Click here to do these on a digital whiteboard. Note that these are a repeat of the holiday questions.
Q1
Answer
A circle has equation $x^2 + y^2 + 6x - 4y - 4 = 0$
  1. Find the centre and radius of the circle.
  2. Find the coordinates of the points where the circle meets the line with equation $y = 3x+4$.
  1. $(-3, 2)$ radius $\sqrt{17}$
  2. $\left(\dfrac{1}{5}, \dfrac{23}{5}\right)$ and $(-2,-2)$
Q2
Answer
Find $\dfrac{\mathrm{d}y}{\mathrm{d}x}$ for the following
  1. $y = 5x+3$
  2. $y = \dfrac{2}{x^2}$
  3. $y = (2x+1)(5x-7)$
  1. $5$
  2. $-4x^{-3}$
  3. $20x - 9$
Q3
Answer
  1. Simplify $(x+4)(5x-3) - 3(x-2)^2$.
  2. The coefficient of $x^2$ in the expansion of $$(x+2)(x+k)(2x-5)$$ is $-3$. Find $k$.
  1. $2x^2 + 29x - 24$
  2. $-2$
Q4
Answer
The value of $y$ increases exponentially with respect to $x$. When $x = 0$, $y = 275$ and when $x = 10$, $y = 440$. Find the value of $y$ when $x = 20$.
$704$