| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Ambiguous case (two solutions) |
| Difficulty | Standard +0.3 This is a standard sine rule application with the ambiguous case, which is a well-known textbook scenario in C2. Part (a) requires straightforward sine rule application, and part (b) tests awareness that sin(x) = sin(π-x), requiring students to find both solutions. While it requires understanding of the ambiguous case concept, this is a routine exercise once the topic is learned, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\frac{\sin x}{8} = \frac{\sin 0.5}{7}\) or \(\frac{8}{\sin x} = \frac{7}{\sin 0.5}\), \(\sin x = \frac{8\sin 0.5}{7}\) | M1, A1ft | Sine rule attempt; A1ft follows through for wrong way round |
| \(\sin x = 0.548\) | A1 | (3 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x = 0.58\) \((\alpha)\) | B1 | This mark may be earned in (a) |
| \(\pi - \alpha = 2.56\) | M1, A1ft | (3 marks) |
## Question 7:
**(a)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{\sin x}{8} = \frac{\sin 0.5}{7}$ or $\frac{8}{\sin x} = \frac{7}{\sin 0.5}$, $\sin x = \frac{8\sin 0.5}{7}$ | M1, A1ft | Sine rule attempt; A1ft follows through for wrong way round |
| $\sin x = 0.548$ | A1 | (3 marks) |
**(b)**
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x = 0.58$ $(\alpha)$ | B1 | This mark may be earned in (a) |
| $\pi - \alpha = 2.56$ | M1, A1ft | (3 marks) |
*Note: Too many d.p. given: maximum 1 mark penalty in complete question (deduct on first occurrence).*
---7. In the triangle $A B C , A B = 8 \mathrm {~cm} , A C = 7 \mathrm {~cm} , \angle A B C = 0.5$ radians and $\angle A C B = x$ radians.
\begin{enumerate}[label=(\alph*)]
\item Use the sine rule to find the value of $\sin x$, giving your answer to 3 decimal places.
Given that there are two possible values of $x$,
\item find these values of $x$, giving your answers to 2 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2005 Q7 [6]}}