| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Sequential triangle calculations (basic) |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring direct application of the cosine rule followed by the area formula (½ab sin C). Both are standard procedures with no problem-solving required, making it easier than average but not trivial since it involves multi-step calculation with the cosine rule. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| \(9.0\) or \(8.96\) or \(8.960\) | B3 | M1 for \([BC^2=]6.8^2+4.1^2-2×4.1×6.8×\cos 108\). A1 for \(80.2(8...)\), \(8.37\)(grads), \(6.49\) (rads). Correctly rounded to 3 or more sf. M1 for \(0.5×4.1×6.8×\sin108\). For complete long methods using BC, allow M1 and A1 for 13.2 to 13.3 |
| \(13.2577\) | B2 | |
| 5 marks | ||
| [16] |
$9.0$ or $8.96$ or $8.960$ | B3 | M1 for $[BC^2=]6.8^2+4.1^2-2×4.1×6.8×\cos 108$. A1 for $80.2(8...)$, $8.37$(grads), $6.49$ (rads). Correctly rounded to 3 or more sf. M1 for $0.5×4.1×6.8×\sin108$. For complete long methods using BC, allow M1 and A1 for 13.2 to 13.3
$13.2577$ | B2 |
| | 5 marks |
| | [16] |4
Fig. 4
For triangle ABC shown in Fig. 4, calculate\\
(i) the length of BC ,\\
(ii) the area of triangle ABC .
\hfill \mbox{\textit{OCR MEI C2 2005 Q4 [5]}}