OCR MEI C3 2016 June — Question 1 3 marks

Exam BoardOCR MEI
ModuleC3 (Core Mathematics 3)
Year2016
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeTrigonometric integration
DifficultyModerate -0.8 This is a straightforward integration question requiring only basic knowledge of integrating constants and cosine functions, with a simple substitution for the coefficient. The limits are clean and the 'exact value' requirement is routine for this topic. Below average difficulty as it's purely procedural with no problem-solving element.
Spec1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)
Find the exact value of \(\int_0^{\frac{1}{4}\pi} (1 + \cos \frac{1}{2}x) dx\). [3]
AnswerMarks Guidance
Answer: \(x + 2\sin\frac{1}{2}x\)Marks: B1 Guidance: Must be exact, not \(2/\sqrt{2}\); isw from correct answer seen
Answer: Substituting limits (upper – lower)Marks: M1 Guidance: Allow 1 slip
Answer: \(= \frac{\pi}{2} + 2\sin\frac{\pi}{4} - [0] = \frac{\pi}{2} + \sqrt{2}\)Marks: A1cao Guidance: (none)
Total Marks: [3]
**Answer:** $x + 2\sin\frac{1}{2}x$ | **Marks:** B1 | **Guidance:** Must be exact, not $2/\sqrt{2}$; isw from correct answer seen

**Answer:** Substituting limits (upper – lower) | **Marks:** M1 | **Guidance:** Allow 1 slip

**Answer:** $= \frac{\pi}{2} + 2\sin\frac{\pi}{4} - [0] = \frac{\pi}{2} + \sqrt{2}$ | **Marks:** A1cao | **Guidance:** (none)

**Total Marks:** [3]

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Find the exact value of $\int_0^{\frac{1}{4}\pi} (1 + \cos \frac{1}{2}x) dx$. [3]

\hfill \mbox{\textit{OCR MEI C3 2016 Q1 [3]}}
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