CAIE FP1 2018 November — Question 9

Exam BoardCAIE
ModuleFP1 (Further Pure Mathematics 1)
Year2018
SessionNovember
TopicPolynomial Division & Manipulation

9 The curve \(C\) has equation $$y = \frac { 5 x ^ { 2 } + 5 x + 1 } { x ^ { 2 } + x + 1 } .$$
  1. Find the equation of the asymptote of \(C\).
  2. Show that, for all real values of \(x , - \frac { 1 } { 3 } \leqslant y < 5\).
  3. Find the coordinates of any stationary points of \(C\).
  4. Sketch \(C\), stating the coordinates of any intersections with the \(y\)-axis.