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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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