| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Simple rational function analysis |
| Difficulty | Standard +0.3 This is a standard FP1 curve sketching question involving rational functions. It requires identifying vertical asymptotes (x=2, x=-1), finding the horizontal asymptote (y=1) by considering large x behavior, determining approach direction by testing signs, and solving a rational inequality. While it involves multiple techniques, these are all routine procedures for FP1 students with no novel problem-solving required. The 13 marks reflect thoroughness rather than conceptual difficulty, making it slightly easier than average overall. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02n Sketch curves: simple equations including polynomials |
A curve has equation $y = \frac{x^2}{(x-2)(x+1)}$.
\begin{enumerate}[label=(\roman*)]
\item Write down the equations of the three asymptotes. [3]
\item Determine whether the curve approaches the horizontal asymptote from above or from below for
\begin{enumerate}[label=(\Alph*)]
\item large positive values of $x$,
\item large negative values of $x$. [3]
\end{enumerate}
\item Sketch the curve. [4]
\item Solve the inequality $\frac{x^2}{(x-2)(x+1)} > 0$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2006 Q7 [13]}}