OCR MEI FP1 2011 January — Question 7

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2011
SessionJanuary
TopicIntegration with Partial Fractions

7 Fig. 7 shows part of the curve with equation \(y = \frac { x + 5 } { ( 2 x - 5 ) ( 3 x + 8 ) }\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d91a83d-971e-48ca-aa1a-09f2c1a8093a-3_894_890_447_625} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure}
  1. Write down the coordinates of the two points where the curve crosses the axes.
  2. Write down the equations of the two vertical asymptotes and the one horizontal asymptote.
  3. Determine how the curve approaches the horizontal asymptote for large positive and large negative values of \(x\).
  4. On the copy of Fig. 7, sketch the rest of the curve.
  5. Solve the inequality \(\frac { x + 5 } { ( 2 x - 5 ) ( 3 x + 8 ) } < 0\).