# Sample quiz on isolating variables Main home here.

1. The area of a triangle can be given by $A=\frac{bh}{2}$. Isolate $b$ from the equation.
$b=\frac{A}{2h}$
$b=\frac{2h}{A}$
$b=\frac{2A}{h}$
$b=\frac{2A-h}{h}$
2. The equation of a line can be given by $y=mx+b$. Rearrange the equation to isolate $b$.
$b=y-mx$
$b=y+mx$
$b=mx-y$
$b=m-yx$
3. The perimeter of a rectangle can be given by $P=2(l+w)$. Isolate $l$ from the equation.
$l=P-2w$
$l=\frac{P-2w}{2}$
$l=\frac{P+2w}{2}$
$l=\frac{2w-P}{2}$
4. The circumference of a circle can be given by $C=2\pi r$. Isolate $r$ from the equation.
$r=\frac{2C}{\pi}$
$r=\frac{C}{2\pi}$
$r=C-2\pi$
$r=C+2\pi$
5. The perimeter of a square can be given by $P=4l$. Isolate $l$ from the equation.
$l=4P$
$l=\frac{4}{P}$
$l=\frac{P}{4}$
$l=P-4$
6. The area of a trapezoid can be given by $A=\frac{(a+b)h}{2}$. Isolate $h$ from the equation.
$h=\frac{2A}{a+b}$
$h=\frac{a+b}{2A}$
$h=\frac{A}{2(a+b)}$
$h=\frac{2A}{ab}$
7. If $A=\frac{(a+b)h}{2}$, express $a$ in terms of $A,b,h$.
$a=\frac{2A+bh}{h}$
$a=\frac{A-bh}{h}$
$a=\frac{2A-bh}{h}$
$a=\frac{bh-2A}{h}$
8. If $v=u+at$, express $t$ in terms of $v,u,a$.
$t=\frac{u-v}{a}$
$t=\frac{v-u}{a}$
$t=\frac{u+v}{a}$
$t=\frac{a}{v-u}$
9. In a simple interest, we have $A=P+Prt$. Isolate $r$ from the equation.
$r=\frac{P-A}{Pt}$
$r=\frac{A+P}{Pt}$
$r=\frac{A-P}{Pt}$
$r=\frac{A-P}{P-t}$
10. The speed of light $c$ can be given by $c=\eta v$. Isolate $\eta$ from the equation.
$\eta=\frac{c+v}{v}$
$\eta=\frac{c-v}{v}$
$\eta=\frac{v}{c}$
$\eta=\frac{c}{v}$