Advanced level mathematics

Advanced Level (A-Level) Mathematics is a post-16 qualification taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college. Advanced Level Further Mathematics is often taken by students who wish to study a mathematics-based degree at university, or related degree courses such as physics or computer science.

Like other A-Level subjects, mathematics is assessed by examination at the end of the course. The syllabus seeks to develop skills in mathematical modelling, problem-solving, mathematical argument including mathematical language, and data analysis. It came to be regarded as one of the most beneficial A-Level subjects after the Russell Group of research-intensive universities in the United Kingdom published guidance for applicants in 2011 on their preferred A-Levels to prepare candidates for degree-level study at their institutions.^[1] Mathematics featured prominently in their list of A-Levels, which they described as "facilitating subjects". The Russell Group replaced its guidance with a new website in 2019, after a backlash led by the creative industries and criticism that it was unhelpful to disadvantaged applicants. ^{[2] [3]} But the impression that mathematics A-Level is respected and favoured by selective universities and employers has persisted. Mathematics became the most popular A-Level subject by number of entries in 2014, overtaking English literature, and remained so for the next 12 years.^[4]

The linear structure and content were introduced for first teaching in September 2017, as part of far-reaching reforms to A-Levels and GCSEs introduced by Michael Gove during his tenure as Secretary of State for Education from 2010-14. These reforms replaced the modular system of assessment introduced in Curriculum 2000, whereby these qualifications were taught in modules, typically a total six of which three were taught in each year, with examinations after each whose results contributed to an overall final grade. The Gove changes also decoupled the AS-level qualification from A-levels, making AS levels a qualification in their own right.

Specification

There are three papers which must all be taken in the same year. There are three overarching themes - “Argument, language and proof”, “Problem solving” and “Modelling” throughout the assessment.^[5]

Each board structures the three papers as follows:

AQA

• Paper 1: Pure Mathematics
• Paper 2: Content on Paper 1 plus Mechanics
• Paper 3: Content on Paper 1 plus Statistics

^[6]

Edexcel

• Paper 1: Pure Mathematics 1
• Paper 2: Pure Mathematics 2
• Paper 3: Statistics and Mechanics

^[7]

OCR A

• Paper 1: Pure Mathematics
• Paper 2: Pure Mathematics and Statistics
• Paper 3: Pure Mathematics and Mechanics

^[8]

OCR B (MEI)

• Paper 1: Pure Mathematics and Mechanics
• Paper 2: Pure Mathematics and Statistics
• Paper 3: Pure Mathematics and Comprehension

^[9]

Grading

It was suggested by the Department for Education that the high proportion of candidates who obtain grade A makes it difficult for universities to distinguish between the most able candidates. As a result, the 2010 exam session introduced the grade A*—which serves to distinguish between the better candidates.^[10]

Prior to the 2017 reforms, the A* grade in maths was awarded to candidates who achieved an A (480/600) in their overall A Level, as well as achieving a combined score of 180/200 in modules Core 3 and Core 4. For the reformed specification, the A* is given by a more traditional grade boundary based on the raw mark achieved by the candidate over their papers.

List of subjects

1. Core Mathematics:

Covers foundational topics like algebra, calculus, trigonometry, and coordinate geometry.

2. Further Mathematics:

Expands upon Core Mathematics with additional areas such as complex numbers, matrices, differential equations, and numerical methods.

3. Pure Mathematics:

Explores advanced topics in algebra, calculus, and mathematical proofs.

4. Applied Mathematics:

Focuses on practical applications of mathematical concepts to solve real-world problems in various fields.

5. Mechanics:

Focuses on the study of motion, forces, and vectors, particularly relevant for physics or engineering interests.

6. Statistics:

Involves collecting, analysing, and interpreting data, including topics like probability, hypothesis testing, regression analysis, and sampling.

7. Discrete Mathematics:

Deals with separate and distinct mathematical structures, including topics such as combinatorics, graph theory, and algorithms.

8. Decision Mathematics:

Applies mathematical techniques to solve real-world problems related to optimisation, networks, and decision-making.

9. Financial Mathematics:

Applies mathematical concepts to analyse financial markets, investments, and risk management.

Further mathematics

Main article: Further Mathematics

Not all schools are able to offer Further Mathematics, due to a low student number (meaning that the course is not financially viable) or a lack of suitably experienced teachers. To fulfil the demand, extra tutoring is available, with providers such as the Further Mathematics Support Programme.^[11]

Results

The proportion of candidates in England, Wales and Northern Ireland acquiring these grades in 2025 are below, presented as cumulative percentages.^[12]

Mathematics

Entries	112,138
Grade A*	16.7%
Grades A*-A	41.7%
Grades A*-B	61.6%
Grades A*-C	78.2%
Grades A*-D	90.0%
Grades A*-E	96.5%
Grades A*-U	100.0%

Further mathematics

Entries	19,390
Grade A*	28.9%
Grades A*-A	58.2%
Grades A*-B	78.8%
Grades A*-C	89.6%
Grades A*-D	95.2%
Grades A*-E	98.1%
Grades A*-U	100.0%

2000s specification

Prior to the 2017 reform, the basic A-Level course consisted of six modules, four pure modules (C1, C2, C3, and C4) and two applied modules in Statistics, Mechanics and/or Decision Mathematics. The C1 through C4 modules are referred to by A-level textbooks as "Core" modules, encompassing the major topics of mathematics such as logarithms, differentiation/integration and geometric/arithmetic progressions.

The two chosen modules for the final two parts of the A-Level were determined either by a student's personal choices, or the course choice of their school/college, though it commonly took the form of S1 (Statistics) and M1 (Mechanics).