OCR A Level Mathematics B (H640) Past Papers 2026

Pure Mathematics and Mechanics

Duration: 2h

Pure Mathematics and Statistics

Duration: 2h

Pure Mathematics and Comprehension

Duration: 2h

Detailed Reasoning: rationalising surds and manipulating exact forms without calculator support

H640/03 June 2023 Q3 and H640/03 June 2024 Q4: in both years a significant number of candidates 'did not show sufficient detail of their working' and scored 0 because they presented the simplified surd answer with no intermediate rationalisation steps. Many also attempted to combine fractions into a common denominator rather than rationalising each term separately — an approach that 'rarely succeeded' and wasted examination time on a 2–3 mark question.

H640/03

Trigonometric identities involving higher powers: sin⁶θ + cos⁶θ and double angle formulas

H640/03 June 2023 Q10(a): 'In part (a) very few candidates did the whole question correctly.' Many assumed sin⁶θ + cos⁶θ = 1 by incorrect analogy with sin²θ + cos²θ = 1. Others applied the double angle formula incorrectly as 2sin²θcos²θ instead of 4sin²θcos²θ. Only a small minority completed the proof to score full marks.

H640/03

Parametric calculus: finding stationary points and correctly setting dy/dθ = 0 without dividing by a trig factor

H640/03 June 2024 Q12: this was 'probably the question that candidates generally found to be the most challenging on the paper.' Candidates who divided by sin θ rather than factorising lost all four accuracy marks. Unnecessary rewriting via the cos double angle formula introduced sign errors. Many candidates also 'did not explicitly state that they had set dy/dθ equal to zero', which left subsequent steps unsupported.

H640/03

Statistics: identifying and using the correct variance in the distribution of the sample mean

H640/02 June 2023 Q13: 'Many candidates mistook the root mean squared deviation for the standard deviation in the software printout when identifying the distribution of the sample mean.' Using the wrong variance (mean-squared deviation instead of unbiased variance s²) means the distribution of X̄ is set up incorrectly, losing all subsequent marks.

H640/02

Mechanics: omitting weight from Newton's second law in vertical or near-vertical problems

H640/01 June 2023 Q12 and H640/01 June 2024 Q9: in both years a large minority or majority of candidates omitted weight from the equation of motion. In 2024 it was described as 'very common' even after the question noted that the pebble was falling and its mass was given. Candidates found the acceleration correctly but assumed it multiplied by mass gave the resistance force — forgetting that weight also acts.

H640/01

Modelling: explaining specifically why a model is not suitable rather than giving generic comments

H640/01 June 2024 Q10: candidates who compared the initial exponential model with Zac's observation (that area grew by 10% per day) 'did not recognise the need to explicitly compare the initial model with Zac's observation.' Many described the model as linear and the real data as exponential — which is the opposite of what the question showed. The mark required identifying what the model predicts and pointing out the difference.

H640/01

Domain and range of inverse functions — confusing the two or omitting zero

H640/03 June 2024 Q2(a): 'A large number of candidates were unable to state the domain of the inverse function. Some were unclear about the difference between domain and range while others neglected to include zero in the domain.' Many correctly found the inverse formula but could not then state its domain, leaving the accuracy mark unearned.

H640/03

Large Data Set: extracting the correct variable/entry rather than giving generic statistical comments

H640/02 June 2023 and 2024 pre-release LDS questions: candidates who 'did not appear to be familiar with the pre-release material' consistently gave vague or incorrect answers. For example, giving 'median income is different in different areas' without referencing the specific LDA or year from the dataset, or describing outliers without identifying the correct #N/A entries from the spreadsheet printout.

H640/02