(a) Test for functions (b) Domain and Range of functions (c) Composite functions and Inverse functions (d) Asymptotes of functions (e) Harder problems involving Properties of Functions
2.Exponential and Logarithmic Functions
(a)Laws of exponents(I)
Manipulation using laws of exponents
Solving equation
(b) Law of Rational Indices(II)
Manipulation using of Logarithms
Solving Equations
(c) Exponential and Logarithmic Functions
Graphs of Exponential and Logarithmic Functions
Composite functions ,Inverse functions and Asymptotes
(d) Applications of Exponential and Logarithmic Functions
(e) Harder problems involving Exponential and Logarithmic Functions
3.The Natural Exponent “e” and Natural Logarithms
(a) The Natural Exponent “e”
Solving Equations
Graph of Exponential Functions
(b)The Natural Logarithms
Manipulation using Properties of Logarithms
Properties of Logarithms with Functions
Graph of Natural Exponential and Natural Logarithmic Functions
Applications of Natural Exponential and Natural Logarithmic Functions
(c) Harder problems involving The Natural Exponent “e” and Natural Logarithms
4.Quadratic Equations and Functions
(a) FIVE WAYS of solving Quadratic Equations
Factorization
Taking square roots
Completing the square
Completing the square with Functions
Completing the square with Maximum/Minimum Value
Quadratic Formula
GDC Method
(b) Graph of Quadratic Functions and Ray Woo’s ABCD Trick
(c) THREE FORMS of Quadratic Functions
General Form
Vertex Form
Factor Form
(d) Discriminant and Nature of Roots
Discriminant with Solving Equations
Discriminant with Solving Inequalities
Application of Quadratic Functions
Solving Unknowns
Maximum/minimum Problems
(e) Harder problems involving Quadratic Equations and Functions
5.Transformation of Functions
(a) FOUR WAYS of Transformations and Ray Woo’s Trick
Translations up/down
Translations left/right
Stretches
Reflections
(b) Harder problems involving Transformation of Functions
