CAIE P1 2024 March — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionMarch
Marks3
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Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeImproper integral to infinity
DifficultyModerate -0.5 This is a straightforward improper integral requiring only basic integration of x^(-2) and evaluation of a limit. While improper integrals are slightly beyond the most routine exercises, this particular example involves a standard power rule integration and a simple limit that converges clearly, making it easier than average for A-level.
Spec1.08d Evaluate definite integrals: between limits4.08c Improper integrals: infinite limits or discontinuous integrands
1 Find the exact value of \(\int _ { 3 } ^ { \infty } \frac { 2 } { x ^ { 2 } } d x\).
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Integrate to obtain \(-2x^{-1}\)B1 OE
Substitute limits correctly with clear indication seen that upper limit gives 0M1 For integral of form \(-kx^{-n}\), where \(k>0\), \(n>0\)
Obtain \(\frac{2}{3}\)A1 WWW; Accept 0.667
3 
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Integrate to obtain $-2x^{-1}$ | B1 | OE |
| Substitute limits correctly with clear indication seen that upper limit gives 0 | M1 | For integral of form $-kx^{-n}$, where $k>0$, $n>0$ |
| Obtain $\frac{2}{3}$ | A1 | WWW; Accept 0.667 |
| | **3** | |

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1 Find the exact value of $\int _ { 3 } ^ { \infty } \frac { 2 } { x ^ { 2 } } d x$.\\

\hfill \mbox{\textit{CAIE P1 2024 Q1 [3]}}
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