| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2021 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Parallelogram problems |
| Difficulty | Standard +0.3 This is a straightforward application of the parallelogram area formula (area = ab sin θ) to find an angle, followed by using the cosine rule. Both parts are standard textbook exercises requiring direct formula application with no problem-solving insight needed. Slightly easier than average due to the routine nature of the calculations. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(50 = 7\times14\sin(SPQ)\) | B1 | Sets up area formula correctly |
| \(180° - \arcsin\!\left(\dfrac{50}{98}\right)\) | M1 | Correct method to find obtuse \(\angle SPQ\) |
| \(= 149.32°\) | A1 | awrt \(149.32°\) |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(SQ^2 = 14^2+7^2-2\times14\times7\cos(149.32°)\) | M1 | Correct method using their \(\angle SPQ\) |
| \(SQ = 20.3\text{ cm}\) | A1 | awrt \(20.3\) cm; condone lack of units |
# Question 7:
## Part (a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $50 = 7\times14\sin(SPQ)$ | B1 | Sets up area formula correctly |
| $180° - \arcsin\!\left(\dfrac{50}{98}\right)$ | M1 | Correct method to find obtuse $\angle SPQ$ |
| $= 149.32°$ | A1 | awrt $149.32°$ |
## Part (b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $SQ^2 = 14^2+7^2-2\times14\times7\cos(149.32°)$ | M1 | Correct method using their $\angle SPQ$ |
| $SQ = 20.3\text{ cm}$ | A1 | awrt $20.3$ cm; condone lack of units |\begin{enumerate}
\item A parallelogram $P Q R S$ has area $50 \mathrm {~cm} ^ { 2 }$
\end{enumerate}
Given
\begin{itemize}
\item $P Q$ has length 14 cm
\item $Q R$ has length 7 cm
\item angle $S P Q$ is obtuse\\
find\\
(a) the size of angle $S P Q$, in degrees, to 2 decimal places,\\
(b) the length of the diagonal $S Q$, in cm , to one decimal place.
\end{itemize}
\hfill \mbox{\textit{Edexcel AS Paper 1 2021 Q7 [5]}}