| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Triangle with circular sector |
| Difficulty | Standard +0.3 This is a straightforward multi-part question requiring standard applications of sine rule, angle sum in triangles, triangle area formula, and sector area formula. All techniques are routine C2 content with clear signposting. The calculations are direct with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{\sin B}{3} = \frac{\sin 2.2}{7}\) | M1 | |
| \(\sin B = \frac{3}{7} \sin 2.2\) | ||
| \(\angle ABC = 0.354\) (3sf) | M1 A1 | |
| (b) \(\angle BAC = \pi - (2.2 + 0.3538) = 0.588\) (3sf) | M1 A1 | |
| (c) \(= \frac{1}{2} \times 3 \times 7 \times \sin 0.5878 = 5.82\) m² (3sf) | M1 A1 | |
| (d) \(= 5.822 + [\frac{1}{2} \times 2^2 \times (2\pi - 0.5878)] + [\frac{1}{2} \times 1^2 \times (2\pi - 0.3538)]\) | M3 A1 | |
| \(= 20.2\) m² (3sf) | A1 | (12 marks) |
**(a)** $\frac{\sin B}{3} = \frac{\sin 2.2}{7}$ | M1 |
$\sin B = \frac{3}{7} \sin 2.2$ | |
$\angle ABC = 0.354$ (3sf) | M1 A1 |
**(b)** $\angle BAC = \pi - (2.2 + 0.3538) = 0.588$ (3sf) | M1 A1 |
**(c)** $= \frac{1}{2} \times 3 \times 7 \times \sin 0.5878 = 5.82$ m² (3sf) | M1 A1 |
**(d)** $= 5.822 + [\frac{1}{2} \times 2^2 \times (2\pi - 0.5878)] + [\frac{1}{2} \times 1^2 \times (2\pi - 0.3538)]$ | M3 A1 |
$= 20.2$ m² (3sf) | A1 | (12 marks)9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{857bf144-b03e-4b46-b043-1119b30f9e78-4_365_888_1484_479}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Figure 3 shows a design painted on the wall at a karting track. The sign consists of triangle $A B C$ and two circular sectors of radius 2 metres and 1 metre with centres $A$ and $B$ respectively.
Given that $A B = 7 \mathrm {~m} , A C = 3 \mathrm {~m}$ and $\angle A C B = 2.2$ radians,
\begin{enumerate}[label=(\alph*)]
\item use the sine rule to find the size of $\angle A B C$ in radians to 3 significant figures,
\item show that $\angle B A C = 0.588$ radians to 3 significant figures,
\item find the area of triangle $A B C$,
\item find the area of the wall covered by the design.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q9 [12]}}