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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]

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]

Examiners report

[N/A]

a(i).

[N/A]

a(ii).

[N/A]

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.1 » The circle: radian measure of angles; length of an arc; area of a sector.

Show 43 related questions

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16M.1.sl.TZ2.5a: Find ${\rm{A\hat BC}}$ .
16N.2.sl.TZ0.3b: Find the value of $r$ .
16N.2.sl.TZ0.3a: Write down the exact value of $\theta$ in radians.
12N.2.sl.TZ0.8a: Find the length of the chord [AB].
12N.2.sl.TZ0.8b: Find the area of triangle AOB.
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09M.2.sl.TZ1.2b: Find the area of the shaded region.
10M.2.sl.TZ2.8a: Find the size of angle AOC .
10M.2.sl.TZ2.8d: Find EF .
10M.2.sl.TZ2.8b: Hence find the area of the shaded region.
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14M.2.sl.TZ2.1b: Find the area of the shaded sector.
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