Transition to A level Mathematics resources: Essential Skills

These resources are designed to help you to make the transition from GCSE to AS and A level Mathematics.

Many students say that they find the initial transition from GCSE challenging. These resources focus on key skills that will be used across the whole spectrum of AS and A level Mathematics. Each section includes:

skills checks
a chance to practise and explore
some extra ideas that you may want to investigate further

There are six sets of resources, and each set should provide about 3 hours of work. If you really get engaged by the enrichment activities, you may want to spend longer than this. Each set includes either written worked solutions, video solutions or links to websites.

We hope you find these resources useful, that they add depth to your understanding, and that they help you make a smooth and successful transition to AS and A level Mathematics.

Guidance on using these resources

Simplifying

Simplifying numerical and algebraic expressions is an essential component in maths. Here we look at the key skill of simplifying and how it is applied to fractions, indices and surds in particular.

‌ Fractions

‌ Indices

‌ Surds

Expanding

This unit looks at expanding – you will look at visual geometrical approaches, multiplication of numeric values, working through to manipulating algebraic expressions involving single, double, triple brackets and beyond! Expanding and simplifying expressions is a key skill in many areas of maths.

‌ Expanding

‌ Double Brackets

‌ More Brackets

Factorising

In this section we are looking at the topic of factorising. We will look at expressions such as those with common factors or quadratics. Before starting AS or A level Mathematics it is essential that you are confident with factorising expressions and recognising when you can factorise. This skill will become very important when we consider solving and sketching.

‌ Factorising

‌ Further Factorising

‌ Completing the Square

Rearranging

Being able to rearrange formulae or equations is a fundamental process in algebraic manipulation. From simple conversions to more complicated mathematical formulae, rearranging helps to make calculations easier and plays an important role when studying AS or A level Mathematics. For students studying science as well as maths it is hugely important that you can rearrange scientific formulae with confidence.

‌ Rearranging

‌ Rearranging and Factorising

‌ Rearranging and Fractions

Solving

The ability to solve equations is fundamental in maths. Whilst the process of solving equations is essential, the interpretation of solutions gained is equally important in real-world applications. Equations can take many forms from the linear and quadratic ones studied at GCSE to more complex ones studied at AS and A level. In this resource we will also look at inequalities which have many applications including maximising profit in business subject to constraints.

‌ Linear Equations

‌ Quadratic Equations

‌ Other Equations

Sketching

Maybe when studying GCSE Mathematics, and definitely during your A level Mathematics studies, you will hear your teacher ask, “Have you tried drawing a sketch or a diagram?” The use of sketching is a really important tool which can help simplify a written mathematical problem. From geometry in pure maths to mathematical modelling in mechanics, a sketch will help you to make sense of problems which look extremely challenging in written form. In this section we look at uses for sketching and the important role graph drawing packages can play to aid understanding.

‌ Linear Sketching

‌ Quadratic Sketching

‌ Other Sketching