| Exam Board | OCR MEI |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Product & Quotient Rules |
| Type | Show derivative equals given algebraic form |
| Difficulty | Moderate -0.3 This is a straightforward differentiation question using the quotient rule followed by solving a simple equation. Part (i) is routine verification requiring careful algebra, and part (ii) involves setting the derivative to zero where the factored form makes finding stationary points trivial (x=0 or x=-1). The question is slightly easier than average as it's a standard textbook exercise with no conceptual challenges beyond applying the quotient rule correctly. |
| Spec | 1.07n Stationary points: find maxima, minima using derivatives1.07q Product and quotient rules: differentiation |
The equation of a curve is $y = \frac{x^2}{2x + 1}$.
\begin{enumerate}[label=(\roman*)]
\item Show that $\frac{dy}{dx} = \frac{2x(x + 1)}{(2x + 1)^2}$. [4]
\item Find the coordinates of the stationary points of the curve. You need not determine their nature. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C3 Q4 [8]}}