Given that $S=\frac{v^2-u^2}{2a}$,
(a) Find the value of $S$ when $v=4$, $u=3$ and $a=7$.

(b) Make $v$ the subject of the formula.

(a) Solve:
$5\times 2\mathrm{y}=320$

(b) Solve the simultaneous equations:
$bx+y=b$
$ax-y=a$

(a) Make $t$ the subject of the formula:
$P=\frac{\sqrt{t}}{3R}$

(b) Solve:
$96=3y^{\frac{5}{4}}$

Given $4n^2-m^2=171$ and $2n-m=9$.
(a) Calculate the value of $2n+m$.

(b) Find the values of $n$ and $m$.

$p=\frac{\sqrt{hq}}{2}$,
(a) Find the value of $p$ when $h=2$ and $q=18$.

(b) Make $h$ the subject of the formula.

(c) Write a condition for $hq$ so that $p$ is a real number.

Solve:
(a) $\frac{24}{x+1}=3$

(b) $2p+3q=21$
$3p-2q=-1$

(c) $(2t-5)(t+3)=0$

(a) $T=\frac{6k}{\sqrt{m-n}}$
(i) Find $T$ when $m=17$, $n=8$ and $k=13$.

(ii) Make $m$ the subject of the formula.

(b) Find $x$ and $y$ if $y=\frac{x+4}{3}$, and $y=\frac{2x+1}{4}$.

Solve the simultaneous equations:
$3x-2y=4$
$5x-4y=-3$

Given that $\frac{y^4\times \sqrt{y}}{y^{-3}}=y^n$, find the numerical value of $n$.

Solve the simultaneous equations:
$5x+4y=7$
$7x+4y=5$

Given that ${77}^2-{67}^2=5k$, find the value of $k$.

(a) Solve for $t$:
$2^t=\frac{4}{8^3}$

(b) Solve the simultaneous equations:
$y=26-4x$
$\frac{2}{3}y+x=5\frac{2}{3}$

Solve the following equations:
(a) $3x-5(3-x)=41$

(b) $2^{x+1}-32=0$

(c) $2x+y=10$
$7x-3y=9$

Given that $T=\frac{2r\sqrt{p}}{3}$, make $p$ the subject of the formula.

Solve the simultaneous equations:
$2x+2y=3$
$4x-5y=24$

Factorise $x^2-18x+81$.

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$
(i) Find R when R₁ = 4 and R₂ = 6.

(ii) Make R₂ the subject of the formula.

Solve the equation $(2x-3)(x-4)=18$.

(a) Make p subject of the formula.
$2p+q=kp+4$

(b) Express as a single fraction in its simplest form.
$\frac{2x+3}{6}-\frac{5x-3}{7}$

(c) Solve.
$x+1.5=2.5y$
$2y-x=0$

Solve.
(a) $2x>39+15x$

(b) $2x+1.5=2.5y$
$2y-x=0$

(a) Rearrange the formula to make a the subject.
$P=\frac{y^2+a}{y+a}$

(b) Factorise fully.
$(x^2-y^2)-{(x-y)}^2$

(c) Simplify.
(i) $\frac{y-2}{2y^2-3y-2}$

(ii) $\frac{ax-ab+bx+b^2}{a{x}^2-abx}$

$P=\frac{2}{3}m{t}^2-c$
(i) Find the value of P when c = 4, m = 2 and t = −3.

(ii) Make t the subject of the formula.

(a) (i) Factorise completely $2m^2-m-15$.

(ii) Hence, or otherwise simplify $\frac{2m^2-m-15}{4m^2-25}$.

(b) Given that $(a-b{)}^2=20$ and $(a+b{)}^2=36$, find the value of $a^2+b^2$.

Solve the equations:
(i) $\frac{4}{5}x-6=2x-8$,

(ii) $x^2=2x$,

(iii) $2x^2-4x-3=0$, giving your answer to 3 decimal places.

(a) Solve the equation.
$(2x-2)(6x+1)=0$

(b) Factorise completely.
$2a^2+6a-ab-3b$

(c) Express as a single fraction in its simplest form.
Show all your working.
$\frac{1}{p-2}-\frac{2}{4p+3}$

(a) Simplify,
${\left(4x^2{y}^3\right)}^4$

(b) Make a the subject of the formula.
$p=\frac{r}{\sqrt{a}}$

(c) Simplify fully.
$\frac{2x^2+5x-3}{x^2+3x}$

(d) Solve $x^2+5x-3=0$.