OCR MEI C2 — Question 8 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSine and Cosine Rules
TypeBasic sine rule application
DifficultyModerate -0.8 This is a straightforward application of the sine rule to find an angle given two sides and one angle. It requires only direct substitution into the formula a/sin A = b/sin B and solving for the unknown angle, which is a routine C2-level exercise with no problem-solving complexity.
Spec1.05b Sine and cosine rules: including ambiguous case
8 In the triangle ABC shown, \(\mathrm { AB } = 8 \mathrm {~cm}\). \(\mathrm { AC } = 12 \mathrm {~cm}\) and angle \(\mathrm { ABC } = 82 ^ { \circ }\). Find \(\theta\) correct to 3 significant figures. \includegraphics[max width=\textwidth, alt={}, center]{1c52d6b5-84b4-455a-9620-c377ae457069-3_382_540_1492_718}
AnswerMarks Guidance
\(\frac{\sin 82°}{12} = \frac{\sin \theta}{8}\)M1, A1 Use of sine rule
\(\sin \theta = 8 \times \frac{\sin 82°}{12}\)M1 Correct solution process to extract \(\theta\)
\(\theta = 41.3°\)A1 c.a.o 
$\frac{\sin 82°}{12} = \frac{\sin \theta}{8}$ | M1, A1 | Use of sine rule
$\sin \theta = 8 \times \frac{\sin 82°}{12}$ | M1 | Correct solution process to extract $\theta$
$\theta = 41.3°$ | A1 | c.a.o | **Total: 4 marks**
8 In the triangle ABC shown, $\mathrm { AB } = 8 \mathrm {~cm}$. $\mathrm { AC } = 12 \mathrm {~cm}$ and angle $\mathrm { ABC } = 82 ^ { \circ }$. Find $\theta$ correct to 3 significant figures.\\
\includegraphics[max width=\textwidth, alt={}, center]{1c52d6b5-84b4-455a-9620-c377ae457069-3_382_540_1492_718}

\hfill \mbox{\textit{OCR MEI C2  Q8 [4]}}
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Q1 5 Q2 3 Q3 4 Q4 5 Q5 5 Q6 5 Q7 5 Q8 4 Q9 12 Q10 12 Q11 12