OCR MEI FP1 2012 January — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2012
SessionJanuary
TopicIntegration with Partial Fractions

7 A curve has equation \(y = \frac { ( x + 1 ) ( 2 x - 1 ) } { x ^ { 2 } - 3 }\).
  1. Find the coordinates of the points where the curve crosses the axes.
  2. Write down the equations of the three asymptotes.
  3. Determine whether the curve approaches the horizontal asymptote from above or from below for
    (A) large positive values of \(x\),
    (B) large negative values of \(x\).
  4. Sketch the curve.
  5. Solve the inequality \(\frac { ( x + 1 ) ( 2 x - 1 ) } { x ^ { 2 } - 3 } < 2\).