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Date November 2020 Marks available 4 Reference code 20N.2.AHL.TZ0.H_3
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Determine Question number H_3 Adapted from N/A

Question

The following diagram shows part of the graph of y=p+qsin(rx) . The graph has a local maximum point at (-9π4, 5) and a local minimum point at (-3π4, -1).

Determine the values of p, q and r.

[4]
a.

Hence find the area of the shaded region.

[4]
b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

the principal axis is 5+(-1)2(=2)

so p=2       A1

the amplitude is 5-(-1)2(=3)

so q=3       A1


EITHER

one period is 2(-3π4-(-9π4))       (M1)

=3π

2πr=3π


OR

Substituting a point eg -1=2+sin(-3π4r)

sin(-3π4r)=-1-3π4r=-5π2, -π2, 3π2,

Choice of correct solution -3π4r=-π2       (M1)


THEN

r=23       A1

(y=2+3sin(2x3))


Note:
q and r can be both given as negatives for full marks


[4 marks]

a.

roots are x=-1.09459, x=-3.617797       (A1)

-1.09459-3.617797(2+3sin(2x3))dx       (M1)

=-1.66(=-1.66179)       (A1)

so area =1.66  (units2)       A1


[4 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 5 —Calculus » SL 5.5—Integration introduction, areas between curve and x axis
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