CAIE P1 2012 June — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicStandard trigonometric equations
TypeSimple double angle equations (direct substitution)
DifficultyModerate -0.3 This is a straightforward double angle equation requiring division to get tan 2x = 2, then solving in the appropriate range. It's slightly easier than average as it's a direct application of a standard technique with no complications, though students must remember to find all solutions for 2x in [0°, 360°] before dividing by 2.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
1 Solve the equation \(\sin 2 x = 2 \cos 2 x\), for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\tan 2x = 2\)M1
\(2x = 63.4\) or \(243.4\)A1 1 solution sufficient
\(x = 31.7\) or \(121.7\) (allow 122)A1A1 [4] For 2nd A1 allow \(90 + 1^{st}\) soln. Only 2 solns in range. Alt methods possible 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\tan 2x = 2$ | M1 | |
| $2x = 63.4$ or $243.4$ | A1 | 1 solution sufficient |
| $x = 31.7$ or $121.7$ (allow 122) | A1A1 [4] | For 2nd A1 allow $90 + 1^{st}$ soln. Only 2 solns in range. Alt methods possible |

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1 Solve the equation $\sin 2 x = 2 \cos 2 x$, for $0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }$.

\hfill \mbox{\textit{CAIE P1 2012 Q1 [4]}}
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