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
8. Coordinate geometry
15. Financial Mathematics
18. Trigonometric functions
19. Exponential functions
20. Two variable statistics
21. Differential calculus
NB: Sample chapters do not have working links.
Mathematics for the International Student: Mathematical Studies SL has been written for use with the two-year Mathematical Studies 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. The main difference in this
second edition is the inclusion of more questions in the book and the addition of
on the CD. Extra questions have been included throughout, and a new final
chapter with 200 exam-style questions has been added. A clear distinction is made between
core (examinable) and extension material and syllabus references are given for each chapter.
Comprehensive graphics calculator instructions are given for Casio fx-9860G, TI-84 Plus and TI-nspire in an introductory chapter 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.
Note that in the graphics calculator instructions chapter, the programs written to solve quadratic equations for the TI-84 Plus and the TI-nspire can not be taken into examinations.
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.
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 revisit when necessary.
It is not our intention that each chapter be worked through in full. Time constraints will 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.
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 Mathematical Studies SL second edition CD, click here.
Graphics calculator instructions: where additional help may be needed, detailed instructions are available 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 17, Logic, p. 542
| | SYMBOLS AND NOTATION USED IN THIS BOOK | 9 | |
| USEFUL FORMULAE | 11 | ||
| GRAPHICS CALCULATOR INSTRUCTIONS | 15 | ||
| A | Casio fx-9860G | 16 | |
| B | Texas Instruments TI-84 Plus | 25 | |
| C | Texas Instruments TI-nspire | 34 | |
| 1 | NUMBER PROPERTIES | 45 | |
| A | Words used in mathematics | 46 | |
| B | Index notation | 48 | |
| C | Factors of positive integers | 51 | |
| D | Multiples of positive integers | 56 | |
| E | Order of operations | 57 | |
| Review set 1A | 60 | ||
| Review set 1B | 61 | ||
| 2 | MEASUREMENT | 63 | |
| A | Time | 64 | |
| B | Temperature | 68 | |
| C | Scientific notation (standard form) | 70 | |
| D | International system (SI) units | 72 | |
| E | Rounding numbers | 74 | |
| F | Rates | 80 | |
| G | Accuracy of measurements | 86 | |
| H | Error and percentage error | 88 | |
| Review set 2A | 92 | ||
| Review set 2B | 93 | ||
| Review set 2C | 94 | ||
| 3 | SETS AND VENN DIAGRAMS | 95 | |
| A | Set notation | 96 | |
| B | Special number sets | 98 | |
| C | Set builder notation | 101 | |
| D | Complements of sets | 102 | |
| E | Venn diagrams | 105 | |
| F | Venn diagram regions | 108 | |
| G | Numbers in regions | 109 | |
| H | Problem solving with Venn diagrams | 112 | |
| Review set 3A | 115 | ||
| Review set 3B | 117 | ||
| 4 | LAWS OF ALGEBRA | 119 | |
| A | Index laws | 120 | |
| B | The distributive law | 128 | |
| C | The product (a + b)(c + d) | 129 | |
| D | Difference of two squares | 131 | |
| E | Perfect squares expansions | 132 | |
| F | Further expansion | 134 | |
| Review set 4A | 137 | ||
| Review set 4B | 137 | ||
| 5 | EQUATIONS AND FORMULAE | 139 | |
| A | Algebraic substitution | 140 | |
| B | Linear equations | 142 | |
| C | Fractional equations | 146 | |
| D | Solving linear equations using technology | 148 | |
| E | Problem solving with linear equations | 149 | |
| F | Formula substitution | 151 | |
| G | Formula rearrangement | 154 | |
| H | Linear simultaneous equations | 156 | |
| I | Problem solving with simultaneous equations | 161 | |
| J | Exponential equations | 164 | |
| Review set 5A | 166 | ||
| Review set 5B | 167 | ||
| 6 | PYTHAGORAS' THEOREM | 169 | |
| A | Pythagoras' theorem | 170 | |
| B | Right angles in geometry | 175 | |
| C | The converse of Pythagoras' theorem | 180 | |
| D | Problem solving | 182 | |
| E | True bearings | 186 | |
| F | Three-dimensional problems | 189 | |
| Review set 6A | 192 | ||
| Review set 6B | 193 | ||
| Review set 6C | 194 | ||
| Review set 6D | 195 | ||
| 7 | DESCRIPTIVE STATISTICS | 197 | |
| A | Types of data | 199 | |
| B | Simple quantitative discrete data | 200 | |
| C | Grouped quantitative discrete data | 205 | |
| D | Quantitative continuous data | 210 | |
| E | Measuring the centre of data | 213 | |
| F | Measuring the spread of data | 223 | |
| G | Box and whisker plots | 226 | |
| H | Cumulative frequency graphs | 231 | |
| I | Statistics using technology | 235 | |
| J | Standard deviation | 237 | |
| Review set 7A | 245 | ||
| Review set 7B | 246 | ||
| Review set 7C | 248 | ||
| 8 | COORDINATE GEOMETRY | 251 | |
| A | Distance between two points | 253 | |
| B | Midpoints | 257 | |
| C | Gradient | 260 | |
| D | Rates | 267 | |
| E | Vertical and horizontal lines | 269 | |
| F | Equations of lines | 270 | |
| G | Graphing lines | 276 | |
| H | Perpendicular bisectors | 281 | |
| Review set 8A | 282 | ||
| Review set 8B | 283 | ||
| Review set 8C | 284 | ||
| Review set 8D | 285 | ||
| 9 | QUADRATIC ALGEBRA | 287 | |
| A | Factorisation with common factors | 289 | |
| B | The difference of two squares factorisation | 290 | |
| C | Perfect square factorisation | 292 | |
| D | Sum and product factorisation | 293 | |
| E | Factorisation of ax2 + bx + c | 294 | |
| F | Quadratic equations | 297 | |
| G | The Null Factor law | 298 | |
| H | The quadratic formula (extension) | 301 | |
| I | Solving quadratic equations using technology | 303 | |
| J | Problem solving with quadratics | 304 | |
| Review set 9A | 307 | ||
| Review set 9B | 307 | ||
| Review set 9C | 308 | ||
| Review set 9D | 308 | ||
| 10 | FUNCTIONS | 309 | |
| A | Relations and functions | 310 | |
| B | Function notation | 313 | |
| C | Domain and range | 315 | |
| D | Mappings | 317 | |
| E | Linear functions | 321 | |
| Review set 10A | 326 | ||
| Review set 10B | 327 | ||
| Review set 10C | 328 | ||
| 11 | PERIMETER, AREA AND VOLUME | 329 | |
| A | Conversion of units | 331 | |
| B | Perimeter | 333 | |
| C | Area | 337 | |
| D | Volume | 347 | |
| E | Capacity | 353 | |
| F | Density (extension) | 357 | |
| G | Harder applications | 359 | |
| Review set 11A | 360 | ||
| Review set 11B | 361 | ||
| Review set 11C | 363 | ||
| 12 | QUADRATIC FUNCTIONS | 365 | |
| A | Quadratic functions | 366 | |
| B | Graphs of quadratic functions | 369 | |
| C | Axes intercepts | 371 | |
| D | Axis of symmetry | 376 | |
| E | Vertex | 378 | |
| F | Finding a quadratic from its graph | 380 | |
| G | Where functions meet | 382 | |
| H | Quadratic modelling | 383 | |
| Review set 12A | 388 | ||
| Review set 12B | 389 | ||
| Review set 12C | 390 | ||
| 13 | TRIGONOMETRY | 391 | |
| A | Labelling right angled triangles | 392 | |
| B | The trigonometric ratios | 393 | |
| C | Using trigonometry in geometric figures | 399 | |
| D | Problem solving using trigonometry | 403 | |
| E | 3-dimensional problem solving | 406 | |
| F | Areas of triangles | 411 | |
| G | The cosine rule | 414 | |
| H | The sine rule | 416 | |
| I | Using the sine and cosine rules | 418 | |
| J | The ambiguous case (extension) | 421 | |
| K | Bearings (extension) | 423 | |
| Review set 13A | 426 | ||
| Review set 13B | 427 | ||
| Review set 13C | 429 | ||
| 14 | SEQUENCES AND SERIES | 431 | |
| A | Number patterns | 432 | |
| B | Sequences of numbers | 433 | |
| C | Arithmetic sequences | 434 | |
| D | Geometric sequences | 438 | |
| E | Applications of sequences | 441 | |
| F | Series | 446 | |
| Review set 14A | 452 | ||
| Review set 14B | 452 | ||
| Review set 14C | 453 | ||
| 15 | FINANCIAL MATHEMATICS | 455 | |
| A | Foreign exchange | 456 | |
| B | Simple interest | 463 | |
| C | Compound interest | 467 | |
| D | Depreciation | 478 | |
| E | Personal loans | 481 | |
| F | Inflation | 484 | |
| Review set 15A | 486 | ||
| Review set 15B | 487 | ||
| 16 | PROBABILITY | 489 | |
| A | Experimental probability | 491 | |
| B | Sample space | 497 | |
| C | Theoretical probability | 499 | |
| D | Two-dimensional grids | 501 | |
| E | Compound events | 504 | |
| F | Using tree diagrams | 508 | |
| G | Sampling | 511 | |
| H | Probabilities from Venn diagrams | 515 | |
| I | Laws of probability | 518 | |
| J | Independent events | 524 | |
| Review set 16A | 525 | ||
| Review set 16B | 526 | ||
| Review set 16C | 527 | ||
| 17 | LOGIC | 529 | |
| A | Propositions | 530 | |
| B | Compound propositions | 534 | |
| C | Truth tables and logical equivalence | 539 | |
| D | Implication and equivalence | 543 | |
| E | Converse, inverse and contrapositive | 545 | |
| F | Valid arguments (extension) | 548 | |
| Review set 17A | 553 | ||
| Review set 17B | 554 | ||
| Review set 17C | 555 | ||
| 18 | TRIGONOMETRIC FUNCTIONS | 557 | |
| A | Observing periodic behaviour | 559 | |
| B | The sine function | 562 | |
| C | The cosine function | 568 | |
| D | Modelling using sine and cosine functions | 570 | |
| E | Trigonometric equations | 572 | |
| F | Using trigonometric models | 575 | |
| Review set 18A | 577 | ||
| Review set 18B | 578 | ||
| Review set 18C | 579 | ||
| 19 | EXPONENTIAL FUNCTIONS | 581 | |
| A | Evaluating exponential functions | 583 | |
| B | Graphs of exponential functions | 583 | |
| C | Growth and decay | 586 | |
| Review set 19A | 592 | ||
| Review set 19B | 592 | ||
| 20 | TWO VARIABLE STATISTICS | 593 | |
| A | Correlation | 594 | |
| B | Measuring correlation | 597 | |
| C | Line of best fit by eye | 604 | |
| D | Linear regression | 608 | |
| E | The χ2 test of independence | 614 | |
| Review set 20A | 621 | ||
| Review set 20B | 623 | ||
| 21 | DIFFERENTIAL CALCULUS | 625 | |
| A | Rates of change | 626 | |
| B | Limits | 632 | |
| C | The derivative function | 634 | |
| D | Simple rules of differentiation | 638 | |
| E | Tangents to curves | 641 | |
| F | The second derivative | 642 | |
| Review set 21A | 645 | ||
| Review set 21B | 645 | ||
| Review set 21C | 646 | ||
| 22 | APPLICATIONS OF DIFFERENTIAL CALCULUS | 647 | |
| A | Properties of curves | 648 | |
| B | Rates of change | 655 | |
| C | Optimisation | 660 | |
| Review set 22A | 666 | ||
| Review set 22B | 666 | ||
| Review set 22C | 667 | ||
| 23 | UNFAMILIAR FUNCTIONS | 669 | |
| A | Properties of functions | 670 | |
| B | Asymptotes | 673 | |
| C | Optimisation | 676 | |
| D | Where functions meet | 678 | |
| Review set 23A | 680 | ||
| Review set 23B | 681 | ||
| 24 | MISCELLANEOUS PROBLEMS | 683 | |
| A | Short questions | 684 | |
| B | Long questions | 712 | |
| Answers | 735 | ||
| INDEX | 806 | ||