(a)[2]
Simplify $\left(25x^6\right)^{\frac{3}{2}}$.
(b)[2]
Find the $n$th-term expression for the sequence.
(c)[3]
Expand and simplify $(x+4)(x-3)(3x-1)$.
(d(i))[4]
Show that $(3x+5) + \frac{7}{x-2} = x$ reduces to $2x^2 + x - 3 = 0$.
(d(ii))[3]
Solve $2x^2 + x - 3 = 0$ by factorisation.
(e)[4]
Show that $x^2 = \frac{75y^2}{8}$.