| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Sector area calculation |
| Difficulty | Easy -1.2 This is a straightforward application of standard sector formulas (A = ½r²θ and arc length = rθ) with simple arithmetic. Part (b)(ii) adds one extra step of finding a square's area from its perimeter, but requires no problem-solving insight—just direct formula recall and calculation. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Area of sector} = \frac{1}{2}r^2\theta\) | M1 | \(\frac{1}{2}r^2\theta\) stated or used for area of sector. PI |
| \(= \frac{1}{2} \times 10^2 \times 0.8 = 40 \text{ [cm}^2\text{]}\) | A1 | 2 marks total |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Arc} = r\theta\) ... \(= 8\) | M1, A1 | \(r\theta\) stated or used for arc length. PI |
| \(\text{Perimeter} = 20 + r\theta = 28 \text{ (cm)}\) | A1ft | ft on \(20 + r\theta\). 3 marks total |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Area of square} = \left[\frac{\text{c's answer for (b)(i)}}{4}\right]^2 = 49 \text{ [cm}^2\text{]}\) | M1, A1cao | PI. 2 marks total |
**1(a)**
$\text{Area of sector} = \frac{1}{2}r^2\theta$ | M1 | $\frac{1}{2}r^2\theta$ stated or used for area of sector. PI
$= \frac{1}{2} \times 10^2 \times 0.8 = 40 \text{ [cm}^2\text{]}$ | A1 | 2 marks total
**1(b)(i)**
$\text{Arc} = r\theta$ ... $= 8$ | M1, A1 | $r\theta$ stated or used for arc length. PI
$\text{Perimeter} = 20 + r\theta = 28 \text{ (cm)}$ | A1ft | ft on $20 + r\theta$. 3 marks total
**1(b)(ii)**
$\text{Area of square} = \left[\frac{\text{c's answer for (b)(i)}}{4}\right]^2 = 49 \text{ [cm}^2\text{]}$ | M1, A1cao | PI. 2 marks total
**Total for Q1: 7 marks**
---1 The diagram shows a sector $O A B$ of a circle with centre $O$ and radius 10 cm .\\
\includegraphics[max width=\textwidth, alt={}, center]{0e19665b-5ee5-49e4-8de2-6c8dd17f61eb-2_371_378_555_824}
The angle $A O B$ is 0.8 radians.
\begin{enumerate}[label=(\alph*)]
\item Find the area of the sector.
\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 perimeter of a square. Find the area of the square.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C2 2009 Q1 [7]}}