In the first week of Year 12 I ask every new student the same question: “Is the quadratic formula in the A-level formula booklet?” Most say yes. It was on their GCSE sheet, after all. It is not in the A-level booklet — on any board — and nor are the sine rule, the cosine rule or the double-angle identities.
This guide sets out exactly what the A-level maths formula booklet contains, the full national list of formulae students must memorise instead, and how the Edexcel, AQA and OCR versions differ. Everything here is taken from the boards' own specifications rather than a revision-site summary.
The distinction matters more than students expect. Knowing where a formula is in the booklet saves a minute; knowing a memorise-list formula cold saves a whole question. Over three two-hour papers, that adds up to a grade.
What You Get in the A-Level Maths Exam
Every board provides formulae in every A-level maths paper, but the format differs. Pearson Edexcel hands out a separate booklet titled Mathematical Formulae and Statistical Tables, which is used for all three papers. AQA provides its own separate formulae and statistical tables booklet. OCR prints its formulae on pages 2 and 3 of each question paper, including a table of percentage points of the normal distribution.
What none of them does is give you everything. Underneath all three sits a list, set nationally by the Department for Education, of formulae and identities students are expected to know. Edexcel prints it as Appendix 1 of its specification, AQA as Appendix B and OCR as section 5d, and the list is the same. Anything on that list is left out of the booklet by design.
OCR's specification spells out the one exception: a memorise-list formula may appear in a question only when it is the starting point for a proof or the result you are being asked to prove. Otherwise you are on your own.
Pure Formulae You Must Memorise
Pure maths makes up the bulk of the list, and it is where most of the dropped marks come from. Here is the full set, grouped the way the specifications group it.
Two groups do the most damage. Trigonometry is the first: students expect the double-angle identities to be printed beside the compound-angle ones, and they are not. The second is calculus, where the booklet gives the awkward derivatives — tan, sec, cosec, cot and the quotient rule — but not the basic ones, nor the product rule or chain rule, which are assumed knowledge.
| Topic | Formulae you must know (not in the booklet) |
|---|---|
| Quadratics | Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a |
| Indices | aˣ × aʸ = aˣ⁺ʸ; aˣ ÷ aʸ = aˣ⁻ʸ; (aˣ)ʸ = aˣʸ |
| Logarithms | logₐx = n ⇔ x = aⁿ; log x + log y = log xy; log x − log y = log(x/y); k log x = log xᵏ |
| Coordinate geometry | y − y₁ = m(x − x₁); perpendicular when m₁m₂ = −1 |
| Sequences | nth term of an arithmetic sequence a + (n − 1)d; of a geometric sequence arⁿ⁻¹ |
| Triangles | Sine rule; cosine rule a² = b² + c² − 2bc cos A; area = ½ab sin C |
| Trig identities | cos²A + sin²A ≡ 1; sec²A ≡ 1 + tan²A; cosec²A ≡ 1 + cot²A |
| Double angles | sin 2A ≡ 2 sin A cos A; cos 2A ≡ cos²A − sin²A; tan 2A ≡ 2 tan A / (1 − tan²A) |
| Mensuration | Circle C = 2πr, A = πr²; Pythagoras; trapezium area; prism volume; arc s = rθ; sector A = ½r²θ |
| Differentiation | xⁿ, sin kx, cos kx, eᵏˣ, ln x; sum rule; product rule; chain rule |
| Integration | xⁿ (n ≠ −1), cos kx, sin kx, eᵏˣ, 1/x; reverse chain rule; area under a curve = ∫y dx |
| Vectors | Magnitude of xi + yj + zk = √(x² + y² + z²) |
Statistics and Mechanics Formulae to Memorise
The applied list is much shorter, which is exactly why students neglect it. Every item below turns up year after year, usually early in a question where a slip costs you the rest of it.
The mechanics entries are the ones I see forgotten most. Students remember the suvat equations — which are given anyway — and forget that the calculus links between displacement, velocity and acceleration are not. Any question with acceleration as a function of time depends on them.
| Area | Formulae you must know (not in the booklet) |
|---|---|
| Statistics | Mean of a data set: x̄ = Σx / n = Σfx / Σf |
| Statistics | Standard normal variable: Z = (X − μ) / σ, where X ~ N(μ, σ²) |
| Mechanics | Weight = mass × g |
| Mechanics | Friction: F ≤ μR |
| Mechanics | Newton's second law: F = ma |
| Mechanics | Variable acceleration: v = dr/dt, a = dv/dt = d²r/dt², r = ∫v dt, v = ∫a dt |
What the Formula Booklet Gives You
Here is what you can rely on being printed. The list below follows the OCR A (H240) formulae sheet, which is reproduced in full in its specification; the Edexcel and AQA booklets cover the same ground in their own layouts, with fuller statistical tables.
Notice the theme: the booklet gives you formulae that are long, easily misremembered or rarely used — the binomial expansion for any n, the compound-angle identities, the trapezium rule. That is a gift only if you have used them often enough to know which one you need and where it is on the page.
- Series: the sum of an arithmetic series, the sum of a geometric series and its sum to infinity, and the binomial expansion, including the general form for any rational n.
- Differentiation: derivatives of tan kx, sec x, cot x and cosec x, the quotient rule, and the definition of differentiation from first principles.
- Integration: a short table of standard integrals and the integration by parts formula.
- Trigonometry: the compound-angle identities for sin(A ± B), cos(A ± B) and tan(A ± B), and the small-angle approximations for sin θ, cos θ and tan θ (θ in radians).
- Numerical methods: the trapezium rule and the Newton–Raphson iteration.
- Statistics: probability rules, standard deviation, the binomial distribution with its mean np and variance np(1 − p), the hypothesis test for the mean of a normal distribution, and a table of percentage points of the normal distribution.
- Mechanics: the constant-acceleration (suvat) equations, both for motion in a straight line and in vector form for two dimensions.
The GCSE-to-A-Level Gap: Formulae That Disappear
This is the trap I most want Year 12 students to know about. At GCSE, students are now given a formulae sheet in maths, and in May 2026 Ofqual confirmed they will stay for the lifetime of the current GCSE specifications. On the Higher tier GCSE sheet, students are given the quadratic formula, the sine rule, the cosine rule and ½ab sin C.
Every one of those is on the A-level memorise list. So a student who has spent Year 11 looking the quadratic formula up — perfectly sensibly — arrives in Year 12 never having needed to learn it. The first A-level mock then finds the gap for them. If your child has just finished GCSE, my guide to the GCSE maths formula sheet shows exactly what they were given, so you can see what now needs learning.
| Formula | GCSE Higher formulae sheet | A-level maths |
|---|---|---|
| Quadratic formula | Given | Must memorise |
| Sine rule | Given | Must memorise |
| Cosine rule | Given | Must memorise |
| Area = ½ab sin C | Given | Must memorise |
| Sum of an arithmetic series | Not on the course | Given |
Edexcel, AQA and OCR: How the Booklets Compare
The memorise list is identical on every board, so a student who changes board — or uses another board's textbook — is not learning the wrong formulae. What changes is layout and the statistical tables, and that is what students need to practise with.
Pearson Edexcel (9MA0) uses one booklet, Mathematical Formulae and Statistical Tables, for all three papers, including the statistics and mechanics paper. Because it is a separate document, students can keep it open beside the question paper. AQA (7357) also supplies a separate formulae and statistical tables booklet. OCR A (H240) builds the formulae into the first pages of each question paper, which means students flick back and forth — a small thing, but worth practising.
The practical advice is the same for all three: download your board's booklet from its website on the first day of Year 12, and use that exact document, never a homemade sheet, every time you do a past paper. By the summer of Year 13 you should be able to find the trapezium rule without reading the headings. My comparison of AQA, Edexcel and OCR covers the other differences between the boards.
How to Revise A-Level Maths Formulae
Formulae are learnt by using them, not by reading a list. A student who has applied the cosine rule in thirty questions does not need to memorise it; a student who has stared at it on a flashcard thirty times often still mixes up the sign. The aim is automatic recall under exam conditions, which only comes from practice.
The method I use with students is simple. Write the memorise list from blank paper once a week in Year 12 — it takes five minutes — and check it against the specification. Anything wrong goes on a short list, and those formulae appear in that week's questions. By Christmas of Year 13 the list should come out perfect every time, and the remaining revision time can go where marks are really won: method, accuracy and finishing long questions. That is the core of my approach in how hard A-level maths really is, and it is why full timed past papers matter so much.
- Write the list from memory weekly. Five minutes, blank paper, checked against the specification. Errors go on a short list for that week.
- Learn by using. Follow every recall session with questions that need the formulae you got wrong.
- Derive, then memorise. Knowing that cos 2A comes from cos(A + A) gives you a fallback, but learn the result so you never need it.
- Practise with the real booklet. Use your board's official booklet in every past paper so finding a formula takes seconds.
- Don't neglect mechanics and statistics. The applied list is short, which is exactly why it is forgotten. F ≤ μR and Z = (X − μ)/σ are free marks.
Sources & further reading
- Pearson Edexcel — A Level Mathematics (9MA0) specification, Issue 4, Appendix 1: Formulae
- Pearson Edexcel — AS and A level Mathematics (2017) qualification page
- OCR — A Level Mathematics A (H240) specification, section 5d and formulae sheet
- AQA — A-level Mathematics (7357) specification, Appendix B: Mathematical formulae and identities
- AQA — A-level Mathematics (7357) assessment resources
- Department for Education — GCE AS and A level subject content for mathematics
The memorise list and the OCR formulae sheet were read directly from the Pearson Edexcel and OCR specifications in October 2026, and the two memorise lists match. The detailed list of given formulae follows OCR's published sheet; Edexcel and AQA print the same non-memorise formulae in their own booklets, with their own layouts and statistical tables. Always download the current booklet from your board's website and confirm your child's specification with their school.