CAIE Further Paper 1 2023 June — Question 6

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2023
SessionJune
TopicCurve Sketching
TypeSolve |f(x)| > k using sketch

6 The curve \(C\) has equation \(\mathrm { y } = \frac { \mathrm { x } ^ { 2 } + 2 \mathrm { x } - 15 } { \mathrm { x } - 2 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Show that \(C\) has no stationary points.
  3. Sketch \(C\), stating the coordinates of the intersections with the axes.
  4. Sketch the curve with equation \(\mathrm { y } = \left| \frac { \mathrm { x } ^ { 2 } - 2 \mathrm { x } - 15 } { \mathrm { x } - 2 } \right|\).
  5. Find the set of values of \(x\) for which \(\left| \frac { 2 x ^ { 2 } + 4 x - 30 } { x - 2 } \right| < 15\).