OCR MEI FP1 2014 June — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2014
SessionJune
TopicPolynomial Division & Manipulation

7 A curve has equation \(y = \frac { x ^ { 2 } - 5 } { ( x + 3 ) ( x - 2 ) ( a x - 1 ) }\), where \(a\) is a constant.
  1. Find the coordinates of the points where the curve crosses the \(x\)-axis and the \(y\)-axis.
  2. You are given that the curve has a vertical asymptote at \(x = \frac { 1 } { 2 }\). Write down the value of \(a\) and the equations of the other asymptotes.
  3. Sketch the curve.
  4. Find the set of values of \(x\) for which \(y > 0\).