A-Level Maths: Pure (Year 1 / AS)

A-Level Maths: Pure (Year 1 / AS) is a course for anyone studying A-Level Maths:

This course covers all the pure content in A-Level AS maths, usually covered in the first year of study (Year 12). The course is suitable for all major exam boards, including Edexcel, OCR, AQA and MEI. It is also a great introduction to pure maths for anyone interested in getting started.

The main sections of the course are:

– Equations and Inequalities – we will look at a wide range of different functions, including quadratic, linear and cubic functions.

– Graphs – we will learn how to sketch and work with graphs, including higher-order polynomials, as well as graph transformations.

– Straight Line Graphs – we take this topic, familiar from GCSE, and push it to the next level, introducing new ways of using straight line graphs.

– Circles – we learn how to represent circles in the coordinate plane, find tangents to circles and solve intersections with lines.

– Polynomial Division – we learn new and powerful algebraic techniques that allow us to divide, factorise and solve higher order polynomials.

– Proof – we learn a range of different techniques for proving mathematical claims.

– Binomial expansion – here we learn a new algebraic technique for expanding brackets raise to large powers.

– Trigonometry – in the two trigonometry chapters we look at how to use trigonometry to solve triangle problems, but also solve trigonometric equations, sketch tri graphs, and prove trigonometric identities.

– Vectors – we extend GCSE vector ideas to much more complex problems, including vector proofs.

– Differentiation – in this huge chapter we introduce one of the most powerful and exciting ideas in mathematics. We look at gradients of curves, tangents, stationary points and optimization problems.

– Integration – here we look at the other side of calculus, and learn how to use integration to find areas under curves.

– Exponentials and Logarithms – we learn about the exponential function, logarithms, and the natural log, as well as how to use these ideas to model a range of real-world scenarios.