OCR MEI C2 2007 June — Question 5 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRadians, Arc Length and Sector Area
TypeSector area calculation
DifficultyModerate -0.8 This is a straightforward application of the sector area formula A = ½r²θ, requiring simple algebraic rearrangement to find θ, then using the arc length formula s = rθ to find perimeter. It involves direct formula recall with minimal problem-solving, making it easier than average but not trivial since students must remember to add the two radii to the arc length for the perimeter.
Spec1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta
5 A sector of a circle of radius 5 cm has area \(9 \mathrm {~cm} ^ { 2 }\).
Find, in radians, the angle of the sector.
Find also the perimeter of the sector.
Question 5:
AnswerMarks Guidance
Area \(= \frac{1}{2}r^2\theta \Rightarrow 9 = \frac{1}{2}(25)\theta\)M1
\(\theta = \frac{18}{25} = 0.72\) radiansA1
Arc length \(= r\theta = 5 \times 0.72 = 3.6\)M1
Perimeter \(= 3.6 + 5 + 5 = 13.6\) cmA1 A1 A1 arc length, A1 perimeter 
## Question 5:

Area $= \frac{1}{2}r^2\theta \Rightarrow 9 = \frac{1}{2}(25)\theta$ | M1 |

$\theta = \frac{18}{25} = 0.72$ radians | A1 |

Arc length $= r\theta = 5 \times 0.72 = 3.6$ | M1 |

Perimeter $= 3.6 + 5 + 5 = 13.6$ cm | A1 A1 | A1 arc length, A1 perimeter

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5 A sector of a circle of radius 5 cm has area $9 \mathrm {~cm} ^ { 2 }$.\\
Find, in radians, the angle of the sector.\\
Find also the perimeter of the sector.

\hfill \mbox{\textit{OCR MEI C2 2007 Q5 [5]}}
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