CAIE P2 2016 June — Question 2 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2016
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeDouble angle equations requiring identity expansion and factorisation
DifficultyStandard +0.3 This requires using the double angle formula for tan(2θ) and converting cot to tan, then solving a resulting quadratic in tan(θ). It's a standard double angle equation with straightforward algebraic manipulation, slightly above average due to the multiple steps and need to handle the quadratic, but well within typical A-level expectations with no novel insight required.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals
2 Solve the equation \(5 \tan 2 \theta = 4 \cot \theta\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).
AnswerMarks
Use \(\cot\theta = 1 + \tan\theta\)B1
Form equation involving \(\tan\theta\) only and with no denominators involving \(\theta\)M1
Obtain \(\tan^2\theta = \frac{2}{3}\)A1
Obtain 28.1A1
Obtain 151.9A1
Allow other valid methods[5] 
Use $\cot\theta = 1 + \tan\theta$ | B1 |
Form equation involving $\tan\theta$ only and with no denominators involving $\theta$ | M1 |
Obtain $\tan^2\theta = \frac{2}{3}$ | A1 |
Obtain 28.1 | A1 |
Obtain 151.9 | A1 |
Allow other valid methods | [5]
2 Solve the equation $5 \tan 2 \theta = 4 \cot \theta$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.

\hfill \mbox{\textit{CAIE P2 2016 Q2 [5]}}
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