CAIE P1 2016 March — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionMarch
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 (including negative powers) and finding a constant using given coordinates. It's simpler than average A-level questions as it involves no problem-solving, just routine technique with standard integrals.
Spec1.02a Indices: laws of indices for rational exponents1.08a Fundamental theorem of calculus: integration as reverse of differentiation
2 A curve for which \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - \frac { 2 } { x ^ { 3 } }\) passes through \(( - 1,3 )\). Find the equation of the curve.
Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(y = \dfrac{3x^3}{3} - \dfrac{2x^{-2}}{-2}\) \((+c)\)B1B1
\(3 = -1 + 1 + c\)M1 Sub \(x = -1, y = 3\). \(c\) must be present
\(y = x^3 + x^{-2} + 3\)A1 [4] Accept \(c = 3\) www 
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $y = \dfrac{3x^3}{3} - \dfrac{2x^{-2}}{-2}$ $(+c)$ | B1B1 | |
| $3 = -1 + 1 + c$ | M1 | Sub $x = -1, y = 3$. $c$ must be present |
| $y = x^3 + x^{-2} + 3$ | A1 [4] | Accept $c = 3$ www |

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2 A curve for which $\frac { \mathrm { d } y } { \mathrm {~d} x } = 3 x ^ { 2 } - \frac { 2 } { x ^ { 3 } }$ passes through $( - 1,3 )$. Find the equation of the curve.

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