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With new SELF TUTOR CD

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 SELF TUTOR icon.

Book Information

Series:

Mathematics for the International Student (IB Diploma)

Title:

Mathematics SL (2nd edition)

Price:

Australia: AU$67.10 (inc. GST)
Overseas: AU$61.00 (ex. GST)

Authors:

Marjut Mäenpää
John Owen
Michael Haese
Robert Haese
Sandra Haese
Mark Humphries

Year Published:

2009

ISBN-13:

978-1-921500-09-1

Extent:

768 pages

Availability:

Available from US warehouse only

Sample chapters for download

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.

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To view the sample chapters you must have Adobe Reader installed.

About the book

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 SELF TUTOR for every worked example. SELF TUTOR 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.

Using the interactive student CD

IB SL CD INTERACTIVE LINK Calculator icons

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:

  • SELF TUTOR
  • Graphics calculator instructions
  • Background knowledge (as printable pages)
  • Interactive links to spreadsheets, graphing and geometry software, computer demonstrations and simulations

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 SELF TUTOR icon on each worked example denotes an active link on the CD.

Simply ‘click’ on the SELF TUTOR (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.

SELF TUTOR EXAMPLE

See Chapter 13, Lines and planes in space, p. 356

Table of contents

  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