| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| 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 (arc length = rθ, perimeter = 2r + rθ) with simple algebraic manipulation. Part (a) requires solving a linear equation, and part (b) is direct substitution into the area formula. Both parts are routine exercises with no problem-solving insight required, making it easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \(\text{Arc} = r\theta\) \((= 1.25r)\) | M1 | Within (a), \(r\theta\) or 15 used for arc length |
| \(P = r + r + r\theta = 39\) | m1 | Use of \(r + r + r\theta\) for perimeter. m0 if no indication that '15' comes from \(r\theta\) |
| \(3.25r = 39 \quad r = \frac{39}{3.25} = 12\) | A1 | CSO AG |
| Total: 3 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Area of sector \(= \frac{1}{2}r^2\theta\) | M1 | \(\frac{1}{2}r^2\theta\) stated or used for sector area |
| \(= \frac{1}{2} \times 12^2 \times 1.25 = 90 \text{ cm}^2\) | A1 | NMS: 90 scores 2 marks |
| Total: 2 marks |
# Question 1:
## Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| $\text{Arc} = r\theta$ $(= 1.25r)$ | M1 | Within (a), $r\theta$ or 15 used for arc length |
| $P = r + r + r\theta = 39$ | m1 | Use of $r + r + r\theta$ for perimeter. m0 if no indication that '15' comes from $r\theta$ |
| $3.25r = 39 \quad r = \frac{39}{3.25} = 12$ | A1 | CSO AG |
| **Total: 3 marks** | | |
## Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| Area of sector $= \frac{1}{2}r^2\theta$ | M1 | $\frac{1}{2}r^2\theta$ stated or used for sector area |
| $= \frac{1}{2} \times 12^2 \times 1.25 = 90 \text{ cm}^2$ | A1 | NMS: 90 scores 2 marks |
| **Total: 2 marks** | | |
---1 The diagram shows a sector $O A B$ of a circle with centre $O$ and radius $r \mathrm {~cm}$.\\
\includegraphics[max width=\textwidth, alt={}, center]{bfe96138-9587-4efb-95c5-84c4d5eadfbe-2_382_351_379_826}
The angle $A O B$ is 1.25 radians. The perimeter of the sector is 39 cm .
\begin{enumerate}[label=(\alph*)]
\item Show that $r = 12$.
\item Calculate the area of the sector $O A B$.
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2013 Q1 [5]}}