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# An Introduction to Pre-University Mathematics

### Overview

This course introduces some of the basic ideas and methods of mathematics with an emphasis on their application.

It works at an elementary level with the aim of developing sophisticated mathematical skills and bridging the gap between school leavers and undergraduate study.

At the end of the mathematics course, you should be able to:

• Manipulate and use algebraic expressions

• Graph, differentiate and integrate simple functions

• Calculate basis quantities in financial mathematics

Related skills developed during this course include Algebra, Basic Math, Calculus, Differential Calculus, Elementary Algebra, Integral Calculus, Linear Equations.

### Syllabus

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 as 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

### Taught by

James Ward and Siri Kouletsis

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