| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/1 (Pre-U Further Mathematics Paper 1) |
| Year | 2015 |
| Session | June |
| Marks | 11 |
| Topic | Curve Sketching |
| Type | Sketch rational with quadratic numerator |
| Difficulty | Standard +0.8 This is a Further Maths question requiring multiple techniques: polynomial division to find the oblique asymptote, differentiation using the quotient rule, solving a quadratic for turning points, and synthesizing all information into a sketch. While each step is methodical, the combination of techniques and the oblique asymptote (less routine than vertical/horizontal) elevates this above a standard A-level question. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02y Partial fractions: decompose rational functions1.07n Stationary points: find maxima, minima using derivatives |
A curve has equation $y = \frac{2x^2 + 5x - 25}{x - 3}$.
\begin{enumerate}[label=(\roman*)]
\item Determine the equations of the asymptotes. [3]
\item Find the coordinates of the turning points. [5]
\item Sketch the curve. [3]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2015 Q5 [11]}}