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 second of two books to choose from for the Pre-Diploma Grade/Year: this book (MYP 5 Plus – second edition) aims to cover the Presumed Knowledge required for ‘Mathematics SL’ and/or ‘Mathematics HL’ at Diploma level; its companion (MYP 5) aims to cover the Presumed Knowledge required for ‘Mathematical Studies SL’ at Diploma level.
Pre-Diploma SL and HL (MYP 5 Plus) second edition is our interpretation of the Presumed Knowledge required for the IB Diploma courses ‘Mathematics SL’ and ‘Mathematics HL’. It is not our intention to define the PK and we encourage teachers to use a variety of resources. The text is not endorsed by the International Baccalaureate Organization (IBO). We have developed the book independently of the IBO with advice from several experienced teachers of IB Mathematics.
This book may also be used as a general textbook at about Grade 10 level in schools where students are expected to complete a rigorous course in preparation for the study of mathematics at a high level in their final two years of high school.
A URL may be made available so that teachers can preview the content – email firstname.lastname@example.org.
The complete middle years 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 5 Plus second edition 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|
|1||Sets and Venn diagrams||29|
|D||Union and intersection||36|
|E||Problem solving with Venn diagrams||40|
|F||The algebra of sets (Extension)||42|
|Review set 1A||43|
|Review set 1B||44|
|2||Algebraic expansion and factorisation||45|
|A||Revision of expansion laws||46|
|B||Revision of factorisation||48|
|D||The binomial expansion||51|
|E||Factorising expressions with four terms||54|
|F||Factorising quadratic trinomials||55|
|G||Factorisation by splitting||57|
|Review set 2A||61|
|Review set 2B||62|
|3||Radicals and surds||63|
|A||Basic operations with radicals||65|
|B||Properties of radicals||67|
|C||Multiplication of radicals||70|
|D||Division by radicals||72|
|E||Equality of surds||74|
|Review set 3A||77|
|Review set 3B||78|
|B||The converse of Pythagoras’ theorem||85|
|C||Problem solving using Pythagoras’ theorem||88|
|F||More difficult problems (Extension)||98|
|Review set 4A||100|
|Review set 4B||101|
|A||Distance between two points||105|
|C||Gradient (or slope)||110|
|D||Using coordinate geometry||116|
|E||Equations of straight lines||118|
|F||Distance from a point to a line||127|
|G||3-dimensional coordinate geometry (Extension)||129|
|Review set 5A||130|
|Review set 5B||131|
|6||Congruence and similarity||133|
|A||Congruence of figures||134|
|E||Areas and volumes of similar figures||150|
|Review set 6A||152|
|Review set 6B||153|
|Review set 7A||167|
|Review set 7B||168|
|8||Univariate data analysis||169|
|B||Quantitative (numerical) data||176|
|C||Grouped discrete data||179|
|E||Measuring the centre||184|
|G||Measuring the spread||194|
|I||Statistics from technology||200|
|K||The normal distribution||206|
|Review set 8A||209|
|Review set 8B||211|
|A||Quadratic equations of the form x2 = k||215|
|B||Solution by factorisation||216|
|C||Completing the square||220|
|E||The quadratic formula||227|
|Review set 9A||231|
|Review set 9B||232|
|B||Trigonometric problem solving||240|
|C||3-dimensional problem solving||246|
|D||The unit circle||250|
|E||Area of a triangle using sine||252|
|F||The sine rule||255|
|G||The cosine rule||257|
|H||Problem solving with the sine and cosine rules||259|
|I||Trigonometric identities (Extension)||261|
|Review set 10A||264|
|Review set 10B||265|
|B||Probabilities from tabled data||271|
|C||Representing combined events||272|
|F||Using tree diagrams||280|
|G||Sampling with and without replacement||283|
|H||Mutually exclusive and non-mutually exclusive events||285|
|I||Venn diagrams and conditional probability||287|
|Review set 11A||292|
|Review set 11B||293|
|A||Simplifying algebraic fractions||296|
|B||Multiplying and dividing algebraic fractions||300|
|C||Adding and subtracting algebraic fractions||302|
|D||More complicated fractions||305|
|Review set 12A||307|
|Review set 12B||308|
|D||Formulae by induction||318|
|E||More difficult rearrangements||320|
|Review set 13A||323|
|Review set 13B||324|
|14||Relations, functions and sequences||325|
|A||Relations and functions||326|
|E||Transforming y = f(x)||335|
|G||The modulus function||340|
|H||Where functions meet||343|
|Review set 14A||354|
|Review set 14B||355|
|A||Directed line segment representation||358|
|E||Vectors in component form||367|
|H||Parallelism of vectors||374|
|I||The scalar product of two vectors||376|
|J||Vector proof (Extension)||380|
|Review set 15A||382|
|Review set 15B||384|
|16||Exponential functions and logarithms||385|
|B||Rational (fractional) indices||389|
|D||Growth and decay||393|
|H||Expansion and factorisation||401|
|Review set 16A||410|
|Review set 16B||411|
|B||Graphs of quadratic functions||416|
|D||Axis of symmetry and vertex||429|
|Review set 17A||435|
|Review set 17B||436|
|B||Trigonometric ratios from the unit circle||441|
|C||The multiples of 30° and 45°||444|
|D||Graphing trigonometric functions||448|
|E||Modelling with sine functions||451|
|G||Negative and complementary angle formulae||457|
|Review set 18A||461|
|Review set 18B||462|
|D||The arithmetic mean - geometric mean inequality (Extension)||473|
|Review set 19A||476|
|Review set 19B||476|
|20||Matrices and linear transformations||477|
|A||Introduction to matrices||478|
|B||Operations with matrices||480|
|D||The determinant of a matrix||487|
|E||Multiplicative identity and inverse matrices||489|
|H||Proofs with 2×2 matrices (Extension)||503|
|Review set 20A||504|
|Review set 20B||505|
|B||Further circle theorems||513|
|Review set 21A||526|
|Review set 21B||527|
|22||Introduction to calculus||529|
|A||Estimating gradients of tangents to curves||530|
|B||Gradients using quadratic theory||531|
|C||Gradients using limit theory||532|
|F||Areas under curves||543|
|H||The definite integral||547|
|Review set 22A||549|
|Review set 22B||550|
|23||Counting and probability||CD|
|A||The product and sum principles||CD|
|D||Counting with combinations||CD|
|E||Probabilities using permutations and combinations||CD|
|F||The hypergeometric distribution||CD|
|Review set 23A||CD|
|Review set 23B||CD|
|D||Other locus problems (Extension)||CD|
|Review set 24A||CD|
|Review set 24B||CD|
|B||Isomorphism and adjacency matrices||CD|
|D||Problem solving with networks||CD|
|Review set 25A||CD|
|Review set 25B||CD|
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:
Pre-Diploma SL and HL (MYP 5 Plus) second edition is an attempt to cover, in one volume, the Presumed Knowledge required for the IB Diploma courses ‘Mathematics SL’ and ‘Mathematics HL’. It may also be used as a general textbook at about 10th Grade level in classes where students complete a rigorous course in preparation for the study of mathematics at a high level in their final two years of high school.
Feedback from teachers using the first edition suggested that while it provided satisfactory preparation for prospective Mathematics SL students, several sections needed to be more rigorous to prepare students thoroughly for Mathematics HL. The first edition has been revised throughout and the highlighted topics in the table of contents show at a glance the main areas that have been substantially revised and extended.
In terms of the IB Middle Years Programme (MYP), this book 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 book that would prepare students for Mathematics SL and Mathematics HL. We have developed the book independently of the International Baccalaureate Organization (IBO) in consultation with experienced teachers of IB Mathematics. The text is not endorsed by the IBO.
It is not our intention that each chapter be worked through in full. 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.
Three additional chapters appear on the CD as printable pages:
These chapters were selected because the content could be regarded as extension beyond what might be regarded as an essential prerequisite for IB Diploma mathematics.
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 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 everyday uses and practical applications of the mathematics they are studying.
We welcome your feedback.