| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2018 |
| Session | November |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
6 The curve $C$ has equation
$$y = \frac { x ^ { 2 } + a x - 1 } { x + 1 }$$
where $a$ is constant and $a > 1$.\\
(i) Find the equations of the asymptotes of $C$.\\
(ii) Show that $C$ intersects the $x$-axis twice.\\
(iii) Justifying your answer, find the number of stationary points on $C$.\\
(iv) Sketch $C$, stating the coordinates of its point of intersection with the $y$-axis.
\hfill \mbox{\textit{CAIE FP1 2018 Q6}}