| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2020 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sine and Cosine Rules |
| Type | Quadrilateral with diagonal |
| Difficulty | Standard +0.3 This is a straightforward multi-step application of sine and cosine rules in a quadrilateral. Students find AC using cosine rule in triangle ABC, then use sine rule in triangle ACD with given angles. The 'exact value' requirement adds minor complexity but the angles (60°, 75°) have manageable exact forms. Slightly easier than average due to clear structure and standard technique application. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Cosine rule in triangle ABC: \(AC^2 = 5^2 + 6^2 - 2\times5\times6\cos60° = 31\) | M1, A1 (AO 1.1a, 1.1) | Attempt to use cosine rule; need not be evaluated |
| Sine rule in triangle ACD: \(\frac{AD}{\sin60°} = \frac{AC}{\sin45°}\) | M1 (AO 1.1a) | Using their \(AC\) (not \(AC^2\)) in sine rule |
| \(AD = \frac{\sqrt{3}}{2}\times\sqrt{31}\times\sqrt{2} = \frac{1}{2}\sqrt{186}\) | A1 [4] (AO 1.1) | Must be surd form FT their \(AC\) |
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cosine rule in triangle ABC: $AC^2 = 5^2 + 6^2 - 2\times5\times6\cos60° = 31$ | M1, A1 (AO 1.1a, 1.1) | Attempt to use cosine rule; need not be evaluated |
| Sine rule in triangle ACD: $\frac{AD}{\sin60°} = \frac{AC}{\sin45°}$ | M1 (AO 1.1a) | Using their $AC$ (not $AC^2$) in sine rule |
| $AD = \frac{\sqrt{3}}{2}\times\sqrt{31}\times\sqrt{2} = \frac{1}{2}\sqrt{186}$ | A1 [4] (AO 1.1) | Must be surd form FT their $AC$ |
---2 Fig. 2 shows a quadrilateral ABCD . The lengths AB and BC are 5 cm and 6 cm respectively. The angles $\mathrm { ABC } , \mathrm { ACD }$ and DAC are $60 ^ { \circ } , 60 ^ { \circ }$ and $75 ^ { \circ }$ respectively.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{a1b6c827-7d74-4527-9b60-58872e3d5ef7-3_547_643_740_242}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
Calculate the exact value of the length AD.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2020 Q2 [4]}}