A1 – Functions and Graphs
Graphs and Properties of Functions [24Hrs Free]
1.1 Introduction to Graph Sketching
1.3 Exponential Functions [Free]
1.5 Trigonometric Functions Background Knowledge
Polynomial Functions
Transformation of Graphs
3.1 Transformation 1: Translation
3.2 Transformation 2: Dilation
3.3 Transformation 3: Reflections
3.4 Combination of Transformations
3.5 Transformation of Polynomial Functions
3.6 Transformations of Exponential Functions
Relationship of Transformations
4.1 Transformations with a Single Parameter
4.2 Background: Introduction to Matrices
4.3 Using Matrices for Transformations and its Inverse
Real Life Applications using Function Models
5.1 Application of Polynomial Functions
5.2 Applications of Circular Functions
A2 – Algebra
Functions and Relations
1.1 Set Notations and Sets of Numbers
1.2 Describing a Set and Function
Polynomial Functions and Algebraic Operations
2.1 Polynomial Function Introduction and Algebraic Operations
2.2 Remainder Theorem, Factor Theorem and The Rational-Root Theorem
Functional Relations [24Hrs Free]
3.1 Introduction to Functional Relations
Solving Equation Systems
5.3 Solution of Trigonometric Equations
5.4 Solving Exponential and Logarithmic Equations
Literal and Parametric Equation Systems
6.1 Revision for Linear Systems
6.2 Literal Equation Systems: Polynomials
6.3 Families of Functions and Solving Literal Equations
Solving Simultaneous Linear Equations
A3 – Calculus
Rates of Changes, Tangents and Derivative Functions
1.1 Derivatives Basic Concepts – Rate of Changes
1.2 Derivatives Basic Concepts – Tangent and Derivatives
1.3 Further Exploring Derivatives
1.4 Algebra of Limits (Not Required)
Graphs of Derivatives and Antiderivatives
Derivatives of Functions
3.1 Differentiation Rules for Polynomials
3.2 Finding Gradient of a Tangent Line
Application of Differentiation on Graph Properties
5.1 Finding Tangents and Normals
5.2 Rates of Change, Motion in a Straight Line
5.3 First Derivative and Function Characteristics
5.4 Maximum and Minimum Points
5.5 Second Derivatives and Concavity
Antiderivatives of Functions
Sum of Area and Definite Integrals
Anti-Differentiation
Fundamental Theorem of Calculus
Properties of Antiderivatives
Real Life Applications of Integrations
11.1 Finding Area Under a Curve
A4 – Probability and Statistics
Basic Concepts of Probabilities
1.1 Sample Spaces, Events, Tree Diagrams
Discrete Random Variables
2.1 Discrete Probability Distributions and Mass Functions
2.3 Variance and Standard Deviation