| Exam Board | OCR MEI |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 14 |
| 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. While it requires multiple techniques (finding intercepts, asymptotes, and behavior at infinity), each step follows routine procedures: factoring the numerator, identifying discontinuities, and analyzing limits. The algebraic manipulation is straightforward (numerator factors as (x-2)(x+2)), and determining asymptotic behavior requires only basic limit reasoning. This is slightly above average difficulty due to being Further Maths content and requiring coordination of several concepts, but it's a textbook-style question with no novel problem-solving required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials |
A curve has equation $y = \frac{x^2 - 4}{(x-3)(x+1)(x-1)}$.
\begin{enumerate}[label=(\roman*)]
\item Write down the coordinates of the points where the curve crosses the axes. [3]
\item Write down the equations of the three vertical asymptotes and the one horizontal asymptote. [4]
\item Determine whether the curve approaches the horizontal asymptote from above or 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]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI FP1 2007 Q8 [14]}}