OCR A-level Mathematics A · H240

Functions

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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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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

The function f is defined by $f(x)=\ln\left(\frac{x+3}{x-3}\right)$ for $x>3$ .

(a)

Show that f has an inverse. Find the inverse and state its domain.

[4]

(b)

Find the exact value of $\int_{6}^{9}f(x)dx$ .

[5]

Question reference: ocr-a-level-extreme-05-01Report a question →

Answer booklet

Question 1 · Show your working

(a)

Answer booklet · Question 1(a)

(b)

Answer booklet · Question 1(b)

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