The inverse of a transformation | 402 | |
G | Combinations of transformations | 403 | |
Review set 24A | 404 | ||
Review set 24B | 406 | ||
25 | FUNCTIONS | 407 | |
A | Mapping diagrams | 407 | |
B | Functions | 410 | |
C | Function notation | 412 | |
D | Composite functions | 414 | |
E | The absolute value function | 415 | |
F | Reciprocal functions | 419 | |
G | Graphs of functions | 421 | |
H | Transforming functions | 423 | |
I | Inverse functions | 427 | |
Review set 25A | 429 | ||
Review set 25B | 431 | ||
26 | POLYNOMIAL FUNCTIONS | 433 | |
A | Quadratic functions | 434 | |
B | Graphs of quadratic functions | 435 | |
C | Axes intercepts | 440 | |
D | Axis of symmetry of a quadratic | 444 | |
E | Vertex of a quadratic | 445 | |
F | Finding a quadratic function | 447 | |
G | Problem solving with quadratic functions | 449 | |
H | Cubic functions | 450 | |
Review set 26A | 454 | ||
Review set 26B | 455 | ||
27 | SEQUENCES | 457 | |
A | Number sequences | 458 | |
B | Formulae for sequences | 459 | |
C | Geometric sequences | 462 | |
D | The difference method for sequences | 463 | |
Review set 27A | 468 | ||
Review set 27B | 469 | ||
28 | EXPONENTIALS | 471 | |
A | Rational exponents | 471 | |
B | Exponential functions | 473 | |
C | Graphs of exponential functions | 474 | |
D | Exponential equations | 477 | |
E | Problem solving with exponential functions | 479 | |
F | Exponential modelling | 481 | |
Review set 28A | 482 | ||
Review set 28B | 484 | ||
29 | LOGARITHMS | 485 | |
A | Logarithms | 485 | |
B | The logarithmic function | 487 | |
C | Laws of logarithms | 488 | |
D | Logarithms in base $10$ | 490 | |
E | Logarithmic equations | 492 | |
F | Solving exponential equations | 494 | |
Review set 29A | 495 | ||
Review set 29B | 496 | ||
30 | ADVANCED TRIGONOMETRY | 497 | |
A | The unit circle | 498 | |
B | The multiples of 30° and 45° | 502 | |
C | The area of a triangle | 504 | |
D | The sine rule | 506 | |
E | The cosine rule | 509 | |
F | Problem solving with the sine and cosine rules | 512 | |
G | Graphs from the unit circle | 514 | |
H | Trigonometric functions | 515 | |
I | Transformations of trigonometric functions | 517 | |
Review set 30A | 520 | ||
Review set 30B | 521 | ||
31 | CIRCLE GEOMETRY | 523 | |
A | Angle in a semi-circle theorem | 524 | |
B | Chords of a circle theorem | 526 | |
C | Radius-tangent theorem | 528 | |
D | Tangents from an external point theorem | 531 | |
E | Angle between a tangent and a chord theorem | 533 | |
F | Angle at the centre theorem | 535 | |
G | Angles subtended by the same arc theorem | 537 | |
H | Cyclic quadrilaterals | 539 | |
I | Tests for cyclic quadrilaterals | 542 | |
Review set 31A | 545 | ||
Review set 31B | 547 | ||
32 | PROBABILITY | 549 | |
A | Probability | 550 | |
B | Experimental probability | 552 | |
C | Expectation | 556 | |
D | Sample space and events | 557 | |
E | Theoretical probability | 559 | |
F | The addition law of probability | 563 | |
G | Independent events | 565 | |
H | Dependent events | 568 | |
Review set 32A | 571 | ||
Review set 32B | 573 | ||
33 | VARIATION AND POWER MODELLING | 575 | |
A | Direct variation | 576 | |
B | Powers in direct variation | 579 | |
C | Inverse variation | 582 | |
D | Powers in inverse variation | 586 | |
E | Power models | 587 | |
Review set 33A | 590 | ||
Review set 33B | 591 | ||
34 | VECTORS | 593 | |
A | Directed line segment representation | 594 | |
B | Vector equality | 595 | |
C | Vector addition | 596 | |
D | Vector subtraction | 599 | |
E | Vectors in component form | 601 | |
F | Operations in component form | 604 | |
G | Scalar multiplication | 607 | |
H | Parallel vectors | 608 | |
Review set 34A | 611 | ||
Review set 34B | 612 | ||
35 | INEQUALITIES | 613 | |
A | Linear inequalities | 614 | |
B | Solving linear inequalities | 614 | |
C | Sign diagrams | 617 | |
D | Quadratic inequalities | 619 | |
E | Solving inequalities using technology | 621 | |
F | Linear inequalities in the Cartesian plane | 622 | |
Review set 35A | 626 | ||
Review set 35B | 627 | ||
36 | MULTI-TOPIC QUESTIONS | 629 | |
37 | INVESTIGATION AND MODELLING QUESTIONS | 637 | |
A | Investigation questions | 637 | |
B | Modelling questions | 640 | |
ANSWERS | 643 | ||
INDEX | 736 |
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.
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.
Graphics Calculator Instructions
For TI-84 Plus CE, Casio fx-CG20, Casio fx-9860G Plus, and TI-nspire
Graphics calculator instructions for TI-84 Plus CE, Casio fx-CG20, Casio fx-9860G 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.
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.
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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