AQA FP1 2009 January — Question 6

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2009
SessionJanuary
TopicPartial Fractions
TypeCurve sketching with asymptotes

6 A curve has equation $$y = \frac { ( x - 1 ) ( x - 3 ) } { x ( x - 2 ) }$$
    1. Write down the equations of the three asymptotes of this curve.
    2. State the coordinates of the points at which the curve intersects the \(x\)-axis.
    3. Sketch the curve.
      (You are given that the curve has no stationary points.)
  1. Hence, or otherwise, solve the inequality $$\frac { ( x - 1 ) ( x - 3 ) } { x ( x - 2 ) } < 0$$