OCR A-level Maths (H240): papers, marks and grade boundaries

OCR A-level Maths at a glance

OCR has two A-level maths courses: Mathematics A (H240), covered here, and Mathematics B (MEI) (H640). Mathematics A is linear, with every paper sat at the end of the two years in one May and June series. The AS Level is a separate qualification (H230), so the A-level code is H240.

That is 300 marks. Paper 1 is a single 100 mark section of pure maths. Papers 2 and 3 each have two sections of about 50 marks, pure maths and then statistics (Paper 2) or mechanics (Paper 3). Each section has a gradient of difficulty with a mix of long and short questions, so the early questions are accessible and the last ones stretch the A* students.

What each paper covers

• Pure Mathematics (all three papers): proof, algebra and functions, coordinate geometry, sequences and series, trigonometry, exponentials and logarithms, differentiation, integration, numerical methods and vectors.
• Statistics (Paper 2): sampling, data presentation and interpretation, probability, statistical distributions (binomial and normal) and statistical hypothesis testing, including questions set in the context of the pre-release large data set.
• Mechanics (Paper 3): kinematics (SUVAT and variable acceleration with calculus), forces and Newton’s laws, and moments.

The overarching themes (mathematical argument, language and proof, mathematical problem solving and mathematical modelling) run through every paper. All three papers contain some synoptic assessment, extended response questions and stretch and challenge questions.

Calculator, formulae and the large data set

OCR allows a scientific or graphical calculator in all three papers, subject to the JCQ rules. OCR expects it to have an iterative function such as an ANS key and the ability to compute summary statistics and access probabilities from the binomial and normal distributions. You still have to support answers with working.

Learners are given formulae in each assessment, on pages 2 and 3 of the question paper, so do not waste revision time on memorising what is printed. The list is in Section 5d of the specification: use it from the first week of the course.

The large data set is real data that OCR publishes on its website for the life of the specification. It is for you to explore with spreadsheets or statistics software during the course, and some Paper 2 statistics questions are set in its context. A question may rely on knowing the variables and the main features of the data, so working with it in advance pays off.

Worked examples in OCR style

Pure: integration by parts

Find the integral of x e^(2x) with respect to x. Let u = x and dv/dx = e^(2x), so du/dx = 1 and v = ½e^(2x).

To check, differentiate the answer: (½)e^(2x) + x e^(2x) − ½e^(2x) = x e^(2x). Always include the constant c for an indefinite integral. Practise related skills in our Calculus course.

Statistics: a binomial hypothesis test

A manufacturer claims that 30% of bags contain a prize. A sample of 20 bags has 10 prizes. Test at the 5% level whether the true proportion is higher than 30%.

Let X be the number of prizes. H₀: p = 0.3 and H₁: p > 0.3, with X ~ B(20, p). The test is one-tailed because the claim is that p is higher.

0.0480 is less than 0.05, so reject H₀. The sample supports the view that more than 30% of bags contain a prize. The conclusion must be in context and not definite: you are not proving the claim, only saying the evidence supports it. Try a distribution question in our Probability course:

Mechanics: velocity and displacement with calculus

A particle moves along a straight line with velocity v = 3t² − 18t + 24 m s⁻¹, for time t in seconds. Find the total distance it travels in the first 4 seconds.

The particle is momentarily at rest when v = 0, which gives 3(t − 2)(t − 4) = 0, so at t = 2 and t = 4. At t = 2, s = 8 − 36 + 48 = 20 m. At t = 4, s = 64 − 144 + 96 = 16 m. The displacement after 4 seconds is therefore 16 m.

Distance travelled is not the same as displacement. The particle moves 20 m forward, then turns and comes back 4 m, so the distance is 20 + 4 = 24 m. Splitting at the turning point is the step that earns the final mark.

Grades and June 2026 grade boundaries

OCR adds your three papers into a total out of 300 and compares it with the boundaries. The table is from OCR’s document published on 14 September 2026 and covers the June 2026 series. The A* boundary on Paper 1 was 90 marks, while on Paper 3 it was 77, because papers vary in difficulty.

Worked through: 72, 66 and 60 give 198 out of 300, which is a B (172) and 10 marks below an A (208).

Using the daily paper as a short timed mock

Uni-Sine publishes a free daily paper on four A-level maths tracks, with a new one every day. Each is a short timed paper of 8 questions worth 25 to 35 marks, marked instantly with worked answers. It is not an OCR paper and it is far shorter than a 2 hour paper, so use it for quick, regular practice between past papers.

• Algebra and Functions: coordinate geometry, logarithms, sequences, trigonometric identities, binomial expansion, functions, transformations, polynomials, partial fractions and proof. This supports the pure sections of all three papers.
• Calculus: chain, product and quotient rules, integration techniques, tangents and normals, stationary points, rates of change, parametric differentiation, differential equations and area under a curve.
• Statistics: hypothesis testing, the normal and binomial distributions, sampling, measures of location and spread, probability, correlation and regression. It matches the statistics section of Paper 2.
• Mechanics: SUVAT, forces and Newton’s laws, velocity-time graphs, projectiles, inclined planes, variable acceleration, moments, connected particles and friction. It matches the mechanics section of Paper 3.

For advice on running mocks, see our A-level Maths mocks guide and the A-level Maths guide.

Exam answers

Uni-Sine does not publish official answers or mark schemes for OCR A-level Maths papers. The answers and a worked mark scheme for each question come with today’s paper once you have submitted it and it has been marked, so you can see where every mark was won or lost.

Common mistakes in OCR A-level Maths

• Sign errors and missing brackets when expanding or substituting negative values.
• Leaving out the constant of integration or the limits in a definite integral.
• Giving a calculator answer without working. OCR expects supporting working, and method marks depend on it.
• Conclusions that are not in context. A hypothesis test ends with a statement about bags, people or whatever the question is about.
• Confusing displacement with distance in mechanics when the velocity changes sign.

Read next

UK · A-levelOCR A-level Maths formula booklet: what is on itThe OCR A-level Maths A formula booklet for H240: every formula on it, what you must memorise, how it differs from other boards, and worked examples.