| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2020 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Given sin/cos/tan, find other expressions |
| Difficulty | Standard +0.3 This question requires applying the double angle formula sin 2θ = 2sin θ cos θ, then solving a quadratic equation to find sin θ, followed by straightforward use of Pythagorean identity and double angle formula for cosine. While it involves multiple steps and exact value manipulation, the techniques are standard and the path is clear once the double angle formula is applied. Slightly above average due to the algebraic manipulation required, but well within typical P2 expectations. |
| Spec | 1.05g Exact trigonometric values: for standard angles1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Use \(\sin 2\theta = 2\sin\theta\cos\theta\) | B1 | |
| Obtain \(\sin\theta = \frac{1}{6}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Use correct identity or identities to find value of \(\sec\theta\) | M1 | |
| Obtain \(\frac{6}{\sqrt{35}}\) or exact equivalent | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Use correct identity or identities to find value of \(\cos 2\theta\) | M1 | |
| Obtain \(\frac{17}{18}\) or exact equivalent | A1 |
## Question 6(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Use $\sin 2\theta = 2\sin\theta\cos\theta$ | B1 | |
| Obtain $\sin\theta = \frac{1}{6}$ | B1 | |
## Question 6(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Use correct identity or identities to find value of $\sec\theta$ | M1 | |
| Obtain $\frac{6}{\sqrt{35}}$ or exact equivalent | A1 | |
## Question 6(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Use correct identity or identities to find value of $\cos 2\theta$ | M1 | |
| Obtain $\frac{17}{18}$ or exact equivalent | A1 | |6 It is given that $3 \sin 2 \theta = \cos \theta$ where $\theta$ is an angle such that $0 ^ { \circ } < \theta < 90 ^ { \circ }$.
\begin{enumerate}[label=(\alph*)]
\item Find the exact value of $\sin \theta$.
\item Find the exact value of $\sec \theta$.
\item Find the exact value of $\cos 2 \theta$.
\end{enumerate}
\hfill \mbox{\textit{CAIE P2 2020 Q6 [6]}}