CAIE P2 2020 Specimen — Question 2 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2020
SessionSpecimen
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeDouble angle with reciprocal functions
DifficultyStandard +0.3 This is a straightforward double angle equation requiring expansion of sin 2θ to 2sin θ cos θ, then simplifying with tan θ = sin θ/cos θ to get a basic trigonometric equation. It's slightly easier than average as it follows a standard procedure with no conceptual surprises, though it does require knowing the double angle formula and careful algebraic manipulation.
Spec1.05o Trigonometric equations: solve in given intervals

2 Solve the equation \(3 \sin 2 \theta \tan \theta = 2\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Use \(\sin 2\theta = 2\sin\theta\cos\theta\)B1
Simplify to obtain form \(c_1\sin^2\theta = c_2\cos\theta\) or equivalentM1
Find at least one value of \(\theta\) from equation of form \(\sin\theta = k\)M1
Obtain \(35.3°\) and \(144.7°\)A1 And no others between \(0°\) and \(180°\). Unsupported answer receives 0 marks.
Total4
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use $\sin 2\theta = 2\sin\theta\cos\theta$ | B1 | |
| Simplify to obtain form $c_1\sin^2\theta = c_2\cos\theta$ or equivalent | M1 | |
| Find at least one value of $\theta$ from equation of form $\sin\theta = k$ | M1 | |
| Obtain $35.3°$ and $144.7°$ | A1 | And no others between $0°$ and $180°$. Unsupported answer receives 0 marks. |
| **Total** | **4** | |

---
2 Solve the equation $3 \sin 2 \theta \tan \theta = 2$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.\\

\hfill \mbox{\textit{CAIE P2 2020 Q2 [4]}}