CAIE FP1 2018 November — Question 6

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCurve Sketching

6 The curve \(C\) has equation $$y = \frac { x ^ { 2 } + a x - 1 } { x + 1 }$$ where \(a\) is constant and \(a > 1\).
  1. Find the equations of the asymptotes of \(C\).
  2. Show that \(C\) intersects the \(x\)-axis twice.
  3. Justifying your answer, find the number of stationary points on \(C\).
  4. Sketch \(C\), stating the coordinates of its point of intersection with the \(y\)-axis.

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}}