1. Algebra Basics

1.1 The Real Number System

1.2 Algebraic Expressions

1.2.1 Indices and Index Rules

1.2.2 Simplifying Algebraic expressions

1.2.3 Factorisation

1.2.4 Fractions

1.3 Equations

1.3.1 Linear Equations

1.3.2 Quadratic Equations

1.3.3 Simultaneous Equations

1.3.4 Applications of Equations

2. Matrices

2.1 Matrix addition and Scalar Multiplication and Matrix Multiplication

2.2 Solutions of systems of Linear Equations by Matrices

3. Functions

3.1 Definition: Notation and Evaluation

3.2 The Arithmetic of Functions

3.3 Graphs in Rectangular Coordinates

3.3.1 Straight Lines and Equations of a Line

3.3.2 Graphs of Quadratic Equations (Parabolas)

3.4 Applications of Functions in Business and Economics

3.4.1 Cost, Revenue and Profit Functions

3.4.2 Break Even Analysis

3.4.3 Demand and Supply Functions

4. Differentiation

4.1 Limit of a Function

4.2 Basic Rules for Differentiation

4.3 Successive Differentiation

4.4 The Sign of the Derivative and Nature of Function

4.5 Relative Maximum and Relative Minimum points of a Function

4.6 Applications of Differentiation

4.6.1 The derivative as a rate of change

4.6.2 Marginal Functions

4.6.3 Optimization of Functions in Business and Economics

4.6.4 Elasticity

5. Functions of Several Variables and Partial Derivatives

5.1 Functions of Several Variables

5.2 Partial Derivatives

5.3 Applications of Partial Derivatives

5.4 Second Order Partial derivatives

5.5 Optimization of Functions Two Variables

6. Integration

6.1 Indefinite Integration

6.2 Basic Rules of Integration

6.3 The Definite Integration

6.4 Area Between Curves

6.5 Applications of Integrations in Business and Economics

6.5.1 Integration of Marginal Functions

6.5.2 Total Change of Functions

6.5.3 Consumers’ Surplus and Producers’ Surplus

7. Mathematics of Finance

7.1 Simple Interest and Compound Interest

7.2 Present Value

7.3 Investment Appraisal

7.4 Annuities

7.5 Sinking Funds and Amortization