(a(i))[1]
Factorise $4x^3-10xy$ completely.
(a(ii))[1]
Factorise $9a^2-b^2$ completely.
(b)[2]
Solve $\frac{7}{3-2m}=4$ for $m$.
(c(i))[2]
A right-angled triangle has a height of $h\text{ cm}$ and a base that is $7\text{ cm}$ longer than the height. Its hypotenuse is $23\text{ cm}$. Show that $h$ satisfies $h^2+7h-240=0$.
(c(ii))[1]
Write an expression for the area of the triangle in terms of $h$.
(c(iii))[1]
Hence state the triangle’s exact area.
(c(iv))[3]
Solve $h^2+7h-240=0$, and give your answers correct to $1$ decimal place.
(c(v))[1]
Calculate the perimeter of the triangle.