Transition to A level Mathematics: Essential Skills

The most popular choice at A level is Mathematics; however, many students say that they find the initial transition from GCSE to A level challenging.

These resources were designed for students to complete independently and will develop fluency in the fundamental techniques and the key mathematical concepts that underpin A level Mathematics. They can be paired with support and additional guidance from a teacher where this is available.

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. Each set includes either written worked solutions, video solutions or links to websites.

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

Guidance on using these resources

Printable resources

We have produced printable versions of the Essential Skills resources for students with limited access to technology.

Download

Simplifying

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

Expanding

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

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.

Rearranging

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.

Solving

The ability to solve equations and interpret solutions is fundamental in maths. 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.

Sketching

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.