OCR MEI C4 2006 January — Question 4 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2006
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeDouble angle equations requiring identity expansion and factorisation
DifficultyModerate -0.3 This is a straightforward double angle equation requiring substitution of standard identities (sin 2θ and cos 2θ), rearrangement into a single trigonometric function, and solving within a given range. While it involves multiple steps, the techniques are standard C4 material with no novel problem-solving required, making it slightly easier than average.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
4 Solve the equation \(2 \sin 2 \theta + \cos 2 \theta = 1\), for \(0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }\).
Question 4(i): Relationship between interval endpoints and Table 5
AnswerMarks Guidance
AnswerMark Guidance
The endpoints correspond to values \(\frac{V_k}{N_k}\) from Table 5B1
Example given, e.g. upper endpoint 22.2 corresponds to \(V_A/N_A = 22.2/1 = 22.2\)B1 Correct example stated
Question 4(ii): Complete the table
AnswerMarks Guidance
AnswerMark Guidance
Seats=3: \(13.5 < a \leq 16.6\); Seats=4: \(11.1 < a \leq 13.5\); Seats=5: \(11.1 < a \leq 11.2\); Seats=7: \(10.6 < a \leq 11.1\)B1 All missing intervals correct 
# Question 4(i): Relationship between interval endpoints and Table 5

| Answer | Mark | Guidance |
|--------|------|----------|
| The endpoints correspond to values $\frac{V_k}{N_k}$ from Table 5 | B1 | |
| Example given, e.g. upper endpoint 22.2 corresponds to $V_A/N_A = 22.2/1 = 22.2$ | B1 | Correct example stated |

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# Question 4(ii): Complete the table

| Answer | Mark | Guidance |
|--------|------|----------|
| Seats=3: $13.5 < a \leq 16.6$; Seats=4: $11.1 < a \leq 13.5$; Seats=5: $11.1 < a \leq 11.2$; Seats=7: $10.6 < a \leq 11.1$ | B1 | All missing intervals correct |

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4 Solve the equation $2 \sin 2 \theta + \cos 2 \theta = 1$, for $0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C4 2006 Q4 [6]}}
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