| Exam Board | AQA |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Sequential triangle calculations (basic) |
| Difficulty | Easy -1.2 This is a straightforward two-part question requiring direct application of standard formulas: (a) area = ½ab sin C with all values given, and (b) cosine rule with two sides and included angle. Both are routine calculations with no problem-solving or conceptual challenge beyond formula recall. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{Area} = \frac{1}{2} \times 5 \times 12 \times \sin 47°\) | M1 | Use of \(\frac{1}{2}ab\sin C\) with correct values |
| \(= 21.94... \approx 22 \text{ cm}^2\) | A1 | Accept 22 |
| Answer | Marks | Guidance |
|---|---|---|
| \(BC^2 = 5^2 + 12^2 - 2(5)(12)\cos 47°\) | M1 | Use of cosine rule |
| \(BC^2 = 25 + 144 - 120\cos 47°\) | A1 | Correct substitution |
| \(BC^2 = 169 - 81.846... = 87.15...\) | ||
| \(BC = 9.3 \text{ cm}\) | A1 |
# Question 1:
## Part (a):
| $\text{Area} = \frac{1}{2} \times 5 \times 12 \times \sin 47°$ | M1 | Use of $\frac{1}{2}ab\sin C$ with correct values |
|---|---|---|
| $= 21.94... \approx 22 \text{ cm}^2$ | A1 | Accept 22 |
## Part (b):
| $BC^2 = 5^2 + 12^2 - 2(5)(12)\cos 47°$ | M1 | Use of cosine rule |
| $BC^2 = 25 + 144 - 120\cos 47°$ | A1 | Correct substitution |
| $BC^2 = 169 - 81.846... = 87.15...$ | | |
| $BC = 9.3 \text{ cm}$ | A1 | |
---1 The diagram shows a triangle $A B C$.
The size of angle $B A C$ is $47 ^ { \circ }$ and the lengths of $A B$ and $A C$ are 5 cm and 12 cm respectively.
\begin{enumerate}[label=(\alph*)]
\item Calculate the area of the triangle $A B C$, giving your answer to the nearest $\mathrm { cm } ^ { 2 }$.
\item Calculate the length of $B C$, giving your answer, in cm , to one decimal place.\\[0pt]
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA C2 2014 Q1 [5]}}