| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find second derivative |
| Difficulty | Moderate -0.8 This question tests basic understanding of differentiation of quadratics. Part (a) requires recognizing that the derivative of a quadratic is linear, with the graph passing through the x-axis at the turning point. Part (b) requires knowing that the second derivative of a quadratic is constant. Both parts are conceptual recall with minimal calculation, making this easier than average A-level questions. |
| Spec | 1.07a Derivative as gradient: of tangent to curve1.07c Sketch gradient function: for given curve1.07d Second derivatives: d^2y/dx^2 notation |
The diagram shows the graph of $y = f(x)$, where $f(x)$ is a quadratic function of $x$.
A copy of the diagram is given in the Printed Answer Booklet.
\includegraphics{figure_2}
\begin{enumerate}[label=(\alph*)]
\item On the copy of the diagram in the Printed Answer Booklet, draw a possible graph of the gradient function $y = f'(x)$. [3]
\item State the gradient of the graph of $y = f''(x)$. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q3 [4]}}