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A-level Maths formula booklet: what each board gives you

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Formula sheet

The card below opens today's A-level Maths paper with this sheet in the drawer. It holds the formulae that the Edexcel, AQA and OCR booklets all print, grouped in our own layout and words. Each board adds a little more, so check AQA's booklet, Pearson's booklet, OCR's sample paper, WJEC's booklet or CCEA's booklet for your own.

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

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)

Differentiation

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}differentiation from first principles
\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}quotient rule

Integration

\int u\frac{dv}{dx}dx=uv-\int v\frac{du}{dx}dxintegration by parts

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 and the binomial distribution

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

Mechanics: constant acceleration

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 none of the booklets will do for you

  • No board prints the quadratic formula. It sits on every board's recall list.
  • Which booklet you need depends on your exam entry, not on the subject. A guide cannot tell you whether your paper lets you off the sine rule.
  • Statistical tables are the biggest difference. Edexcel and CCEA put them in the booklet, OCR gives one normal table, and AQA and WJEC give none.

Choosing the right booklet before the exam

Find your board and specification on your exam entry confirmation. Six specifications are covered here: Edexcel, AQA, OCR A, OCR MEI, WJEC and CCEA. Eduqas does not offer A-level Maths. Then open that board's booklet in the comparison below.

The sheet in the card above is only the overlap, the formulae the Edexcel, AQA and OCR booklets all print. Anything on top of that is in the board pages linked in the comparison.

Use the quadratic formula to find both roots.

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

How the boards' booklets differ

BoardStatistical tables insideMensurationSum to product identitiesConstant acceleration
EdexcelYes: binomial, normal, correlation, random numbersYesYesYes
AQANoNoNoYes
OCR ANormal percentage points onlyNoNoYes
OCR MEINormal percentage points onlyNoNoYes
WJECNoYesYesNo
CCEAYes: six tablesYesYesNo
EduqasNot offered: Eduqas has no A-level Maths

Mensuration appears in Edexcel, WJEC and CCEA but not AQA or OCR. Constant acceleration is printed by Edexcel, AQA and the two OCR booklets but not by WJEC or CCEA. Sum to product identities appear in Edexcel, WJEC and CCEA only. Use the table to decide what to memorise on top of your own sheet.

Exam answers

Mark a daily paper here and you will see worked answers, which are ours and not from any board. They never replace a board mark scheme and we do not publish those.

Four daily papers to match the booklet's sections

The booklet divides into pure, statistics and mechanics, and the daily papers do too: Algebra and Functions, Calculus, Statistics and Mechanics. A fortnight of one paper a day, with the sheet open, is enough to learn the layout.

Mistakes when comparing booklets

  • Revising from the wrong board's sheet and finding a formula missing on exam day.
  • Treating the shared formulae in the card above as the full booklet.
  • Forgetting that the table of values you rely on may not exist in your booklet.

Common questions

Do you get a formula booklet in A-level Maths?
Yes. Edexcel, AQA, OCR (A and MEI), WJEC and CCEA each provide a formula booklet in the exam. It lists many formulae, but not all of them.
What formulae do you need to memorise for A-level Maths?
The ones the booklet leaves out: the quadratic formula, laws of indices and logarithms, the sine and cosine rules, basic identities, standard derivatives and integrals, and the straight line equation.
Is the A-level Maths formula booklet the same for every board?
No. They overlap, but each board prints its own. Edexcel and CCEA include statistical tables, AQA's short booklet does not, and WJEC and CCEA have no kinematics section.
Does the A-level Maths formula booklet have the quadratic formula?
No board prints it. Edexcel's specification lists it as a formula you must be able to recall.
Does Eduqas have an A-level Maths formula booklet?
No, because Eduqas does not offer A-level Maths.

Revision cards

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