OCR MEI FP1 2007 January — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2007
SessionJanuary
TopicPartial Fractions
TypeCurve sketching with asymptotes

7 A curve has equation \(y = \frac { 5 } { ( x + 2 ) ( 4 - x ) }\).
  1. Write down the value of \(y\) when \(x = 0\).
  2. Write down the equations of the three asymptotes.
  3. Sketch the curve.
  4. Find the values of \(x\) for which \(\frac { 5 } { ( x + 2 ) ( 4 - x ) } = 1\) and hence solve the inequality $$\frac { 5 } { ( x + 2 ) ( 4 - x ) } < 1 .$$