Pre-U Pre-U 9795/1 2018 June — Question 2 10 marks

Exam BoardPre-U
ModulePre-U 9795/1 (Pre-U Further Mathematics Paper 1)
Year2018
SessionJune
Marks10
TopicCurve Sketching
TypeSketch rational with quadratic numerator
DifficultyStandard +0.3 This is a straightforward curve sketching question requiring polynomial division to find the oblique asymptote, standard calculus for turning points, and identification of the vertical asymptote. While it involves multiple techniques (algebraic manipulation, differentiation using quotient rule, solving a quadratic), these are all routine A-level procedures with no novel problem-solving required. The 10 marks reflect the working needed rather than conceptual difficulty.
Spec1.02n Sketch curves: simple equations including polynomials1.07n Stationary points: find maxima, minima using derivatives

  1. Determine the asymptotes and turning points of the curve with equation \(y = \frac{x^2+3}{x+1}\). [7]
  2. Sketch the curve. [3]

\begin{enumerate}[label=(\roman*)]
\item Determine the asymptotes and turning points of the curve with equation $y = \frac{x^2+3}{x+1}$. [7]

\item Sketch the curve. [3]
\end{enumerate}

\hfill \mbox{\textit{Pre-U Pre-U 9795/1 2018 Q2 [10]}}