Mathematics at university concentrates more on how mathematics uses abstraction and proof and less on the techniques that you met at A-level. However, skill and accuracy in the use of these techniques is essential, and it should be an important aim to make sure that you can use these techniques well. In the past we have held a test ("Diagnostic Test") in the first week, but we no longer do this. Instead, before you arrive, there are online versions of the tests for you to attempt. We will not use the result of the tests when you try them, but they are designed to make sure you are ready to start your degree, and so you should attempt them all. If you do not score very highly then it suggests a gap in your preparation and you should do some background reading to get those skills back again.
There are three topics: Differentiation, Integration and Trigonometry.
We expect you to be able to differentiate typical functions such as polynomials and trigonometric functions, find the turning points and type for simple functions and be comfortable with differentiating quotients and their products.
We expect you to be confident integrating standard functions such as polynomials and trigonometric functions both leaving a constant of integration and integrating between limits. This extends to working out the area under a graph and between two graphs, and determining the limits to integrate between. We also expect you to be able to "integrate by parts" which is not always covered at school, so you should look up how to do this and practise.
We expect you to be familiar with standard trig identities such as double angle formulae and product and sum formulae, and be able to use them to solve equalities in fixed ranges. You should not use a calculator or formulae book, it is essential that you know your formulae off by heart.
If you cannot pass these tests then you will struggle to follow logical arguments in many of your lectures, which is why we expect you to be able to solve such problems quickly and accurately.