Content for mathematics AS and A level for teaching from 2017

1. AS and A level subject content sets out the knowledge, understanding and
skills common to all AS and A level specifications in mathematics.

2. A level mathematics provides a framework within which a large number of
young people continue the subject beyond GCSE level. It supports their mathematical needs across a broad range of other subjects at this level and provides a basis for subsequent quantitative work in a very wide range of higher education courses and in employment. It also supports the study of AS and A level further mathematics.
3. 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.
4. AS mathematics, which can be co-taught with the A level as a separate
qualification, is a very useful qualification in its own right. It consolidates and
develops GCSE level mathematics and supports transition to higher education or employment in any of the many disciplines that make use of quantitative analysis, including those involving calculus.
Aims and objectives
5. AS and A level specifications in mathematics must encourage students to:
• understand mathematics and mathematical processes in a way that promotes
confidence, fosters enjoyment and provides a strong foundation for progress to
further study
• extend their range of mathematical skills and techniques
• understand coherence and progression in mathematics and how different
areas of mathematics are connected
• apply mathematics in other fields of study and be aware of the relevance of
mathematics to the world of work and to situations in society in general
• use their mathematical knowledge to make logical and reasoned decisions in
solving problems both within pure mathematics and in a variety of contexts,
and communicate the mathematical rationale for these decisions clearly
• reason logically and recognise incorrect reasoning
• generalise mathematically
• construct mathematical proofs
• use their mathematical skills and techniques to solve challenging problems
which require them to decide on the solution strategy
• recognise when mathematics can be used to analyse and solve a problem in
• represent situations mathematically and understand the relationship between
problems in context and mathematical models that may be applied to solve
• draw diagrams and sketch graphs to help explore mathematical situations and interpret solutions
• make deductions and inferences and draw conclusions by using mathematical
• interpret solutions and communicate their interpretation effectively in the
context of the problem
• read and comprehend mathematical arguments, including justifications of
methods and formulae, and communicate their understanding
• read and comprehend articles concerning applications of mathematics and
communicate their understanding
• use technology such as calculators and computers effectively and recognise
when such use may be inappropriate
• take increasing responsibility for their own learning and the evaluation of their own mathematical development

Subject content

Background knowledge

6. AS and A level mathematics specifications must build on the skills, knowledge and understanding set out in the whole GCSE subject content for mathematics for first teaching from 2015

Overarching themes
7. A level specifications in mathematics must require students to demonstrate the following overarching knowledge and skills. These must be applied, along with associated mathematical thinking and understanding, across the whole of the detailed content set out below.

  • Expert guidance through this complex study.


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