The CD has our new ‘self-tutoring’ software. For every worked
example in this book, a student can listen to a teacher’s voice explain
each step in the worked example – ‘click’ anywhere in the
worked example where you see the
icon.
Introductory chapter. Graphics calculator instructions
On CD. Background knowledge
10. Advanced trigonometry
15. Probability
21. Integration
22. Applications of integration
NB: Sample chapters do not have working links.
Mathematics for the International Student: Mathematics SL has been written to embrace the syllabus for the two-year Mathematics SL Course, which is one of the courses of study in the IB Diploma Programme. It is not our intention to define the course. Teachers are encouraged to use other resources. We have developed this book independently of the International Baccalaureate Organization (IBO) in consultation with many experienced teachers of IB Mathematics. The text is not endorsed by the IBO.
The second edition builds on the strength of the first edition. Chapters are arranged to follow the same order as the chapters in our Mathematics HL (Core) second edition, making it easier for teachers who have combined classes of SL and HL students.
Syllabus references are given at the beginning of each chapter. The new edition reflects the Mathematics SL syllabus more closely, with several sections from the first edition being consolidated in this second edition for greater teaching efficiency. Topics such as Pythagoras' theorem, coordinate geometry, and right angled triangle trigonometry, which appeared in Chapters 7 and 10 in the first edition, are now in the ‘Background Knowledge’ at the beginning of the book and accessible as printable pages on the CD.
Changes have been made in response to the introduction of a calculator-free examination paper. A large number of questions have been added and categorised as ‘calculator’ or ‘non calculator’. In particular, the final chapter contains over 150 examination-style questions.
Comprehensive graphics calculator instructions are given for Casio fx-9860G, TI-84 Plus and TI-nspire in an introductory chapter (see p. 17) and, occasionally, where additional help may be needed, more detailed instructions are available as printable pages on the CD. The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application, and appropriate use of technology. No single aspect of technology has been favoured. It is as important that students work with a pen and paper as it is that they use their calculator or graphics calculator, or use a spreadsheet or graphing package on computer.
This package is language rich and technology rich. The combination of textbook
and interactive Student CD will foster the mathematical development of students
in a stimulating way. Frequent use of the interactive features on the CD is
certain to nurture a much deeper understanding and appreciation of mathematical
concepts. The CD also offers
for every worked example.
is accessed via the CD – click anywhere on any worked example to hear a teacher's voice explain each
step in that worked example. This is ideal for catch-up and revision, or for
motivated students who want to do some independent study outside school hours.
For students who may not have a good understanding of the necessary background knowledge for this course, we have provided printable pages of information, examples, exercises, and answers on the Student CD – see ‘Background knowledge’ (p. 12). To access these pages, click on the ‘Background knowledge’ icon when running the CD.
The interactive features of the CD allow immediate access to our own specially designed geometry software, graphing software and more. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.
It is not our intention that each chapter be worked through in full. Time constraints may not allow for this. Teachers must select exercises carefully, according to the abilities and prior knowledge of their students, to make the most efficient use of time and give as thorough coverage of work as possible. Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Many investigations are suitable for portfolio assignments.
In this changing world of mathematics education, we believe that the contextual approach shown in this book, with the associated use of technology, will enhance the students' understanding, knowledge and appreciation of mathematics, and its universal application.
The interactive CD is ideal for independent study.
Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home.
By clicking on the relevant icon, a range of interactive features can be accessed:

For a complete list of all the active links on the Mathematics SL second edition CD, click here.
Graphics calculator instructions: where additional help may be needed, detailed instructions are availabkle on the CD, as printable pages. Click on the relevant icon for TI-nspire, TI-84 Plus or Casio fx-9860G.
SELF TUTOR is an exciting feature of this book.
The
icon on
each worked example denotes an active link on the CD.
Simply ‘click’ on the
(or anywhere in the example box) to access the worked example, with
a teacher's voice explaining each step necessary to reach the answer.
Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen.
Ideal for students who have missed lessons or need extra help.
See Chapter 13, Lines and planes in space, p. 356
| Symbols and notation used in this book | 10 | ||
| Background knowledge | 12 | ||
| A | Surds and radicals | CD | |
| B | Scientific notation (standard form) | CD | |
| C | Number systems and set notation | CD | |
| D | Algebraic simplification | CD | |
| E | Linear equations and inequalities | CD | |
| F | Modulus or absolute value | CD | |
| G | Product expansion | CD | |
| H | Factorisation | CD | |
| Investigation: Another factorisation technique | CD | ||
| I | Formula rearrangement | CD | |
| J | Adding and subtracting algebraic fractions | CD | |
| K | Congruence and similarity | CD | |
| L | Pythagoras' theorem | CD | |
| M | Coordinate geometry | CD | |
| N | Right angled triangle trigonometry | CD | |
| Summary of circle properties | 12 | ||
| Summary of measurement facts | 14 | ||
| Graphics calculator instructions | 17 | ||
| A | Casio fx-9860G | 18 | |
| B | Texas Instruments TI-84 Plus | 26 | |
| C | Texas Instruments TI-nSpire | 35 | |
| 1 | Functions | 45 | |
| A | Relations and functions | 46 | |
| B | Function notation | 49 | |
| C | Domain and range | 51 | |
| Investigation 1: Fluid filling functions | 54 | ||
| D | Composite functions | 55 | |
| E | Sign diagrams | 56 | |
| F | The reciprocal function | 60 | |
| G | Asymptotes of other rational functions | 61 | |
| Investigation 2: Finding asymptotes | 61 | ||
| H | Inverse functions | 62 | |
| Review set 1A | 65 | ||
| Review set 1B | 66 | ||
| Review set 1C | 68 | ||
| 2 | Sequences and series | 69 | |
| A | Number patterns | 70 | |
| B | Sequences of numbers | 71 | |
| C | Arithmetic sequences | 72 | |
| D | Geometric sequences | 76 | |
| E | Series | 82 | |
| Investigation: Von Koch's snowflake curve | 89 | ||
| Review set 2A | 90 | ||
| Review set 2B | 90 | ||
| Review set 2C | 91 | ||
| 3 | Exponentials | 93 | |
| A | Index notation | 94 | |
| B | Evaluating powers | 95 | |
| C | Index laws | 96 | |
| D | Rational indices | 99 | |
| E | Algebraic expansion and factorisation | 101 | |
| F | Exponential equations | 104 | |
| G | Graphs of exponential functions | 105 | |
| Investigation 1: Exponential graphs | 106 | ||
| H | Growth and decay | 109 | |
| I | The natural exponential ‘e’ | 113 | |
| Investigation 2: Continuous compound interest | 113 | ||
| Review set 3A | 116 | ||
| Review set 3B | 117 | ||
| Review set 3C | 118 | ||
| 4 | Logarithms | 119 | |
| A | Logarithms | 120 | |
| B | Logarithms in base 10 | 122 | |
| C | Laws of logarithms | 125 | |
| Investigation: Discovering the laws of logarithms | 125 | ||
| D | Natural logarithms | 128 | |
| E | Exponential equations using logarithms | 131 | |
| F | The change of base rule | 133 | |
| G | Graphs of logarithmic functions | 134 | |
| H | Growth and decay | 137 | |
| Review set 4A | 140 | ||
| Review set 4B | 140 | ||
| Review set 4C | 141 | ||
| 5 | Graphing and transforming functions | 143 | |
| A | Families of functions | 144 | |
| Investigation: Function families | 144 | ||
| B | Transformation of graphs | 146 | |
| Review set 5A | 151 | ||
| Review set 5B | 152 | ||
| Review set 5C | 153 | ||
| 6 | Quadratic equations and functions | 155 | |
| A | Quadratic equations | 157 | |
| B | The discriminant of a quadratic | 162 | |
| C | Graphing quadratic functions | 164 | |
| Investigation 1: Graphing y=a(x-p)(x-q) | 164 | ||
| Investigation 2: Graphing y=a(x-h)2+k | 165 | ||
| D | Finding a quadratic from its graph | 173 | |
| Investigation 3: Finding quadratic functions | 176 | ||
| E | Where functions meet | 177 | |
| F | Problem solving with quadratics | 179 | |
| G | Quadratic optimisation | 182 | |
| Investigation 4: Sum and product of roots | 185 | ||
| Review set 6A | 185 | ||
| Review set 6B | 186 | ||
| Review set 6C | 187 | ||
| 7 | The binomial expansion | 189 | |
| A | Binomial expansions | 190 | |
| Investigation 1: The binomial expansion of (a+b)n, n≥4 | 191 | ||
| B | The binomial theorem | 193 | |
| Investigation 2: The binomial coefficient | 193 | ||
| Review set 7 | 196 | ||
| 8 | The unit circle and radian measure | 197 | |
| A | Radian measure | 198 | |
| B | Arc length and sector area | 200 | |
| C | The unit circle and the basic trigonometric ratios | 203 | |
| Investigation: Parametric equations | 209 | ||
| D | The equation of a straight line | 213 | |
| Review set 8A | 214 | ||
| Review set 8B | 215 | ||
| Review set 8C | 216 | ||
| 9 | Non-right angled triangle trigonometry | 217 | |
| A | Areas of triangles | 218 | |
| B | The cosine rule | 221 | |
| C | The sine rule | 224 | |
| Investigation: The ambiguous case | 225 | ||
| D | Using the sine and cosine rules | 229 | |
| Review set 9A | 232 | ||
| Review set 9B | 233 | ||
| Review set 9C | 234 | ||
| 10 | Advanced trigonometry | 235 | |
| A | Observing periodic behaviour | 237 | |
| B | The sine function | 240 | |
| Investigation 1: The family y=a sin x | 241 | ||
| Investigation 2: The family y=sin bx, b>0 | 242 | ||
| Investigation 3: The families y=sin(x-c) and y=sin x + d | 244 | ||
| C | Modelling using sine functions | 246 | |
| D | The cosine function | 249 | |
| E | The tangent function | 251 | |
| F | General trigonometric functions | 254 | |
| G | Trigonometric equations | 255 | |
| H | Using trigonometric models | 261 | |
| I | Trigonometric relationships | 263 | |
| J | Double angle formulae | 266 | |
| Investigation 4: Double angle formulae | 266 | ||
| K | Trigonometric equations in quadratic form | 269 | |
| Review set 10A | 269 | ||
| Review set 10B | 270 | ||
| Review set 10C | 271 | ||
| 11 | Matrices | 273 | |
| A | Matrix structure | 274 | |
| B | Matrix operations and definitions | 276 | |
| C | The inverse of a 2×2 matrix | 291 | |
| D | 3×3 matrices | 297 | |
| E | Solving systems of linear equations | 299 | |
| Investigation: Using matrices in cryptography | 302 | ||
| Review set 11A | 304 | ||
| Review set 11B | 305 | ||
| Review set 11C | 307 | ||
| 12 | Vectors in 2 and 3 dimensions | 309 | |
| A | Introduction | 310 | |
| B | Geometric operations with vectors | 314 | |
| C | 2-D vectors in component form | 322 | |
| D | 3-D coordinate geometry | 327 | |
| E | 3-D vectors in component form | 330 | |
| F | Algebraic operations with vectors | 333 | |
| G | Parallelism | 337 | |
| H | Unit vectors | 338 | |
| I | The scalar product of two vectors | 341 | |
| Review set 12A | 347 | ||
| Review set 12B | 349 | ||
| Review set 12C | 351 | ||
| 13 | Lines and planes in space | 353 | |
| A | Lines in 2-D and 3-D | 355 | |
| B | Applications of a line in a plane | 360 | |
| C | Relationships between lines | 368 | |
| Review set 13A | 371 | ||
| Review set 13B | 371 | ||
| Review set 13C | 372 | ||
| 14 | Descriptive statistics | 375 | |
| A | Key statistical concepts | 376 | |
| B | Measuring the centre of data | 381 | |
| Investigation: Merits of the mean and median | 384 | ||
| C | Measuring the spread of data | 394 | |
| D | Cumulative frequency graphs | 399 | |
| E | Statistics using technology | 404 | |
| F | Variance and standard deviation | 406 | |
| G | The significance of standard deviation | 412 | |
| Review set 14A | 414 | ||
| Review set 14B | 415 | ||
| Review set 14C | 416 | ||
| 15 | Probability | 419 | |
| A | Experimental probability | 422 | |
| Investigation 1: Tossing drawing pins | 422 | ||
| Investigation 2: Coin tossing experiments | 423 | ||
| Investigation 3: Dice rolling experiments | 424 | ||
| B | Sample space | 426 | |
| C | Theoretical probability | 427 | |
| D | Tables of outcomes | 431 | |
| E | Compound events | 433 | |
| Investigation 4: Probabilities of compound events | 433 | ||
| Investigation 5: Revisiting drawing pins | 434 | ||
| F | Using tree diagrams | 438 | |
| G | Sampling with and without replacement | 440 | |
| Investigation 6: Sampling simulation | 442 | ||
| H | Binomial probabilities | 444 | |
| I | Sets and Venn diagrams | 446 | |
| J | Laws of probability | 452 | |
| K | Independent events | 456 | |
| Review set 15A | 457 | ||
| Review set 15B | 458 | ||
| Review set 15C | 459 | ||
| Investigation 7: How many should I plant? | 460 | ||
| 16 | Introduction to calculus | 461 | |
| A | Limits | 462 | |
| B | Finding asymptotes using limits | 466 | |
| Investigation 1: Limits in number sequences | 467 | ||
| C | Rates of change | 468 | |
| Investigation 2: Instantaneous speed | 468 | ||
| Investigation 3: The gradient of a tangent | 470 | ||
| D | Calculation of areas under curves | 471 | |
| Investigation 4: Estimating ∫-33e(-x2/2) dx | 476 | ||
| Review set 16 | 477 | ||
| 17 | Differential calculus | 479 | |
| A | The derivative function | 480 | |
| Investigation 1: Finding gradients of functions | 482 | ||
| B | Derivatives at a given x-value | 483 | |
| C | Simple rules of differentiation | 485 | |
| Investigation 2: Simple rules of differentiation | 485 | ||
| D | The chain rule | 489 | |
| Investigation 3: Differentiating composites | 490 | ||
| E | The product rule | 493 | |
| F | The quotient rule | 495 | |
| G | Tangents and normals | 497 | |
| H | The second derivative | 501 | |
| Review set 17A | 503 | ||
| Review set 17B | 504 | ||
| Review set 17C | 505 | ||
| 18 | Applications of differential calculus | 507 | |
| A | Time rate of change | 508 | |
| B | General rates of change | 509 | |
| C | Motion in a straight line | 513 | |
| Investigation: Displacement, velocity and acceleration graphs | 517 | ||
| D | Some curve properties | 520 | |
| E | Rational functions | 528 | |
| F | Inflections and shape | 533 | |
| G | Optimisation | 538 | |
| Review set 18A | 547 | ||
| Review set 18B | 548 | ||
| Review set 18C | 549 | ||
| 19 | Derivatives of exponential and logarithmic functions | 551 | |
| A | Exponential e | 552 | |
| Investigation 1: The derivative of y=ax | 552 | ||
| Investigation 2: Finding a when y=a and dy/dx=a | 553 | ||
| B | Natural logarithms | 557 | |
| C | Derivatives of logarithmic functions | 560 | |
| Investigation 3: The derivative of ln x | 560 | ||
| D | Applications | 563 | |
| Review set 19A | 566 | ||
| Review set 19B | 567 | ||
| Review set 19C | 568 | ||
| 20 | Derivatives of trigonometric functions | 569 | |
| A | Derivatives of trigonometric functions | 570 | |
| Investigation: Derivatives of sin t and cos t | 570 | ||
| B | Optimisation with trigonometry | 575 | |
| Review set 20 | 577 | ||
| 21 | Integration | 579 | |
| A | Antidifferentiation | 580 | |
| B | The fundamental theorem of calculus | 582 | |
| Investigation: The area function | 582 | ||
| C | Integration | 587 | |
| D | Integrating f(ax+b) | 594 | |
| E | Definite integrals | 598 | |
| Review set 21A | 602 | ||
| Review set 21B | 602 | ||
| Review set 21C | 603 | ||
| 22 | Applications of integration | 605 | |
| Investigation: ∫ab f(x) dx and areas | 606 | ||
| A | Finding areas between curves | 606 | |
| B | Motion problems | 612 | |
| C | Problem solving by integration | 617 | |
| D | Solids of revolution | 619 | |
| Review set 22A | 625 | ||
| Review set 22B | 626 | ||
| Review set 22C | 627 | ||
| 23 | Statistical distributions of discrete random variables | 629 | |
| A | Discrete random variables | 630 | |
| B | Discrete probability distributions | 632 | |
| C | Expectation | 635 | |
| D | The binomial distribution | 639 | |
| Review set 23A | 643 | ||
| Review set 23B | 643 | ||
| Review set 23C | 644 | ||
| 24 | Statistical distributions of continuous random variables | 645 | |
| A | Continuous probability density functions | 646 | |
| B | Normal distributions | 648 | |
| Investigation 1: Standard deviation significance | 650 | ||
| C | The standard normal distribution (Z-distribution) | 653 | |
| Investigation 2: Properties of z=(x-μ)/σ | 653 | ||
| D | Quantiles or k-values | 659 | |
| E | Applications of the normal distribution | 661 | |
| Review set 24A | 664 | ||
| Review set 24B | 665 | ||
| Review set 24C | 666 | ||
| 25 | Miscellaneous questions | 667 | |
| A | Non-calculator questions | 668 | |
| B | Calculator questions | 681 | |
| Answers | 695 | ||
| Index | 763 | ||