# Test: Formulae - Ambitious

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Question 1:   Find the value of $d$ in the following formula: $d=\frac{x}{y}$, if $x=5,y=2$
$d=2$
$d=5$
$d=\frac{5}{2}$
$d=\frac{2}{5}$
Question 2:   Find the value of $\Delta$ in the following formula: $\Delta ={b}^{2}-4ac$, if $b=5,a=1,c=4$
$\Delta =16$
$\Delta =15$
$\Delta =3$
$\Delta =9$
Question 3:   Transpose the following formula for $h$: $s=\frac{1}{2}ah$
$h=2\frac{a}{s}$
$h=\frac{1}{2}as$
$h=2as$
$h=2\frac{s}{a}$
Question 4:   Transpose the following formula for $x$: $y=\frac{x+1}{3}$
$x=3y-1$
$x=y-3$
$y=x+\frac{1}{3}$
$x=\frac{y+1}{3}$
Question 5:   Transpose the following formula for $c$: $E=m{c}^{2}$
$c=\frac{E}{m}$
$c=E{m}^{2}$
$c=\sqrt{\frac{E}{m}}$
$c=\sqrt{\frac{m}{E}}$
Question 6:   Transpose the following formula for $q$: $p=\frac{2}{\sqrt{q}}$
$q=\frac{1}{2\sqrt{p}}$
$q=\frac{1}{2{p}^{2}}$
$q=\frac{2}{\sqrt{p}}$
$q=\frac{4}{{p}^{2}}$
Question 7:   Transpose the following formula for $x$: $y=\frac{x+1}{x-1}+2$
$x=\frac{y+2}{y-3}-1$
$x=\frac{y-3}{y-1}$
$x=\frac{y-1}{y-2}-2$
$x=\frac{y-1}{y-3}$
Question 8:   Transpose the following formula for $b$ : $y=a{x}^{2}+bx+c$
$b=y-a{x}^{2}-c$
$b=\frac{y-a{x}^{2}-c}{x}$
$b=y+2a{x}^{2}-c$
$b=\frac{y-a{x}^{2}+c}{y}$
Question 9:   Rearrange the formula $u=\sqrt{v-1}+1$ to make $v$ a subject
$v={u}^{2}-1$
$v={\left(u-1\right)}^{2}+1$
$v=\sqrt{u-1}+1$
$v={u}^{2}-2$
Question 10:   Rearrange the formula $2ax+by=3ay-bx$ to make $x$ a subject
$x=3ay-by-2a-b$
$x=\frac{y\left(2a+b\right)}{3a-b}$
$x=3ay-by+2a+b$
$x=\frac{y\left(3a-b\right)}{2a+b}$