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Date November 2019 Marks available 2 Reference code 19N.1.AHL.TZ0.H_7
Level Additional Higher Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Question number H_7 Adapted from N/A

Question

Write 2xx2 in the form a(xh)2+k, where ahkR.

[2]
a.

Hence, find the value of 321212xx2dx.

[5]
b.

Markscheme

attempt to complete the square or multiplication and equating coefficients       (M1)

2xx2=(x1)2+1      A1

a=1h=1k=1

[2 marks]

a.

use of their identity from part (a) (321211(x1)2dx)        (M1)

=[arcsin(x1)]3212 or [arcsin(u)]1212       A1

Note: Condone lack of, or incorrect limits up to this point.

=arcsin(12)arcsin(12)        (M1)

=π6(π6)       (A1)

=π3       A1

[5 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 —Calculus » AHL 5.15—Further derivatives and indefinite integration of these, partial fractions
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Topic 5 —Calculus

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