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Date	November 2021	Marks available	4	Reference code	21N.1.SL.TZ0.2
Level	Standard Level	Paper	Paper 1 (without calculator)	Time zone	Time zone 0
Command term	Find	Question number	2	Adapted from	N/A

Question

Given that $\frac{d y}{d x} = \cos (x - \frac{π}{4})$ and $y = 2$ when $x = \frac{3 π}{4}$ , find $y$ in terms of $x$ .

Markscheme

METHOD 1

recognition that $y = \int \cos (x - \frac{π}{4}) d x$ (M1)

$y = \sin (x - \frac{π}{4}) (+ c)$ (A1)

substitute both $x$ and $y$ values into their integrated expression including $c$ (M1)

$2 = \sin \frac{π}{2} + c$

$c = 1$

$y = \sin (x - \frac{π}{4}) + 1$ A1

METHOD 2

$\int_{2}^{y} d y = \int_{\frac{3 π}{4}}^{x} \cos (x - \frac{π}{4}) d x$ (M1)(A1)

$y - 2 = \sin (x - \frac{π}{4}) - \sin \frac{π}{2}$ A1

$y = \sin (x - \frac{π}{4}) + 1$ A1

[4 marks]

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Syllabus sections

Topic 5 —Calculus » SL 5.10—Indefinite integration, reverse chain, by substitution

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