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CCEA A-level Maths formulae and tables: 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. Because CCEA shares one booklet between Maths and Further Maths, the drawer holds all the formulae pages, Further Maths pages included, and the cycle indices in our own layout and words, without the six statistical tables, and the contents below repeat the sections A-level Maths uses. Check against CCEA's Mathematical Formulae and Tables 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

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

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

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

\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}quotient rule
\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^2 xderivative of cot x
\frac{d}{dx}(\csc x)=-\csc x\cot xderivative of cosec x

Integration

\int\tan x\ dx=\ln|\sec x|+cintegral of tan x
\int\cot x\ dx=\ln|\sin x|+cintegral of cot x
\int\sec^2 kx\ dx=\frac{1}{k}\tan kx+cintegral of sec² kx
\int u\frac{dv}{dx}dx=uv-\int v\frac{du}{dx}dxintegration by parts

Numerical mathematics

\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 and the binomial distribution

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(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

Also in the same booklet

SectionWhat it holds
Further Maths pure contentsummations, complex numbers, Maclaurin series, hyperbolic functions, vectors, matrices
Mechanicsmotion in a circle, centres of mass, the universal law of gravitation
Statistical tablesnormal, binomial, Poisson, chi-squared, Student t and correlation tables
Discrete and decision mathematicscycle indices for 3-D rotational symmetry groups

The statistical tables in the CCEA booklet

CCEA's contents list names six tables: normal probability, the binomial cumulative distribution function, the Poisson cumulative distribution function, percentage points of the chi-squared distribution, percentage points of Student's t distribution, and critical values for correlation coefficients. Not every table is needed for A-level Maths, but the booklet is the same in each exam, so learn which table your paper needs.

What CCEA does not print

  • No constant acceleration section. The mechanics pages cover motion in a circle, centres of mass and the universal law of gravitation.
  • No hyperbolic or Further Maths content for A-level Maths questions: ignore those pages.
  • The usual recall list is also absent: quadratic formula, triangle rules and basic derivatives.

Working with a booklet that holds the tables

CCEA's Mathematical Formulae and Tables is the one booklet in this set that puts the statistical tables between the same covers as the formulae. That is a convenience, and also a trap: students who revise from a formulae-only sheet forget the tables exist.

Candidates in Northern Ireland sitting the CCEA papers receive this booklet in the exam. Its contents list is on page 3, so find the table you want from the list rather than turning pages blindly.

Use the quadratic formula to find both roots.

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

Worked example: arithmetic series

The first term is 3 and the common difference is 4. Find the sum of the first 20 terms.

S_{20}=\frac{1}{2}(20)[2(3)+19(4)]=10\times82=820

The booklet prints both forms of the sum. With a and d known, the second form is quicker; you would use the first if you knew the last term l.

The CCEA 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 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
CCEA (this guide)Mathematical Formulae and TablesOne booklet for both subjects, with statistical tables inside

Edexcel and CCEA are the two boards that give you the tables inside the booklet. Edexcel lists four tables for A-level Maths, whereas CCEA lists six: normal, binomial, Poisson, chi-squared, Student t and correlation. CCEA also adds a discrete and decision mathematics page that no other board has.

Exam answers

Worked answers appear in the daily paper once you have marked it. They are written for this site, with no CCEA mark scheme behind them.

Daily papers for CCEA candidates

The Statistics daily paper makes the most of CCEA's tables, because many questions end in a probability that is quicker with the table open. The other tracks are Algebra and Functions, Calculus and Mechanics. All are short 8-question papers rather than full CCEA units.

Booklet traps for CCEA students

  • Using the Further Maths summation formulae in an A-level Maths proof.
  • Reading from the Poisson table when the question is binomial.
  • Assuming the booklet lists suvat because the board's other documents do.

Common questions

Do you get a formula booklet in CCEA A-level Maths?
Yes. CCEA's Mathematical Formulae and Tables is for use by candidates taking AS and A level Mathematics and Further Mathematics, from 2018.
Does the CCEA booklet have statistical tables?
Yes. The contents list normal, binomial, Poisson, chi-squared, Student t and correlation tables.
Is the CCEA booklet the same for Maths and Further Maths?
Yes. One booklet covers both, so some pages are Further Maths content.
Where can I find the CCEA formulae booklet?
CCEA lists a Mathematical Formulae and Tables PDF on its GCE Mathematics support page.
Does CCEA have a decision maths page?
Yes. The booklet includes a Discrete and Decision Mathematics page with cycle indices for 3D rotational symmetry groups.

Revision cards

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