(a)[2]
Factorise completely $3a^2b - ab^2$.
(b)[2]
Solve the inequality $3x + 12 < 5x - 3$.
(c)[2]
Simplify $(3x^2y^4)^3$.
(d)[3]
Solve $\frac{2}{x} = \frac{6}{2 - x}$.
(e)[3]
Expand and simplify $(x - 2)(x + 5)(2x - 1)$.
(f(i))[3]
Show that, after simplifying, $r^2 + 200r - 323 = 0$.
(f(ii))[3]
Solve the equation $r^2 + 200r - 323 = 0$ to determine the interest rate. Show all your working and give your answer correct to 2 decimal places.