OCR MEI C4 2013 January — Question 5 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2013
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeSolve equation using Pythagorean identities
DifficultyModerate -0.3 This is a straightforward application of the Pythagorean identity sec²θ = 1 + tan²θ to convert to a quadratic in tan θ, then solve. It requires standard technique (substitution and factorization) with no novel insight, making it slightly easier than average but still requiring proper execution of multiple steps.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05o Trigonometric equations: solve in given intervals
5 Solve the equation \(2 \sec ^ { 2 } \theta = 5 \tan \theta\), for \(0 \leqslant \theta \leqslant \pi\).
Question 5:
AnswerMarks Guidance
AnswerMark Guidance
Routes from \((0,0)\) to \((3,2)\): \(\binom{5}{2} = 10\)M1 Correct method for either sub-journey
Routes from \((3,2)\) to \((4,3)\): \(\binom{2}{1} = 2\)
\(10 \times 2 = 20\) routes pass through \((3,2)\)A1 [2] 
# Question 5:

| Answer | Mark | Guidance |
|--------|------|----------|
| Routes from $(0,0)$ to $(3,2)$: $\binom{5}{2} = 10$ | M1 | Correct method for either sub-journey |
| Routes from $(3,2)$ to $(4,3)$: $\binom{2}{1} = 2$ | | |
| $10 \times 2 = 20$ routes pass through $(3,2)$ | A1 | [2] |

---
5 Solve the equation $2 \sec ^ { 2 } \theta = 5 \tan \theta$, for $0 \leqslant \theta \leqslant \pi$.

\hfill \mbox{\textit{OCR MEI C4 2013 Q5 [6]}}
This paper (7 questions)
View full paper
Q2 6 Q3 7 Q4 8 Q5 6 Q6 5 Q7 17 Q8 19