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 $x^2 + y^2 + 2x - 4y - 8 = 0$
  1. Find the centre and radius of the circle.
  2. The circle passes through the point $(-3, k)$ where $k < 0$. Find $k$.
  3. Find the coordinates of the points where the circle meets the line $x + y = 6$.
  1. $(-1, 2)$ radius $\sqrt{13}$
  2. $-1$
  3. $(1, 5)$ and $(2,4)$
Q2
Answer
For the curve $y = x^3 - 3x^2 + 4$
  1. Find the coordinates of the stationary points
  2. Determine whether each is a maximum or minimum
  3. For what values of $x$ is the curve increasing?
  1. $(0, 4)$ and $(2,0)$
  2. max, min
  3. $x < 0$, $x > 2$
Q3
Answer
Express the following as a single logarithm
  1. $\log_a 2 + \log_a 3$
  2. $2\log_{10} x - 3\log_{10} y$
  1. $\log_a 6$
  2. $\log_{10}\dfrac{x^2}{y^3}$
Q4
Answer
Express $\sqrt{45} + \dfrac{20}{\sqrt{5}}$ in the form $k\sqrt{5}$ where $k$ is an integer.
$7\sqrt{5}$