| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Bearings and navigation |
| Difficulty | Moderate -0.8 This is a straightforward multi-part trigonometry question testing standard C2 content: bearings using sine rule, triangle area formula, arc length to find angle, and sector area calculation. All parts follow routine procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks |
|---|---|
| 1 | i |
| Answer | Marks |
|---|---|
| iiiB | Correct attempt at cos rule |
| Answer | Marks |
|---|---|
| 5315 to 5340 | M1 |
| Answer | Marks |
|---|---|
| A1 | any vertex, any letter |
| Answer | Marks |
|---|---|
| dep on sector > triangle | 4 |
Question 1:
1 | i
ii
iiiA
iiiB | Correct attempt at cos rule
correct full method for C
C = 141.1…
bearing = [0]38.8 cao
½ × 118 × 82 × sin their C or
supp.
3030 to 3050 [m2]
sin (θ/2) = ( ½ × 189)/130
1.6276 → 1.63
0.5 × 1302 × sin 1.63
0.5 × 1302 × 1.63
their sector − their triangle AOB
5315 to 5340 | M1
M1
A1
A1
M1
A1
M1
A1
M1
M1
M1
A1 | any vertex, any letter
or B4
or correct use of angle A or angle B
or cosθ = (1302+1302-
1892)/(2x130x130)
In all methods, the more accurate
number to be seen.
condone their θ (8435)
condone their θ in radians (13770)
dep on sector > triangle | 4
2
2
4Fig. 11.1 shows a village green which is bordered by 3 straight roads AB, BC and CA. The road AC runs due North and the measurements shown are in metres.
\includegraphics{figure_1}
\begin{enumerate}[label=(\roman*)]
\item Calculate the bearing of B from C, giving your answer to the nearest 0.1°. [4]
\item Calculate the area of the village green. [2]
\end{enumerate}
The road AB is replaced by a new road, as shown in Fig. 11.2. The village green is extended up to the new road.
\includegraphics{figure_2}
The new road is an arc of a circle with centre O and radius 130 m.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item (A) Show that angle AOB is 1.63 radians, correct to 3 significant figures. [2]
(B) Show that the area of land added to the village green is 5300 m² correct to 2 significant figures. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 Q1 [12]}}