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OCR A-level Mathematics A · H240

Curve sketching

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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.

OCR format & instructions

Calculator permitted. Give clear working in the answer booklet and label each part. Formulae are provided in the official question paper.

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

  • 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

For a real constant k, f(x)=(x2−9)2−kf(x)=(x^2-9)^2-k.

(a)

Find the stationary points in terms of k.

[3]

(b)

Determine the number of distinct real roots of f(x)=0 for every possible value of k.

[4]

(c)

When k=81k=81, find the total area of the finite regions bounded by the graph and the x-axis.

[5]

Question reference: ocr-a-level-extreme-02-01Report a question →

Answer booklet

Question 1 · Show your working

(a)
(b)
(c)
Need a nudge?Three small hints · no answer revealed