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 2x−x2 in the form a(x−h)2+k, where a, h, k∈R.
[2]
a.
Hence, find the value of ∫32121√2x−x2dx.
[5]
b.
Markscheme
attempt to complete the square or multiplication and equating coefficients (M1)
2x−x2=−(x−1)2+1 A1
a=−1, h=1, k=1
[2 marks]
a.
use of their identity from part (a) (∫32121√1−(x−1)2dx) (M1)
=[arcsin(x−1)]3212 or [arcsin(u)]12−12 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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