| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Proving angle relationships |
| Difficulty | Standard +0.3 This is a straightforward coordinate geometry and circle sector problem requiring standard techniques: distance formula, cosine rule for angles, and sector area formula. All methods are routine C2 content with clear scaffolding through the 'show that' parts, making it slightly easier than average despite multiple steps. |
| 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_1}
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 mm², 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 cm³, the volume of the bar. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [11]}}