AQA C2 2015 June — Question 1 4 marks

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2015
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRadians, Arc Length and Sector Area
TypeSector perimeter calculation
DifficultyModerate -0.8 This is a straightforward sector problem requiring recall of two standard formulas (area = ½r²θ and arc length = rθ). Students find θ from the given area, then calculate perimeter as arc length plus two radii. It's more routine than average A-level questions since it involves direct formula application with no conceptual challenges or problem-solving insight required.
Spec1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta
1 The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius 5 cm . \includegraphics[max width=\textwidth, alt={}, center]{24641e66-b73b-4323-98c8-349727151aba-02_378_451_648_790} The angle \(A O B\) is \(\theta\) radians and the area of the sector is \(15 \mathrm {~cm} ^ { 2 }\).
Find the perimeter of the sector.
[0pt] [4 marks]
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
Area = \(\frac{1}{2}r^2\theta\), so \(15 = \frac{1}{2}(5)^2\theta\)M1 Use of correct area formula
\(\theta = \frac{15 \times 2}{25} = 1.2\) (radians)A1 Correct value of \(\theta\)
Arc length \(= r\theta = 5 \times 1.2 = 6\) (cm)M1 Use of \(s = r\theta\) with their \(\theta\)
Perimeter \(= 6 + 5 + 5 = 16\) cmA1 Correct perimeter 
# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| Area = $\frac{1}{2}r^2\theta$, so $15 = \frac{1}{2}(5)^2\theta$ | M1 | Use of correct area formula |
| $\theta = \frac{15 \times 2}{25} = 1.2$ (radians) | A1 | Correct value of $\theta$ |
| Arc length $= r\theta = 5 \times 1.2 = 6$ (cm) | M1 | Use of $s = r\theta$ with their $\theta$ |
| Perimeter $= 6 + 5 + 5 = 16$ cm | A1 | Correct perimeter |

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1 The diagram shows a sector $O A B$ of a circle with centre $O$ and radius 5 cm .\\
\includegraphics[max width=\textwidth, alt={}, center]{24641e66-b73b-4323-98c8-349727151aba-02_378_451_648_790}

The angle $A O B$ is $\theta$ radians and the area of the sector is $15 \mathrm {~cm} ^ { 2 }$.\\
Find the perimeter of the sector.\\[0pt]
[4 marks]

\hfill \mbox{\textit{AQA C2 2015 Q1 [4]}}
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Q1 4 Q2 7 Q3 7 Q4 10 Q5 6 Q6 10 Q7 14 Q8 5 Q9 14