| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Compound shape area |
| Difficulty | Standard +0.3 This is a straightforward multi-part question testing basic coordinate geometry (distance formula), radian measure (using cosine rule or dot product), and sector area formulas. All steps are routine applications of standard techniques with clear guidance ('show that' questions provide the answer). The geometric setup is given explicitly with coordinates, requiring no novel insight—slightly easier than average for C2. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta1.10c Magnitude and direction: of vectors |
\includegraphics{figure_10}
Figure 1 shows the cross-section $ABCD$ of a chocolate bar, where $AB$, $CD$ and $AD$ are straight lines and $M$ is the mid-point of $AD$. The length $AD$ is 28 mm, and $BC$ is an arc of a circle with centre $M$.
Taking $A$ as the origin, $B$, $C$ and $D$ have coordinates $(7, 24)$, $(21, 24)$ and $(28, 0)$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that the length of $BM$ is 25 mm. [1]
\item Show that, to 3 significant figures, $\angle BMC = 0.568$ radians. [3]
\item Hence calculate, in mm$^2$, the area of the cross-section of the chocolate bar. [5]
\end{enumerate}
Given that this chocolate bar has length 85 mm,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item calculate, to the nearest cm$^3$, the volume of the bar. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q39 [11]}}