| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 4 |
| 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 two-part question applying standard sector formulas (A = ½r²θ and perimeter = 2r + rθ). Part (a) requires rearranging the area formula to find θ, and part (b) is direct substitution. Both are routine calculations with no problem-solving or conceptual challenges beyond formula recall. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks |
|---|---|
| \(\frac{1}{2} \times 9.2^2 \times \angle AOB = 37.4\) | M1 |
| \(\angle AOB = 0.884\) radians (3sf) | A1 |
| Answer | Marks |
|---|---|
| \(= (2 \times 9.2) + (9.2 \times 0.8837) = 26.5\) cm (3sf) | M1 A1 |
**Part (a)**
$\frac{1}{2} \times 9.2^2 \times \angle AOB = 37.4$ | M1 |
$\angle AOB = 0.884$ radians (3sf) | A1 |
**Part (b)**
$= (2 \times 9.2) + (9.2 \times 0.8837) = 26.5$ cm (3sf) | M1 A1 |
---1.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9215e382-406c-41a3-8907-f465b134dd87-2_509_538_248_657}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the sector $O A B$ of a circle of radius 9.2 cm and centre $O$.\\
Given that the area of the sector is $37.4 \mathrm {~cm} ^ { 2 }$, find to 3 significant figures
\begin{enumerate}[label=(\alph*)]
\item the size of $\angle A O B$ in radians,
\item the perimeter of the sector.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q1 [4]}}