OCR MEI C4 2009 June — Question 6 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyStandard +0.3 This is a straightforward trigonometric identity manipulation using the standard identity cosec²θ = 1 + cot²θ, followed by solving a simple quadratic equation in cotθ. The 'show that' structure guides students through the algebraic steps, and the final solving requires only basic knowledge of cotangent values. Slightly easier than average due to the scaffolding and routine techniques involved.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
Given that \(\cos\text{ec}^2\theta - \cot\theta = 3\), show that \(\cot^2\theta - \cot\theta - 2 = 0\). Hence solve the equation \(\cos\text{ec}^2\theta - \cot\theta = 3\) for \(0° \leq \theta \leq 180°\). [6]
AnswerMarks
(i) All scores are increased by two points per roundB1
(ii) The same player wins. No difference/change. The rank order of the players remains the same.B1 
**(i)** All scores are increased by two points per round | B1 |
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**(ii)** The same player wins. No difference/change. The rank order of the players remains the same. | B1 |
Given that $\cos\text{ec}^2\theta - \cot\theta = 3$, show that $\cot^2\theta - \cot\theta - 2 = 0$.

Hence solve the equation $\cos\text{ec}^2\theta - \cot\theta = 3$ for $0° \leq \theta \leq 180°$. [6]

\hfill \mbox{\textit{OCR MEI C4 2009 Q6 [6]}}
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Q1 7 Q2 7 Q3 4 Q4 5 Q5 7 Q6 6 Q7 17 Q8 19