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OCR MEI A-level Maths formula booklet (H640): what is on it and what is not

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Formula sheet

The card below opens today's A-level Maths paper with this sheet in the drawer, so you practise the way you will sit the exam. The contents follow, grouped like the real booklet in our own layout and words. OCR prints the booklet in each paper, so we checked it against the H640/02 sample paper (OCR 2025). Check the booklet in your own paper before you rely on anything here.

Formula sheet

A-level Maths: Algebra & Functions

Open formula sheet

Arithmetic series

S_n=\frac{1}{2}n(a+l)=\frac{1}{2}n[2a+(n-1)d]arithmetic series, sum of the first n terms

Geometric series

S_n=\frac{a(1-r^n)}{1-r}geometric series, sum of the first n terms
S_\infty=\frac{a}{1-r}geometric series, sum to infinity (for |r| < 1)

Binomial series

(a+b)^n=a^n+\binom{n}{1}a^{n-1}b+\binom{n}{2}a^{n-2}b^2+\cdots+\binom{n}{r}a^{n-r}b^r+\cdots+b^nbinomial theorem for a positive whole number n
\binom{n}{r}=\frac{n!}{r!(n-r)!}the binomial coefficient
(1+x)^n=1+nx+\frac{n(n-1)}{1\times2}x^2+\cdots+\frac{n(n-1)\cdots(n-r+1)}{1\times2\times\cdots\times r}x^r+\cdotsbinomial series for any n, when |x| < 1

Differentiation

\frac{d}{dx}(\tan kx)=k\sec^2 kxderivative of tan kx
\frac{d}{dx}(\sec x)=\sec x\tan xderivative of sec x
\frac{d}{dx}(\cot x)=-\csc^2xderivative of cot x
\frac{d}{dx}(\csc x)=-\csc x\cot xderivative of cosec x
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}quotient rule
f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}differentiation from first principles

Integration

\int\frac{f'(x)}{f(x)}dx=\ln|f(x)|+cintegral of f′(x)/f(x)
\int f'(x)[f(x)]^n\ dx=\frac{[f(x)]^{n+1}}{n+1}+cintegral of f′(x) times a power of f(x)
\int u\frac{dv}{dx}dx=uv-\int v\frac{du}{dx}dxintegration by parts

Small angle approximations

\sin\theta\approx\thetasine for a small angle (θ in radians)
\cos\theta\approx1-\frac{\theta^2}{2}cosine for a small angle (θ in radians)
\tan\theta\approx\thetatangent for a small angle (θ in radians)

Trigonometric identities

\sin(A\pm B)=\sin A\cos B\pm\cos A\sin Bsine of a sum or difference
\cos(A\pm B)=\cos A\cos B\mp\sin A\sin Bcosine of a sum or difference
\tan(A\pm B)=\frac{\tan A\pm\tan B}{1\mp\tan A\tan B}tangent of a sum or difference (A ± B not an odd multiple of π/2)

Numerical methods

\int_a^b y\ dx\approx\frac{1}{2}h[(y_0+y_n)+2(y_1+y_2+\cdots+y_{n-1})]the trapezium rule (h = (b − a)/n)
x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}Newton-Raphson iteration for solving f(x) = 0

Probability

P(A\cup B)=P(A)+P(B)-P(A\cap B)addition rule
P(A\cap B)=P(A)P(B|A)=P(B)P(A|B)\quad\text{or}\quad P(A|B)=\frac{P(A\cap B)}{P(B)}multiplication rule and conditional probability

Standard deviation

s=\sqrt{\text{variance}}standard deviation of a sample
s^2=\frac{1}{n-1}S_{xx}\text{ where }S_{xx}=\sum x^2-\frac{(\sum x)^2}{n}=\sum x^2-n\bar{x}^2sample variance

The binomial distribution

P(X=r)={}^nC_rp^rq^{n-r},\quad q=1-p,\quad E(X)=npbinomial distribution B(n, p): probability and mean

Hypothesis test for the mean of a normal distribution

X\sim N(\mu,\sigma^2)\Rightarrow\bar{X}\sim N\left(\mu,\frac{\sigma^2}{n}\right),\quad\frac{\bar{X}-\mu}{\sigma/\sqrt{n}}\sim N(0,1)sample mean from a normal population

Kinematics: motion in a straight line

v=u+atfinal velocity
s=ut+\frac{1}{2}at^2displacement from the start velocity
s=vt-\frac{1}{2}at^2displacement from the final velocity
s=\frac{1}{2}(u+v)tdisplacement from the average velocity
v^2=u^2+2asvelocity without time

What MEI adds to the OCR A booklet

Compared with the OCR A booklet, the MEI one adds the sample variance formula, s² = Sₓₓ/(n − 1), and presents its normal percentage points table for p = 10, 5, 2 and 1, giving z = 1.645, 1.960, 2.326 and 2.576. Those are the two-tailed critical values you reach for in hypothesis tests. MEI students also meet the booklet used for the further content in H645, which has its own Further Maths booklet.

What is missing from the MEI booklet

  • There is no logarithm or exponential line, so the change of base is left to you.
  • The normal table has just four entries, 10, 5, 2 and 1 per cent. A probability like 0.8 needs the calculator or a value given in the question.
  • Mensuration, summations and the double angle formulae are not printed.

Using the booklet with MEI's style of question

MEI questions tend to put maths in context, with long statements about a real situation, and then ask for a formula from the booklet in the middle. The skill is to read through the context to the one line of the booklet that applies.

MEI is the only board here that prints the sample variance, s² = Sₓₓ/(n − 1), in the booklet. If a question gives a sample and asks for an unbiased estimate, this is the line.

Use the quadratic formula to find both roots.

Press Mark to have your answer marked in the Algebra course.

Worked example: sample variance

A sample of five values has Σx = 20 and Σx² = 90. Find the sample variance.

The mean is 4. Sₓₓ is Σx² minus n times the mean squared.

S_{xx}=90-5(4)^2=10,\quad s^2=\frac{S_{xx}}{n-1}=\frac{10}{4}=2.5

Dividing by 5 instead of 4 gives the population variance, 2, which is the usual wrong answer.

The OCR MEI booklet and the other boards

BoardBookletWhat it adds or leaves out
EdexcelMathematical Formulae and Statistical TablesMensuration, logarithm change of base, sum to product identities, and the statistical tables, all in one booklet for AS, A-level Maths and Further Maths
AQAFormulae for A-level Mathematics (7357)A shorter booklet with no statistical tables, no mensuration and no sum to product identities
OCR AFormulae, A Level Mathematics A (H240)Short, with a hypothesis test line, a normal percentage points table and kinematics in two dimensions
OCR MEI (this guide)Formulae, A Level Mathematics B (MEI) (H640)Close to OCR A, plus the sample variance formula
WJECGCE AS/A Level Mathematics and Further Mathematics Formula BookletOne booklet for both subjects, formulae only, including sum to product identities
CCEAMathematical Formulae and TablesOne booklet for both subjects, with statistical tables inside

The MEI and OCR A booklets are close cousins, and a sheet from one would nearly pass for the other. The details that separate them are the sample variance line and the table: MEI's normal table is for p = 10, 5, 2 and 1, giving 1.645, 1.960, 2.326 and 2.576, where OCR A lists a row for each probability from 0.75 up.

Exam answers

Once you mark a paper here, the answers show worked steps in our own words. They come from us, not from OCR, and there are no official mark schemes involved.

Using the daily papers for an MEI course

MEI students often study statistics and mechanics in the same paper as pure maths, so do not worry about which track to choose. Pick a topic: Statistics is the best match for the sample variance and the binomial line, and Algebra and Functions for the series entries. Calculus and Mechanics are also available.

Common MEI booklet errors

  • Using the sample variance formula when the question asks for the variance of the data as a whole.
  • Treating the 10, 5, 2, 1 table as one-tailed probabilities.
  • Missing that kinematics is printed for two dimensions as well as one.

Common questions

Do you get a formula booklet in MEI A-level Maths?
Yes. The formulae for A Level Mathematics B (MEI) (H640) are printed in the papers, and OCR's sample paper shows them.
Is the MEI formula booklet the same as OCR A?
Almost. MEI adds the sample variance formula and uses a normal percentage points table for p = 10, 5, 2 and 1 per cent.
What is not in the MEI formula booklet?
The quadratic formula, indices and logarithm rules, triangle rules and the basic derivatives and integrals.
Does the MEI booklet have statistical tables?
Only a small table of normal percentage points.
Is there a separate MEI Further Maths booklet?
Yes. OCR publishes a Formulae Booklet for AS and A Level Further Mathematics B (MEI) (H635 and H645).

Revision cards

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