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WJEC A-level Maths formula booklet: 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 WJEC shares one booklet between Maths and Further Maths, the drawer holds the whole booklet, Further Maths pages included, in our own layout and words, and the contents below repeat the sections A-level Maths uses. Check against WJEC's Formula Booklet 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

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

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 x)=\sec^2 xderivative of tan x
\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^2x\ dx=\tan x+cintegral of sec² x
\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 (Further Maths content)

SectionWhat it holds
Summationssums of r² and r³
Complex numbersroots of unity
Maclaurin and Taylor seriesstandard series
Hyperbolic functionsidentities and inverse forms
Vectors and matricesplanes, distances, 2-D and 3-D transformations
Mechanicsmotion in a circle and centres of mass
StatisticsBayes, Poisson, continuous, sampling, regression

The rest of the WJEC booklet

The same booklet continues past the A-level Maths content into Further Maths: summations, complex numbers and the roots of unity, Maclaurin and Taylor series, hyperbolic functions, vectors, matrix transformations in two and three dimensions, motion in a circle, centres of mass of uniform bodies, Bayes' theorem, the Poisson distribution, continuous distributions, sampling distributions and regression. If you sit A-level Maths, you can skip those pages, but knowing they exist stops you wasting time looking for a result that is not there.

Where the WJEC booklet stops

  • No kinematics. The constant acceleration equations are not in the booklet, whose mechanics section covers motion in a circle and centres of mass.
  • No small angle approximations, and no statistical tables: the booklet is formulae only.
  • No logarithm change of base. Only the exponential line aˣ = e^(x ln a) appears under logarithms and exponentials.

A booklet built for two courses

WJEC wrote one booklet for AS and A-level Maths and for Further Maths, issued in October 2018. That makes it unusually wide: complex numbers, matrices and the Poisson distribution sit between the pages you actually use. Decide beforehand which pages you will use and which you can ignore, because the exam copy must stay unmarked.

The trigonometry page adds the tan(A/2) = t forms for sin A and cos A, alongside the sum to product identities, which is more than AQA or OCR print.

Use the quadratic formula to find both roots.

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

Worked example: Newton-Raphson for a square root

Use one step of Newton-Raphson on f(x) = x² − 5 from x₀ = 2.

f(2)=-1,\quad f'(2)=4,\quad x_1=2-\frac{-1}{4}=2.25

The true root is 2.236, so one step already gets within 0.014. Run the iteration again and you reach 2.2361.

The WJEC 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
WJEC (this guide)GCE 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

Of the six boards' booklets, WJEC's is the only A-level Maths one that is formulae only and shared with Further Maths. CCEA shares its booklet too but adds tables. If you have used an AQA or Edexcel sheet before, notice that the standard constant acceleration equations are absent here.

Exam answers

After you mark your paper, the answers on this site are worked through for you. They are written by us and have no link to WJEC mark schemes.

Daily papers for WJEC Maths

Because the booklet has no kinematics section, Mechanics is the daily paper to try without any sheet help for the equations of motion, with the booklet open only for centres of mass and circular motion. For the pure content use Algebra and Functions and Calculus, and for the booklet's probability pages Statistics.

WJEC booklet pitfalls

  • Looking for suvat and not finding it.
  • Searching Further Maths pages for A-level content. Use the contents page.
  • Applying a Further Maths integral that needs hyperbolic functions to an A-level question.

Common questions

Do you get a formula booklet in WJEC A-level Maths?
Yes. WJEC publishes a Formula Booklet for GCE AS/A Level Mathematics and GCE AS/A Level Further Mathematics, from September 2017.
Does the WJEC booklet include the suvat equations?
No. Its mechanics section covers motion in a circle and centres of mass, so learn constant acceleration yourself.
Does the WJEC booklet have statistical tables?
No. It holds formulae only.
Is the WJEC booklet the same for Maths and Further Maths?
Yes. It is one booklet for both, so some pages are Further Maths content.
Does Eduqas have an A-level Maths formula booklet?
No. Eduqas does not offer A-level Maths.

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