| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2023 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Bearings and navigation |
| Difficulty | Moderate -0.3 This is a straightforward application of the cosine rule in a bearings context. Students need to find the angle at C (72° - 39° = 33°) and apply the cosine rule with two given sides. Part (b) is a simple interpretation question. Slightly easier than average due to being a direct single-technique application with clear setup. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Angle \(ACB = 33°\) | B1 | 33 seen anywhere; allow \(72 - 39\); may be on diagram |
| \(AB^2 = 8.2^2 + 15.6^2 - 2 \times 8.2 \times 15.6 \cos 33°\) | M1 | Uses cosine rule with a value for the angle |
| Distance \(= \) awrt \(9.8\) {km} | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Valid reason: road is not straight so distance greater; objects in the way; masts not in same horizontal plane | B1 | Must be based on model assumptions (plane not horizontal, or journey not straight line); do not accept comments about accuracy of given values alone |
# Question 3:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Angle $ACB = 33°$ | B1 | 33 seen anywhere; allow $72 - 39$; may be on diagram |
| $AB^2 = 8.2^2 + 15.6^2 - 2 \times 8.2 \times 15.6 \cos 33°$ | M1 | Uses cosine rule with a value for the angle |
| Distance $= $ awrt $9.8$ {km} | A1 | |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Valid reason: road is not straight so distance greater; objects in the way; masts not in same horizontal plane | B1 | Must be based on model assumptions (plane not horizontal, or journey not straight line); do not accept comments about accuracy of given values alone |
---3.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{ce4f8375-0d88-4e48-85de-35f7e90b014d-06_478_513_283_776}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 is a sketch showing the position of three phone masts, $A , B$ and $C$.\\
The masts are identical and their bases are assumed to lie in the same horizontal plane.\\
From mast $C$
\begin{itemize}
\item mast $A$ is 8.2 km away on a bearing of $072 ^ { \circ }$
\item mast $B$ is 15.6 km away on a bearing of $039 ^ { \circ }$
\begin{enumerate}[label=(\alph*)]
\item Find the distance between masts $A$ and $B$, giving your answer in km to one decimal place.
\end{itemize}
An engineer needs to travel from mast $A$ to mast $B$.
\item Give a reason why the answer to part (a) is unlikely to be an accurate value for the distance the engineer travels.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 2023 Q3 [4]}}