Q1
Answer
The curve $C$ has equation $y = x^2 - 4x + 2$.
  1. Find the equation of the normal to $C$ at the point where $x = 4$.
  2. The normal meets the curve again. Find the coordinates of the second point of intersection.
  1. $y = -\dfrac{1}{4}x + 3$
  2. $\left(-\dfrac{1}{4},\dfrac{49}{16}\right)$
Q2
Answer
Find the equation of the normal to the curve with equation $x^2y = 2x + 2y^2$ at the point $(0,0)$.
$y = 0$
Q3
Answer
Write $\dfrac{6x^2-5x-2x^3}{(x-2)(1-x)}$ in partial fractions.
$2x + \dfrac{2}{x-2} + \dfrac{1}{1-x}$