An Introduction to Pre-University Mathematics

This course will provide you with:

1. A grounding in arithmetic and algebra
2. An overview of functions and the fundamentals of calculus
3. An introduction to financial mathematics

You can review the full syllabus below:

Arithmetic and Algebra

• A review of arithmetic and the manipulation of algebraic expressions (including the use of brackets and power laws).
• Solving linear equations and the relationship between linear expressions and straight lines.
• Solving quadratic equations
• The relationship between quadratic expressions and parabolae.

Functions

• An introduction to functions such a polynomials, exponentials, logarithms, and trigonometric functions.
• The existence of inverse functions and how to find them.
• The laws of logarithms and their uses.

Calculus

• The meaning of the derivative and how to find it (including the product, quotient, and chain rules).
• Using derivatives to find approximations and solve simple optimisation problems with economic applications.
• Curve sketching
• Integration of simple functions and using integrals to find areas.

Financial mathematics

• Compound interest over different compounding intervals.
• Arithmetic and geometric sequences.
• Investment schemes
• Assessing the value of an investment