A-level Maths 2027: formula booklet, exam dates, papers and grade boundaries

A-level Maths formula booklet: what you get

People call it the formula sheet, formula book or formula booklet. Each board does it slightly differently:

• AQA: a booklet called Formulae for A-level Mathematics, required for every AS and A-level Maths exam.
• Edexcel: a booklet called Mathematical Formulae and Statistical Tables, provided with every paper. The Edexcel A-level Maths specification lists, in Appendix 1, every formula you must know that is not in it.
• OCR: no separate booklet. A formulae page is printed at the front of each paper, as on the June 2023 H240/01 paper.

What is in the formula booklet

This is what AQA's booklet gives you. OCR's formulae page covers the same ground and adds a little more, such as a table of percentage points of the normal distribution.

Formulae you must memorise for A-level Maths

Edexcel's Appendix 1 is the clearest official list of what is not given. Neither AQA's booklet nor OCR's page gives these either, so learn them whatever your board:

• Algebra: the quadratic formula, the laws of indices and the laws of logarithms
• Coordinate geometry: y − y₁ = m(x − x₁), and perpendicular gradients multiply to −1
• Sequences: the nth term of an arithmetic progression, a + (n − 1)d, and of a geometric progression, arⁿ⁻¹
• Trigonometry: the sine rule, area = ½ab sin C, sin²A + cos²A ≡ 1, sec²A ≡ 1 + tan²A, cosec²A ≡ 1 + cot²A, and the double angle formulae for sin 2A, cos 2A and tan 2A
• Circles and radians: circumference and area of a circle, arc length s = rθ and sector area A = ½r²θ
• Calculus: the derivatives and integrals of xⁿ, sin kx, cos kx, eᵏˣ and 1/x, the product rule and the chain rule, and area under a curve as a definite integral
• Vectors and statistics: the magnitude of a vector, √(x² + y² + z²), and the mean of a data set
• Mechanics: F = ma, and v = dr/dt, a = dv/dt for motion with variable acceleration

A-level Maths papers

Every board sets three papers of 2 hours and 100 marks, and you can use a calculator on all of them. Pure maths runs through every paper. The difference is where statistics and mechanics sit.

AQA says each paper's marks split roughly 50% for using standard techniques, 25% for reasoning and communicating, and 25% for problem solving and modelling. So half of each paper rewards methods you can practise until they are automatic.

A-level Maths topics

• Pure: proof, algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods and vectors.
• Statistics: sampling, data presentation and interpretation, probability, statistical distributions and hypothesis testing. Each board also publishes a large data set, and questions assume you have worked with it.
• Mechanics: quantities and units, kinematics, forces and Newton's laws, and moments.

A-level Maths exam dates 2027

All three boards sit A-level Maths on the same afternoons, according to the final timetables from AQA, Edexcel and OCR.

• Results day: Thursday 12 August 2027.
• Contingency day: Wednesday 23 June 2027, in case of serious national disruption.
• Entries: your school must enter you by 21 February 2027 (JCQ key dates).

A-level Maths grade boundaries

Grade boundaries are set on your total out of 300 and change every year. These are from June 2026 (AQA, Edexcel and OCR).

Edexcel A-level Maths grade boundaries in percentages

With Edexcel in June 2026, an A* took 254 out of 300 (84.7%) and an A took 210 (70.0%). AQA's A was higher at 219 (73.0%), and OCR's lower at 208 (69.3%). Spread over three papers, an Edexcel A is about 70 marks a paper and an A* about 85.

Worked examples, from the booklet and beyond

These questions were written for this guide. Each one uses a formula you must memorise or one the booklet gives you, so you can see where the marks really are.

Radians: arc length and sector area

Question: sector OAB has radius 6 cm and angle 1.2 radians at O. Find its arc length, area and perimeter.

The perimeter is the arc plus two radii: 7.2 + 6 + 6 = 19.2 cm. Neither formula is in the booklet, and both only work with the angle in radians.

Trigonometric equations with a double angle

Question: solve cos 2x = sin x for 0° ≤ x ≤ 360°.

1. Pick the version of cos 2x that matches the other side: cos 2x = 1 − 2sin²x.
2. So 1 − 2sin²x = sin x, which rearranges to 2sin²x + sin x − 1 = 0.
3. Factorise as a quadratic in sin x: (2sin x − 1)(sin x + 1) = 0.
4. So sin x = ½, giving x = 30° or 150°, or sin x = −1, giving x = 270°.

Check one: cos 60° = 0.5 and sin 30° = 0.5. The commonest slip is stopping at 30° and missing the other solutions in the range, so sketch the sine curve. The double angle formulae aren't in the booklet. Now try a trigonometry question from our Trigonometry course and press Mark.

Integration by parts

Question: find ∫ x e²ˣ dx. The booklet gives the formula, so the skill is choosing u. Let u = x, because it gets simpler when differentiated, and dv/dx = e²ˣ, so v = ½e²ˣ.

Check by differentiating your answer with the product rule: you get back x e²ˣ. Try more in the Integral Calculator.

SUVAT equations in A-level Maths

Question: a ball is thrown straight up at 14 m s⁻¹. Taking g = 9.8 m s⁻², find its greatest height and the time it takes to get there.

At the top v = 0. Use v² = u² + 2as with a = −9.8: 0 = 196 − 19.6s, so s = 10 m. Then v = u + at gives 0 = 14 − 9.8t, so t = 1.43 s to 3 significant figures. The SUVAT equations are in the booklet, but only for constant acceleration. Our SUVAT equations guide goes through all five, and the SUVAT Calculator checks your answers.

A-level Maths past papers

The current specifications were first examined in 2018. Past papers and mark schemes are free from AQA, Edexcel and OCR. The newest are kept back: Pearson keeps them for teachers so that at least one can be used as a mock, and releases most once they are nine months old.

If you are sitting mocks now, the A-level Maths mocks guide shows how to sit a paper at home and turn your mark into a rough grade.

A-level Maths revision that works

1. Learn the missing formulae first. Make flash cards for everything in the memorise list above and test yourself until you don't need them.
2. Practise by topic, then mixed. Do a set of questions on one topic, then mixed papers, because the real exam doesn't tell you which topic a question is.
3. Mark against the mark scheme. Method marks need the method on the page. Compare your working, not just your answer.
4. Know your large data set. Questions assume you know what it contains and its quirks.
5. Time yourself. 2 hours for 100 marks is 1.2 minutes a mark. Practise finishing a paper in that time.

Common A-level Maths mistakes

• Calculator answers where working is required. If a question asks you to show your working or reasoning, a bare answer scores nothing.
• Degrees in calculus. Differentiating and integrating trigonometric functions only works in radians.
• Missing solutions. Trigonometric equations usually have more than one answer in the range. Sketch the graph.
• Forgetting + c on an indefinite integral, or the limits on a definite one.
• No conclusion in context. A hypothesis test ends with a sentence about the situation, not just "reject H₀".
• The wrong g. Use 9.8 m s⁻² unless the question gives another value.

Use a daily paper as a short timed mock

Year 13 mocks run through the winter, and a full paper takes 2 hours. On busier days, sit one topic's daily paper: Algebra and Functions, Calculus, Statistics or Mechanics. Each covers one part of the course, so rotate through all four.

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