The OCR A level Maths formula sheet (H240)
OCR does not hand out a separate booklet for A Level Mathematics A: the formulae are printed on pages 2 and 3 of every H240 question paper. Here is exactly what is on them, read from an official 2025 paper, and what you must still learn.
On this page
Where the formulae are
For OCR A Level Mathematics A (H240), the formulae are printed at the start of each question paper, on pages 2 and 3. The same formulae appear in Paper 1 (pure mathematics), Paper 2 (pure mathematics and statistics) and Paper 3 (pure mathematics and mechanics). Download a recent OCR paper and you have the exact sheet you will see in the exam.
Everything on the H240 formulae pages
Pure mathematics
- Arithmetic series: Sn = ½n(a + l) = ½n{2a + (n − 1)d}.
- Geometric series: Sn = a(1 − rn)/(1 − r) and S∞ = a/(1 − r) for |r| < 1.
- Binomial series for positive whole-number n, with nCr, and for rational n with |x| < 1.
- Differentiation: derivatives of tan kx, sec x, cot x and cosec x, the quotient rule, and differentiation from first principles.
- Integration: the integral of f′(x)/f(x), the integral of f′(x)(f(x))n, and integration by parts.
- Small angle approximations: sin θ ≈ θ, cos θ ≈ 1 − ½θ², tan θ ≈ θ, with θ in radians.
- Trigonometric identities: the compound angle formulas for sin, cos and tan.
- Numerical methods: the trapezium rule and the Newton-Raphson iteration.
Statistics
- P(A ∪ B) and P(A ∩ B), including conditional probability.
- The standard deviation formula, for data and for frequency tables.
- The binomial distribution: probabilities, mean np and variance np(1 − p).
- The distribution of the sample mean for a hypothesis test about a normal mean.
- A short table of percentage points of the normal distribution, such as z = 1.645 for p = 0.95 and z = 1.960 for p = 0.975.
Mechanics
- The constant acceleration equations, for motion in a straight line and in vector form for motion in two dimensions.
What is not on it
- Standard derivatives and integrals of xn, sin x, cos x, ex and ln x.
- The product and chain rules: only the quotient rule is given.
- Double angle formulas and the identities sin²x + cos²x = 1 and 1 + tan²x = sec²x.
- The quadratic formula, laws of indices and logarithms, and coordinate geometry results.
- The sine and cosine rules, arc length and sector area.
- F = ma, weight and friction, and moments.
Using the sheet: integration by parts
Find the integral of x cos x.
- By parts (given): u = x, dv/dx = cos x, so du/dx = 1 and v = sin x. The integral of cos x is not given, so you must know it.
- Integral = x sin x − ∫ sin x dx = x sin x + cos x + c.
Using the normal table
X ~ N(50, 16). A sample of 25 has mean 51.8. Test at 5% (one-tailed, upper) whether the mean has increased.
- Under H0, the sample mean ~ N(50, 16/25), so its standard deviation is 0.8.
- z = (51.8 − 50) / 0.8 = 2.25.
- The sheet gives the critical value 1.645 for p = 0.95. Since 2.25 > 1.645, reject H0: there is evidence the mean has increased.
A must-know identity
Solve cos 2x = cos x for 0 ≤ x < 2π.
- cos 2x = 2cos²x − 1 (not on the sheet).
- 2cos²x − cos x − 1 = 0 gives (2 cos x + 1)(cos x − 1) = 0.
- cos x = 1 gives x = 0; cos x = −½ gives x = 2π/3 or 4π/3. So x = 0, 2π/3, 4π/3.
How to train with it
- Print pages 2 and 3 from a recent OCR paper and use them for every practice paper.
- Learn the missing results above until they are automatic, especially calculus and double angles.
- Know the normal table values by sight, so you can find a critical value in seconds.
- Compare with other boards' sheets if you practise with their papers: they differ.
OCR compared with Edexcel and AQA
- Like AQA and Edexcel, OCR leaves out the standard derivatives, the product and chain rules, and the double angle formulas.
- Unlike AQA's Maths-only booklet, OCR includes a short table of normal distribution percentage points.
- Unlike Edexcel, OCR prints its formulae inside each question paper rather than as a separate booklet.
A quick self-test: without looking, write the derivatives of e3x, ln(2x) and sin 5x, and the formulas for sin 2A and cos 2A in all three forms. Anything you hesitate on belongs on your daily practice list.
Common mistakes
- Expecting the product rule or chain rule on the sheet.
- Forgetting the constant of integration in indefinite integrals.
- Using degrees with small angle approximations, which need radians.
- Reading the normal percentage points table the wrong way round.
Practice questions
Try each one before opening the answer.
Q1. Is the quotient rule on OCR's H240 formulae pages?
Show answer
Q2. Is the derivative of sin x given?
Show answer
Q3. Which z-value does the table give for p = 0.975?
Show answer
Q4. Differentiate tan 3x.
Show answer
Frequently asked questions
Does OCR give a separate formula booklet for A Level Maths?
No. For H240 the formulae are printed on pages 2 and 3 of each question paper.
Is OCR MEI the same?
No. OCR MEI (H640) is a different specification with its own formulae. Check an MEI paper.
Are the formulae the same in all three papers?
Yes, the same formulae appear at the front of Papers 1, 2 and 3.
Key takeaways
- OCR H240 prints formulae on pages 2 and 3 of every paper.
- Series, some derivatives and integrals, small angles, compound angles, numerical methods.
- Statistics: probability, binomial, sample mean, a normal percentage points table.
- No product rule, chain rule, double angles or standard derivatives.
- Practise with the sheet from a recent paper.