| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 10 |
| Topic | Applied differentiation |
| Type | Kinematics: displacement-velocity-acceleration |
| Difficulty | Moderate -0.3 This is a straightforward calculus application question requiring routine differentiation and finding stationary points. All parts follow standard procedures (substitution, differentiation for velocity/acceleration, solving quadratic for maximum), making it slightly easier than average despite being multi-part with 10 marks total. |
| Spec | 1.07i Differentiate x^n: for rational n and sums3.02f Non-uniform acceleration: using differentiation and integration |
A student is attempting to model the flight of a boomerang.
She throws the boomerang from a fixed point $O$ and catches it when it returns to $O$.
She suggests the model for the displacement, $s$ metres, after $t$ seconds is given by
$s = 9t^2 - \frac{3}{2}t^3$, $0 \leq t \leq 6$.
For this model,
\begin{enumerate}[label=(\alph*)]
\item determine what happens at $t = 6$, [2]
\item find the greatest displacement of the boomerang from $O$, [4]
\item find the velocity of the boomerang 1 second before the student catches it, [2]
\item find the acceleration of the boomerang 1 second before the student catches it. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q10 [10]}}