CAIE P1 2012 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicStandard Integrals and Reverse Chain Rule
TypeFind curve equation from derivative (straightforward integration + point)
DifficultyEasy -1.2 This is a straightforward integration question requiring only basic power rule application and using a point to find the constant of integration. It involves routine manipulation of negative powers with no problem-solving insight needed, making it easier than average.
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 \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 8 } { x ^ { 3 } } - 1\) and the point \(( 2,4 )\) lies on the curve. Find the equation of the curve.

AnswerMarks Guidance
\(y = \frac{4}{x^2} - x\) \((+c)\)M1A1 Attempt integration. cao
Sub \((2, 4) \to c = 5\)DM1A1 Dependent on \(c\) present
$y = \frac{4}{x^2} - x$ $(+c)$ | M1A1 | Attempt integration. cao
Sub $(2, 4) \to c = 5$ | DM1A1 | Dependent on $c$ present | [4]
2 A curve is such that $\frac { \mathrm { d } y } { \mathrm {~d} x } = - \frac { 8 } { x ^ { 3 } } - 1$ and the point $( 2,4 )$ lies on the curve. Find the equation of the curve.

\hfill \mbox{\textit{CAIE P1 2012 Q2 [4]}}