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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 (for Middle Years)

Title:

Mathematics for the International Student 8 (MYP 3)

Price:

Australia: AU$54.45 (inc. GST)
Overseas: AU$49.50 (ex. GST)

Authors:

Pamela Vollmar
Michael Haese
Robert Haese
Sandra Haese
Mark Humphries

Year Published:

2008

ISBN-13:

978-1-876543-35-8

Extent:

544 pages

Availability:

Available now

Sample chapters for download

Graphics calculator instructions
1. Number
3. Percentage
8. Indices
13. Coordinate geometry
18. Comparing categorical data
24. Introduction to networks

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 third book in our new Middle Years series for international schools (for use with MYP 3, approx. Grade/Year 8).

This book may also be used as a general textbook at about Grade 8 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 contents - email hannah@haesemathematics.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:

  • Areas of interaction links to printable pages
  • graphing and geometry software
  • computer demonstrations and simulations
  • statistics package
  • video clips

For a complete list of all the active links on the MYP 3 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
       
  Challenge sets 25
       
1 Number 27
  A Natural numbers 28
  B Divisibility tests 30
  C Integers 32
  D Order of operations 34
  E Fractions and rational numbers 37
  F Decimal numbers 41
  G Ratio 46
  H Prime numbers and index notation 50
    Review set 1A 53
    Review set 1B 54
       
2 Algebraic operations 55
  A Algebraic notation 56
  B The language of mathematics 59
  C Changing words to symbols 60
  D Generalising arithmetic 63
  E Algebraic substitution 64
  F Collecting like terms 67
  G Product and quotient simplification 69
    Review set 2A 71
    Review set 2B 71
       
3 Percentage 73
  A Percentage 74
  B The unitary method in percentage 78
  C Finding a percentage of a quantity 80
  D Percentage increase and decrease 81
  E Percentage change using a multiplier 85
  F Finding the original amount 89
  G Simple interest 90
  H Compound interest 93
    Review set 3A 97
    Review set 3B 98
       
4 Algebraic expansion 99
  A The distributive law 100
  B The expansion of (a + b)(c + d) 105
  C The expansion rules 106
  D Expansion of radical expressions 112
    Review set 4A 115
    Review set 4B 116
       
5 Interpreting and drawing graphs 117
  A Interpreting graphs and charts 118
  B Travel graphs 123
  C Information from line graphs 126
  D Using technology to graph data 127
    Review set 5A 129
    Review set 5B 131
       
6 Solving equations 133
  A The solution of an equation 134
  B Maintaining balance 136
  C Isolating the unknown 137
  D Formal solution of linear equations 138
  E Equations with a repeated unknown 141
  F Fractional equations 143
  G Unknown in the denominator 146
    Review set 6A 148
    Review set 6B 148
       
7 The geometry of polygons 149
  A Review of geometrical facts 151
  B Triangles 156
  C Isosceles triangles 159
  D Quadrilaterals and other polygons 162
  E Deductive geometry 165
  F Special quadrilaterals 167
    Review set 7A 170
    Review set 7B 171
       
8 Indices 173
  A Algebraic products and quotients in index notation 174
  B Index laws 176
  C Expansion laws 178
  D Zero and negative indices 180
  E Scientific notation (Standard form) 183
  F Significant figures 186
    Review set 8A 188
    Review set 8B 188
       
9 Radicals and pythagoras 189
  A Square roots 191
  B Rules for square roots 192
  C Solving equations of the form x2 = k 194
  D The theorem of Pythagoras 196
  E The converse of Pythagoras’ theorem 202
  F Pythagorean triples 203
  G Problem solving using Pythagoras 205
  H Three dimensional problems (Extension) 208
  I Cube roots 209
    Review set 9A 211
    Review set 9B 212
       
10 Length and area 213
  A Lengths and perimeters 214
  B Circumference of a circle 218
  C Area 223
  D Areas of circles and ellipses 228
  E Areas of composite figures 230
  F Surface area 233
  G Problem solving 238
    Review set 10A 240
    Review set 10B 241
       
11 Algebra 243
  A Converting into algebraic form 244
  B Forming equations 246
  C Problem solving using equations 248
  D Finding an unknown from a formula 251
  E Linear inequations 253
  F Solving linear inequations 255
    Review set 11A 259
    Review set 11B 260
       
12 Volume and capacity 261
  A Units of volume 262
  B Volume formulae 263
  C Capacity 268
  D Problem solving 271
    Review set 12A 274
    Review set 12B 275
       
13 Coordinate geometry 277
  A Plotting points 279
  B Linear relationships 281
  C Plotting linear graphs 284
  D The equation of a line 286
  E Gradient or slope 287
  F Graphing lines from equations 291
  G Other line forms 294
  H Finding equations from graphs 298
  I Points on lines 299
    Review set 13A 301
    Review set 13B 302
       
14 Simultaneous equations 303
  A Trial and error solution 304
  B Graphical solution 305
  C Solution by substitution 306
  D Solution by elimination 308
  E Problem solving with simultaneous equations 311
    Review set 14A 314
    Review set 14B 314
       
15 Estimating probabilities 315
  A Probability by experiment 317
  B Probabilities from tabled data 319
  C Probabilities from two way tables 320
  D Chance investigations 322
    Review set 15A 327
    Review set 15B 327
       
16 Transformations, similarity and congruence 329
  A Translations 330
  B Reflections and line symmetry 331
  C Rotations and rotational symmetry 334
  D Enlargements and reductions 337
  E Similar figures 338
  F Similar triangles 340
  G Areas and volumes of similar objects 341
  H Congruence of triangles 346
    Review set 16A 350
    Review set 16B 351
       
17 Algebraic factorisation 353
  A Common factors 354
  B Factorising with common factors 356
  C Difference of two squares factorising 359
  D Perfect square factorisation 361
  E Factorising quadratic trinomials 363
  F Miscellaneous factorisation 366
    Review set 17A 367
    Review set 17B 367
       
18 Comparing categorical data 369
  A Categorical data 372
  B Examining categorical data 376
  C Comparing and reporting categorical data 380
  D Data collection 382
  E Misleading graphs 384
    Review set 18A 385
    Review set 18B 387
       
19 Quadratic equations 389
  A The Null Factor law 390
  B Equations of the form ax2 + bx = 0 391
  C Solving equations using the ‘difference of squares’ 392
  D Solving equations of the form x2 + bx + c = 0 393
  E Problem solving with quadratic equations 394
  F Simultaneous equations involving quadratic equations 398
    Review set 19A 399
    Review set 19B 399
       
20 Quantitative statistics 401
  A Quantitative data 402
  B Grouped discrete data 406
  C Measuring the centre 409
  D Comparing and reporting discrete data 415
    Review set 20A 417
    Review set 20B 419
       
21 Algebraic fractions 421
  A Evaluating algebraic fractions 422
  B Simplifying algebraic fractions 423
  C Multiplying and dividing algebraic fractions 425
  D Adding and subtracting algebraic fractions 427
  E Simplifying more complicated fractions 430
    Review set 21A 435
    Review set 21B 436
       
22 Theoretical probability 437
  A Sample space 438
  B Theoretical probability 439
  C Using grids to find probabilities 442
  D Multiplying probabilities 444
  E Using tree diagrams 445
  F Expectation 448
  G Odds 450
    Review set 22A 451
    Review set 22B 452
       
23 Trigonometry 453
  A Using scale diagrams in geometry 454
  B Trigonometry 455
  C The trigonometric ratios 460
  D Problem solving with trigonometry 464
    Review set 23A 468
    Review set 23B 469
       
24 Introduction to networks 471
  A Network diagrams 472
  B Constructing networks 474
  C Precedence networks 477
  D Counting pathways 480
    Review set 24A 482
    Review set 24B 483
       
25 Locus 485
  A Everyday applications of loci 486
  B Experiments in locus 488
  C Locus in geometry 491
    Review set 25 493
       
25 Activities 495
  1 Triangular numbers 496
  2 Word maze 496
  3 Cops and robbers 497
  4 Translations on a chessboard 497
  5 Shortest distance 498
  6 Engaged couples 499
  7 Number chains 500
  8 Paper 501
  9 Jockeying for truth 502
       
  Answers 503
       
  Index 543

Using the interactive CD

IB MYP 3 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:

  • Self Tutor
  • Areas of Interaction links to printable pages
  • Printable Chapters
  • Interactive Links – to spreadsheets, video clips, graphing and geometry software, computer demonstrations and simulations
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:

  • Approaches to learning
  • Community and service
  • Human ingenuity
  • Environments
  • Health and social education

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 8th Grade (or Year 8) level in classes where students are expected to complete a rigorous course in Mathematics. It is the third 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 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. Neither the series nor this text is 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.

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). Other features worth nothing include ‘Graphics Calculator Instructions’ (p. 9) and ‘Challenge Sets’ on the CD (see p. 25). Chapter 25 is a collection of miscellaneous activities which we hope students will find interesting and challenging (see p. 495).

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.