This book is written for the new Mathematics Extension 2 course, which is being introduced into the NSW syllabus in 2020.
This book has been written with two main objectives: it can be used as a textbook for classroom use, as well as a step-by-step resource to be used independently by students for their own self-study purposes. This book provides sufficiently clear explanations about each topic in the syllabus, with worked out examples and alternative methods, where applicable. Questions are categorised by topic and graded from easy to hard, to help guide students in their learning. Each chapter also contains a set of review exercises and challenge problems, as well as fully worked solutions for each question. The review exercises will help consolidate students’ skills and knowledge, while improving their competence and confidence. The book also features challenge problems. While they may extend beyond the syllabus, they are designed to provide extra stimulus for highly motivated students and increase confidence for the harder questions in the Higher School Certificate examination.
While this book is written specifically for the new Mathematics Extension 2 course, it also covers various topics in the Advanced Mathematics and Mathematics Extension 1 courses, including Mathematical Induction, Vectors, Integration and Elementary Dynamics. This book provides clear explanations of the basic concepts underpinning these topics to help provide students with a strong foundation upon which they can develop a more thorough understanding of the complex and challenging concepts in Mathematics Extension 2.
This book also features colour-coding throughout to highlight various theorems and study tips – this makes the book a study reference and more enjoyable to read. Students are advised to complete as many questions in this book as possible to master the course.
This book builds upon what the Terry Lee series has been famous for: it includes many fully explained tips and tricks to help students understand and solve problems efficiently, while ultimately developing a greater enjoyment of the course. The joy in being able to complete Mathematics Extension 2 questions, including harder questions, in half the time is immeasurably worthwhile.
Author(s): Terry H. Lee
Edition: First edition.
Year: 2019
Language: English
Tags: HSC
Preface
Chapter 1: The nature of proof
1.1 The nature of proof
Exercise 1.1
1.2 Induction proofs
Exercise 1.2
1.3 Inequality proofs
Exercise 1.3
1.4 Review Exercise 1
Challenge Problems 1
Solutions
Chapter 2: Vectors
2.1 Two-dimensional vectors
Exercise 2.1
2.2 Geometrical applications
Exercise 2.2
2.3 Three-dimensional vectors
Exercise 2.3
2.4 More geometrical applications
Exercise 2.4
2.5 Review Exercise 2
Challenge Problems 2
Solutions
Chapter 3: Complex numbers
3.1 Introduction
Exercise 3.1
3.2 Operations on complex numbers
Exercise 3.2
3.3 The Conjugate theorems
Exercise 3.3
3.4 Argand diagram
Exercise 3.4
3.5 Product and Quotient
Exercise 3.5
3.6 Geometrical Applications
Exercise 3.6
3.7 Locus problems
Exercise 3.7
3.8 Locus problems by algebraic method
Exercise 3.8
3.9 De Moivre's theorem
Exercise 3.9
3.10 The nth roots of complex numbers
Exercise 3.10
3.11 Trigonometric applications
Exercise 3.11
3.12 Review Exercise 3
Challenge Problems 3
Solutions
Chapter 4: Integration
4.1 Understanding the SI t able
Exercise 4.1
4.2 Trigonometric functions
Exercise 4.2
4.3 Splitting the numerator
Exercise 4.3
4.4 Partial fractions
Exercise 4.4
4.5 Use of t-formulae
Exercise 4.5
4.6 Definite Integrals
Exercise 4.6
4.7 Integration by parts
Exercise 4.7
4.8 Reduction formula
Exercise 4.8
4.9 Applications of Integration
Exercise 4.9
4.10 Review Exercise 4
Challenge Problems 4
Solutions
Chapter 5: Mechanics
5.1 Simple harmonic motion
Exercise 5.1
5.2 Motion without resistance
Exercise 5.2
5.3 Resisted motion
Exercise 5.3
5.4 Projectiles and resisted motion
Exercise 5.4
5.5 Review Exercse 5
Challenge Problems 5
Solutions
