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 first of two books to choose from for the Pre-Diploma Grade/Year: this book (MYP 5) aims to cover the Presumed Knowledge required for ‘Mathematical Studies SL’ at Diploma level; its companion (MYP 5 Plus) aims to cover the Presumed Knowledge required for either ‘Mathematics SL’ or ‘Mathematics HL’ at Diploma level.
Pre-Diploma Studies SL (MYP 5) is our interpretation of the Presumed Knowledge required for the IB Diploma course ‘Mathematical Studies’. 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 might be expected to embark on an ‘Applications’ type of Mathematics course 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 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||Measurement and units||25|
|Review set 1A||40|
|Review set 1B||41|
|A||Operations with integers||44|
|B||Operations with fractions||49|
|D||Laws of indices||57|
|Review set 2A||59|
|Review set 2B||60|
|3||Sets, sequences and logic||61|
|B||Important number sets||63|
|C||Constructing sets (Interval notation)||66|
|E||Union and intersection||69|
|F||Simple set problems||72|
|H||Introduction to logic||75|
|Review set 3A||79|
|Review set 3B||80|
|4||Rounding and estimation||81|
|C||One figure approximations||86|
|D||Rounding decimal numbers||88|
|E||Using a calculator to round off||90|
|F||Significant figure rounding||92|
|Review set 4A||95|
|Review set 4B||96|
|5||The Rule of Pythagoras||97|
|A||The Rule of Pythagoras (Review)||99|
|B||Further problem solving||103|
|C||Testing for right angles||106|
|Review set 5A||109|
|Review set 5B||110|
|A||Changing words into symbols||112|
|C||Converting into algebraic form||115|
|E||Number patterns and rules||118|
|F||The value of an expression||120|
|Review set 6A||124|
|Review set 6B||125|
|7||Length and area||127|
|A||Perimeter and length||128|
|Review set 7A||147|
|Review set 7B||148|
|8||Decimals and percentage||149|
|C||Working with percentages||154|
|D||Unitary method in percentage||156|
|E||Percentage increase and decrease||157|
|F||Scientific notation (Standard form)||159|
|Review set 8A||163|
|Review set 8B||164|
|9||Algebraic simplification and expansion||167|
|A||Collecting like terms||168|
|C||The distributive law||172|
|D||The expansion of (a+b)(c+d)||177|
|E||The expansion rules||179|
|F||Perimeters and areas||183|
|Review set 9A||185|
|Review set 9B||185|
|A||Terminology for the study of statistics||189|
|B||Quantitative (numerical) data||194|
|C||Grouped discrete data||197|
|E||Measuring the centre||202|
|G||Measuring the spread||211|
|I||Statistics from technology||217|
|Review set 10A||218|
|Review set 10B||219|
|A||Solution by inspection or trial and error||223|
|C||Formal solution of linear equations||226|
|D||Equations with a repeated unknown||228|
|F||Unknown in the denominator||231|
|H||Problem solving using equations||235|
|I||Finding an unknown from a formula||237|
|Review set 11A||243|
|Review set 11B||244|
|12||Ratios and rates||245|
|D||The unitary method for ratios||251|
|E||Using ratios to divide quantities||252|
|Review set 12A||262|
|Review set 12B||264|
|B||Factorising with common factors||268|
|C||Factorising expressions with four terms||272|
|D||Factorising quadratic trinomials||273|
|E||Factorisation of ax2+bx+c (a ≠ 1)||275|
|F||Difference of two squares factorising||278|
|Review set 13A||278|
|Review set 13B||279|
|14||Congruence and similarity||281|
|A||Congruence of figures||282|
|E||Problem solving with similar triangles||292|
|Review set 14A||295|
|Review set 14B||296|
|15||Volume and capacity||297|
|Review set 15A||309|
|Review set 15B||310|
|A||Labelling sides of a right angled triangle||312|
|C||Using the sine ratio||316|
|D||Using the cosine ratio||318|
|E||Using the tangent ratio||319|
|F||Problem solving with trigonometry||321|
|Review set 16A||326|
|Review set 16B||328|
|17||Coordinates and lines||329|
|A||Plotting points on the Cartesian plane||330|
|B||Distance between two points||332|
|D||Gradient (or slope)||335|
|G||Finding equations of straight lines||342|
|I||Points on lines||348|
|J||Other line forms||349|
|K||Parallel and perpendicular lines||350|
|Review set 17A||354|
|Review set 17B||355|
|18||Simultaneous linear equations||357|
|A||The point of intersection of linear graphs||358|
|C||Algebraic methods for solving simultaneous equations||362|
|E||Using a graphics calculator to solve simultaneous equations||368|
|Review set 18A||370|
|Review set 18B||370|
|A||Probability by experiment||373|
|D||Probabilities from tabled data||378|
|E||Representing combined events||379|
|F||Probabilities from lists and diagrams||381|
|H||Using tree diagrams||385|
|I||Sampling with and without replacement||388|
|J||Mutually exclusive and non-mutually exclusive events||390|
|Review set 19A||393|
|Review set 19B||394|
|20||Functions, graphs and notation||395|
|B||Interpreting line graphs||398|
|D||Time series data||402|
|Review set 20A||410|
|Review set 20B||412|
|D||Angles of a quadrilateral||427|
|F||The exterior angles of a polygon||433|
|G||Nets of solids||434|
|Review set 21A||435|
|Review set 21B||437|
|22||Quadratic and other equations||439|
|B||Problem solving with quadratics||443|
|D||Solving harder equations with technology||447|
|Review set 22A||449|
|Review set 22B||450|
|A||Profit and loss||452|
|B||Percentage profit and loss||454|
|D||Using a multiplier||459|
|E||Chain percentage problems||461|
|Review set 23A||472|
|Review set 23B||474|
|A||Graphs of quadratic functions||476|
|C||The axis of symmetry||480|
|Review set 24A||485|
|Review set 24B||486|
|25||Transformation geometry (Chapter on CD only)||487|
|Review set 25A||14|
|Review set 25B||15|
|26||Sine and cosine rules (chapter on CD only)||488|
|Chapter on CD only|
|B||Area of a triangle using sine||4|
|C||The sine rule||5|
|D||The cosine rule||10|
|E||Problem solving with the sine and cosine rules||13|
|Review set 26A||14|
|Review set 26B||15|
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 Studies SL (MYP 5) is an attempt to cover, in one volume, the Presumed Knowledge required for the IB Diploma course “Mathematical Studies SL” as well as including some extension topics. It may also be used as a general textbook at about Grade 10 level in classes where students might be expected to embark on an “Applications” type of Mathematics course in their final two years of high school.
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 Mathematical Studies SL at Diploma level. 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. Time constraints may 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 beyond what might be regarded as an essential prerequisite for Diploma.
This package is language rich and technology rich. We hope 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 should nurture a much deeper understanding and appreciation of mathematical concepts. The inclusion of our new software (see p. 5) is intended to help students who have been absent from classes or who experience difficulty understanding the material.
The book contains many problems from the basic to the advanced, to cater for a range of student abilities and interests. While some of the exercises are simply designed to build skills, every effort has been made to contextualise problems, so that students can see everyday uses and practical applications of the mathematics they are studying, and appreciate the universality of 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. 8).
The interactive CD also allows immediate access to our own specially designed geometry packages, graphing packages and more.
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.
We welcome your feedback.