OCR A-level Mathematics A · H240

Iteration & Newton–Raphson

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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

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QUESTION PAPER

Mathematics · A levelPure mathematics · H240/01

Torus Maths original · OCR style

The curve $y=x\mathrm e^{-3x}$ is intersected by $y=1/(6\mathrm e)$ .

(a)

Show that there are exactly two intersections with x>0.

[4]

(b)

Put $t=3x$ . Obtain a Newton–Raphson formula for the larger root and use $t_0=3$ to calculate $t_1,t_2,t_3$ . Give the corresponding approximation to x to 3 decimal places.

[5]

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Answer booklet

Question 1 · Show your working

(a)

Answer booklet · Question 1(a)

(b)

Answer booklet · Question 1(b)

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