A-Level Maths formulae booklet: What's in it and what you still need to know
Every A-Level Maths candidate gets a formulae booklet in the exam. It is provided across all boards (AQA, Edexcel, OCR, OCR MEI) and contains the more complex standard results in Pure, Mechanics and Statistics that examiners decided you should not have to recall from memory.
That is a help, but it is also a trap. The booklet gives you the standard derivatives and the Pythagorean trig identities, so students who do not check it sometimes burn time deriving things that are already printed. At the same time, the basic Mechanics relation W = mg, the product and chain rules and the quadratic formula are NOT in the booklet, and they appear in questions regularly.
This guide walks through what is in the booklet and where each result is used, then sets out the major formulae you should still know from memory.
Booklet provided
Every exam
the A-Level Maths formulae booklet is given to every candidate in every paper – Pure, Mechanics and Statistics – across all UK exam boards
The booklet is the same length across boards, but the exact contents differ slightly. This guide follows the Edexcel and AQA booklets, which cover almost identical material. Check your own board's specification appendix for the official list.
What's in the Pure section
The Pure section of the booklet covers the trigonometric identities, integration standard forms and a handful of iterative formulae that are too long to memorise reliably. The table below lists the most commonly used ones.
| Result | Statement | When you use it |
|---|---|---|
| Pythagorean trig identities | cos²A + sin²A ≡ 1; sec²A ≡ 1 + tan²A; cosec²A ≡ 1 + cot²A | Simplifying trig expressions, swapping between sin/cos and tan/sec forms, integration of trig |
| Sine rule, cosine rule and triangle area | a/sin A = b/sin B = c/sin C; a² = b² + c² - 2bc·cos A; Area = (1/2)ab·sin C | Printed in the Trigonometry section of the Edexcel, AQA and OCR A-Level Maths booklets |
| Compound angle formulae | sin(A ± B) = sin A cos B ± cos A sin B; cos(A ± B) = cos A cos B ∓ sin A sin B; tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B) | Proofs, simplifying expressions, solving trig equations with non-standard angles |
| Double angle formulae | sin 2A = 2 sin A cos A; cos 2A = cos²A - sin²A = 2cos²A - 1 = 1 - 2sin²A; tan 2A = 2tan A / (1 - tan²A) | Integration of sin²x or cos²x, solving equations involving 2x and x |
| R-method form | a sin θ + b cos θ = R sin(θ + α) where R = √(a² + b²) and tan α = b/a | Solving equations of the form a sin θ + b cos θ = c, or finding max/min values |
| Standard derivatives | d/dx(sin x) = cos x; d/dx(cos x) = -sin x; d/dx(tan x) = sec²x; d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x | Almost every Pure differentiation question. Listed in the Differentiation section of Edexcel and AQA booklets |
| Standard integral 1/x | ∫(1/x) dx = ln|x| + c | Integrating any 1/(linear) expression, often combined with substitution |
| Standard integral sec²x | ∫sec²x dx = tan x + c | Trigonometric integration, especially after substitution |
| Integration by parts | ∫u (dv/dx) dx = uv - ∫v (du/dx) dx | Integrating products like x·eˣ, x·sin x or x·ln x |
| Newton-Raphson iteration | xₙ₊₁ = xₙ - f(xₙ)/f'(xₙ) | Numerical methods: Finding roots of f(x) = 0 to a given accuracy |
| Maclaurin / Taylor series (some boards) | f(x) = f(0) + xf'(0) + (x²/2!)f''(0) + ... (Maclaurin form) | Series expansions in Pure Year 2 / Further Maths |
What's in the Mechanics section
Mechanics has a shorter formulae section than Pure. Most of Mechanics is built on Newton's laws and free body diagrams, which you have to set up yourself. The booklet provides a handful of constant-acceleration and rotational results.
| Result | Statement | When you use it |
|---|---|---|
| SUVAT (constant acceleration) | v = u + at; s = ut + (1/2)at²; v² = u² + 2as; s = ((u + v)/2)t; s = vt - (1/2)at² | Any constant-acceleration problem: Projectiles, vertical motion, kinematics |
| Newton's law of gravitation (some boards) | F = Gm₁m₂/r² | Further Maths / specific syllabuses only |
What's in the Statistics section
The Statistics section is mostly distribution-related. It includes the formulae for the binomial, normal and (for some boards) the Poisson and uniform distributions, plus the normal distribution probability tables themselves in an appendix.
The statistical tables are often a separate booklet handed out with the formulae booklet. They give cumulative binomial probabilities, percentage points of the normal distribution, and critical values for hypothesis tests.
| Result | Statement | When you use it |
|---|---|---|
| Binomial distribution | P(X = r) = ⁿCᵣ pʳ (1-p)ⁿ⁻ʳ where X ~ B(n, p) | Discrete distributions, hypothesis tests on a proportion |
| Normal distribution standardising | Z = (X - μ) / σ where Z ~ N(0, 1) | Converting any normal to the standard normal so you can use the tables |
| Mean and variance of a sample mean | E(X̄) = μ; Var(X̄) = σ²/n | Hypothesis tests on the mean of a normal distribution |
| Cumulative binomial tables | Tabulated values of P(X ≤ x) for X ~ B(n, p) at standard n and p | Quick lookup in binomial hypothesis tests instead of summing terms |
| Normal distribution tables | Tabulated values of Φ(z) = P(Z ≤ z) for the standard normal | Any normal-distribution probability or hypothesis test |
| Critical values for hypothesis tests | 5%, 2.5%, 1%, 0.5% one-tailed and two-tailed values of Z | Quickly reading off critical values without interpolating from the main table |
What's NOT in the booklet – formulae you must still know
A lot of basic results are not in the booklet. Examiners assume these are part of your working knowledge from GCSE or core A-Level content, and they test them constantly. If any of the formulae below feel uncertain, build them into your daily revision drill.
This list is not exhaustive but it covers the high-leverage results that come up most often across past papers.
| Topic | Formula you must know | Notes |
|---|---|---|
| Quotient rule | d/dx(u/v) = (v·u' - u·v') / v² | Some boards include this (Edexcel does); others do not. Check your own booklet |
| Product rule | d/dx(uv) = u·v' + v·u' | Not in most booklets. Drill it |
| Chain rule | d/dx(f(g(x))) = f'(g(x))·g'(x) | Not in the booklet. Used in almost every differentiation question |
| Logarithm laws | log(ab) = log a + log b; log(a/b) = log a - log b; log(aⁿ) = n·log a | Including the change of base formula log_a(x) = log(x)/log(a) |
| Vector magnitude | |a| = √(x² + y² + z²) | Vector questions in Pure 2 |
| Quadratic formula | x = [-b ± √(b² - 4ac)] / 2a | Was on the GCSE Higher sheet, but NOT in the A-Level booklet |
| Weight | W = mg | Assumed knowledge. Not printed in the A-Level Maths booklet. Use g = 9.8 m s⁻² unless told otherwise |
| Arithmetic and geometric series (some boards) | Sₙ = (n/2)(2a + (n-1)d); Sₙ = a(1 - rⁿ)/(1 - r); S∞ = a/(1-r) for |r| < 1 | Edexcel, AQA and OCR booklets do include these; if you sit a less common syllabus, check yours |
Don't waste exam time looking up the basics. The booklet has sin²x + cos²x = 1 and d/dx(sin x), but flicking pages to find them costs seconds you cannot get back. Know the foundations cold and reserve the booklet for the longer-tailed results like compound angles, Newton-Raphson and integration by parts.
How to use the booklet effectively
The booklet is a safety net for the long, low-frequency results – not a substitute for knowing the fundamentals. Three habits will help you use it well.
First, learn the layout before the exam. Download your board's exact booklet from their website and use it during every past paper. By the real exam, you should know without looking that Newton-Raphson is on page 2 and the binomial formula is on page 4.
Second, only reach for the booklet when you genuinely need it. If a question asks you to differentiate sin x, do not flick through pages looking for a derivative table. If you cannot do that one from memory, the booklet will not save you in the real time pressure of the exam.
Third, practise applying the booklet results in the exact form they are given. The R-method formula in the booklet is stated as a sin θ + b cos θ = R sin(θ + α). If a question asks for the form R cos(θ - α) instead, you need to recognise that it is the same idea with the cos identity rearranged.
Statistical tables are sometimes a separate booklet from the formulae booklet. Open both at the start of any Statistics paper so you don't waste time looking for one when you need it.
Differences between exam boards
All four major A-Level Maths boards (Edexcel, AQA, OCR A, OCR MEI) provide a formulae booklet. The content is broadly the same, with three small differences worth knowing.
Edexcel and AQA booklets are nearly identical for the standard A-Level Maths qualification. Both cover the Pure trig identities, integration standard forms, Newton-Raphson, integration by parts, SUVAT and the main distribution formulae.
OCR booklets sometimes include the arithmetic and geometric series formulae and the binomial expansion (1 + x)ⁿ for any rational n. Edexcel includes the binomial expansion as well. AQA puts the binomial expansion in the Pure section but expects you to recall the basic version for positive integer n from memory.
Further Maths booklets are different from regular A-Level Maths and include matrix results, complex number identities and hyperbolic function definitions. If you are doing Further Maths, you get the Further booklet in your Further papers – not the regular one.
Building deeper fluency
Top-scoring A-Level Maths students treat the formulae booklet like an emergency reference, not a working tool. Three habits build that fluency.
One, write out the off-booklet formulae weekly. Set a timer for five minutes and write the standard derivatives, the trig identity sin²x + cos²x = 1 and its rearrangements, the chain rule and the product rule from memory. Check against your notes and any slips become flashcards.
Two, do past papers under timed conditions with the booklet next to you. Mark them honestly. Any question where you used the booklet for something basic – say, looking up d/dx(eˣ) – should be flagged as a memory gap to fix.
Three, practise the rearrangement of booklet formulae. The cosine rule appears in the form a² = b² + c² - 2bc·cos A for some boards, and you may need cos A = (b² + c² - a²) / 2bc. The double angle cos 2A has three forms and you need to pick the right one for the question (integrating cos²x uses cos 2A = 2cos²x - 1).
A-Level Maths formulae booklet checklist
Work through this list once a week during exam season to make sure you are getting full value from the booklet.
- Download your board's exact formulae booklet PDF and use it during every past paper
- Know where the booklet prints the standard derivatives (sin x, cos x, tan x, eˣ, ln x) and the Pythagorean identities so you can find them in seconds
- Memorise the chain and product rules. They are NOT in the booklet on Edexcel, AQA or OCR
- Drill sin²x + cos²x = 1 and its rearrangements 1 + tan²x = sec²x, 1 + cot²x = cosec²x. The identities are printed, but speed of recall still wins time
- Memorise W = mg and the quadratic formula. These are NOT in the A-Level booklet. The sine rule, cosine rule and (1/2)ab·sin C ARE printed in the Trigonometry section, but knowing them cold still saves time
- Practise picking the right form of cos 2A (three versions) depending on the question
- For Mechanics, drill SUVAT from memory rather than reading off the booklet every time
- For Statistics, learn the layout of the cumulative binomial tables before exam day
- Practise R-method questions until converting a sin θ + b cos θ to R sin(θ + α) is automatic
