CAIE P2 2018 November — Question 2 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2018
SessionNovember
Marks5
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TopicStandard Integrals and Reverse Chain Rule
TypeDefinite integral with logarithmic form
DifficultyModerate -0.5 This is a straightforward application of the standard integral for 1/x with a linear substitution. Students need to recognize the reverse chain rule pattern (constant 6 matches the derivative of 2x+1), integrate to get 3ln|2x+1|, and evaluate between limits—all routine techniques for P2 level with no conceptual challenges beyond careful arithmetic to reach ln 125.
Spec1.06f Laws of logarithms: addition, subtraction, power rules1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08d Evaluate definite integrals: between limits
Show that \(\int_1^7 \frac{6}{2x + 1} \, dx = \ln 125\). [5]
Question 2:
AnswerMarks Guidance
2Integrate to obtain form kln(2x+1) M1
Obtain correct 3ln(2x+1)A1
Use subtraction law of logarithms correctlyM1 Dependent on first M1
Use power law of logarithms correctlyM1 Dependent on first M1
Confirm ln125A1
5
AnswerMarks Guidance
QuestionAnswer Marks 
Question 2:
2 | Integrate to obtain form kln(2x+1) | M1
Obtain correct 3ln(2x+1) | A1
Use subtraction law of logarithms correctly | M1 | Dependent on first M1
Use power law of logarithms correctly | M1 | Dependent on first M1
Confirm ln125 | A1
5
Question | Answer | Marks | Guidance
Show that $\int_1^7 \frac{6}{2x + 1} \, dx = \ln 125$. [5]

\hfill \mbox{\textit{CAIE P2 2018 Q2 [5]}}
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Q1 5 Q2 5 Q3 5 Q4 11 Q5 9 Q6 8 Q7 10