OCR MEI Paper 1 2019 June — Question 1 3 marks

Exam BoardOCR MEI
ModulePaper 1 (Paper 1)
Year2019
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeShow definite integral equals value
DifficultyEasy -1.2 This is a straightforward definite integration question requiring only basic integration rules (power rule for x and x^{1/2}) and arithmetic evaluation at limits. It's easier than average because it's purely procedural with no problem-solving element—students simply apply standard techniques and verify the given answer through calculation.
Spec1.08b Integrate x^n: where n != -1 and sums1.08d Evaluate definite integrals: between limits
1 In this question you must show detailed reasoning. Show that \(\int _ { 4 } ^ { 9 } ( 2 x + \sqrt { x } ) \mathrm { d } x = \frac { 233 } { 3 }\).
Question 1:
DR (Detailed Reasoning required)
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\int_4^9 \left(2x + x^{\frac{1}{2}}\right) dx = \left[x^2 + \frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_4^9\)M1* AO2.1 — Attempt to integrate using fractional power
\(\left(9^2 + \frac{2}{3} \times 9^{\frac{3}{2}}\right) - \left(4^2 + \frac{2}{3} \times 4^{\frac{3}{2}}\right)\)M1(dep) AO2.1 — Use of limits must be seen
\(\left[81 + 18 - 16 - \frac{16}{3}\right] = \frac{233}{3}\)A1 AO2.1 — AG: Any interim working must be correct
[3] 
## Question 1:

**DR** (Detailed Reasoning required)

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\int_4^9 \left(2x + x^{\frac{1}{2}}\right) dx = \left[x^2 + \frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_4^9$ | M1* | AO2.1 — Attempt to integrate using fractional power |
| $\left(9^2 + \frac{2}{3} \times 9^{\frac{3}{2}}\right) - \left(4^2 + \frac{2}{3} \times 4^{\frac{3}{2}}\right)$ | M1(dep) | AO2.1 — Use of limits must be seen |
| $\left[81 + 18 - 16 - \frac{16}{3}\right] = \frac{233}{3}$ | A1 | AO2.1 — AG: Any interim working must be correct |
| **[3]** | | |

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1 In this question you must show detailed reasoning.
Show that $\int _ { 4 } ^ { 9 } ( 2 x + \sqrt { x } ) \mathrm { d } x = \frac { 233 } { 3 }$.

\hfill \mbox{\textit{OCR MEI Paper 1 2019 Q1 [3]}}
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Q1 3 Q2 3 Q3 8 Q4 3 Q5 4 Q6 7 Q7 4 Q8 7 Q9 7 Q10 7 Q11 5 Q12 6 Q13 5 Q14 8 Q15 12 Q16 14