| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Marks | 9 |
| Topic | Curve Sketching |
| Type | Sketch rational with quadratic numerator |
| Difficulty | Standard +0.3 This is a standard curve sketching question involving rational functions. Finding asymptotes (vertical from denominator, oblique from polynomial division) and x-intercepts (factoring numerator) are routine A-level techniques. While it requires multiple steps and careful algebraic manipulation, it follows a well-established procedure without requiring novel insight or particularly challenging problem-solving. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^2 |
The curve $C$ has equation
$$y = \frac{x^2 - 2x - 3}{x + 2}.$$
\begin{enumerate}[label=(\roman*)]
\item Find the equations of the asymptotes of $C$. [4]
\item Draw a sketch of $C$, which should include the asymptotes, and state the coordinates of the points of intersection of $C$ with the $x$-axis. [5]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q8 [9]}}