| Exam Board | CAIE |
|---|---|
| Module | P2 (Pure Mathematics 2) |
| Year | 2017 |
| Session | March |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Reciprocal Trig & Identities |
| Type | Double angle with reciprocal functions |
| Difficulty | Standard +0.3 This question requires applying the double angle formula for tan and the reciprocal identity for cot, then algebraic manipulation to reach a quadratic in tan θ. Part (i) is a structured 'show that' guiding students to the key result, and part (ii) is straightforward application once tan²θ is known. The multi-step nature and combination of identities elevates it slightly above average, but the scaffolding and standard techniques keep it accessible. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Use identity \(\cot\theta = \frac{1}{\tan\theta}\) | B1 | |
| Attempt use of identity for \(\tan 2\theta\) | M1 | |
| Confirm given \(\tan^2\theta = \frac{3}{4}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Obtain \(40.9\) | B1 | |
| Obtain \(139.1\) | B1 |
## Question 2(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| Use identity $\cot\theta = \frac{1}{\tan\theta}$ | B1 | |
| Attempt use of identity for $\tan 2\theta$ | M1 | |
| Confirm given $\tan^2\theta = \frac{3}{4}$ | A1 | |
## Question 2(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| Obtain $40.9$ | B1 | |
| Obtain $139.1$ | B1 | |
---2 (i) Given that $\tan 2 \theta \cot \theta = 8$, show that $\tan ^ { 2 } \theta = \frac { 3 } { 4 }$.\\
(ii) Hence solve the equation $\tan 2 \theta \cot \theta = 8$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$.\\
\hfill \mbox{\textit{CAIE P2 2017 Q2 [5]}}