CAIE Further Paper 1 2022 November — Question 7

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2022
SessionNovember
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCurve Sketching

7 The curve \(C\) has equation \(y = \frac { 5 x ^ { 2 } } { 5 x - 2 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Find the coordinates of the stationary points on \(C\).
  3. Sketch \(C\).
  4. Sketch the curve with equation \(y = \left| \frac { 5 x ^ { 2 } } { 5 x - 2 } \right|\) and find in exact form the set of values of \(x\) for which \(\left| \frac { 5 x ^ { 2 } } { 5 x - 2 } \right| < 2\).
    If you use the following page to complete the answer to any question, the question number must be clearly shown.

7 The curve $C$ has equation $y = \frac { 5 x ^ { 2 } } { 5 x - 2 }$.\\
(a) Find the equations of the asymptotes of $C$.\\

(b) Find the coordinates of the stationary points on $C$.\\

(c) Sketch $C$.\\
(d) Sketch the curve with equation $y = \left| \frac { 5 x ^ { 2 } } { 5 x - 2 } \right|$ and find in exact form the set of values of $x$ for which $\left| \frac { 5 x ^ { 2 } } { 5 x - 2 } \right| < 2$.\\

If you use the following page to complete the answer to any question, the question number must be clearly shown.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2022 Q7}}