| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector perimeter calculation |
| Difficulty | Moderate -0.8 This is a straightforward application of standard sector formulas (area = ½r²θ, arc length = rθ) with all values given directly. Part (b)(ii) adds a simple equation-solving step (2πx = perimeter) but requires no problem-solving insight. Easier than average for A-level. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Area} = \frac{1}{2}r^2\theta = \frac{1}{2} \times 8^2 \times 1.4\) | M1 | Use of correct formula |
| \(= 44.8 \text{ m}^2\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Arc length \(= r\theta = 8 \times 1.4 = 11.2\) | M1 | Use of correct arc length formula |
| Perimeter \(= 11.2 + 8 + 8\) | M1 | Adding two radii |
| \(= 27.2 \text{ m}\) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| \(2\pi x = 27.2\) | M1 | Equating circumference to perimeter found in (b)(i) |
| \(x = \frac{27.2}{2\pi} = 4.33 \text{ m}\) | A1 | 3 significant figures |
# Question 1:
## Part (a)
| $\text{Area} = \frac{1}{2}r^2\theta = \frac{1}{2} \times 8^2 \times 1.4$ | M1 | Use of correct formula |
|---|---|---|
| $= 44.8 \text{ m}^2$ | A1 | cao |
## Part (b)(i)
| Arc length $= r\theta = 8 \times 1.4 = 11.2$ | M1 | Use of correct arc length formula |
|---|---|---|
| Perimeter $= 11.2 + 8 + 8$ | M1 | Adding two radii |
| $= 27.2 \text{ m}$ | A1 | cao |
## Part (b)(ii)
| $2\pi x = 27.2$ | M1 | Equating circumference to perimeter found in (b)(i) |
|---|---|---|
| $x = \frac{27.2}{2\pi} = 4.33 \text{ m}$ | A1 | 3 significant figures |
---1 The diagram shows a sector $O A B$ of a circle with centre $O$.\\
\includegraphics[max width=\textwidth, alt={}, center]{f9a7a4dd-f7fd-4135-8872-2c1270d46a14-2_383_472_566_778}
The radius of the circle is 8 m and the angle $A O B$ is 1.4 radians.
\begin{enumerate}[label=(\alph*)]
\item Find the area of the sector $O A B$.
\item \begin{enumerate}[label=(\roman*)]
\item Find the perimeter of the sector $O A B$.
\item The perimeter of the sector $O A B$ is equal to the circumference of a circle of radius $x \mathrm {~m}$. Calculate the value of $x$ to three significant figures.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C2 2010 Q1 [7]}}