A level Maths topics: the full list

By The STEM-Tutor team · Updated October 2026

Every A level Maths course in England covers the same core content, set nationally. Here is the full topic list, how the papers are split by board, and how to revise.

Pure Mathematics

• Proof
• Algebra and functions
• Coordinate geometry
• Sequences and series, including the binomial expansion
• Trigonometry, including identities and radians
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors

Statistics

• Statistical sampling
• Data presentation and interpretation
• Probability
• Statistical distributions, including the binomial and normal distributions
• Statistical hypothesis testing

Mechanics

• Quantities and units
• Kinematics
• Forces and Newton's laws
• Moments

How the papers are split

The content is the same across English boards, but the papers are organised differently:

• Edexcel: two Pure papers, and a third paper covering Statistics and Mechanics.
• AQA: one Pure paper, one Pure and Mechanics paper, and one Pure and Statistics paper.
• OCR: three papers that combine Pure with Statistics and Mechanics in different ways.
• Cambridge International: a different structure built from separate Pure, Mechanics and Probability and Statistics components. Check which components your school takes.

Pure maths makes up the largest share of the marks on every board, so it deserves the largest share of your revision. Check your board's current specification for exact paper lengths and marks.

How to revise the topics

1. Start with algebra. Weak algebra causes mistakes in every other topic.
2. Learn the formula booklet so you know what is given and what you must remember.
3. Do questions by topic first, then mixed exam papers under timed conditions.
4. Keep a mistakes list and redo those questions a week later.
5. Practise Statistics and Mechanics regularly. They are easy marks to lose if left to the end.

Is A level Maths hard?

It is a big step up from GCSE, mostly because of the amount of algebra and the need to combine topics in one question. Students who practise little and often, and fix gaps early, usually find it very manageable.

A quick example from each section

Pure: proof by contradiction

Prove that √2 is irrational.

• Assume √2 = a/b in lowest terms. Then a² = 2b², so a is even; write a = 2k.
• Then 4k² = 2b², so b² = 2k² and b is even too. This contradicts lowest terms, so √2 is irrational.

Pure: exponentials and logarithms

Solve 3^x = 20.

• Take logs: x = ln 20/ln 3 ≈ 2.73.

Statistics: probability

P(A) = 0.4, P(B) = 0.5 and A and B are independent. Find P(A and B).

• P(A and B) = 0.4 × 0.5 = 0.2.

Mechanics: kinematics

A car accelerates uniformly from rest to 20 m/s in 8 s. Find its acceleration.

• a = 20/8 = 2.5 m/s².

How to plan two years of A level Maths

• Year 12: secure algebra, coordinate geometry, trigonometry, exponentials, basic calculus, and the first parts of statistics and mechanics.
• Year 13: extend to proof, functions, further trigonometry, the chain, product and quotient rules, integration techniques, numerical methods, vectors in 3D, the normal distribution and more mechanics.
• Final months: mixed past papers under timed conditions.

Year 13 builds directly on Year 12, so gaps left early tend to grow. Fixing weak algebra in Year 12 pays off for the whole course.

Exam technique

• Show every step: most marks are for method, not just the final answer.
• Give exact answers when asked, such as surds or multiples of π.
• Use the mark allocation as a guide to how much working is expected.
• Check answers make sense, especially in mechanics and statistics contexts.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is A level Maths the same across boards?

The core content is set nationally, so the topics are the same. Paper structure and question styles differ, so practise with your own board's papers.

Should I take Further Maths too?

It suits students who enjoy maths and plan to study maths, physics, engineering or computer science. It adds topics like complex numbers and matrices.

Key takeaways

• A level Maths is mostly Pure, with Statistics and Mechanics.
• The content is the same across English boards; papers differ.
• Secure algebra early.
• Show every step for method marks.
• Practise mixed past papers in the final months.

Where to go next

Dive into each area.

• Differentiation
• Integration
• Statistics
• Mechanics

What each section is really testing

Pure Mathematics makes up about two thirds of the qualification. It tests algebraic fluency and the ability to build a logical argument. Questions often combine topics, so a single question might use trigonometric identities, differentiation and solving an equation. The strongest students are those whose algebra is fast and accurate, which frees up thinking time for the harder steps.

Statistics tests whether you can choose a sensible model, calculate with it and interpret the result. Communication matters: conclusions must refer to the context. Familiarity with your board's large data set, if it has one, helps you answer questions quickly.

Mechanics tests modelling. You turn a physical situation into equations using forces, motion and moments, then solve and interpret. A clear diagram is the single most useful habit, and many marks come from setting up the equations correctly.

How to use past papers well

Past papers are most useful once you have covered the content. Do the first few with notes open and no time limit, focusing on method. Later, sit full papers under timed conditions and mark them strictly with the mark scheme. Keep a log of every question you lost marks on and the reason. Before the exam, revisit that log rather than redoing questions you already find easy. Examiner reports are also worth reading: they list the mistakes many students made on each question.

Common reasons students lose marks

• Weak algebra: slips in expanding, factorising or rearranging cost marks in every topic.
• Skipping steps: an answer with no working may get no credit, even if it is correct.
• Calculator mode: using degrees when a question needs radians, especially in calculus.
• Missing context: statistics and mechanics answers need a sentence that relates back to the situation.
• Running out of time: practising full timed papers builds the pace you need on the day.

Each of these can be fixed with steady, focused practice, and fixing them often lifts a grade without learning any new content.

Choosing resources

Your board's specification lists exactly what can be examined, so keep a copy and tick topics off as you master them. Use your textbook for explanations, past papers and mark schemes for practice, and the formula booklet so you know what is given and what you must memorise. Short, regular sessions spread over the week work better than one long session, because spacing helps you remember.