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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 dydx=cos(x-π4) and y=2 when x=3π4, find y in terms of x.

Markscheme

METHOD 1

recognition that y=cos(x-π4)dx                 (M1)

y=sin(x-π4)(+c)                 (A1)

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

2=sinπ2+c

c=1

y=sin(x-π4)+1                 A1

 

METHOD 2

y2dy=x3π4cos(x-π4)dx                 (M1)(A1)

y-2=sin(x-π4)-sinπ2                 A1

y=sin(x-π4)+1                 A1

 

[4 marks]

Examiners report

[N/A]

Syllabus sections

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