Expected Prior Knowledge
In your first semester it will be assumed that you have a good knowledge of all the Pure Mathematics that you learned at A-level. There will be some tests on this core A-level material within the first few weeks. The purpose of this is to ensure that all students start with an appropriate level of knowledge. Revision material and exercises will be provided at the start of the course. You should find this work straightforward, provided that you are familiar with the following:
- Basic algebraic processes: simplifying and substituting into expressions. Expanding brackets. Factorisation.
- Solution of equations: linear, quadratic, simultaneous. Inequalities. Changing the subject of formulae.
- Function Notation. Domain and Range. Composite and inverse functions.
- Indices and Logarithms. The exponential ex and natural logarithm ln(x) functions.
- Functions defined parametrically or implicitly.
- Partial Fractions.
- The Binomial Theorem.
- Algebraic division and the Factor Theorem.
- Graphs of simple functions: straight line, quadratic, cubic, reciprocal.
- Arithmetic and Geometric series. Formulae for nth term and sum of first n terms.
- Trigonometric functions (sin, cos, tan, cosec, sec, cot). Addition and double-angle formulae. Trigonometric equations and identities. Radians. Graphs of trigonometric functions.
- Differentiation of powers of x, sums, differences, products, quotients, composite functions, exponential, logarithmic and trigonometric functions.
- Applications of differentiation to gradients, tangents and normals, maximum and minimum values, rates of change.
- Integration of powers of x, sums, differences, exponential and trigonometric functions.
- Integration using partial fractions, by substitution and by parts.
- Applications of integration to areas and volumes, and to solving simple differential equations.
- Vector notation.
To test yourself in these areas have a go at our question sheet (40K pdf-file). The answer sheet (40K pdf-file) is also available.
