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Date	May 2017	Marks available	2	Reference code	17M.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 40 cm.

M17/5/MATME/SP2/ENG/TZ2/01

The points A, B and C are on the circumference of the circle and ${\rm{A\hat OC}} = 1.9{\text{ radians}}$ .

Find the length of arc ABC.

[2]

Find the perimeter of sector OABC.

[2]

Find the area of sector OABC.

[2]

Markscheme

correct substitution into arc length formula (A1)

eg $\,\,\,\,\,$ $(40)(1.9)$

${\text{arc length}} = 76{\text{ (cm)}}$ A1 N2

[2 marks]

valid approach (M1)

eg $\,\,\,\,\,$ ${\text{arc}} + 2r,{\text{ }}76 + 40 + 40$

${\text{perimeter}} = 156{\text{ (cm)}}$ A1 N2

[2 marks]

correct substitution into area formula (A1)

eg $\,\,\,\,\,$ $\frac{1}{2}(1.9){(40)^2}$

${\text{area}} = 1520{\text{ (c}}{{\text{m}}^{\text{2}}}{\text{)}}$ A1 N2

[2 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.1

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17M.2.sl.TZ2.1a: Find the length of arc ABC.
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15M.1.sl.TZ1.2a: Find the length of ${\text{arc ACB}}$ .
12M.2.sl.TZ1.9b: Write down the length of BD.
12N.2.sl.TZ0.8a: Find the length of the chord [AB].
12N.2.sl.TZ0.8b: Find the area of triangle AOB.
12N.2.sl.TZ0.8c: Angle BOC is 2.4 radians. Find the length of arc ADC.
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08M.2.sl.TZ1.3c: Find the area of sector OABC.
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10M.2.sl.TZ2.8d: Find EF .
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15N.2.sl.TZ0.1b: Find the area of the shaded region.

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