| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Compound shape area |
| Difficulty | Moderate -0.3 This is a straightforward C2 question testing basic applications of circle geometry, sector area, and arc length formulas. Part (a) requires equating two areas using standard formulas (rectangle + semicircle = sector), which is algebraically simple. Parts (b)-(d) are routine calculations with given values. The question involves multiple steps but each is standard bookwork with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_4}
Figure 1 shows the cross-sections of two drawer handles.
Shape $X$ is a rectangle $ABCD$ joined to a semicircle with $BC$ as diameter. The length $AB = d$ cm and $BC = 2d$ cm.
Shape $Y$ is a sector $OPQ$ of a circle with centre $O$ and radius $2d$ cm. Angle $POQ$ is $\theta$ radians.
Given that the areas of the shapes $X$ and $Y$ are equal,
\begin{enumerate}[label=(\alph*)]
\item prove that $\theta = 1 + \frac{1}{4}\pi$. [5]
\end{enumerate}
Using this value of $\theta$, and given that $d = 3$, find in terms of $\pi$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the perimeter of shape $X$, [2]
\item the perimeter of shape $Y$. [3]
\item Hence find the difference, in mm, between the perimeters of shapes $X$ and $Y$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q7 [12]}}