| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2012 |
| Session | January |
| Marks | 4 |
| 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 s = rθ) with direct substitution. Part (a) requires simple rearrangement to find θ, and part (b) is immediate once θ is known. No problem-solving or conceptual insight needed—pure formula recall and arithmetic. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Area of sector \(= \frac{1}{2}r^2\theta = \frac{1}{2} \times 6^2 \times \theta\) | M1 | \(\frac{1}{2}r^2\theta\) seen in (a) or used for the area |
| \(21.6 = 18\theta\) so \(\theta = 1.2\) | A1 (Total: 2) | Must be exact, not rounded |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| Arc \(= r\theta\) | M1 | \(r\theta\) seen in (b) or used for arc length |
| \(= 7.2\) {cm} | A1F (Total: 2) | Ft on \(6\times\)c's value for \(\theta\) provided \(4 < \text{arc} < 10\) |
## Question 1:
**Part (a):**
| Working | Mark | Guidance |
|---------|------|----------|
| Area of sector $= \frac{1}{2}r^2\theta = \frac{1}{2} \times 6^2 \times \theta$ | M1 | $\frac{1}{2}r^2\theta$ seen in (a) or used for the area |
| $21.6 = 18\theta$ so $\theta = 1.2$ | A1 (Total: 2) | Must be exact, not rounded |
**Part (b):**
| Working | Mark | Guidance |
|---------|------|----------|
| Arc $= r\theta$ | M1 | $r\theta$ seen in (b) or used for arc length |
| $= 7.2$ {cm} | A1F (Total: 2) | Ft on $6\times$c's value for $\theta$ provided $4 < \text{arc} < 10$ |
---1 The diagram shows a sector $O A B$ of a circle with centre $O$ and radius 6 cm .\\
\includegraphics[max width=\textwidth, alt={}, center]{02e5dfac-18d7-480d-ac23-dfd2ca348cba-2_358_332_358_829}
The angle between the radii $O A$ and $O B$ is $\theta$ radians.\\
The area of the sector $O A B$ is $21.6 \mathrm {~cm} ^ { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\theta$.
\item Find the length of the $\operatorname { arc } A B$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2012 Q1 [4]}}