OCR MEI Paper 1 2018 June — Question 3 4 marks

Exam BoardOCR MEI
ModulePaper 1 (Paper 1)
Year2018
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyStandard +0.3 This is a standard trigonometric equation requiring the Pythagorean identity sec²θ = 1 + tan²θ to convert to a quadratic in tan θ, then solve and find angles in the given range. It's slightly easier than average as it follows a well-practiced procedure with no conceptual surprises, though it does require multiple steps and careful angle finding.
Spec1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
3 In this question you must show detailed reasoning.
Solve the equation \(\sec ^ { 2 } \theta + 2 \tan \theta = 4\) for \(0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }\).
Question 3:
AnswerMarks Guidance
AnswerMarks Guidance
\((1+\tan^2\theta) + 2\tan\theta = 4\)M1 Using appropriate trig identity; must attempt to reach equation with only one trig function
\(\tan^2\theta + 2\tan\theta - 3 = 0\)M1 Showing algebraic method for solving their quadratic
\((\tan\theta - 1)(\tan\theta + 3) = 0\)
When \(\tan\theta = 1\): \(\theta = 45°, 225°\)A1 Any two correct values for \(\theta\)
When \(\tan\theta = -3\): \(\theta = 108.4°, 288.4°\)A1 [4] All correct values for \(\theta\) and no extras in interval; ignore values outside required interval 
## Question 3:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $(1+\tan^2\theta) + 2\tan\theta = 4$ | M1 | Using appropriate trig identity; must attempt to reach equation with only one trig function |
| $\tan^2\theta + 2\tan\theta - 3 = 0$ | M1 | Showing algebraic method for solving their quadratic |
| $(\tan\theta - 1)(\tan\theta + 3) = 0$ | | |
| When $\tan\theta = 1$: $\theta = 45°, 225°$ | A1 | Any two correct values for $\theta$ |
| When $\tan\theta = -3$: $\theta = 108.4°, 288.4°$ | A1 [4] | All correct values for $\theta$ and no extras in interval; ignore values outside required interval |

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3 In this question you must show detailed reasoning.\\
Solve the equation $\sec ^ { 2 } \theta + 2 \tan \theta = 4$ for $0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }$.

\hfill \mbox{\textit{OCR MEI Paper 1 2018 Q3 [4]}}
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Q1 3 Q2 2 Q3 4 Q4 4 Q5 4 Q6 6 Q7 3 Q8 6 Q9 10 Q10 8 Q11 7 Q12 14 Q13 12 Q14 17