| Exam Board | OCR |
|---|---|
| Module | H240/01 (Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Radians, Arc Length and Sector Area |
| Type | Simultaneous equations with arc/area |
| Difficulty | Moderate -0.3 This is a straightforward application of standard sector formulas (arc length = rθ, area = ½r²θ) to form simultaneous equations, followed by finding segment area using the triangle formula. The problem requires only direct formula recall and basic algebraic manipulation with no conceptual challenges or novel insights. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
The diagram shows a sector $AOB$ of a circle with centre $O$ and radius $r$ cm.
\includegraphics{figure_4}
The angle $AOB$ is $\theta$ radians. The arc length $AB$ is 15 cm and the area of the sector is 45 cm$^2$.
\begin{enumerate}[label=(\alph*)]
\item Find the values of $r$ and $\theta$. [4]
\item Find the area of the segment bounded by the arc $AB$ and the chord $AB$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/01 2017 Q4 [7]}}