| 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 \(\rm{O}\) and radius \(5 \rm\,{cm}\).
The points \(\rm{A}\), \(rm{B}\) and \(rm{C}\) lie on the circumference of the circle, and \({\rm{A\hat OC}} = 0.7\) radians.
Find the length of the arc \({\text{ABC}}\).
[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 \(0.7 \times 5\)
arc length \(= 3.5\) (cm) A1 N2
[2 marks]
a(i).
valid approach (M1)
eg \(3.5 + 5 + 5,{\text{ arc}} + 2r\)
perimeter \(= 13.5\) (cm) A1 N2
[2 marks]
a(ii).
correct substitution into area formula (A1)
eg \(\frac{1}{2}(0.7){(5)^2}\)
\({\text{area}} = 8.75{\text{ (c}}{{\text{m}}^2}{\text{)}}\) 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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