OCR MEI C2 — Question 7 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicQuadratic trigonometric equations
TypeDirect solve: sin²/cos² substitution
DifficultyModerate -0.3 This is a straightforward trigonometric equation requiring the standard substitution sin²θ = 1 - cos²θ to form a quadratic in cos²θ, then solving for θ in the given range. It's slightly easier than average as it follows a well-practiced method with no conceptual surprises, though it does require multiple steps and careful attention to finding all solutions in the range.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
7 Showing your method clearly, solve the equation \(4 \sin ^ { 2 } \theta = 3 + \cos ^ { 2 } \theta\), for values of \(\theta\) between \(0 ^ { \circ }\) and \(360 ^ { \circ }\).
Question 7:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Substitution of \(1-\cos^2\theta\) or \(1-\sin^2\theta\)M1
\(5\cos^2\theta = 1\) or \(5\sin^2\theta = 4\)A1
\(\cos\theta = \pm\sqrt{\text{their }\frac{1}{5}}\) or \(\sin\theta = \pm\sqrt{\text{their }\frac{4}{5}}\) o.e.M1
\(63.4, 116.6, 243.4, 296.6\)B2 Accept to nearest degree or better; B1 for 2 correct (ignore any extra values in range) 
## Question 7:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Substitution of $1-\cos^2\theta$ or $1-\sin^2\theta$ | M1 | |
| $5\cos^2\theta = 1$ or $5\sin^2\theta = 4$ | A1 | |
| $\cos\theta = \pm\sqrt{\text{their }\frac{1}{5}}$ or $\sin\theta = \pm\sqrt{\text{their }\frac{4}{5}}$ o.e. | M1 | |
| $63.4, 116.6, 243.4, 296.6$ | B2 | Accept to nearest degree or better; **B1** for 2 correct (ignore any extra values in range) |

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7 Showing your method clearly, solve the equation $4 \sin ^ { 2 } \theta = 3 + \cos ^ { 2 } \theta$, for values of $\theta$ between $0 ^ { \circ }$ and $360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C2  Q7 [5]}}
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Q1 5 Q2 11 Q3 3 Q4 3 Q5 5 Q6 4 Q7 5 Q8 5 Q9 5 Q10 5