CAIE P2 2023 November — Question 1 3 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2023
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeGiven sin/cos/tan, find other expressions
DifficultyModerate -0.8 This is a straightforward application of the addition formula sin(A+B) = sinAcosB + cosAsinB with standard angle 60°. Students need to find cos θ from sin θ using Pythagoras, then substitute known values. It's routine bookwork with clear method and minimal steps, making it easier than average.
Spec1.05l Double angle formulae: and compound angle formulae
1 It is given that \(\theta\) is an acute angle in degrees such that \(\sin \theta = \frac { 2 } { 3 }\).
Find the exact value of \(\sin \left( \theta + 60 ^ { \circ } \right)\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
State or imply that \(\cos\theta = \frac{1}{3}\sqrt{5}\)B1 or exact equivalent
Substitute appropriate values into \(\sin\theta\cos60° + \cos\theta\sin60°\)M1
Obtain \(\frac{1}{3} + \frac{1}{6}\sqrt{15}\)A1 or exact equivalent
Total3 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| State or imply that $\cos\theta = \frac{1}{3}\sqrt{5}$ | B1 | or exact equivalent |
| Substitute appropriate values into $\sin\theta\cos60° + \cos\theta\sin60°$ | M1 | |
| Obtain $\frac{1}{3} + \frac{1}{6}\sqrt{15}$ | A1 | or exact equivalent |
| **Total** | **3** | |

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1 It is given that $\theta$ is an acute angle in degrees such that $\sin \theta = \frac { 2 } { 3 }$.\\
Find the exact value of $\sin \left( \theta + 60 ^ { \circ } \right)$.\\

\hfill \mbox{\textit{CAIE P2 2023 Q1 [3]}}
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