17M.2.SL.TZ2.S_1

pestleMathematicsAISLPaper 217M· ahl-3-7-radianssource ↗

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 / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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]