CAIE P1 2006 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2006
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve equation with combined sin2x and cos2x
DifficultyModerate -0.8 This is a straightforward application of the R-formula or simple rearrangement (tan 2x = -3) followed by calculator work. It requires only one standard technique with no conceptual difficulty, making it easier than average but not trivial since students must handle the double angle and find all solutions in the given range.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
2 Solve the equation $$\sin 2 x + 3 \cos 2 x = 0$$ for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).
AnswerMarks Guidance
\(\tan 2x = -3\)M1 Use of \(\tan = \sin/\cos\) with "\(2x\)" "\(2x\)" in second quadrant.
\(2x = 180 - 71.6\) or \(2x = 360 - 71.6\)DM1
\(x = 54.2°\) or \(144.2°\)A1 A1 co. For \(90 + 1°\) answer.
Total: [4]
$\tan 2x = -3$ | M1 | Use of $\tan = \sin/\cos$ with "$2x$" "$2x$" in second quadrant.
$2x = 180 - 71.6$ or $2x = 360 - 71.6$ | DM1 | 
$x = 54.2°$ or $144.2°$ | A1 A1 | co. For $90 + 1°$ answer.

**Total: [4]**

---
2 Solve the equation

$$\sin 2 x + 3 \cos 2 x = 0$$

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

\hfill \mbox{\textit{CAIE P1 2006 Q2 [4]}}
This paper (11 questions)
View full paper
Q1 3 Q2 4 Q3 5 Q4 5 Q5 6 Q6 6 Q7 8 Q8 8 Q9 9 Q10 10 Q11 11