OCR MEI C2 — Question 5 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
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Mark schemeDownload PDF ↗
TopicSine and Cosine Rules
TypeTriangle area calculation
DifficultyModerate -0.8 This is a straightforward application of the cosine rule to find an angle, followed by using the standard triangle area formula (½ab sin C). It's a routine two-step calculation with no conceptual challenges—easier than average since it's a direct application of standard formulas with all three sides given.
Spec1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C)
5 Fig. 7 shows a sketch of a village green ABC which is bounded by three straight roads. \(\mathrm { AB } = 92 \mathrm {~m}\), \(\mathrm { BC } = 75 \mathrm {~m}\) and \(\mathrm { AC } = 105 \mathrm {~m}\). Fig. 7 Calculate the area of the village green.
Question 5:
AnswerMarks Guidance
AnswerMark Guidance
\(\cos A = \frac{105^2 + 92^2 - 75^2}{2 \times 105 \times 92}\) oeM1 or \(\cos B = \frac{75^2 + 92^2 - 105^2}{2 \times 75 \times 92}\) oe; or \(\cos C = \frac{105^2 + 75^2 - 92^2}{2 \times 105 \times 75}\) oe
\(0.717598...\) soiA1 \(0.2220289...\) soi; \(0.519746...\) soi
\(A = 44.14345...°\) soi \([0.770448553...]\)A1 \(B = 77.1717719...°\) soi \([1.346901422]\); \(C = 58.6847827...°\) soi \([1.024242678...]\); ignore minor errors due to premature rounding for second A1; condone \(A\), \(B\) or \(C\) wrongly attributed
\(\frac{1}{2} \times 92 \times 105 \times \sin(\text{their }A)\)M1 or \(\frac{1}{2} \times 75 \times 92 \times \sin(\text{their }B)\); or \(\frac{1}{2} \times 75 \times 105 \times \sin(\text{their }C)\)
3360 or 3361 to 3365A1 or M3 for \(\sqrt{136(136-75)(136-105)(136-92)}\); A2 for correct answer 3360 or 3363–3364 
## Question 5:

| Answer | Mark | Guidance |
|--------|------|----------|
| $\cos A = \frac{105^2 + 92^2 - 75^2}{2 \times 105 \times 92}$ oe | M1 | or $\cos B = \frac{75^2 + 92^2 - 105^2}{2 \times 75 \times 92}$ oe; or $\cos C = \frac{105^2 + 75^2 - 92^2}{2 \times 105 \times 75}$ oe |
| $0.717598...$ soi | A1 | $0.2220289...$ soi; $0.519746...$ soi |
| $A = 44.14345...°$ soi $[0.770448553...]$ | A1 | $B = 77.1717719...°$ soi $[1.346901422]$; $C = 58.6847827...°$ soi $[1.024242678...]$; ignore minor errors due to premature rounding for second A1; condone $A$, $B$ or $C$ wrongly attributed |
| $\frac{1}{2} \times 92 \times 105 \times \sin(\text{their }A)$ | M1 | or $\frac{1}{2} \times 75 \times 92 \times \sin(\text{their }B)$; or $\frac{1}{2} \times 75 \times 105 \times \sin(\text{their }C)$ |
| 3360 or 3361 to 3365 | A1 | **or M3** for $\sqrt{136(136-75)(136-105)(136-92)}$; **A2** for correct answer 3360 or 3363–3364 |

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5 Fig. 7 shows a sketch of a village green ABC which is bounded by three straight roads. $\mathrm { AB } = 92 \mathrm {~m}$, $\mathrm { BC } = 75 \mathrm {~m}$ and $\mathrm { AC } = 105 \mathrm {~m}$.

Fig. 7

Calculate the area of the village green.

\hfill \mbox{\textit{OCR MEI C2  Q5 [5]}}
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Q2 14 Q3 5 Q4 11 Q5 5 Q6 5