CAIE FP1 2003 November — Question 11 EITHER

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2003
SessionNovember
TopicPartial Fractions
TypeCurve sketching with asymptotes

The curve \(C\) has equation \(y = \frac { 5 ( x - 1 ) ( x + 2 ) } { ( x - 2 ) ( x + 3 ) }\).
  1. Express \(y\) in the form \(P + \frac { Q } { x - 2 } + \frac { R } { x + 3 }\).
  2. Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 0\) for exactly one value of \(x\) and find the corresponding value of \(y\).
  3. Write down the equations of all the asymptotes of \(C\).
  4. Find the set of values of \(k\) for which the line \(y = k\) does not intersect \(C\).