CAIE P1 2016 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIntegration by Substitution
TypeFinding curve equation from derivative
DifficultyModerate -0.3 This is a straightforward integration problem requiring a simple substitution (u = 5-2x) to find y, followed by using the given point to determine the constant of integration. While it requires knowledge of integration by substitution, the substitution is standard and the algebraic manipulation is minimal, making it slightly easier than an average A-level question.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation
2 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 8 } { ( 5 - 2 x ) ^ { 2 } }\). Given that the curve passes through ( 2,7 ), find the equation of the curve.
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(f(x) = \frac{8(5-2x)^{-1}}{-1} \div -2\) (+c)B1 Correct without (\(\div\) by \(-2\))
B1An attempt at integration (\(\div\) by \(-2\))
Uses \(x = 2\), \(y = 7\)M1 Substitution of correct values into an integral to find \(c\)
\(c = 3\)A1 
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $f(x) = \frac{8(5-2x)^{-1}}{-1} \div -2$ (+c) | B1 | Correct without ($\div$ by $-2$) |
| | B1 | An attempt at integration ($\div$ by $-2$) |
| Uses $x = 2$, $y = 7$ | M1 | Substitution of correct values into an integral to find $c$ |
| $c = 3$ | A1 | |
2 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 8 } { ( 5 - 2 x ) ^ { 2 } }$. Given that the curve passes through ( 2,7 ), find the equation of the curve.

\hfill \mbox{\textit{CAIE P1 2016 Q2 [4]}}
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