Sample chapters for download

1. Functions
5. Graphing and transforming functions
8. Counting and binomial expansion
12. Advanced trigonometry
30. Miscellaneous questions

NB: Sample chapters do not have working links.

About the book

Mathematics for the International Student: Mathematics HL has been written to reflect the syllabus for the two-year IB Diploma Mathematics HL course. It is not our intention to define the course. Teachers are encouraged to use other resources. We have developed the book independently of the International Baccalaureate Organization (IBO) in consultation with many experienced teachers of IB Mathematics. The text is not endorsed by the IBO.

This second edition builds on the strengths of the first edition. Many excellent suggestions were received from teachers around the world and these are reflected in the changes. In some cases sections have been consolidated to allow for greater efficiency. Changes have also been made in response to the introduction of a calculator-free examination paper. A large number of questions, including some to challenge even the best students, have been added. In particular, the final chapter contains over 200 miscellaneous questions, some of which require the use of a graphics calculator. These questions have been included to provide more difficult challenges for students and to give them experience at working with problems that may or may not require the use of a graphics calculator.

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 is certain to nurture a much deeper understanding and appreciation of mathematical concepts.

The book contains many problems from the basic to the advanced, to cater for a wide 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.

Emphasis is placed on the gradual development of concepts with appropriate worked examples, but we have also provided extension material for those who wish to go beyond the scope of the syllabus. Some proofs have been included for completeness and interest although they will not be examined.

For students who may not have a good understanding of the necessary background knowledge for this course, we have provided printable pages of information, examples, exercises and answers on the Student CD. To access these pages, simply click on the ‘Background knowledge’ icons when running the CD.

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 work as possible.

Investigations throughout the book will add to the discovery aspect of the course and enhance student understanding and learning. Many Investigations could be developed into portfolio assignments. Teachers should follow the guidelines for portfolio assignments to ensure they set acceptable portfolio pieces for their students that meet the requirement criteria for the portfolios. Review sets appear at the end of each chapter and a suggested order for teaching the two-year course is given at the end of this Foreword.

The extensive use of graphics calculators and computer packages throughout the book enables students to realise the importance, application and appropriate use of technology. No single aspect of technology has been favoured. It is as important that students work with a pen and paper as it is that they use their calculator or graphics calculator, or use a spreadsheet or graphing package on computer.

The interactive features of the CD allow immediate access to our own specially designed geometry packages, graphing packages and more. Teachers are provided with a quick and easy way to demonstrate concepts, and students can discover for themselves and re-visit when necessary.

Instructions appropriate to each graphic calculator problem are on the CD and can be printed for students. These instructions are written for Texas Instruments and Casio calculators.

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.

Using the interactive student CD

The interactive CD is ideal for independent study. Frequent use will nurture a deeper understanding of Mathematics. 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.

The icon denotes an Interactive Link on the CD. Simply ‘click’ the icon to access a range of interactive features:

• spreadsheets
• video clips
• graphing and geometry software
• graphics calculator instructions
• computer demonstrations and simulations
• background knowledge (as printable pages)

For a complete list of all the active links on the Mathematics HL CORE second edition CD, click here.

For those who want to make sure they have the prerequisite levels of understanding for this course, printable pages of background informations, examples, exercises and answers and provided on the CD. Click the ‘Background knowledge’ icon on pages 12 and 248.

Graphics calculators: Instructions for using graphics calculators are also given on the CD and can be printed. Instructions are given for Texas Instruments and Casio calculators. Click on the relevant icon (TI or C) to access the instructions for the other type of calculator.

Note on accuracy

Students are reminded that in assessment tasks, including examination papers, unless otherwise stated in the question, all numerical answers must be given exactly or to three significant figures.

HL and SL combined classes

Click Use in combined SL & HL classes for guidance in using this textbook in HL and SL combined classes, or email hannah@haesemathematics.com.au.

HL Options

This is a companion to the Mathematics HL (Core) textbook. It offers coverage of each of the following options:

• Topic 8 – Statistics and probability
• Topic 9 – Sets, relations and groups
• Topic 10 – Series and differential equations
• Topic 11 – Discrete mathematics

In addition, coverage of the Geometry option for students undertaking the IB Diploma course Further Mathematics is presented on the CD that accompanies the HL Options book.

Supplementary books

A separated book of WORKED SOLUTIONS give the fully worked solutions for every question (discussions, investigations and projects excepted) in each chapter of the Mathematics HL (Core) textbook. The HL (CORE) EXAMINATION PREPARATION & PRACTICE GUIDE offers additional questions and practice exams to help students prepare for the Mathematics HL examination. For more information email info@haesemathematics.com.au.

Table of contents