New Advanced Mathematics: A Complete HSC Mathematics Extension 2 Course

Author: Terry Lee, Publisher: Terry Lee

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.


  • Preface
  • Chapter 1: The nature of proof
    • 1.1 The nature of proof
    • 1.2 Induction proofs
    • 1.3 Inequality proofs
    • 1.4 Review Exercise 1
    • Solutions
  • Chapter 2: Vectors
    • 2.1 Two-dimensional vectors
    • 2.2 Geometrical applications
    • 2.3 Three-dimensional vectors
    • 2.4 More geometrical applications
    • 2.5 Review Exercise 2
    • Solutions
  • Chapter 3: Complex numbers
    • 3.1 Introduction
    • 3.2 Operations on complex numbers
    • 3.3 The Conjugate theorems
    • 3.4 Argand diagram
    • 3.5 Product and Quotient
    • 3.6 Geometrical applications
    • 3.7 Locus problems
    • 3.8 Locus problems by algebraic method
    • 3.9 De Moivre’s theorem
    • 3.10 The nth roots of complex numbers
    • 3.11 Trigonometric applications
    • 3.12 Review Exercise 3
    • Solutions
  • Chapter 4: Integration
    • 4.1 Understanding the SI table
    • 4.2 Trigonometric functions
    • 4.3 Splitting the numerator
    • 4.4 Partial fractions
    • 4.5 Use of t-formulae
    • 4.6 Definite Integrals
    • 4.7 Integration by parts
    • 4.8 Reduction formula
    • 4.9 Applications of Integration
    • 4.10 Review Exercise 4
    • Solutions
  • Chapter 5: Mechanics
    • 5.1 Simple harmonic motion
    • 5.2 Motion without resistance
    • 5.3 Resisted motion
    • 5.4 Projectiles and resisted motion
    • 5.5 Review Exercise 5
    • Solutions
More Information
Year Level Year 12
Edition 1st
Date of Publication March 2019
ISBN 9780957742888
Subject Maths, Mathematics Extension 2
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