CAIE P2 2015 November — Question 1 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2015
SessionNovember
Marks5
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Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeDefinite integral with logarithmic form
DifficultyModerate -0.8 This is a straightforward application of the standard integral ∫1/(ax+b)dx = (1/a)ln|ax+b| + c with simple substitution of limits. It requires only recognition of the logarithmic form and careful arithmetic with the constant factor, making it easier than average but not trivial since students must handle the exact form and absolute values correctly.
Spec1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)
1 Find the exact value of \(\int _ { - 1 } ^ { 35 } \frac { 3 } { 2 x + 5 } \mathrm {~d} x\), giving the answer in the form \(\ln k\).
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
Integrate to obtain \(k\ln(2x+5)\)M1
Obtain correct \(\frac{3}{2}\ln(2x+5)\)A1
Apply limits and use logarithm law for \(\ln a - \ln b\)M1
Use logarithm power lawM1
Obtain \(\ln 125\)A1 [5] 
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| Integrate to obtain $k\ln(2x+5)$ | M1 | |
| Obtain correct $\frac{3}{2}\ln(2x+5)$ | A1 | |
| Apply limits and use logarithm law for $\ln a - \ln b$ | M1 | |
| Use logarithm power law | M1 | |
| Obtain $\ln 125$ | A1 | [5] |

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1 Find the exact value of $\int _ { - 1 } ^ { 35 } \frac { 3 } { 2 x + 5 } \mathrm {~d} x$, giving the answer in the form $\ln k$.

\hfill \mbox{\textit{CAIE P2 2015 Q1 [5]}}
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