Edexcel A-level Mathematics · 9MA0

Applications of differentiation

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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

The curve $C$ has equation $y=\frac{\ln x}{x}$ , $x>0$ . The tangent to C at P passes through the origin O.

(a)

Find the exact coordinates of P.

(4)

Working

(b)

Show that this is the only tangent to C that passes through O.

(3)

Working

(c)

The region R is bounded by OP, the x-axis and the arc of C from its x-intercept to P. Find the exact area of R.

(5)

Working

(Total for Question 1 is 12 marks)

Question reference: edexcel-stretch-calculus-02Report a question →

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