If you're sitting OCR B MEI A-Level Maths (specification H640) in 2027, every exam paper is printed with the formula booklet on pages 2 and 3. The H640 specification 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.'
The first thing to know, because the question comes up often: MEI stands for Mathematics in Education and Industry, which is an educational charity that developed the specification jointly with OCR. MEI isn't a separate awarding body, H640 is an OCR qualification, OCR issues the certificates, and the booklet is published by OCR under the OCR B heading. Students sometimes assume MEI is an independent board, which it isn't.
The second thing to know, since it matters more than the admin: the A-Level Maths formula booklet is permanent and spec-mandated since the 2017 reform. It's a fixed feature of the reformed qualification across all boards (AQA, Edexcel, OCR, OCR B MEI). The booklet exists so papers can test problem-solving and modelling on top of fluency, which is where MEI's design intent, strong on modelling and real-world application, lives.
The DfE sets the content students must know across all boards, so the OCR A (H240) and OCR B MEI (H640) booklets cover very similar formulae, but each board designs its own booklet and the statistics sections differ. What differs is the formatting, section ordering, notation and one visible difference in the statistics section. This guide walks through MEI's booklet specifically. For OCR A, see our OCR A A-Level Maths formula booklet guide. For a guide covering all boards, see our general A-Level Maths formulae guide.
MEI is OCR B, not a separate awarding body. The H640 specification (H630 AS, H640 A-Level) was developed by MEI (Mathematics in Education and Industry) jointly with OCR, who issues the qualification. The booklet is permanent since 2017, not a pandemic-era provision.
This article was last checked against the OCR B (MEI) A-Level Mathematics qualification page and the H640 specification PDF on **14 October 2026**. OCR occasionally revises specification wording and booklet formatting, so download the current year's booklet from OCR's assessment-resources page before you rely on any specific detail.
How the booklet works in the exam
The booklet is printed on pages 2 and 3 of every H640 question paper. You don't carry it in, you don't request it, and every candidate gets a fresh clean copy. It's included in all three papers: Paper 1 (Pure Mathematics and Mechanics), Paper 2 (Pure Mathematics and Statistics) and Paper 3 (Pure Mathematics and Comprehension).
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, sample variance, the binomial distribution, the normal-distribution hypothesis test, a critical-values table for the standard normal distribution, and kinematics equations in one and two dimensions.
The booklet gives you the longer, less-memorable standard results. Section 5d of the H640 specification lists what you ARE expected to recall. MEI's content on both documents is subject-level identical to OCR A, because of DfE standardisation, but a handful of notation and layout choices make the two booklets feel different in practice.
Verify the exact booklet content against the current year's provision on OCR's A-Level Mathematics B (MEI) 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. The content matches OCR A at subject level; MEI's formatting groups things slightly differently, but the formulae themselves are the same.
| 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)
MEI's mechanics section on the booklet is deliberately short, like OCR A's. You get the constant-acceleration kinematic equations in both one-dimensional and vector (two-dimensional) form. One visible MEI quirk: the kinematics equations are often presented in a two-column side-by-side layout (1D on the left, 2D vector on the right), which some students find clearer than OCR A's separated listing. The underlying content is the same.
Everything else in mechanics, Newton's laws, equilibrium, friction modelling, variable acceleration via calculus, comes from first principles. The booklet is light here because MEI's mechanics is modelling-first by design.
| 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 is where MEI's booklet differs most visibly from OCR A. MEI phrases variance as sample variance s2 explicitly, uses Sxx notation, uses r (not x) for the binomial probability mass function, and publishes a shorter critical-values table.
| 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 |
| Sample variance | s<sup>2</sup> = (1/(n − 1)) × S<sub>xx</sub>, where S<sub>xx</sub> = Σ(x<sub>i</sub> − x̄)<sup>2</sup> = Σx<sub>i</sub><sup>2</sup> − (Σx<sub>i</sub>)<sup>2</sup>/n = Σx<sub>i</sub><sup>2</sup> − nx̄<sup>2</sup>; standard deviation s = √variance | Computing sample variance from a dataset |
| Binomial distribution | X ~ B(n, p): P(X = r) = <sup>n</sup>C<sub>r</sub> p<sup>r</sup> q<sup>n−r</sup> where q = 1 − p; Mean = np | 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 = 10, 5, 2, 1 (percentages) | 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. This is identical to OCR A, a common exam-day mistake across both specs.
Ready to boost your grades?
Join 1M+ students who have used Cognito to ace their exams.
Get started for free!
What you still need to recall, Section 5d
Section 5d of the H640 specification lists the formulae and identities students must use 'without these formulae and identities being provided'. The list is substantively identical to OCR A's, because the DfE standardises the content. Treat it as a parallel document to the booklet, not 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 isn't required). 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: MEI's Section 5d quotes the magnitude in 3D form |xi + yj + zk| = √(x2 + y2 + z2). The 2D case is treated as the obvious projection.
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 MEI vs OCR A: Where they differ
The two OCR A-Level Maths booklets are close to identical at content level, because the DfE standardises the required knowledge across all A-Level Maths specifications. The formulae on the Pure section of MEI's booklet are the same as OCR A's. The kinematics equations are the same. The compound-angle identities, small-angle approximations, trapezium rule and Newton-Raphson are the same.
The visible differences live in the statistics section and in formatting.
The critical-values table is the biggest practical difference. OCR A publishes a wider table of normal-distribution critical values (as one-tailed cumulative probabilities, P(Z ≤ z)). MEI publishes a shorter table using two-tailed significance percentages (p = 10, 5, 2, 1); the z-values are the same (1.645, 1.960, 2.326, 2.576), it's the labelling convention that differs. Students sometimes practise with OCR A past papers and end up expecting a wider table; MEI students should drill with MEI's own table.
MEI phrases sample variance s2 explicitly, using Sxx notation (Sxx = Σ(xi − x̄)2). OCR A uses the raw-form standard deviation formula without the Sxx shortcut. For hypothesis-testing questions on sample means, the two formulations are algebraically equivalent, but the notation on the page looks different.
MEI's binomial PMF uses r (and q = 1 − p). OCR A uses x (and (1 − p) written out). Minor, but if you memorise MEI's version and sit in front of OCR A notation, there's a small cognitive overhead.
Section numbering and layout differ throughout. The kinematics side-by-side layout (1D | 2D vector) is distinctive to MEI's presentation; OCR A separates the two cases. The row ordering within the Pure differentiation table is not identical.
None of these differences change what you're expected to know. They change what you'll see on the page under exam pressure. Practise with your own board's current booklet, not OCR A's version. Our OCR A A-Level Maths formula booklet guide covers the OCR A version in detail.
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 MEI booklet and keep it next to every past paper you sit at home. The physical layout matters, knowing that the Sxx sample-variance formula is in the lower half of the statistics section, or that the kinematics equations are in a two-column side-by-side block, saves seconds per look-up.
MEI's critical-values table deserves its own revision time. Four columns, percentage labels. Students who've seen OCR A's 9-column table in textbooks sometimes expect more detail than MEI's booklet provides. If a question needs a value that isn't in the table, use your calculator's inverse Normal function rather than the nearest table value.
Section 5d is a parallel document to the booklet, not a bonus. 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 A-Level Maths A* guide covers this and other exam-time decisions that separate A* work from fluent work.
For MEI specifically, practise sample-variance questions using the Sxx shortcut rather than the long form. The booklet gives you the Sxx decomposition (Σxi2 − (Σxi)2/n), which is faster to compute than the raw-deviation form. Students who revise from OCR A or AQA textbooks sometimes miss this shortcut.
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 B MEI 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 MEI booklet items, the Sxx sample-variance formula, the compound-angle identities, 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.
For statistics specifically, the course includes worked examples of hypothesis tests using MEI's 4-column critical-values table layout, so you're drilling with the exact format you'll meet in the exam. 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.
Six practical steps for using the booklet well across all three papers.
- Download the current year's booklet from [OCR's A-Level Mathematics B (MEI) qualification page](https://www.ocr.org.uk/qualifications/as-and-a-level/mathematics-b-mei-h630-h640-from-2017/)
- 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 MEI's 4-column critical-values table layout, don't practise with OCR A's 9-column version
- Drill the S<sub>xx</sub> sample-variance shortcut rather than the raw-deviation form
