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Q1
Answer
A circle has equation $x^2 + y^2 + 2x - 4y - 8 = 0$
Find the centre and radius of the circle.
The circle passes through the point $(-3, k)$ where $k < 0$. Find $k$.
Find the coordinates of the points where the circle meets the line $x + y = 6$.
$(-1, 2)$ radius $\sqrt{13}$
$-1$
$(1, 5)$ and $(2,4)$
Q2
Answer
For the curve $y = x^3 - 3x^2 + 4$
Find the coordinates of the stationary points
Determine whether each is a maximum or minimum
For what values of $x$ is the curve increasing?
$(0, 4)$ and $(2,0)$
max, min
$x < 0$, $x > 2$
Q3
Answer
Express the following as a single logarithm
$\log_a 2 + \log_a 3$
$2\log_{10} x - 3\log_{10} y$
$\log_a 6$
$\log_{10}\dfrac{x^2}{y^3}$
Q4
Answer
Express $\sqrt{45} + \dfrac{20}{\sqrt{5}}$ in the form $k\sqrt{5}$ where $k$ is an integer.
$7\sqrt{5}$