Rearranging Formulae (AQA GCSE Further Maths): Exam Questions

Rearrange $\frac{1}{xy}=4-\frac{3}{y}$ to make $x$ the subject.

Rearrange $y=\frac{8\left(w-x\right)}{x}$ to make $x$ the subject.

Rearrange $t=\frac{3w^3+a}{w^3-2}$ to make $w$the subject.

Rearrange $\frac{a+x}{x+t}=\frac{by}{t}$ to make $t$ the subject.

Rearrange $\frac{4-v^{{\displaystyle \frac{1}{3}}}}{16-v^{\frac{1}{3}}}=\frac{2+h}{1-h}$ to make $v$ the subject.

You do not need to expand your final answer.

Rearrange $m=\frac{2p+1}{p}+\frac{p+5}{3p}$ to make $p$ the subject.

$3y^2-12y\equiv a{\left(y-b\right)}^2+c$ where $a$, $b$ and $c$ are integers.

Work out the values of $a$, $b$ and $c$.

Using your answer from part (a), or otherwise, rearrange $\frac{4}{3y^2-m^2}=\frac{1}{3y}$ to make $y$ the subject.

Rearrange $\frac{1}{z^3}+\frac{x^3}{z^3{w}^3}=\frac{1}{x^3}$ to make $w$ the subject, simplifying your answer.