Q1
Answer
Find $\displaystyle\int x\sqrt{x^2+4}\ \mathrm{d}x$
$\dfrac{1}{3}(x^2+4)^{\frac{3}{2}} + c$
Q2
Answer
$A$ is the centre of a circle $C$ with equation $x^2-8x+y^2+10y+1=0$. $P$, $Q$ and $R$ are points on the circle and the lines $l_1$, $l_2$ and $l_3$ are tangents to the circle at these points respectively. $l_2$ intersects $l_1$ at $B$ and $l_3$ at $D$.
  1. Find the centre and radius of $C$.
  2. Given that the $x$ coordinate of $Q$ is 10, and that the gradient of $AQ$ is positive, find the $y$ coordinate of $Q$.
  3. Find the equation of $l_2$ in the form $y=mx+c$.
  4. Given that $APBQ$ is a square find the equation of $l_1$.
  5. $l_1$ intercepts the $y$ axis at $E$. Find the area of triangle $EPA$.
  1. $(4,-5)$, radius $\sqrt{40}$
  2. $(10,-3)$
  3. $y = -3x + 27$
  4. $y = \dfrac{1}{3}x + \dfrac{1}{3}$
  5. $\dfrac{20}{3}$