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Edexcel A-level Maths formula booklet (9MA0): 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. Check against Pearson's Mathematical Formulae and Statistical Tables (Issue 1, July 2017) before you rely on anything here.

Formula sheet

A-level Maths: Algebra & Functions

Open formula sheet

Mensuration

A=4\pi r^2surface area of a sphere
A=\pi r\times\text{slant height}curved surface area of a cone

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

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

Logarithms and exponentials

\log_a x=\frac{\log_b x}{\log_b a}change of base for logarithms
a^x=e^{x\ln a}exponential in terms of the natural logarithm

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)

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)
\sin A+\sin B=2\sin\frac{A+B}{2}\cos\frac{A-B}{2}sum of sines
\sin A-\sin B=2\cos\frac{A+B}{2}\sin\frac{A-B}{2}difference of sines
\cos A+\cos B=2\cos\frac{A+B}{2}\cos\frac{A-B}{2}sum of cosines
\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}difference of cosines

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)

Differentiation

f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}differentiation from first principles
\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

Integration

\int\sec^2 kx\ dx=\frac{1}{k}\tan kx+cintegral of sec² kx
\int\tan kx\ dx=\frac{1}{k}\ln|\sec kx|+cintegral of tan kx
\int\cot kx\ dx=\frac{1}{k}\ln|\sin kx|+cintegral of cot kx
\int\csc kx\ dx=-\frac{1}{k}\ln|\csc kx+\cot kx|+cintegral of cosec kx
\int\sec kx\ dx=\frac{1}{k}\ln|\sec kx+\tan kx|+cintegral of sec kx
\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
P(A\cap B)=P(A)P(B)independent events

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

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

Which paper uses which part

The 9MA0 qualification has Paper 1 and Paper 2 in Pure Mathematics and Paper 3 in Statistics and Mechanics. The series, trigonometry, calculus and numerical sections of the booklet therefore matter in the first two papers, and the probability, distribution, constant acceleration and table sections matter in the third. The booklet is the same in every paper, so you can open it at the right page without hunting. Learn its layout in the weeks before the exam, not in the exam room.

Statistical tables in the booklet

Pearson lists four tables as required for A-level Maths: the binomial cumulative distribution function, the percentage points of the normal distribution, critical values for correlation coefficients, and random numbers. The binomial table covers set values of n and p, so a question that uses another value will ask for a calculator method instead.

What Edexcel expects you to recall

  • Pearson's specification, in Appendix 1, names the formulae you must be able to recall: the quadratic formula, laws of indices and logarithms, the equation of a straight line and the perpendicular gradient test, the nth terms of arithmetic and geometric sequences, the sine and cosine rules, the area of a triangle as ½ab sin C, and the basic trigonometric identities.
  • Calculus basics are on the same recall list: the derivatives and integrals of xⁿ, sin kx, cos kx, eᵏˣ and ln x, with the product and chain rules. The booklet only adds the awkward ones.
  • Mechanics and statistics also have a recall list: weight, friction as F ≤ μR, F = ma, the calculus link between displacement, velocity and acceleration, the mean of grouped data and the standardising formula Z = (X − μ)/σ.

Finding your way round the booklet

Because this one booklet serves AS, A-level Maths and Further Maths, the first thing to learn is which section is yours. Section 2 is A-level Maths. Sections 1 and 3 are for the AS papers and AS Further Maths, so a result that looks perfect in section 3 may be outside your course.

Pearson says candidates sitting Further Maths may also need the A-level Maths formulae, but the reverse does not hold. If you are on 9MA0, stay in section 2 and the tables at the back.

Pearson also tells candidates that the exam copy belongs to Pearson: it is not to be removed from the examination room or marked in any way. Learning the layout beforehand is therefore the only preparation that counts, and a good drill is to name the section of the booklet that each question in a past practice set would use before you start solving it.

Three habits pay off on the day. First, locate the entry before you read the rest of the question, so you know whether the formula is on the page or has to come from memory. Second, write the formula you use with its letters before substituting. Third, note the conditions beside it, such as |x| < 1 for the binomial series or θ in radians for the small angle approximations, because mark schemes often award a mark for stating them.

Use the quadratic formula to find both roots.

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

Worked example: Newton-Raphson in section 2

Take one step of the iteration for f(x) = x³ − x − 2, starting at x₀ = 1.5.

The booklet prints the iteration but not the derivative. Differentiate first, f′(x) = 3x² − 1, then evaluate both functions at 1.5.

f(1.5)=-0.125,\quad f'(1.5)=5.75,\quad x_1=1.5-\frac{-0.125}{5.75}=1.5217

f(1.5) is negative, so subtracting it pushes the estimate upwards. Students who write a plus sign in the formula land on 1.478 instead.

Worked example: a table lookup in the statistics pages

A fair-looking coin is tossed 12 times and lands heads 9 times. Is P(X ≥ 9) small enough to doubt the coin at the 5% level, one-tailed?

The binomial cumulative table for n = 12 and p = 0.5 gives P(X ≤ 8) = 0.9270, so the upper tail follows by subtraction.

P(X\ge9)=1-P(X\le8)=1-0.9270=0.0730

That is above 0.05, so there is no evidence against the coin. The slip to avoid is reading P(X ≤ 9) and treating it as the tail.

The Edexcel 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 and 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

Edexcel's booklet is the longest of the A-level Maths set because it keeps every qualification in one place and adds the tables. If you have been revising from an AQA or OCR sheet, expect to find mensuration, the change of base for logarithms and the sum to product identities here, and do not rely on features of the other sheets.

Exam answers

Papers on this site come with a worked mark scheme after you finish and mark them. Use it to see which line of the booklet each question needed. We have no official Edexcel mark schemes and do not claim any.

Practising with the booklet open

Open any of the four A-level Maths daily papers with the sheet in the drawer: Algebra and Functions, Calculus, Statistics or Mechanics. Each is a short paper of 8 questions, so it mirrors one paper section rather than a full 2-hour 9MA0 paper. Statistics and Mechanics suit the booklet best, because they lean on its distribution and constant acceleration entries.

Slips Edexcel candidates make with the booklet

  • Reaching for section 3 or 4 because a formula looks familiar. Check the section title first.
  • Using the binomial series (1 + x)ⁿ without checking that |x| < 1, or applying it to a negative or fractional n with a positive-integer formula.
  • Quoting the standard deviation formula with n − 1 on the bottom. The booklet divides by n for this qualification.
  • Reading the correlation critical value table for a two-tailed test when it is printed one-tailed.

Common questions

Do you get a formula booklet in Edexcel A-level Maths?
Yes. Pearson says the booklet Mathematical Formulae and Statistical Tables is provided for use in the assessments for the Advanced GCE in Mathematics (9MA0).
What is in the Edexcel A-level Maths formula booklet?
Pure formulae such as series, trigonometric identities, small angle approximations, some derivatives and integrals and numerical methods, then probability, standard deviation and distributions, then the constant acceleration equations, then statistical tables.
Which formulae do I need to memorise for Edexcel A-level Maths?
Pearson's specification lists them in Appendix 1: the quadratic formula, laws of indices and logarithms, straight line equations, nth terms of sequences, the sine and cosine rules, basic identities, standard derivatives and integrals, and a few in statistics and mechanics.
Is the Edexcel booklet the same for AS, A-level and Further Maths?
It is one booklet arranged by qualification. A-level Maths students use section 2, and Further Maths students may also need the formulae listed for A-level Maths.
Are the Edexcel booklet and the AQA booklet the same?
No. They share most of the pure content, but AQA's is shorter and has no statistical tables, while Edexcel's adds mensuration and tables.

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UK · A-levelA-level Maths formula booklet: every board comparedWhat is in the A-level Maths formula booklet for Edexcel, AQA, OCR, MEI, WJEC and CCEA, what is not, and how to use it in the exam.