| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 7 |
| Topic | Stationary points and optimisation |
| Type | Determine constant from stationary point condition |
| Difficulty | Moderate -0.8 This is a straightforward application of differentiation requiring students to find dy/dx, substitute x=2 and set equal to zero to find k, then use the second derivative test. All steps are routine with no problem-solving insight needed, making it easier than average but not trivial since it requires correct execution of multiple standard techniques. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07n Stationary points: find maxima, minima using derivatives |
4 The curve $y = 2 x ^ { 3 } + 3 x ^ { 2 } - k x + 4$ has a stationary point where $x = 2$.
\begin{enumerate}[label=(\alph*)]
\item Determine the value of the constant $k$.
\item Determine whether this stationary point is a maximum or a minimum point.
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q4 [7]}}