Solve $$\log_{10}(x^2-10) - \log_{10}x = 2\log_{10}3$$
$10$
Prove that no number of the form $3^n$ has $5$ as its final digit.
$3^n$ is not divisible by $5$, every number which ends in a $5$ is a multiple of $5$.
The curve $$y = x^3 + px^2 + 2$$ has a stationary point at $x = 4$. Find $p$ and determine the nature of the stationary point.
$p = -6$, min
A line $l$ has gradient $-2$ and passes through the point $A(3,5)$. $B$ is a point on $l$ such that the distance $AB$ is $6\sqrt{5}$. Find the possible coordinates of $B$.
$(-3, 17)$ or $(9,-7)$
Prove by contradiction that $\sqrt[3]{2}$ is irrational.
$\sqrt[3]{2} = \dfrac{a}{b}$ and manipulate to find $a$ and $b$ are both even.