Sample quiz on isolating variables
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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.
    
    $\eta=\frac{c+v}{v}$
    $\eta=\frac{c-v}{v}$
    $\eta=\frac{v}{c}$
    $\eta=\frac{c}{v}$