| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Simultaneous equations with arc/area |
| Difficulty | Moderate -0.3 This is a straightforward application of standard arc length and sector area formulas (s=rθ, A=½r²θ) leading to simple simultaneous equations that solve immediately by division. Part (b) requires subtracting triangle area using ½r²sinθ, which is routine once r and θ are known. Slightly below average difficulty as it's purely procedural with no problem-solving insight required. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
4 The diagram shows a sector $A O B$ of a circle with centre $O$ and radius $r \mathrm {~cm}$.\\
\includegraphics[max width=\textwidth, alt={}, center]{6c16d9e2-7698-48e4-a3ed-5aae3b6f041e-05_510_606_1745_274}
The angle $A O B$ is $\theta$ radians. The arc length $A B$ is 15 cm and the area of the sector is $45 \mathrm {~cm} ^ { 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $r$ and $\theta$.
\item Find the area of the segment bounded by the arc $A B$ and the chord $A B$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 Q4 [7]}}