If you're sitting OCR A A-Level Maths (specification H240) in 2027, every exam paper is printed with the formula booklet on pages 2 and 3. The spec itself confirms this: 'Learners will be given formulae in each assessment on pages 2 and 3 of the question paper. See Section 5d for a list of these formulae.'
One thing to get straight at the start, because it comes up often: the A-Level Maths formula booklet is permanent and spec-mandated under the current A-Level Mathematics specification (unlike the GCSE Maths formulae sheet, which Ofqual confirmed on 5 May 2026 to continue for the life of the current specifications).
OCR runs two separate A-Level Maths specifications: OCR A (H230/H240) and OCR B MEI (H630/H640). Each board decides what goes in its booklet, so the contents differ. This guide covers OCR A specifically. For OCR MEI, see our OCR MEI A-Level Maths formula booklet guide.
This article was last checked against official sources on **14 October 2026**. Specifications and admissions wording change often, so cross-check each named source before relying on specific detail.
Unlike the GCSE equation sheets introduced by Ofqual in 2022, A-Level Maths formula booklets are spec-mandated under the current OCR A specification. Section 5d of the OCR spec lists what you must still recall from memory; the booklet gives you everything else.
How the booklet works in the exam
The booklet is printed on pages 2 and 3 of every H240 question paper. You don't need to carry it in, you don't need to request it, and every candidate gets a fresh clean copy. It's included in all three papers: Paper 1 (Pure Mathematics), Paper 2 (Pure Mathematics and Statistics) and Paper 3 (Pure Mathematics and Mechanics).
Content is organised by topic: arithmetic and geometric series, binomial series, differentiation standard results, integration standard results, small-angle approximations, trigonometric compound-angle identities, numerical methods, probability, standard deviation, the binomial distribution, the normal-distribution hypothesis test, a percentage-points table for the normal distribution, and kinematics equations in one and two dimensions.
The booklet is comprehensive on the longer, less-memorable standard results. Students aren't expected to recall the compound-angle identities, the trapezium rule or the Newton-Raphson iteration from memory. Instead, Section 5d of the specification lists what you ARE expected to recall, and the booklet lists what you're given.
Verify the current year's provision on OCR's A-Level Mathematics A qualification page before your exam.
What's in the booklet, Pure Mathematics
The Pure block covers series, binomial expansions, differentiation beyond the Section 5d basics, integration standard forms, small-angle approximations, compound-angle trig identities and numerical methods. These are the longer, more awkward results that don't belong in your head on exam day.
| Result | Statement | When you use it |
|---|---|---|
| Arithmetic series | S<sub>n</sub> = ½n(a + l) = ½n{2a + (n-1)d} | Sum of the first n terms of an arithmetic progression |
| Geometric series (finite) | S<sub>n</sub> = a(1 − r<sup>n</sup>) / (1 − r) | Sum of the first n terms of a geometric progression |
| Geometric series (infinite) | S<sub>∞</sub> = a / (1 − r) for |r| < 1 | Sum to infinity of a convergent GP |
| Binomial expansion (n ∈ ℕ) | (a + b)<sup>n</sup> = a<sup>n</sup> + <sup>n</sup>C<sub>1</sub> a<sup>n−1</sup>b + ... + b<sup>n</sup>, with <sup>n</sup>C<sub>r</sub> = n! / (r!(n−r)!) | Expanding (a + b)<sup>n</sup> for positive-integer n |
| Binomial expansion (n ∈ ℝ) | (1 + x)<sup>n</sup> = 1 + nx + n(n−1)/2! × x<sup>2</sup> + ... for |x| < 1 | Series expansions with non-integer or negative n |
| Trig derivatives | d/dx(tan kx) = k sec<sup>2</sup> kx; d/dx(sec x) = sec x tan x; d/dx(cot x) = −cosec<sup>2</sup> x; d/dx(cosec x) = −cosec x cot x | Differentiating reciprocal and compound trig functions |
| Quotient rule | y = u/v, dy/dx = (v du/dx − u dv/dx) / v<sup>2</sup> | Differentiating ratios |
| First-principles derivative | f'(x) = lim<sub>h→0</sub> [f(x+h) − f(x)] / h | Formal differentiation from the definition |
| Integration by ln | ∫ f'(x)/f(x) dx = ln|f(x)| + c | Integrating any ratio where numerator is derivative of denominator |
| Integration (reverse chain) | ∫ f'(x)(f(x))<sup>n</sup> dx = (f(x))<sup>n+1</sup> / (n+1) + c | Reverse chain rule for polynomials in f(x) |
| Integration by parts | ∫ u (dv/dx) dx = uv − ∫ v (du/dx) dx | Products like x·e<sup>x</sup>, x·sin x, x·ln x |
| Small-angle approximations | sin θ ≈ θ; cos θ ≈ 1 − ½θ<sup>2</sup>; tan θ ≈ θ (θ in radians) | Approximations in series and limit arguments |
| Compound-angle identities | sin(A ± B), cos(A ± B), tan(A ± B) | Transforming trig expressions in proof and solving equations |
| Trapezium rule | ∫<sub>a</sub><sup>b</sup> y dx ≈ ½h{(y<sub>0</sub> + y<sub>n</sub>) + 2(y<sub>1</sub> + ... + y<sub>n−1</sub>)}, h = (b−a)/n | Numerical integration |
| Newton-Raphson | x<sub>n+1</sub> = x<sub>n</sub> − f(x<sub>n</sub>)/f'(x<sub>n</sub>) | Numerical root-finding |
What's in the booklet, Mechanics (kinematics)
The mechanics content on the booklet is deliberately short. OCR A gives you the constant-acceleration kinematic equations in both one-dimensional and vector (two-dimensional) form. Everything else in mechanics, Newton's laws, equilibrium, friction, variable acceleration via calculus, comes from first principles and your own setup. The booklet is light here because most mechanics is modelling, not formula-recall.
| Form | Equations | Where it applies |
|---|---|---|
| 1D (straight line) | v = u + at; s = ut + ½at<sup>2</sup>; s = ½(u + v)t; v<sup>2</sup> = u<sup>2</sup> + 2as; s = vt − ½at<sup>2</sup> | Constant-acceleration straight-line motion |
| 2D (vectors) | v = u + at; s = ut + ½at<sup>2</sup>; s = ½(u + v)t; s = vt − ½at<sup>2</sup> | Projectile motion and vector-form kinematics |
What's in the booklet, Statistics
The statistics section covers probability, standard deviation, the binomial distribution, hypothesis testing for the mean of a normal distribution, and a table of critical values from the standard normal distribution.
| Result | Statement | When you use it |
|---|---|---|
| Probability (union) | P(A ∪ B) = P(A) + P(B) − P(A ∩ B) | Combining two events |
| Probability (conditional) | P(A ∩ B) = P(A)P(B | A) = P(B)P(A | B); P(A | B) = P(A ∩ B)/P(B) | Conditional and dependent events |
| Standard deviation (frequency) | √(Σ(x − x̄)<sup>2</sup> / n) = √(Σx<sup>2</sup>/n − x̄<sup>2</sup>); frequency-weighted equivalents | Computing SD from data or frequency tables |
| Binomial distribution | X ~ B(n, p): P(X = x) = <sup>n</sup>C<sub>x</sub> p<sup>x</sup>(1−p)<sup>n−x</sup>; Mean = np; Variance = np(1−p) | Discrete probability with fixed n and p |
| Normal distribution (sample mean) | X ~ N(μ, σ<sup>2</sup>) implies X̄ ~ N(μ, σ<sup>2</sup>/n); (X̄ − μ) / (σ/√n) ~ N(0, 1) | Hypothesis testing on the mean |
| Normal critical values | Table at p = 0.75, 0.90, 0.95, 0.975, 0.99, 0.995, 0.9975, 0.999, 0.9995 | Looking up z-values for one- and two-tailed tests |
The compound-angle identities for sin, cos and tan are printed on the booklet. The double-angle versions (sin 2A, cos 2A, tan 2A) are NOT, those are in Section 5d of the specification as items you must recall. A common exam-day mistake is scanning the booklet for sin 2A and not finding it.
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What you still need to recall, Section 5d
Section 5d of the OCR specification lists the formulae and identities students must use 'without these formulae and identities being provided'. This is the memorise list. It's not short, treat it as a parallel document to the booklet rather than an afterthought.
Pure Mathematics recall items
The quadratic formula x = (−b ± √(b2 − 4ac)) / 2a. Laws of indices (three identities around aman, (am)n, a−n). Laws of logarithms (the definition x = an ⇔ n = logax, plus loga(xy), loga(x/y) and loga(xn); change of base is excluded from the spec). Coordinate geometry: y − y1 = m(x − x1) for a straight line, and the perpendicular condition m1m2 = −1.
Sequences: nth-term formulae un = a + (n−1)d for arithmetic and un = arn−1 for geometric.
Trigonometry: sine rule, cosine rule, area ½ab sin C, Pythagorean identities cos2A + sin2A = 1 and the sec/cosec versions, double-angle identities sin 2A, cos 2A (Section 5d prints cos 2A ≡ cos2A − sin2A; the 2cos2A − 1 and 1 − 2sin2A equivalents follow from cos2A + sin2A = 1), tan 2A.
Mensuration: C = 2πr, A = πr2, Pythagoras, trapezium area, prism volume, arc length s = rθ and sector area A = ½r2θ.
Calculus and vectors recall items
Standard derivatives: xn, sin kx, cos kx, ekx, ln x. Sum rule, product rule, chain rule.
Standard integrals: xn, sin kx, cos kx, ekx, 1/x. Sum rule, reverse chain rule for linear substitutions.
Vectors: |xi + yj| = √(x2 + y2) for 2D, |xi + yj + zk| = √(x2 + y2 + z2) for 3D.
Mechanics and Statistics recall items
Mechanics: weight W = mg, friction inequality F ≤ μR, Newton's second law F = ma. Variable-acceleration kinematics via calculus (v = dr/dt, a = dv/dt = d2r/dt2). The booklet gives you constant-acceleration suvat; variable acceleration via calculus is on you.
Statistics: mean x̄ = Σx/n (also Σfx/Σf for frequency data), and the standard normal transformation Z = (X − μ)/σ.
OCR A vs OCR B MEI: Which is which
OCR runs two A-Level Maths specifications and they're not interchangeable. OCR A (covered in this guide) is H230 at AS, H240 at full A-Level. OCR B is the MEI (Mathematics in Education and Industry) specification, H630 at AS, H640 at full A-Level. Students sit different papers and get different formatted booklets.
Each board decides what goes in its own booklet. Formatting, section numbering, ordering and presentational choices differ between OCR A and MEI.
One visible delta is the percentage-points table in the Statistics section. OCR A's booklet lists normal-distribution critical values at p = 0.75, 0.90, 0.95, 0.975, 0.99, 0.995, 0.9975, 0.999 and 0.9995. If you're on OCR A, practise with the OCR A table rather than any cross-board version, because layout familiarity under time pressure matters.
Our OCR MEI formula booklet guide covers MEI specifically.
Study tips for using the booklet well
The booklet is comprehensive but not helpful under time pressure if you don't know your way around it. Students who treat it as a reference of last resort hunt through the pages when they should be reaching across for a specific result they've found in practice.
Print the current OCR A booklet and keep it next to every past paper you sit at home. The physical layout matters, knowing that Newton-Raphson is on the right-hand page under 'numerical methods', or that the binomial PMF is on the lower half under 'statistics', saves seconds per look-up.
Mark the places that trip you up most often. The compound-angle identities get used in integration, trig equations and proof, if you reach for them often, highlight them. The small-angle approximations are easy to miss because they're grouped under a heading some students skim past.
Section 5d is a parallel document to the booklet, not a bonus. Treat the two together: whenever you work on a topic, know which formulae are on the booklet and which are expected recall. The double-angle identities trip students up for exactly this reason, compound-angle is on the booklet, double-angle isn't, and the exam often asks for both in the same question.
Memorise the short items in Section 5d anyway. The quadratic formula, laws of indices and logs, standard derivatives (sin x, cos x, ex, ln x), and the Pythagorean identities. Looking these up in the booklet costs seconds, and across a two-hour paper the seconds add up. Fluency on the short results is where the extra marks come from.
Our hardest A-Level Maths topics guide covers the areas where booklet fluency makes the most practical difference.
How Cognito helps
If your revision runs on structured lessons rather than reading the spec cover to cover, Cognito's OCR A A-Level Maths course walks through every formula on your booklet with worked examples. Pure Mathematics, Mechanics and Statistics each get a dedicated topic area, and the booklet-versus-recall split is called out explicitly inside each lesson.
Specific booklet items, compound-angle identities, small-angle approximations, Newton-Raphson, integration by parts, each have a worked-example video showing when and how to apply them. The Section 5d recall list is covered in the fundamentals block, with quiz questions that test fluency on the short results rather than let you look them up.
If you're starting booklet revision from scratch six weeks before the exam, the topic-by-topic structure is the fastest way to get both knowledgeable and quick, and you can slot your actual booklet alongside it as you work.
Six practical steps for using the booklet well across all three papers.
- Download the current year's booklet from OCR's A-Level Mathematics A assessment-resources page
- Print it and keep it next to every past paper you sit at home
- Highlight the compound-angle identities, Newton-Raphson, the trapezium rule and integration by parts for quick access
- Memorise the Section 5d recall list, especially the quadratic formula, laws of indices and logs, Pythagorean identities and double-angle identities
- Learn the OCR A normal critical-value table layout rather than any cross-board version
- Write each formula out explicitly before substituting numbers in every practice question
