CAIE P2 2012 November — Question 3 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2012
SessionNovember
Marks4
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 the standard substitution cos 2θ = 2cos²θ - 1, leading to a quadratic in cos θ. The restricted domain and simple coefficients make it slightly easier than average, though it does require multiple steps (substitution, factorization, solving, checking domain).
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
3 Solve the equation $$2 \cos 2 \theta = 4 \cos \theta - 3$$ for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).
AnswerMarks Guidance
Make relevant use of the \(\cos 2\theta\) formulaM1
Obtain a correct quadratic in \(\cos \theta\)A1
Solve a quadratic in \(\cos \theta\)M1
Obtain answer \(\theta = 60\) and no others in the range (Ignore answers outside the given range)A1 [4] 
Make relevant use of the $\cos 2\theta$ formula | M1 |
Obtain a correct quadratic in $\cos \theta$ | A1 |
Solve a quadratic in $\cos \theta$ | M1 |
Obtain answer $\theta = 60$ and no others in the range (Ignore answers outside the given range) | A1 | [4]
3 Solve the equation

$$2 \cos 2 \theta = 4 \cos \theta - 3$$

for $0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }$.

\hfill \mbox{\textit{CAIE P2 2012 Q3 [4]}}
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