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Examaced turns CIE A Level past papers into topical questions with the mark scheme beside your working, timed mock exams, and automatic progress tracking.

Paper 2

Further Pure Mathematics 2

Topic

114 questionsNewest first

Question 39 marks

100%

TopicIntegration Further Pure Mathematics 2

How hard was it?

The integral $I_{n}$ is defined by $I_{n} = \int_{0}^{1} {(1 + x^{2})}^{n} d x .$

(a)

By considering $\frac{d}{d x} (x {(1 + x^{2})}^{n})$ , or otherwise, show that

(2 n + 1) I_{n} = 2^{n} + 2 n I_{n - 1} .

[5]

(b)

Find the exact value of $I_{- 2} .$ [4]

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Paper 2

Further Pure Mathematics 2

Topic

337 questionsNewest first

Question 15 marks

100%

TopicHyperbolic functions Differentiation Further Pure Mathematics 2

How hard was it?

Find the first three terms in the Maclaurin’s series for $\sinh^{- 1} (x + 1)$ in the form $\ln a + b x + c x^{2}$ , giving the exact values of the constants $a$ , $b$ and $c .$ [5]

Choose a topic, and 337 questions become 114.Choose a topic, and 337 questions become 114.

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The CIE A Level topical question bank brings extracted past-paper questions and mark schemes together by syllabus topic, exam component, and session. The number of topical questions in each subject and paper is shown in brackets [ ].

CIE A Level Mathematics (9709)[2,416]

6 papers, 2020–2026, 49 past papers in each

CIE A Level Further Mathematics (9231)[1,178]

4 papers, 2020–2026, 42 past papers in each

CIE A Level Physics (9702)[2,172]

5 papers, 2022–2026

[Total: 5,766]

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Which subjects does it cover?

Three Cambridge International A Level subjects: Mathematics 9709 (2,416 questions, 2020–2026), Further Mathematics 9231 (1,178 questions, 2020–2026) and Physics 9702 (2,172 questions, 2022–2026).

Why do topic counts add up to more than the paper?

A question can sit under more than one topic, so it counts in each.

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