Moderate -0.8 This is a straightforward integration question requiring only the power rule and finding a constant using a given point. It's simpler than average A-level questions as it involves routine technique with no problem-solving, geometric insight, or multi-step reasoning beyond basic substitution.
The gradient of a curve is given by \(\frac{dy}{dx} = \frac{18}{x^3} + 2\). The curve passes through the point \((3, 6)\). Find the equation of the curve. [5]
\(kx^2\); \(-9x^2\); \(+ 2x + c\); substitution of \(x = 3\) and \(y = 6\) in their expression following integration; \(c = 1\)
M1*, A1, M1*, M1dep, A1
may be awarded later; \(c\) may appear at substitution stage; on award of either of previous M1s; A0 if spoiled by further working; for full marks, must see "\(y =\)" at some stage; eg \(6 = k3^{-2} + 2x3 + c\)
$kx^2$; $-9x^2$; $+ 2x + c$; substitution of $x = 3$ and $y = 6$ in their expression following integration; $c = 1$ | M1*, A1, M1*, M1dep, A1 | may be awarded later; $c$ may appear at substitution stage; on award of either of previous M1s; A0 if spoiled by further working; for full marks, must see "$y =$" at some stage; eg $6 = k3^{-2} + 2x3 + c$
The gradient of a curve is given by $\frac{dy}{dx} = \frac{18}{x^3} + 2$. The curve passes through the point $(3, 6)$. Find the equation of the curve. [5]
\hfill \mbox{\textit{OCR MEI C2 2013 Q3 [5]}}