CAIE P2 2019 November — Question 2 5 marks

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2019
SessionNovember
Marks5
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TopicStandard Integrals and Reverse Chain Rule
DifficultyModerate -0.8 This question requires expanding the squared bracket to get 4e^(4x) - 4e^(2x) + 1, then integrating term-by-term using standard exponential rules, and finally evaluating between limits. It's a straightforward multi-step problem testing algebraic manipulation and standard integration techniques, but requires no problem-solving insight or novel approaches—slightly easier than average.
Spec1.08d Evaluate definite integrals: between limits
2 Find the exact value of \(\int _ { 1 } ^ { 2 } \left( 2 \mathrm { e } ^ { 2 x } - 1 \right) ^ { 2 } \mathrm {~d} x\). Show all necessary working.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
Expand integrand to obtain \(4e^{4x} - 4e^{2x} + 1\)B1
Integrate to obtain at least two terms of form \(k_1e^{4x} + k_2e^{2x} + k_3x\)\*M1
Obtain correct \(e^{4x} - 2e^{2x} + x\)A1
Apply both limits correctly to their integralDM1
Obtain \(e^8 - 3e^4 + 2e^2 + 1\)A1
Total5 
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Expand integrand to obtain $4e^{4x} - 4e^{2x} + 1$ | B1 | |
| Integrate to obtain at least two terms of form $k_1e^{4x} + k_2e^{2x} + k_3x$ | \*M1 | |
| Obtain correct $e^{4x} - 2e^{2x} + x$ | A1 | |
| Apply both limits correctly to their integral | DM1 | |
| Obtain $e^8 - 3e^4 + 2e^2 + 1$ | A1 | |
| **Total** | **5** | |
2 Find the exact value of $\int _ { 1 } ^ { 2 } \left( 2 \mathrm { e } ^ { 2 x } - 1 \right) ^ { 2 } \mathrm {~d} x$. Show all necessary working.\\

\hfill \mbox{\textit{CAIE P2 2019 Q2 [5]}}
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Q1 5 Q2 5 Q3 5 Q4 7 Q5 9 Q6 9 Q7 10