OCR MEI C4 2008 January — Question 1 7 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2008
SessionJanuary
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicHarmonic Form
TypeExpress and solve equation
DifficultyModerate -0.3 This is a standard two-part harmonic form question requiring routine application of the R cos(θ - α) formula (R = 5, α = arctan(4/3)) followed by solving a straightforward trigonometric equation. While it involves multiple steps, both parts follow textbook procedures with no novel insight required, making it slightly easier than average.
Spec1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc1.05o Trigonometric equations: solve in given intervals
1 Express \(3 \cos \theta + 4 \sin \theta\) in the form \(R \cos ( \theta - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
Hence solve the equation \(3 \cos \theta + 4 \sin \theta = 2\) for \(- \pi \leqslant \theta \leqslant \pi\).
AnswerMarks Guidance
4, 1, 5, 6, 11, 17B1 B1 for 11 and 17; for 1 and 4 
4, 1, 5, 6, 11, 17 | B1 B1 | for 11 and 17; for 1 and 4
1 Express $3 \cos \theta + 4 \sin \theta$ in the form $R \cos ( \theta - \alpha )$, where $R > 0$ and $0 < \alpha < \frac { 1 } { 2 } \pi$.\\
Hence solve the equation $3 \cos \theta + 4 \sin \theta = 2$ for $- \pi \leqslant \theta \leqslant \pi$.

\hfill \mbox{\textit{OCR MEI C4 2008 Q1 [7]}}
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Q1 7 Q2 8 Q3 5 Q4 7 Q5 6 Q6 3 Q7 18 Q8 18