This combined book is written for the new Year 12 Mathematics Advanced + Extension 1 courses, which are 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.
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.
Author(s): Terry H. Lee
Edition: First edition.
Year: 2019
Language: English
Tags: HSC
Graphing Techniques
1.1 Transformation of graphs
1.2 Rational functions
1.3 Using graphs
1.4 Review Exercise 1
Solutions
Differential Calculus
2.1 Review
2.2 Geometrical significance of f'(x)
2.3 Geometrical significance of f"(x)
2.4 Maximum and minimum problems
2.5 Review Exercise 2
Solutions
Integral Calculus
3.1 Review
3.2 More Integration Techniques
3.3 Definite Integration
3.4 Volume of solids of revolution
3.5 Approximations to Definite Integrals
3.6 Review Exercise 3
Solutions
Exponential and Logarithmic Functions
4.1 Differentiation of exponential functions
4.2 Integration of exponential functions
4.3 Differentiation oflogarithmic functions
4.4 Integration involving logarithmic functions
4.5 Review Exercise 4
Solutions
Trigonometric Functions
5.1 Review 1
5.2 Review 2
5.3 Graphs of trigonometric functions
5.4 Trigonometric equations
5.5 Small angles
5.6 Differentiation of Trigonometric functions
5.7 Integration of Trigonometric functions
5.8 Review Exercise 5
Solutions
Inverse Trigonometric Functions
6.1 Review
6.2 Derivatives oflnverse Trig functions
6.3 Integrals involving Inverse trig functions
6.4 Review Exercise 6
Solutions
Applications of Calculus
7.1 Review
7.2 Rates of change
7.3 Displacement and Velocity as Integrals
7.4 Differential Equations
7.5 Acceleration as a function of v or x
7.6 The Laws of Growth and Decay
7.7 Review Exercise 7
Solutions
Introduction to Vectors
8.1 Two-dimensional vectors
8.2 Geometrical applications
8.3 Projectile motion
8.4 Review Exercise 8
Solutions
Financial Mathematics
9.1 Introduction
9.2 The partial sum of a series
9.3 The terms of an Arthmetic Sequence
9.4 The sum of an Arithmetic Series
9.5 The terms of a Geometric Sequence
9.6 The sum of a Geometric Series
9. 7 Infinite series
9. 8 Financial Mathematics
9.9 Review Exercise 9
Solutions
Proof by Induction
10.1 Induction proofs
10.2 Review Exercise 10
Solutions
Data Analysis
11.1 Displaying data
11.2 Central tendencies and disperson
11.3 The normal distribution
11.4 Correlation and Regression
11.5 Review Exercise 11
Solutions
Binomial Distribution
12.1 Binomial distribution
12.2 Normal approximation
12.3 Review Exercise 12
Solutions
Random number table
The z-score table
