### Written by Gregory Hine

## CONTENTS

**UNIT 1**

1. Functions I

2. Functions II

3. Trigonometry I

4. Trigonometry II

5. Counting Techniques

6. Probability and Sets**UNIT 2**

7. Exponents and Exponential Functions

8. Sequences and Recursion

9. Introduction to Differential Calculus

10. Applications of Differential Calculus

11. Introduction to Integral Calculus

TRIAL TESTS

SOLUTIONS TO PROBLEMS

SOLUTIONS TO TRIAL TESTS

## FOREWORD

The purpose of this text is to assist Year 11 students with their preparation for tests and examinations in the new Mathematical Methods course for Western Australia.

The Syllabus Checklist indicates to students which skills they must have acquired and the objectives they need to meet under each of the major headings of the course.

The Worked Examples are presented in a detailed manner, with brief notes and explanations being used to amplify the understanding for the particular question. Some of these worked examples could be used in the written notes that students are permitted to take into an examination.

The Problems to Solve section in each chapter provides students with a broad range of questions without the repetitive nature of problems usually associated with a course textbook.

The Trial Tests are an additional component to this text, and these allow students to familiarise themselves with examination questions. Suggested times are given for these tests, and students should be encouraged to adhere to these times to prepare properly for final examinations. Fully worked solutions are provided for students to receive immediate, accurate and useful feedback on their performance.

About the Units

In Unit 1, students review the basic algebraic concepts and techniques required for a successful introduction to the study of functions and calculus. Simple relationships between variable quantities are reviewed, and these are used to introduce the key concepts of a function and its graph. The study of probability and statistics begins with a review of the fundamentals of probability together with the concepts of conditional probability and independence. The study of the trigonometric functions commences with a consideration of the unit circle using degrees, the trigonometry of triangles, and the application of trigonometry. Students are then introduced to radian measure, the graphs of the trigonometric functions, and the application of trigonometric functions.

In Unit 2, students are introduced to exponential functions, their properties and graphs. Arithmetic and geometric sequences and their applications are explored and their recursive definitions applied. Rates and average rates of change are introduced, and this is followed by an examination of the key concept of the derivative as an ‘instantaneous rate of change’. These concepts are reinforced numerically (by calculating difference quotients), geometrically (as slopes of chords and tangents), and algebraically. This first calculus topic concludes with differentiating polynomial functions, using simple applications of the derivative to sketch curves, determining slopes and equations of tangents, calculating instantaneous velocities, and solving optimisation problems.

Dr Gregory Hine, Ph.D.