Edexcel A-level Mathematics · 9MA0

Definite integration & areas

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Extreme practice · Multi-step problems within A-level pure maths. Difficulty is an editorial judgement. These questions are self-reviewed, not ranked.

Edexcel format & instructions

Calculator permitted. Show sufficient working in the spaces provided. Give inexact answers to 3 significant figures unless specified otherwise. The official exam provides a formulae and statistical tables booklet.

Original topic practice. This set is not a full official paper. Written work is self-reviewed against our worked solutions.

01 · Pure 1 · 100 marks · 2 hours
02 · Pure 2 · 100 marks · 2 hours
03 · Statistics & mechanics · 100 marks · 2 hours

Official specification ↗ · Official past papers ↗

QUESTION PAPER

Mathematics · A levelPure Mathematics practice · 9MA0

Torus Maths original · Edexcel style

For a real constant b, define $I_b=\int_{-3}^{3}\frac{x^2+9}{1+\mathrm e^{bx}}dx$ .

(a)

Find an exact expression for I_b. Show that it does not depend on b.

(5)

Working

(b)

Hence evaluate $\int_{-3}^{3}\frac{(x^2+9)\mathrm e^{bx}}{1+\mathrm e^{bx}}dx$ .

(2)

Working

(Total for Question 1 is 7 marks)

Question reference: edexcel-a-level-extreme-16-01Report a question →

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