**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