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OCR A-level Mathematics A · H240

Polynomials

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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.

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  • 01 · Pure · 100 marks · 2 hours
  • 02 · Pure & statistics · 100 marks · 2 hours
  • 03 · Pure & mechanics · 100 marks · 2 hours
Official specification ↗ · Official past papers ↗
QUESTION PAPER
Mathematics · A levelPure mathematics · H240/01
Torus Maths original · OCR style
1

Let p(x)=x3−9x2+18x−27p(x)=x^3-9x^2+18x-27.

(a)

Show that p(x)=0 has exactly one real root α, and that 6<α<96<\alpha<9.

[5]

(b)

Find a cubic equation with integer coefficients whose unique real root is 1/α. Give bounds for this root.

[4]

Question reference: ocr-a-level-extreme-12-01Report a question →

Answer booklet

Question 1 · Show your working

(a)
(b)
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