A Levels (Advanced Level qualifications) are a U.K subject-based qualification for students aged 16 and above. They are usually studied over the course of 2 years, and lead to qualifications recognised for entrance to higher education institutes in the UK and many others worldwide. 

A level mathematics builds from GCSE level mathematics and introduces calculus and its applications. It emphasises how mathematical ideas are interconnected and how mathematics can be applied to model situations mathematically using algebra and other representations, to help make sense of data, to understand the physical world and to solve problems in a variety of contexts, including social sciences and business. It prepares students for further study and employment in a wide range of disciplines involving the use of mathematics.

A level specifications in mathematics must include the following content. 

  • Proof

  • Algebra and functions

  • Coordinate geometry in the (x,y) plane

  • Sequences and series

  • Trigonometry

  • Exponentials and logarithms

  • Differentiation

  • Integration

  • Numerical methods

  • Vectors

  • Statistical sampling

  • Data presentation and interpretation

  • Probability

  • Statistical distributions

  • Statistical hypothesis testing

  • Quantities and units in mechanics

  • Kinematics

  • Forces and Newton’s laws

  • Moments

Reference: gov.uk, Guidance AS and A-Level Maths