CAIE FP1 2013 June — Question 10

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCurve Sketching

10 The curve \(C\) has equation \(y = \frac { 2 x ^ { 2 } - 3 x - 2 } { x ^ { 2 } - 2 x + 1 }\). State the equations of the asymptotes of \(C\). Show that \(y \leqslant \frac { 25 } { 12 }\) at all points of \(C\). Find the coordinates of any stationary points of \(C\). Sketch \(C\), stating the coordinates of any intersections of \(C\) with the coordinate axes and the asymptotes.

10 The curve $C$ has equation $y = \frac { 2 x ^ { 2 } - 3 x - 2 } { x ^ { 2 } - 2 x + 1 }$. State the equations of the asymptotes of $C$.

Show that $y \leqslant \frac { 25 } { 12 }$ at all points of $C$.

Find the coordinates of any stationary points of $C$.

Sketch $C$, stating the coordinates of any intersections of $C$ with the coordinate axes and the asymptotes.

\hfill \mbox{\textit{CAIE FP1 2013 Q10}}