| Date | May 2014 | Marks available | 2 | Reference code | 14M.2.sl.TZ2.1 |
| Level | SL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
The following diagram shows a circle with centre O and radius 5cm.
The points A, rmB and rmC lie on the circumference of the circle, and AˆOC=0.7 radians.
Find the length of the arc ABC.
[2]
a(i).
Find the perimeter of the shaded sector.
[2]
a(ii).
Find the area of the shaded sector.
[2]
b.
Markscheme
correct substitution into arc length formula (A1)
eg 0.7×5
arc length =3.5 (cm) A1 N2
[2 marks]
a(i).
valid approach (M1)
eg 3.5+5+5, arc+2r
perimeter =13.5 (cm) A1 N2
[2 marks]
a(ii).
correct substitution into area formula (A1)
eg 12(0.7)(5)2
area=8.75 (cm2) A1 N2
[2 marks]
b.
Examiners report
[N/A]
a(i).
[N/A]
a(ii).
[N/A]
b.
Syllabus sections
Topic 3 - Circular functions and trigonometry » 3.1 » The circle: radian measure of angles; length of an arc; area of a sector.
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