Question 1 of 3 · No calculator needed
Which conclusion follows deductively from the assumption that n is divisible by 6?
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
OCR · A LevelMathematics,
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Specification H240. Explore a topic, practise the skill, and see where to focus next.
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Question 2 of 3 · No calculator needed
Rationalise 4/(3 - √5).
Multiply by (3 + √5)/(3 + √5). The denominator is 9 - 5 = 4, so the expression becomes 4(3 + √5)/4 = 3 + √5.
Question 3 of 3 · No calculator needed
Simplify sin x/(1 + cos x) by rationalising the trigonometric denominator.
Multiply by (1-cos x)/(1-cos x). This gives sin x(1-cos x)/sin²x = (1-cos x)/sin x = tan(x/2).
These tiles show your answers to three questions. They are a starting point, not a mastery score or grade prediction.
Proof
Correct answer: n is divisible by 3
If n is divisible by 6, n = 6k = 3(2k) for some integer k. Hence n is divisible by 3.
Algebra and functions
Correct answer: 3 + √5
Multiply by (3 + √5)/(3 + √5). The denominator is 9 - 5 = 4, so the expression becomes 4(3 + √5)/4 = 3 + √5.
Trigonometry
Correct answer: tan(x/2)
Multiply by (1-cos x)/(1-cos x). This gives sin x(1-cos x)/sin²x = (1-cos x)/sin x = tan(x/2).
For parents: look at the explanation together. A correct answer is encouraging; a missed answer gives you something specific to work on. Broader practice over time is needed to understand progress.
YOUR TOPIC MAP
19 areasFind your starting point.
01Proof
Specification reference: H240 1.01
Proof requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Proof requires. Keep exact values until the final step and check signs, units and reasonableness.
02Algebra and functions
Specification reference: H240 1.02
Algebra and functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Algebra and functions requires. Keep exact values until the final step and check signs, units and reasonableness.
03Coordinate geometry in the (x, y) plane
Specification reference: H240 1.03
Coordinate geometry in the (x, y) plane requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Coordinate geometry in the (x, y) plane requires. Keep exact values until the final step and check signs, units and reasonableness.
04Sequences and series
Specification reference: H240 1.04
Sequences and series requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Sequences and series requires. Keep exact values until the final step and check signs, units and reasonableness.
05Trigonometry
Specification reference: H240 1.05
Trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
06Exponentials and logarithms
Specification reference: H240 1.06
Exponentials and logarithms requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Exponentials and logarithms requires. Keep exact values until the final step and check signs, units and reasonableness.
07Differentiation
Specification reference: H240 1.07
Differentiation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Differentiation requires. Keep exact values until the final step and check signs, units and reasonableness.
08Integration
Specification reference: H240 1.08
Integration requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Integration requires. Keep exact values until the final step and check signs, units and reasonableness.
09Numerical methods
Specification reference: H240 1.09
Numerical methods requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Numerical methods requires. Keep exact values until the final step and check signs, units and reasonableness.
10Vectors
Specification reference: H240 1.10
Vectors requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Vectors requires. Keep exact values until the final step and check signs, units and reasonableness.
11Statistical sampling
Specification reference: H240 2.01
Statistical sampling requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statistical sampling requires. Keep exact values until the final step and check signs, units and reasonableness.
12Data presentation and interpretation
Specification reference: H240 2.02
Data presentation and interpretation requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Data presentation and interpretation requires. Keep exact values until the final step and check signs, units and reasonableness.
13Probability
Specification reference: H240 2.03
Probability requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability requires. Keep exact values until the final step and check signs, units and reasonableness.
14Statistical distributions
Specification reference: H240 2.04
Statistical distributions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statistical distributions requires. Keep exact values until the final step and check signs, units and reasonableness.
15Statistical hypothesis testing
Specification reference: H240 2.05
Statistical hypothesis testing requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Statistical hypothesis testing requires. Keep exact values until the final step and check signs, units and reasonableness.
16Quantities and units in mechanics
Specification reference: H240 3.01
Quantities and units in mechanics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Quantities and units in mechanics requires. Keep exact values until the final step and check signs, units and reasonableness.
17Kinematics
Specification reference: H240 3.02
Kinematics requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Kinematics requires. Keep exact values until the final step and check signs, units and reasonableness.
18Forces and Newton's laws
Specification reference: H240 3.03
Forces and Newton's laws requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Forces and Newton's laws requires. Keep exact values until the final step and check signs, units and reasonableness.
19Moments
Specification reference: H240 3.04
Moments requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Moments requires. Keep exact values until the final step and check signs, units and reasonableness.
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OCR · A Level · Mathematics · H240
Version 3, October 2025, current checked 2026-08-27
Source checked: 2026-08-27. The current official specification controls assessment requirements and option choices.
Can parents and students try LearningP before signing up?
Yes. This page offers three original questions from three different skills on this exact course. Each answer has an explanation, followed by a sample heatmap showing what was correct and what to revisit. No account is needed, and taster answers are not saved.
What does the three-question heatmap tell a parent?
It shows the outcome of these three answers and gives a specific skill to discuss or practise next. It is not a full assessment, a mastery score or a grade prediction. Broader practice over time is needed to understand progress.
What does the OCR A Level Mathematics route cover?
LearningP currently maps 19 assessed areas for specification H240. The visible topic map below is derived from the verified route; the current official specification remains controlling.
How many LearningP questions support this route?
The verified source bank contains 232 original LearningP question records for this route. Every mapped area meets the current publication minimum and passed the latest blocker and review audit.
Does LearningP reproduce official exam questions?
No. LearningP uses official specifications and assessment materials to map content and demand, while its practice questions and explanations are independently authored.
Can this page predict an exam grade?
No. LearningP reports practice evidence, coverage, strengths and gaps. It does not guarantee or automatically predict examination outcomes.
Where should current assessment information be checked?
Use the official OCR specification and assessment-resource pages linked on this page, together with information supplied by the learner’s school.
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