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OCR A-level Further Maths A formula booklet (H245): what is on it

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Formula sheet

The card below opens today's Further Maths paper with this sheet in the drawer. The drawer holds the whole booklet in our own layout and words, apart from four critical value tables, and the results most often used follow: summations, matrix transformations, Maclaurin series and hyperbolic functions. Check against OCR's Formulae Booklet (June 2025 series) for the critical value tables.

Formula sheet

A-level Further Maths

Open formula sheet

Summations

\sum_{r=1}^{n}r^2=\frac{1}{6}n(n+1)(2n+1)sum of the squares of the first n integers
\sum_{r=1}^{n}r^3=\frac{1}{4}n^2(n+1)^2sum of the cubes of the first n integers

Matrix transformations

anticlockwise rotation through θ about the origin. The 2 by 2 matrix with rows (cos θ, −sin θ) and (sin θ, cos θ).

Maclaurin series

f(x)=f(0)+xf'(0)+\frac{x^2}{2!}f''(0)+\cdots+\frac{x^r}{r!}f^{(r)}(0)+\cdotsMaclaurin series of a function
e^x=1+x+\frac{x^2}{2!}+\cdots+\frac{x^r}{r!}+\cdotsseries for e^x, for all x
\ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\cdots+(-1)^{r+1}\frac{x^r}{r}+\cdotsseries for ln(1 + x) (−1 < x ≤ 1)
\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\cdots+(-1)^r\frac{x^{2r+1}}{(2r+1)!}+\cdotsseries for sin x, for all x
\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\cdots+(-1)^r\frac{x^{2r}}{(2r)!}+\cdotsseries for cos x, for all x

Hyperbolic functions

\cosh^2x-\sinh^2x=1hyperbolic identity
\cosh^{-1}x=\ln\left[x+\sqrt{x^2-1}\right]inverse hyperbolic cosine (x ≥ 1)
\sinh^{-1}x=\ln\left[x+\sqrt{x^2+1}\right]inverse hyperbolic sine
\tanh^{-1}x=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right)inverse hyperbolic tangent (−1 < x < 1)

What else is on the sheet

The booklet also holds these sections, which are in the drawer above but not repeated below.

SectionWhat it holds
Pure mathematicsseries, differentiation and integration results, complex numbers, vectors and 3-D coordinate geometry, surfaces and surface area of revolution
Statisticssampling distributions, discrete and continuous distributions, the normal distribution, non-parametric tests, expectation algebra and correlation and regression
Mechanicscentres of mass, motion in a circle, simple harmonic motion and Newton's experimental law
Discrete mathematicsnetwork algorithms such as Dijkstra, nearest neighbour, sorting algorithms and the simplex algorithm
Statistical tablesnormal and Wilcoxon signed rank tables, in the drawer; the correlation, chi-squared and Wilcoxon rank sum tables are not

What the H245 booklet does not contain

  • Proofs and explanations. It gives results and, in the discrete mathematics section, algorithm outlines, not worked methods.
  • The A-level Maths recall list: quadratic formula, triangle rules, ordinary derivatives.
  • Guidance on which options you have chosen. OCR's booklet covers every option, so ignore sections for papers you are not sitting.

Sixteen pages, five topics

The June 2025 series booklet is 16 pages and is printed for the exam, so you will use the same layout you practise with. Its distinctive section is discrete mathematics, with Dijkstra's algorithm, nearest neighbour, sorting algorithms and the simplex algorithm outlined.

Statistics includes the Wilcoxon rank sum and signed rank tests with their critical values (the drawer holds the signed rank table only), and the mechanics section covers simple harmonic motion and Newton's experimental law, both of which other boards place elsewhere.

Use the quadratic formula to find both roots.

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

Worked example: an inverse hyperbolic function

Write arsinh 1 in logarithmic form and as a decimal.

\text{arsinh}\ 1=\ln(1+\sqrt{2})=0.8814

If a question says "exact", leave it as ln(1 + √2). The decimal is for questions that ask to three or four figures.

The OCR A booklet and the other boards

BoardBookletNotes
EdexcelMathematical Formulae and Statistical TablesOne booklet arranged by qualification, with statistical tables for binomial, Poisson, chi-squared, correlation, t and F
AQAFormulae and statistical tables for A-level Mathematics and A-level Further MathematicsVersion 1.5, February 2018, with statistical tables; required for Further Maths and optional for Maths
OCR A (this guide)Formulae Booklet, A Level Further Mathematics A (H245)Pure, statistics, mechanics and a discrete mathematics section with network and sorting algorithms
OCR MEIFormulae Booklet, AS and A Level Further Mathematics B (MEI) (H635, H645)Holds the A-level Maths content too, and a Further Pure with Technology section
WJECGCE AS/A Level Mathematics and Further Mathematics Formula BookletOne booklet shared with Maths, formulae only
CCEAMathematical Formulae and TablesOne booklet shared with Maths, with statistical tables and a decision mathematics page

OCR has two Further Maths booklets: this one for A (H245) and a different one for MEI (H645). The A booklet is the one with a discrete mathematics section. Edexcel and AQA do not print network algorithms.

Exam answers

Our daily paper shows its worked answers after you have marked it. These are our solutions and never OCR's.

Daily practice for Further Maths A

The Further Maths daily paper mixes topics, so you will see pure, statistics and mechanics. It cannot cover every option OCR offers, but it is useful for the core.

H245 booklet slips

  • Opening the MEI booklet instead of the A booklet.
  • Applying the Wilcoxon critical value for the wrong test.
  • Taking a result from the discrete section without noting the algorithm steps.

Common questions

Do you get a formula booklet in OCR A-level Further Maths?
Yes. OCR publishes a Formulae Booklet for H245 and prints it for the examinations.
Does the OCR Further Maths booklet include discrete maths?
Yes. It has a Discrete Mathematics section with network and sorting algorithms.
Is the OCR A Further Maths booklet the same as OCR MEI?
No. OCR A and OCR MEI (H645) each have their own booklet.
How long is the OCR Further Maths A booklet?
The June 2025 series booklet has 16 pages.
What is not in the OCR Further Maths booklet?
Proofs, definitions and A-level Maths basics such as the quadratic formula.

Revision cards

Say the answer first, then flip the card to check it.

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