CAIE P1 2013 June — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeFinding curve equation from derivative
DifficultyModerate -0.8 This is a straightforward integration problem requiring a simple substitution (u = 2x + 5) to find y, followed by using the given point to determine the constant of integration. It's a standard P1 exercise with clear steps and no conceptual challenges, making it easier than average but not trivial since it does require the substitution technique.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
1 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { } ( 2 x + 5 )\) and \(( 2,5 )\) is a point on the curve. Find the equation of the curve.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\frac{(2x+5)^{\frac{3}{2}}}{\frac{3}{2}}\)B1 Everything without "÷2"
\(\div 2 \quad (+c)\)B1 B1 "÷2"
Uses \((2, 5) \rightarrow c = -4\)M1 A1 [4] Uses point in an integral 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $\frac{(2x+5)^{\frac{3}{2}}}{\frac{3}{2}}$ | B1 | Everything without "÷2" |
| $\div 2 \quad (+c)$ | B1 | B1 "÷2" |
| Uses $(2, 5) \rightarrow c = -4$ | M1 A1 [4] | Uses point in an integral |

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1 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \sqrt { } ( 2 x + 5 )$ and $( 2,5 )$ is a point on the curve. Find the equation of the curve.

\hfill \mbox{\textit{CAIE P1 2013 Q1 [4]}}
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