CAIE P2 2019 March — Question 1 4 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2019
SessionMarch
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation with reciprocal functions
DifficultyStandard +0.3 This question requires knowledge of the identity sec²θ = 1 + tan²θ to convert to a quadratic in tan θ, then solve the resulting equation. It's a straightforward application of a standard identity with routine algebraic manipulation, making it slightly easier than average but not trivial due to the multi-step process and restricted domain consideration.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
1 Solve the equation \(\sec ^ { 2 } \theta + \tan ^ { 2 } \theta = 5 \tan \theta + 4\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\). Show all necessary working.
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Use identity \(\sec^2\theta = 1 + \tan^2\theta\)B1
Attempt solution of quadratic equation to find two values of \(\tan\theta\)M1
Obtain \(\tan\theta = -\frac{1}{2}\), \(3\)A1
Obtain \(71.6\) and \(153.4\) and no others between \(0\) and \(180\)A1
Total4 
**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use identity $\sec^2\theta = 1 + \tan^2\theta$ | B1 | |
| Attempt solution of quadratic equation to find two values of $\tan\theta$ | M1 | |
| Obtain $\tan\theta = -\frac{1}{2}$, $3$ | A1 | |
| Obtain $71.6$ and $153.4$ and no others between $0$ and $180$ | A1 | |
| **Total** | **4** | |

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1 Solve the equation $\sec ^ { 2 } \theta + \tan ^ { 2 } \theta = 5 \tan \theta + 4$ for $0 ^ { \circ } < \theta < 180 ^ { \circ }$. Show all necessary working.\\

\hfill \mbox{\textit{CAIE P2 2019 Q1 [4]}}
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Q1 4 Q2 4 Q3 5 Q4 6 Q5 9 Q6 11 Q7 11