| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Real-world application problems |
| Difficulty | Moderate -0.3 This is a straightforward application of the sine rule to find a second side, followed by the standard area formula (1/2)ab sin C. Part (b) requires a simple contextual comment about measurement accuracy. The calculations are routine for AS-level, though the multi-step nature and context interpretation elevate it slightly above pure recall, placing it just below average difficulty. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks |
|---|---|
| 8(a) | Way 1 |
| Answer | Marks |
|---|---|
| sin60(cid:113) sin"50(cid:113)" | Way 2 |
| Answer | Marks | Guidance |
|---|---|---|
| sin70(cid:113) sin"50(cid:113)" | M1 | 2.1 |
| Answer | Marks |
|---|---|
| sin50(cid:113) | 30sin70(cid:113) |
| Answer | Marks | Guidance |
|---|---|---|
| sin50(cid:113) | A1 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| 2 2 | M1 | 3.1a |
| = 478 m2 | A1ft | 1.1b |
| Answer | Marks |
|---|---|
| (b) | Plausible reason e.g. Because the angles and the side length are not |
| Answer | Marks | Guidance |
|---|---|---|
| Or e.g. The lawn may not be flat | B1 | 3.2b |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Scheme | Marks |
Question 8:
--- 8(a) ---
8(a) | Way 1
Finds third angle of triangle
and uses or states
x 30
(cid:32)
sin60(cid:113) sin"50(cid:113)" | Way 2
Finds third angle of triangle and
uses or states
y 30
(cid:32)
sin70(cid:113) sin"50(cid:113)" | M1 | 2.1
30sin60(cid:113)
So x (cid:32) ((cid:32)33.9)
sin50(cid:113) | 30sin70(cid:113)
So y (cid:32) ((cid:32)36.8)
sin50(cid:113) | A1 | 1.1b
Area = 1(cid:117)30(cid:117)x(cid:117)sin70 (cid:113) or 1(cid:117)30(cid:117)y(cid:117)sin60
2 2 | M1 | 3.1a
= 478 m2 | A1ft | 1.1b
(4)
(b) | Plausible reason e.g. Because the angles and the side length are not
given to four significant figures
Or e.g. The lawn may not be flat | B1 | 3.2b
(1)
(5 marks)
Notes:
(a)
M1: Uses sine rule with their third angle to find one of the unknown side lengths
A1: Finds expression for, or value of either side length
M1: Completes method to find area of triangle
A1ft: Obtains a correct answer for their value of x or their value of y
(b)
B1: As information given in the question may not be accurate to 4sf or the lawn may not be
flat so modelling by a plane figure may not be accurate
Question | Scheme | Marks | AOs\includegraphics{figure_1}
A triangular lawn is modelled by the triangle $ABC$, shown in Figure 1. The length $AB$ is to be $30\text{m}$ long.
Given that angle $BAC = 70°$ and angle $ABC = 60°$,
\begin{enumerate}[label=(\alph*)]
\item calculate the area of the lawn to $3$ significant figures.
[4]
\item Why is your answer unlikely to be accurate to the nearest square metre?
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 1 Q8 [5]}}