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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:

Mathematical Studies SL (2nd edition)

Price:

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

Authors:

Mal Coad
Glen Whiffen
Marjut Mäenpää
Mark Humphries
James Foley
Michael Haese
Sandra Haese

Year Published:

2010

ISBN-13:

978-1-921500-13-8

Extent:

808 pages

Availability:

Available now

Sample chapters for download

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.

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

About the book

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 SELF TUTOR 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 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.

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.

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
  • Interactive links to spreadsheets, graphing and geometry software, computer demonstrations and simulations

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 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 17, Logic, p. 542

Table of contents

  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