CAIE Further Paper 1 2020 November — Question 6

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2020
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCurve Sketching

6 The curve \(C\) has equation \(\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Show that there is no point on \(C\) for which \(1 < y < 5\).
  3. Find the coordinates of the intersections of \(C\) with the axes, and sketch \(C\).
  4. Sketch the curve with equation \(\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 } \right|\).

6 The curve $C$ has equation $\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 }$.\\
(a) Find the equations of the asymptotes of $C$.\\

(b) Show that there is no point on $C$ for which $1 < y < 5$.\\

(c) Find the coordinates of the intersections of $C$ with the axes, and sketch $C$.\\

(d) Sketch the curve with equation $\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } + \mathrm { x } - 1 } { \mathrm { x } - 1 } \right|$.

\hfill \mbox{\textit{CAIE Further Paper 1 2020 Q6}}