CAIE P2 2004 November — Question 3 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2004
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 sin 2x = 2sin x cos x, factorising cos x, then solving two simple equations. It's slightly easier than average because it's restricted to the first quadrant only and involves routine algebraic manipulation with no conceptual challenges.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
3 Find the values of \(x\) satisfying the equation $$3 \sin 2 x = \cos x$$ for \(0 ^ { \circ } \leqslant x \leqslant 90 ^ { \circ }\).
Question 3:
AnswerMarks Guidance
Answer/WorkingMark Guidance
State answer \(x = 90°\) (c.w.o)B1
Write equation in form \(6\sin x \cos x = \cos x\)B1
Remove factor of \(\cos x\) and solve equation in \(\sin x\) for \(x\)M1
Obtain answer \(x = 9.59°\) and no others in range (\(9.6°\) OK: rubric)A1 Total: 4
Ignore answers outside given range 
## Question 3:

| Answer/Working | Mark | Guidance |
|---|---|---|
| State answer $x = 90°$ (c.w.o) | B1 | |
| Write equation in form $6\sin x \cos x = \cos x$ | B1 | |
| Remove factor of $\cos x$ and solve equation in $\sin x$ for $x$ | M1 | |
| Obtain answer $x = 9.59°$ and no others in range ($9.6°$ OK: rubric) | A1 | **Total: 4** |
| | | Ignore answers outside given range |

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3 Find the values of $x$ satisfying the equation

$$3 \sin 2 x = \cos x$$

for $0 ^ { \circ } \leqslant x \leqslant 90 ^ { \circ }$.

\hfill \mbox{\textit{CAIE P2 2004 Q3 [4]}}
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Q1 3 Q2 3 Q3 4 Q4 5 Q5 6 Q6 8 Q7 11 Q8 10