CAIE FP1 2011 June — Question 9

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJune
TopicPolynomial Division & Manipulation

9 The curve \(C\) with equation $$y = \frac { a x ^ { 2 } + b x + c } { x - 1 }$$ where \(a , b\) and \(c\) are constants, has two asymptotes. It is given that \(y = 2 x - 5\) is one of these asymptotes.
  1. State the equation of the other asymptote.
  2. Find the value of \(a\) and show that \(b = - 7\).
  3. Given also that \(C\) has a turning point when \(x = 2\), find the value of \(c\).
  4. Find the set of values of \(k\) for which the line \(y = k\) does not intersect \(C\).