OCR MEI C2 2007 January — Question 9 4 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeFind curve from gradient
DifficultyEasy -1.2 This is a straightforward integration question requiring only basic polynomial integration and using one point to find the constant of integration. It's a standard textbook exercise with no problem-solving insight needed, making it easier than average for A-level.
Spec1.08a Fundamental theorem of calculus: integration as reverse of differentiation
9 A curve has gradient given by \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } + 8 x\). The curve passes through the point \(( 1,5 )\). Find the equation of the curve.
Question 9:
AnswerMarks Guidance
\(y = \int(6x^2 + 8x)\,dx = 2x^3 + 4x^2 + c\)M1 A1 Correct integration
Substituting \((1, 5)\): \(5 = 2 + 4 + c\), \(c = -1\)M1 Using point to find \(c\)
\(y = 2x^3 + 4x^2 - 1\)A1 cao 
## Question 9:
$y = \int(6x^2 + 8x)\,dx = 2x^3 + 4x^2 + c$ | M1 A1 | Correct integration
Substituting $(1, 5)$: $5 = 2 + 4 + c$, $c = -1$ | M1 | Using point to find $c$
$y = 2x^3 + 4x^2 - 1$ | A1 | cao

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9 A curve has gradient given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } + 8 x$. The curve passes through the point $( 1,5 )$. Find the equation of the curve.

\hfill \mbox{\textit{OCR MEI C2 2007 Q9 [4]}}
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