CAIE P2 2020 March — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeSolve with multiple compound angles
DifficultyStandard +0.3 This requires expanding the compound angle using the addition formula, collecting terms, and solving a linear trigonometric equation. It's slightly above average due to the algebraic manipulation needed after expansion, but follows a standard procedure with no novel insight required.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
1 Solve the equation \(2 \sin \left( \theta + 30 ^ { \circ } \right) + 5 \cos \theta = 2 \sin \theta\) for \(0 ^ { \circ } < \theta < 90 ^ { \circ }\).
Question 1:
AnswerMarks Guidance
AnswerMark Guidance
Express first term as \(2\sin\theta\cos30 + 2\cos\theta\sin30\)B1
Divide by \(\cos\theta\) to produce linear equation in \(\tan\theta\)M1
Obtain \(\tan\theta = \frac{6}{2-\sqrt{3}}\) or \(22.39...\)A1
Obtain \(87.4\)A1 Or greater accuracy \(87.44297...\)
Total4 
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| Express first term as $2\sin\theta\cos30 + 2\cos\theta\sin30$ | B1 | |
| Divide by $\cos\theta$ to produce linear equation in $\tan\theta$ | M1 | |
| Obtain $\tan\theta = \frac{6}{2-\sqrt{3}}$ or $22.39...$ | A1 | |
| Obtain $87.4$ | A1 | Or greater accuracy $87.44297...$ |
| **Total** | **4** | |

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1 Solve the equation $2 \sin \left( \theta + 30 ^ { \circ } \right) + 5 \cos \theta = 2 \sin \theta$ for $0 ^ { \circ } < \theta < 90 ^ { \circ }$.\\

\hfill \mbox{\textit{CAIE P2 2020 Q1 [4]}}
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Q1 4 Q2 6 Q3 6 Q4 6 Q5 9 Q6 9 Q7 10