OCR MEI C4 2009 June — Question 3 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2009
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferential equations
TypeSeparable variables - standard (polynomial/exponential x-side)
DifficultyModerate -0.5 This is a straightforward separable differential equation requiring only basic integration techniques (∫1/y dy and ∫3x² dx) and application of an initial condition. It's slightly easier than average because it's a standard textbook exercise with a clear method and no conceptual challenges, though it does require correct execution of separation of variables.
Spec1.08k Separable differential equations: dy/dx = f(x)g(y)
A curve satisfies the differential equation \(\frac{dy}{dx} = 3x^2y\), and passes through the point \((1, 1)\). Find \(y\) in terms of \(x\). [4]
AnswerMarks
\(\frac{1 \times 2 + (-2) \times (n-2)}{n} = -1.999\) or equivalent (allow \(n, n+2\))M1, A1
\(n = 6000\) so you have played 6000 rounds.A1 
$\frac{1 \times 2 + (-2) \times (n-2)}{n} = -1.999$ or equivalent (allow $n, n+2$) | M1, A1 |
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$n = 6000$ so you have played 6000 rounds. | A1 |
A curve satisfies the differential equation $\frac{dy}{dx} = 3x^2y$, and passes through the point $(1, 1)$. Find $y$ in terms of $x$. [4]

\hfill \mbox{\textit{OCR MEI C4 2009 Q3 [4]}}
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