| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| 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 testing basic triangle formulas. Part (i) uses the standard area formula (1/2)ab sin C with simple surds, and part (ii) applies the cosine rule directly. Both are routine applications of C2 content with no problem-solving required, making it easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C) |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Area \(= \frac{1}{2} × 5\sqrt{2} × 2 × 8 × \sin 60°\) \(= \frac{1}{2} × 5\sqrt{2} × 2 × 8 × \frac{\sqrt{3}}{2}\) \(= 10\sqrt{6}\) | B1, M1, A1 (3 marks) | State or imply that \(\sin 60° = \frac{\sqrt{3}}{2}\) or exact equiv; Use \(\frac{1}{2}ac \sin B\); Obtain \(10\sqrt{6}\) only, from working in surds |
| (ii) \(AC^2 = (5\sqrt{2})^2 + 8^2 - 2 × 5\sqrt{2} × 8 × \cos 60°\) \(AC = 7.58 \text{ cm}\) | M1, A1, A1 (3 marks) | Attempt to use the correct cosine formula; Correct unsimplified expression for \(AC^2\); Obtain \(AC = 7.58\), or better |
**(i)** Area $= \frac{1}{2} × 5\sqrt{2} × 2 × 8 × \sin 60°$ $= \frac{1}{2} × 5\sqrt{2} × 2 × 8 × \frac{\sqrt{3}}{2}$ $= 10\sqrt{6}$ | B1, M1, A1 (3 marks) | State or imply that $\sin 60° = \frac{\sqrt{3}}{2}$ or exact equiv; Use $\frac{1}{2}ac \sin B$; Obtain $10\sqrt{6}$ only, from working in surds
**(ii)** $AC^2 = (5\sqrt{2})^2 + 8^2 - 2 × 5\sqrt{2} × 8 × \cos 60°$ $AC = 7.58 \text{ cm}$ | M1, A1, A1 (3 marks) | Attempt to use the correct cosine formula; Correct unsimplified expression for $AC^2$; Obtain $AC = 7.58$, or better
**Total: 6 marks**In a triangle $ABC$, $AB = 5\sqrt{2}$ cm, $BC = 8$ cm and angle $B = 60°$.
\begin{enumerate}[label=(\roman*)]
\item Find the exact area of the triangle, giving your answer as simply as possible. [3]
\item Find the length of $AC$, correct to 3 significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C2 2007 Q4 [6]}}