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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

Title:

Mathematics for the International Student 9 (MYP 4)

Price:

Australia: AU$55.55 (inc. GST)
Overseas: AU$50.50 (ex. GST)

Authors:

Pamela Vollmar
Michael Haese
Robert Haese
Sandra Haese
Mark Humphries

Year Published:

2008

ISBN-13:

978-1-876543-29-7

Extent:

576 pages

Availability:

Available now

Order form

IB order form

Sample chapters for download

Graphics calculator instructions
3. Algebraic expansion and simplification
4. Radicals (surds)
8. Quadratic factorisation
10. Probability
23. Vectors

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

This is the fourth book in our new Middle Years series for international schools (for use with MYP 4, approx. Grade/Year 9).

This book may also be used as a general textbook at about Grade 9 level in schools where students are expected to complete a rigorous course in mathematics.

A URL may be made available so that teachers can preview the content - email ray@haeseandharris.com.au.

The complete series comprises:

About the accompanying CD

A feature of the accompanying CD is our new ‘self-tutoring’ software where a teacher’s voice explains each step in every worked example in the book. Click anywhere on any worked example where you see the SELF TUTOR icon to activate the self-tutoring software.

Other features include:

For a complete list of all the active links on the MYP 4 CD, click here.

The CD is ideal for independent study and revision. It also contains the full text of the book so that if students load it onto a home computer, they can keep the textbook at school and access the CD at home.

Table of contents

  Graphics calculator instructions 9
  A Basic calculations 10
  B Basic functions 12
  C Secondary function and alpha keys 15
  D Memory 15
  E Lists 18
  F Statistical graphs 20
  G Working with functions 21
  H Matrices 25
  I Two variable analysis 27
       
1 Algebra (notation and equations) 29
  A Algebraic notation 30
  B Algebraic substitution 32
  C Linear equations 34
  D Rational equations 38
  E Linear inequations 40
  F Problem solving 43
  G Money and investment problems 45
  H Motion problems 47
  I Mixture problems 48
    Review set 1A 49
    Review set 1B 50
       
2 Indices 51
  A Index notation 52
  B Index laws 55
  C Exponential equations 61
  D Scientific notation (Standard form) 63
  E Rational (fractional) indices 66
    Review set 2A 69
    Review set 2B 70
       
3 Algebraic expansion and simplification 71
  A Collecting like terms 72
  B Product notation 73
  C The distributive law 75
  D The product (a + b)(c + d) 76
  E Difference of two squares 78
  F Perfect squares expansion 80
  G Further expansion 82
  H The binomial expansion 84
    Review set 3A 85
    Review set 3B 86
       
4 Radicals (surds) 87
  A Radicals on a number line 88
  B Operations with radicals 89
  C Expansions with radicals 93
  D Division by radicals 96
    Review set 4A 99
    Review set 4B 100
       
5 Sets and Venn diagrams 101
  A Sets 102
  B Special number sets 104
  C Set builder notation 105
  D Complement of sets 106
  E Venn diagrams 108
    Review set 5A 115
    Review set 5B 116
       
6 Coordinate geometry 117
  A The distance between two points 119
  B Midpoints 122
  C Gradient (or slope) 124
  D Using gradients 128
  E Using coordinate geometry 129
  F Vertical and horizontal lines 131
  G Equations of straight lines 132
  H The general form of a line 136
  I Points on lines 138
  J Where lines meet 139
    Review set 6A 141
    Review set 6B 142
       
7 Mensuration 145
  A Error 147
  B Length and perimeter 149
  C Area 156
  D Surface area 162
  E Volume and capacity 167
    Review set 7A 174
    Review set 7B 175
       
8 Quadratic factorisation 177
  A Factorisation by removal of common factors 178
  B Difference of two squares factorisation 180
  C Perfect square factorisation 182
  D Factorising expressions with four terms 183
  E Quadratic trinomial factorisation 184
  F Miscellaneous factorisation 186
  G Factorisation of ax2+bx+c (a ≠ 1) 186
    Review set 8A 191
    Review set 8B 191
       
9 Statistics 193
  A Discrete numerical data 195
  B Continuous numerical data 199
  C Measuring the middle of a data set 201
  D Measuring the spread of data 206
  E Box-and-whisker plots 209
  F Grouped continuous data 212
  G Cumulative data 214
    Review set 9A 217
    Review set 9B 217
       
10 Probability 219
  A Experimental probability 221
  B Probabilities from data 222
  C Life tables 224
  D Sample spaces 226
  E Theoretical probability 227
  F Using 2-dimensional grids 229
  G Compound events 230
  H Events and Venn diagrams 233
  I Expectation 237
    Review set 10A 239
    Review set 10B 240
       
11 Financial mathematics 241
  A Business calculations 242
  B Appreciation 248
  C Compound interest 250
  D Depreciation 255
  E Borrowing 258
    Review set 11A 265
    Review set 11B 265
       
12 Trigonometry 267
  A Using scale diagrams 268
  B Labelling triangles 269
  C The trigonometric ratios 270
  D Trigonometric problem solving 275
  E Bearings 279
  F 3-dimensional problem solving 282
    Review set 12A 285
    Review set 12B 286
       
13 Formulae 289
  A Substituting into formulae 290
  B Rearranging formulae 293
  C Constructing formulae 295
  D Formulae by induction 298
    Review set 13A 301
    Review set 13B 302
       
14 Comparing numerical data 303
  A Graphical comparison 304
  B Parallel boxplots 306
  C A statistical project 311
    Review set 14A 312
    Review set 14B 313
       
15 Transformation geometry 315
  A Translations 318
  B Rotations 320
  C Reflections 324
  D Enlargements and reductions 329
  E Tessellations 333
    Review set 15A 337
    Review set 15B 338
       
16 Quadratic equations 339
  A Quadratic equations of the form x2=k 341
  B The Null Factor law 342
  C Solution by factorisation 343
  D Completing the square 346
  E Problem solving 349
    Review set 16A 351
    Review set 16B 352
       
17 Simultaneous equations 353
  A Linear simultaneous equations 354
  B Problem solving 358
  C Non-linear simultaneous equations 362
    Review set 17A 365
    Review set 17B 365
       
18 Matrices 367
  A Matrix size and construction 368
  B Matrix equality 371
  C Addition and subtraction of matrices 372
  D Scalar multiplication 375
  E Matrix multiplication 376
  F Matrices using technology 378
    Review set 18A 380
    Review set 18B 381
       
19 Quadratic functions 383
  A Quadratic functions 384
  B Graphs of quadratic functions 387
  C Using transformations to sketch quadratics 391
  D Graphing by completing the square 393
  E Axes intercepts 394
  F Quadratic graphs 397
  G Maximum and minimum values of quadratics 399
    Review set 19A 401
    Review set 19B 402
       
20 Tree diagrams and binomial probabilities 403
  A Sample spaces using tree diagrams 404
  B Probabilities from tree diagrams 405
  C Binomial probabilities 411
    Review set 20A 416
    Review set 20B 417
       
21 Algebraic fractions 419
  A Evaluating algebraic fractions 420
  B Simplifying algebraic fractions 421
  C Multiplying and dividing algebraic fractions 427
  D Adding and subtracting algebraic fractions 429
  E More complicated fractions 432
    Review set 21A 433
    Review set 21B 434
       
22 Other functions: their graphs and uses 435
  A Exponential functions 436
  B Graphing simple exponential functions 437
  C Growth problems 440
  D Decay problems 442
  E Simple rational functions 444
  F Optimisation with rational functions 447
  G Unfamiliar functions 449
    Review set 22A 450
    Review set 22B 451
       
23 Vectors 453
  A Vector representation 455
  B Lengths of vectors 456
  C Equal vectors 458
  D Vector addition 459
  E Multiplying vectors by a number 463
  F Vector subtraction 465
  G The direction of a vector 467
  H Problem solving by vector addition 469
    Review set 23A 471
    Review set 23B 472
       
24 Deductive geometry 473
  A Review of facts and theorems 475
  B Circle theorems 479
  C Congruent triangles 485
  D Similar triangles 488
  E Problem solving with similar triangles 492
  F The midpoint theorem 494
  G Euler’s rule 496
    Review set 24A 498
    Review set 24B 499
       
25 Non-right angled triangle trigonometry 501
  A The unit quarter circle 502
  B Obtuse angles 505
  C Area of a triangle using sine 507
  D The sine rule 508
  E The cosine rule 512
  F Problem solving with the sine and cosine rules 514
    Review set 25A 516
    Review set 25B 517
       
26 Variation CD
  A Direct variation CD
  B Inverse variation CD
    Review set 26A CD
    Review set 26B CD
       
27 Two variable analysis CD
  A Correlation CD
  B Pearson’s correlation coefficient, r CD
  C Line of best fit by eye CD
  D Linear regression CD
    Review set 27A CD
    Review set 27B CD
       
28 Logic CD
  A Propositions CD
  B Compound statements CD
  C Constructing truth tables CD
    Review set 28A CD
    Review set 28B CD
       
  Answers 523
       
  Index 573

Using the interactive CD

IB MYP 4 CD INTERACTIVE LINK

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 new interactive features can be accessed:

NEW

SELF TUTOR is a new 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

Areas of interaction

The International Baccalaureate Middle Years Programme focuses teaching and learning through five areas of interaction:

The Areas of Interaction are intended as a focus for developing connections between different subject areas in the curriculum and to promote an understanding of the interrelatedness of different branches of knowledge and the coherence of knowledge as a whole.

In an effort to assist busy teachers, we offer the following printable pages of ideas for projects and investigations:

Foreword

This book may be used as a general textbook at about 9th Grade (or Year 9) level in classes where students are expected to complete a rigorous course in Mathematics. It is the fourth book in our Middle Years series ‘Mathematics for the International Student’.

In terms of the IB Middle Years Programme (MYP), our series does not pretend to be a definitive course. In response to requests from teachers who use ‘Mathematics for the International Student’ at IB Diploma level, we have endeavoured to interpret their requirements, as expressed to us, for a series that would prepare students for the Mathematics courses at Diploma level. We have developed the series independently of the International Baccalaureate Organization (IBO) in consultation with experienced teachers of IB Mathematics. The text is not endorsed by the IBO.

In regard to this book, 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 content as possible.

To avoid producing a book that would be too bulky for students, we have presented these chapters on the CD as printable pages:

The above were selected because the content could be regarded as extension material for most 9th Grade (or Year 9) students.

We understand the emphasis that the IB MYP places on the five Areas of Interaction and in response there are links on the CD to printable pages which offer ideas for projects and investigations to help busy teachers (see p. 5).

Frequent use of the interactive features on the CD should nurture a much deeper understanding and appreciation of mathematical concepts. The inclusion of our new SELF TUTOR software (see p. 4) is intended to help students who have been absent from classes or who experience difficulty understanding the material.

The book contains many problems to cater for a range of student abilities and interests, and efforts have been made to contextualise problems so that students can see the practical applications of the mathematics they are studying.

We welcome your feedback.