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OCR A-level Maths formula booklet (H240): 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 at the front of each paper, so we checked it against the H240/01 sample assessment material (2018). 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 kx)=k\sec kx\tan kxderivative of sec kx
\frac{d}{dx}(\cot kx)=-k\csc^2 kxderivative of cot kx
\frac{d}{dx}(\csc kx)=-k\csc kx\cot kxderivative of cosec kx
\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)\times P(B|A)multiplication rule

Standard deviation

\sigma=\sqrt{\frac{\sum x^2}{n}-\bar{x}^2}standard deviation from the data

The binomial distribution

P(X=x)=\binom{n}{x}p^x(1-p)^{n-x},\quad \mu=np,\quad \sigma^2=np(1-p)binomial distribution B(n, p): probability, mean, variance

Hypothesis test for the mean of a normal distribution

\frac{\bar{X}-\mu}{\sigma/\sqrt{n}}\sim N(0,1)sample mean from a normal population (sample of n from N(μ, σ²))

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

The table and the two-dimensional kinematics

Besides the formulae above, the OCR booklet holds a table of percentage points of the normal distribution: for each probability p from 0.75 up to 0.9995 it gives the value of z with P(Z ≤ z) = p. It also gives the constant acceleration equations in vector form for motion in two dimensions, with the same shapes as the straight line ones. Use the table for finding critical values in hypothesis tests rather than working them out from scratch.

What the H240 booklet leaves out

  • No logarithm line at all: neither the change of base nor aˣ = e^(x ln a). Edexcel and WJEC print these.
  • No mensuration and no summation results. The surface area of a sphere is not given.
  • The normal table is a single table of percentage points, so binomial and Poisson values are not on the page.
  • As with every board, the quadratic formula, triangle rules and basic derivatives are not printed.

Reading the OCR booklet like a mark scheme

OCR prints this booklet inside the question paper itself, which means you will have the same pages in front of you in the exam that you used for practice. Learn the page order: pure formulae first, then probability and statistics, then kinematics.

The probability section gives P(A ∩ B) = P(A) P(B | A) in the form that suits tree diagrams, and the hypothesis test line sets up the standardised test statistic. The normal table below it lists z-values for p from 0.75 to 0.9995, so you can read critical values straight off.

Use the quadratic formula to find both roots.

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

Worked example: a binomial coefficient

Find the coefficient of x³ in (2 + x)⁵.

Take a = 2 and b = x. The term in b³ has r = 3, so its coefficient is the binomial coefficient times a raised to n − r.

\binom{5}{3}\ 2^{2}\ x^3=10\times4\ x^3=40x^3

Forget that a is squared, not cubed, and you get 80. The check is that the two powers must add up to 5.

The OCR A 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 A (this guide)Formulae, A Level Mathematics A (H240)Short, with a hypothesis test line, a normal percentage points table and kinematics in two dimensions
OCR MEIFormulae, 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

OCR A and OCR MEI have separate booklets that are nearly the same, so a sheet picked up from the wrong specification will mostly work but not entirely. The A booklet gives normal percentage points for p = 0.75 up to 0.9995. MEI uses 10, 5, 2 and 1 per cent. Both give the kinematics formulae twice, once for a straight line and once as vectors in two dimensions.

Exam answers

Answers to the daily papers are our own worked solutions, shown once you have marked your paper. They are not OCR answers and have no connection to any OCR past paper.

Practice for H240-style paper sections

The four A-level Maths daily papers are listed under Algebra and Functions, Calculus, Statistics and Mechanics. OCR splits its H240 papers differently, with pure and mechanics together in one, so use the track that matches the topic you want to drill rather than trying to copy OCR's paper split.

H240 booklet slips

  • Using the integral of f′(x)[f(x)]ⁿ when n = −1, where the logarithm entry applies instead.
  • Reading the percentage points table for the wrong tail.
  • Applying a straight line kinematics formula to a vector problem.

Common questions

Do you get a formula booklet in OCR A-level Maths?
Yes. The formulae for A Level Mathematics A (H240) are printed in the papers, and OCR's sample papers show them.
What is in the OCR A-level Maths formula booklet?
Arithmetic and geometric series, binomial series, differentiation and integration results, small angle approximations, trigonometric identities, numerical methods, probability, the binomial distribution, a hypothesis test for a normal mean, normal percentage points and kinematics.
Is the OCR A and OCR MEI maths booklet the same?
They are very close. The MEI booklet adds the sample variance formula and gives its normal percentage points for p = 10, 5, 2 and 1 per cent.
Does the OCR booklet have statistical tables?
It has the one table of normal percentage points. It does not carry the binomial or other distribution tables that the Edexcel booklet has.
What do I need to memorise for OCR A-level Maths?
Everything the booklet does not list: the quadratic formula, indices and logarithm rules, triangle rules, basic identities, standard derivatives and integrals, and the methods themselves.

Revision cards

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