OCR MEI C4 2006 June — Question 3 8 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2006
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeExpand compound angle then solve
DifficultyStandard +0.3 This is a straightforward two-part question requiring expansion of sin(θ+α) using the addition formula, algebraic manipulation to isolate tan θ, then substitution of α=40° and calculator work. The 'show that' structure guides students through the method, and the techniques are standard C4 material with no novel insight required. Slightly easier than average due to the scaffolding.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

3 Given that \(\sin ( \theta + \alpha ) = 2 \sin \theta\), show that \(\tan \theta = \frac { \sin \alpha } { 2 - \cos \alpha }\). Hence solve the equation \(\sin \left( \theta + 40 ^ { \circ } \right) = 2 \sin \theta\), for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).

Question 3:
AnswerMarks Guidance
AnswerMark Guidance
The linear model gives a record time greater than 120 minutes for all values of \(t\) (i.e. \(R > 120\) for all \(t\) in the model's range)B1 Accept equivalent explanation that the line never reaches 120 minutes
# Question 3:

| Answer | Mark | Guidance |
|--------|------|----------|
| The linear model gives a record time greater than 120 minutes for all values of $t$ (i.e. $R > 120$ for all $t$ in the model's range) | B1 | Accept equivalent explanation that the line never reaches 120 minutes |

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3 Given that $\sin ( \theta + \alpha ) = 2 \sin \theta$, show that $\tan \theta = \frac { \sin \alpha } { 2 - \cos \alpha }$.

Hence solve the equation $\sin \left( \theta + 40 ^ { \circ } \right) = 2 \sin \theta$, for $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C4 2006 Q3 [8]}}