Find \(\int 7x^3 \, dx\). [3]
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Answer Marks
Guidance
\(kx^{2+1}\) M1
\(k\) is any non-zero constant
\(2x^2\) cao A1
\(+ c\) A1
Total: [3] Question 2(i)
Answer Marks
Guidance
\(21\left(\frac{1}{1+2} + \frac{1}{2+2} + \frac{1}{3+2} + \frac{1}{4+2} + \frac{1}{5+2}\right)\) oe, soi M1
may be implied by correct answer; NB \(7 + 5.25 + 4.2 + 3.5 + 3\) gives M0 if extra terms or terms missing
\(22.95\) or \(\frac{459}{20}\) or \(22\frac{19}{20}\) A1
Total: [2] Question 2(ii)
Answer Marks
Guidance
\(a + 45\) cao B1
mark the final answer must be explicitly stated
\(\frac{10}{2}a + a + \text{their}45\) M1
or \(\frac{10}{2}2a + (10-1) \times 5\); condone wrongly attributed answers
\(5(2a + 45)\) or \(10a + 225\) cao isw A1
ignore further work attempting to find \(a\); B2 if correct answer derived from adding terms separately
Total: [3]
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$kx^{2+1}$ | M1 | $k$ is any non-zero constant
$2x^2$ cao | A1 |
$+ c$ | A1 |
**Total: [3]**
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# Question 2(i)
$21\left(\frac{1}{1+2} + \frac{1}{2+2} + \frac{1}{3+2} + \frac{1}{4+2} + \frac{1}{5+2}\right)$ oe, soi | M1 | may be implied by correct answer; NB $7 + 5.25 + 4.2 + 3.5 + 3$ gives M0 if extra terms or terms missing
$22.95$ or $\frac{459}{20}$ or $22\frac{19}{20}$ | A1 |
**Total: [2]**
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# Question 2(ii)
$a + 45$ cao | B1 | mark the final answer must be explicitly stated
$\frac{10}{2}a + a + \text{their}45$ | M1 | or $\frac{10}{2}2a + (10-1) \times 5$; condone wrongly attributed answers
$5(2a + 45)$ or $10a + 225$ cao isw | A1 | ignore further work attempting to find $a$; B2 if correct answer derived from adding terms separately
**Total: [3]**
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Find $\int 7x^3 \, dx$. [3]
\hfill \mbox{\textit{OCR MEI C2 2014 Q1 [3]}}