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OCR MEI A-level Further Maths B formula booklet (H645): 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, 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

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
\text{arcosh}\ x=\ln(x+\sqrt{x^2-1})inverse hyperbolic cosine (x ≥ 1)
\text{arsinh}\ x=\ln(x+\sqrt{x^2+1})inverse hyperbolic sine
\text{artanh}\ 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
A level Mathematicsthe pure, mechanics and statistics results from the Maths booklet, plus statistical tables for A-level Maths
Core Purecomplex numbers, hyperbolic functions, series, calculus, the vector product and the Cartesian equation of a plane, and polar curves
Mechanicsmotion in a circle
Statisticsdistributions, hypothesis tests, confidence intervals and the Pearson and Spearman tests; the drawer holds the t and normal tables, but not the correlation, chi-squared or Wilcoxon ones
Extra Pure and Further Pure with Technologymultivariable calculus, Euler and Runge-Kutta methods and polar tangent gradients; the Numerical Methods section adds Simpson's rule, interpolation and more

Limits of the MEI Further booklet

  • No proofs. Core Pure results are listed, but the arguments behind them are not.
  • The A-level Maths recall list is not covered, even though the booklet includes the A-level Maths results.
  • No instructions for the technology items. The booklet gives the Euler and Runge-Kutta formulae and Simpson's rule, but not how to run them on your calculator.

The booklet is organised as the A level Mathematics results first, then Core Pure, Mechanics, Further Pure with Technology, Extra Pure, Numerical Methods, Statistics and the statistical tables. A candidate sitting H645 can find nearly everything in one place.

The statistics section is unusually full for a Further Maths booklet: Poisson and geometric distributions, hypothesis tests, confidence intervals and the Pearson and Spearman tests are all listed.

Use the quadratic formula to find both roots.

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

Worked example: one step of Euler's method

For dy/dx = x + y with y = 1 when x = 0, use Euler's method with h = 0.1 to estimate y when x = 0.1.

Here f(x, y) = x + y, so f(0, 1) = 1 and y₁ = y₀ + h f(x₀, y₀).

y_1=1+0.1(0+1)=1.1

The estimate is y(0.1) ≈ 1.1. The exact solution y = 2e^x − x − 1 gives 1.1103, so one Euler step slightly underestimates.

The OCR MEI 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 AFormulae Booklet, A Level Further Mathematics A (H245)Pure, statistics, mechanics and a discrete mathematics section with network and sorting algorithms
OCR MEI (this guide)Formulae 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

MEI's booklet is the one that includes Simpson's rule and interpolation in a Numerical Methods section, and numerical solution of differential equations under a technology heading. OCR A has no such section and has discrete mathematics instead, and Edexcel and AQA fit neither.

Exam answers

After marking, the worked answers on our papers are ours. They are not MEI or OCR mark schemes.

Using the Further Maths daily paper alongside MEI

Try the Further Maths daily paper with the sheet open, especially for the statistics and pure entries. MEI's technology topics are not part of the short daily papers.

MEI Further mistakes

  • Using the A-level Maths results from the wrong section of the booklet.
  • Assuming a technology formula needs no justification in a written answer.
  • Mixing the OCR A and MEI booklets.

Common questions

Do you get a formula booklet in OCR MEI A-level Further Maths?
Yes. OCR publishes a Formulae Booklet for H635 and H645 and prints it for the examinations.
Does the MEI Further Maths booklet include A-level Maths?
Yes. It has an A level Mathematics section as well as the further content.
What is Further Pure with Technology?
A section of the MEI booklet for the numerical solution of differential equations (Euler, modified Euler and Runge-Kutta) and the gradient of a tangent to a polar curve.
Is the MEI Further Maths booklet the same as OCR A?
No. OCR A (H245) and OCR MEI (H645) each have their own booklet.
What is not in the MEI Further Maths booklet?
Proofs, definitions and A-level Maths basics such as the quadratic formula.

Revision cards

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