OCR MEI C4 — Question 3 5 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyStandard +0.3 This is a straightforward application of the Pythagorean identity sec²θ = 1 + tan²θ to convert to a quadratic in tan θ, then solve using standard methods. While it requires knowledge of reciprocal trig functions and identities, the problem-solving path is direct and mechanical, making it slightly easier than average.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
3 Solve the equation \(\sec ^ { 2 } \theta = 2 \tan \theta + 4\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\).
Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
\(\sec^2\theta=2\tan\theta+4 \Rightarrow 1+\tan^2\theta=2\tan\theta+4\)M1, A1 Use of identity
\(\Rightarrow \tan^2\theta-2\tan\theta-3=0\)
\(\Rightarrow(\tan\theta-3)(\tan\theta+1)=0\)M1 Factorising
\(\tan\theta=3 \Rightarrow \theta=71.6°,\ 251.6°\)A1 both
\(\tan\theta=-1 \Rightarrow \theta=135°,\ 315°\)A1 both
Total: 5 marks
## Question 3:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\sec^2\theta=2\tan\theta+4 \Rightarrow 1+\tan^2\theta=2\tan\theta+4$ | M1, A1 | Use of identity |
| $\Rightarrow \tan^2\theta-2\tan\theta-3=0$ | |  |
| $\Rightarrow(\tan\theta-3)(\tan\theta+1)=0$ | M1 | Factorising |
| $\tan\theta=3 \Rightarrow \theta=71.6°,\ 251.6°$ | A1 | both |
| $\tan\theta=-1 \Rightarrow \theta=135°,\ 315°$ | A1 | both |

**Total: 5 marks**

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3 Solve the equation $\sec ^ { 2 } \theta = 2 \tan \theta + 4$ for $0 ^ { \circ } < \theta < 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI C4  Q3 [5]}}
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