CAIE P1 2015 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2015
SessionJune
Marks4
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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 + 1, followed by applying a boundary condition to find the constant. The substitution is standard and the integration of u^(1/2) is routine A-level work with no conceptual challenges beyond basic technique.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation1.08b Integrate x^n: where n != -1 and sums
2 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x + 1 ) ^ { \frac { 1 } { 2 } }\) and the point (4,7) lies on the curve. Find the equation of the curve.
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(\left[\frac{(2x+1)^{\frac{3}{2}}}{\frac{3}{2}}\right] \div 2 \quad (+c)\)B1B1
\(7 = 9 + c\)M1 Attempt subst \(x=4\), \(y=7\). \(c\) must be there. Dep. on attempt at integration.
\(y = \frac{(2x+1)^{\frac{3}{2}}}{3} - 2\) or unsimplifiedA1 [4] \(c=-2\) sufficient 
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left[\frac{(2x+1)^{\frac{3}{2}}}{\frac{3}{2}}\right] \div 2 \quad (+c)$ | B1B1 | |
| $7 = 9 + c$ | M1 | Attempt subst $x=4$, $y=7$. $c$ must be there. Dep. on attempt at integration. |
| $y = \frac{(2x+1)^{\frac{3}{2}}}{3} - 2$ or unsimplified | A1 [4] | $c=-2$ sufficient |

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2 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 2 x + 1 ) ^ { \frac { 1 } { 2 } }$ and the point (4,7) lies on the curve. Find the equation of the curve.

\hfill \mbox{\textit{CAIE P1 2015 Q2 [4]}}
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