Pre-U Pre-U 9795 Specimen — Question 7

Exam BoardPre-U
ModulePre-U 9795 (Pre-U Further Mathematics)
SessionSpecimen
TopicPolynomial Division & Manipulation
TypeSketching Rational Functions with Oblique Asymptote
DifficultyStandard +0.3 This is a straightforward rational function sketching question requiring polynomial division to find the oblique asymptote, identification of the vertical asymptote, and finding intercepts. While it involves multiple steps, each is routine and the techniques are standard A-level material with no novel problem-solving required.
Spec1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02n Sketch curves: simple equations including polynomials1.02p Interpret algebraic solutions: graphically

7 The curve \(C\) has equation $$y = \frac { x ^ { 2 } - 2 x - 3 } { x + 2 } .$$
  1. Find the equations of the asymptotes of \(C\).
  2. Sketch \(C\), indicating clearly the asymptotes and any points where \(C\) meets the coordinate axes.

7 The curve $C$ has equation

$$y = \frac { x ^ { 2 } - 2 x - 3 } { x + 2 } .$$

(i) Find the equations of the asymptotes of $C$.\\
(ii) Sketch $C$, indicating clearly the asymptotes and any points where $C$ meets the coordinate axes.

\hfill \mbox{\textit{Pre-U Pre-U 9795  Q7}}