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: Reflection
3.4 Combination of Transformations
3.5 Transformations 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 Applications 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
5.2 Simultaneous Equations: Polynomials
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