OCR MEI C4 — Question 1 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve equation with sin2x/cos2x by substitution
DifficultyModerate -0.3 This is a straightforward double angle equation requiring the standard substitution sin 2θ = 2sin θ cos θ, factorisation, and solving basic trigonometric equations. It's slightly easier than average as it follows a standard template with no unusual complications, though it does require multiple steps and careful consideration of the full range of solutions.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
1 Solve the equation \(2 \sin 2 \theta = \cos \theta\) for \(0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
\(2\sin 2\theta = \cos\theta\)M1 Use of double angle formula
\(\Rightarrow 4\sin\theta\cos\theta = \cos\theta\)
\(\Rightarrow \cos\theta = 0\) or \(4\sin\theta = 1\)M1 Solve
\(\Rightarrow \sin\theta = 0.25\)A1 B1 for last two only
\(\Rightarrow \theta = 90\) or \(270\) or \(14.5\) or \(165.5\)A1
Total: 4 marks 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $2\sin 2\theta = \cos\theta$ | M1 | Use of double angle formula |
| $\Rightarrow 4\sin\theta\cos\theta = \cos\theta$ | | |
| $\Rightarrow \cos\theta = 0$ or $4\sin\theta = 1$ | M1 | Solve |
| $\Rightarrow \sin\theta = 0.25$ | A1 | B1 for last two only |
| $\Rightarrow \theta = 90$ or $270$ or $14.5$ or $165.5$ | A1 | |
| **Total: 4 marks** | | |

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1 Solve the equation $2 \sin 2 \theta = \cos \theta$ for $0 ^ { \circ } \leq \theta \leq 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C4  Q1 [4]}}
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Q1 4 Q2 4 Q3 5 Q4 8 Q5 7 Q6 4 Q7 4 Q8 18 Q9 18