CAIE P1 2013 June — Question 1 3 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionJune
Marks3
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TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyEasy -1.3 This is a straightforward integration question requiring only the power rule (rewriting x^{-2} and integrating to get -6x^{-1}) followed by substituting a point to find the constant. It's a single-step technique with no problem-solving required, making it easier than average but not trivial since students must handle negative powers correctly.
Spec1.08b Integrate x^n: where n != -1 and sums
1 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 } { x ^ { 2 } }\) and \(( 2,9 )\) is a point on the curve. Find the equation of the curve.
AnswerMarks Guidance
\(\frac{dy}{dx} = \frac{6}{x^2}\)B1 M1 A1 Integration only – unsimplified. Uses (2, 9) in an integral
\(y = -6x^{-1} + c\)
Uses (2, 9) → \(c = 12\)
AnswerMarks
\(y = -6x^{-1} + 12\)[3] 
$\frac{dy}{dx} = \frac{6}{x^2}$ | B1 M1 A1 | Integration only – unsimplified. Uses (2, 9) in an integral

$y = -6x^{-1} + c$

Uses (2, 9) → $c = 12$

$y = -6x^{-1} + 12$ | [3] |

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1 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 } { x ^ { 2 } }$ and $( 2,9 )$ is a point on the curve. Find the equation of the curve.

\hfill \mbox{\textit{CAIE P1 2013 Q1 [3]}}
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