| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Arc length calculation |
| Difficulty | Easy -1.2 This is a straightforward application of the standard arc length formula s = rθ to find θ, followed by direct substitution into the sector area formula A = ½r²θ. Both parts require only recall of basic formulas with simple arithmetic, making it 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 |
|---|---|---|
| Answer | Mark | Guidance |
| Arc length formula: \(s = r\theta\) | M1 | Use of correct formula |
| \(4 = 5\theta\) therefore \(\theta = 0.8\) (radians) | A1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Area \(= \frac{1}{2}r^2\theta = \frac{1}{2} \times 25 \times 0.8\) | M1 | Use of correct formula with their \(\theta\) |
| \(= 10 \text{ cm}^2\) | A1 | cao |
# Question 1:
## Part (a)
| Answer | Mark | Guidance |
|--------|------|----------|
| Arc length formula: $s = r\theta$ | M1 | Use of correct formula |
| $4 = 5\theta$ therefore $\theta = 0.8$ (radians) | A1 | cao |
## Part (b)
| Answer | Mark | Guidance |
|--------|------|----------|
| Area $= \frac{1}{2}r^2\theta = \frac{1}{2} \times 25 \times 0.8$ | M1 | Use of correct formula with their $\theta$ |
| $= 10 \text{ cm}^2$ | A1 | cao |
---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]{1c06ba04-575c-4eb8-b4aa-0a7510838cd2-02_415_525_550_794}
The angle between the radii $O A$ and $O B$ is $\theta$ radians.\\
The length of the $\operatorname { arc } A B$ is 4 cm .
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\theta$.
\item Find the area of the sector $O A B$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2011 Q1 [4]}}