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.
NB: Sample chapters do not have working links.
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 firstname.lastname@example.org.
The complete series comprises:
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 icon to activate the self-tutoring software.
Other features include:
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.
|Graphics calculator instructions||9|
|C||Secondary function and alpha keys||15|
|G||Working with functions||21|
|D||Order of operations||34|
|E||Fractions and rational numbers||37|
|H||Prime numbers and index notation||50|
|Review set 1A||53|
|Review set 1B||54|
|B||The language of mathematics||59|
|C||Changing words to symbols||60|
|F||Collecting like terms||67|
|G||Product and quotient simplification||69|
|Review set 2A||71|
|Review set 2B||71|
|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|
|Review set 3A||97|
|Review set 3B||98|
|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|
|C||Information from line graphs||126|
|D||Using technology to graph data||127|
|Review set 5A||129|
|Review set 5B||131|
|A||The solution of an equation||134|
|C||Isolating the unknown||137|
|D||Formal solution of linear equations||138|
|E||Equations with a repeated unknown||141|
|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|
|D||Quadrilaterals and other polygons||162|
|Review set 7A||170|
|Review set 7B||171|
|A||Algebraic products and quotients in index notation||174|
|D||Zero and negative indices||180|
|E||Scientific notation (Standard form)||183|
|Review set 8A||188|
|Review set 8B||188|
|9||Radicals and pythagoras||189|
|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|
|G||Problem solving using Pythagoras||205|
|H||Three dimensional problems (Extension)||208|
|Review set 9A||211|
|Review set 9B||212|
|10||Length and area||213|
|A||Lengths and perimeters||214|
|B||Circumference of a circle||218|
|D||Areas of circles and ellipses||228|
|E||Areas of composite figures||230|
|Review set 10A||240|
|Review set 10B||241|
|A||Converting into algebraic form||244|
|C||Problem solving using equations||248|
|D||Finding an unknown from a formula||251|
|F||Solving linear inequations||255|
|Review set 11A||259|
|Review set 11B||260|
|12||Volume and capacity||261|
|A||Units of volume||262|
|Review set 12A||274|
|Review set 12B||275|
|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|
|A||Trial and error solution||304|
|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|
|A||Probability by experiment||317|
|B||Probabilities from tabled data||319|
|C||Probabilities from two way tables||320|
|Review set 15A||327|
|Review set 15B||327|
|16||Transformations, similarity and congruence||329|
|B||Reflections and line symmetry||331|
|C||Rotations and rotational symmetry||334|
|D||Enlargements and reductions||337|
|G||Areas and volumes of similar objects||341|
|H||Congruence of triangles||346|
|Review set 16A||350|
|Review set 16B||351|
|B||Factorising with common factors||356|
|C||Difference of two squares factorising||359|
|D||Perfect square factorisation||361|
|E||Factorising quadratic trinomials||363|
|Review set 17A||367|
|Review set 17B||367|
|18||Comparing categorical data||369|
|B||Examining categorical data||376|
|C||Comparing and reporting categorical data||380|
|Review set 18A||385|
|Review set 18B||387|
|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|
|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|
|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|
|C||Using grids to find probabilities||442|
|E||Using tree diagrams||445|
|Review set 22A||451|
|Review set 22B||452|
|A||Using scale diagrams in geometry||454|
|C||The trigonometric ratios||460|
|D||Problem solving with trigonometry||464|
|Review set 23A||468|
|Review set 23B||469|
|24||Introduction to networks||471|
|Review set 24A||482|
|Review set 24B||483|
|A||Everyday applications of loci||486|
|B||Experiments in locus||488|
|C||Locus in geometry||491|
|Review set 25||493|
|3||Cops and robbers||497|
|4||Translations on a chessboard||497|
|9||Jockeying for truth||502|
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 is a new 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.
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:
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 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.