# Test: Formulae - Challenging

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Question 1:   Find the value of $x$ in the formula $c=a{x}^{2}+5$ , if $a=8$ , $c=7$
$x=4$
$x=\frac{1}{2}$ $\vee$ $x=-\frac{1}{2}$
$x=2$
$x=\frac{1}{4}$ $\vee$ $x=-\frac{1}{4}$
Question 2:   Find the value of $x$ in the formula $t=\sqrt[3]{x}+{s}^{2}$ , if $s=\frac{1}{2}$ , $t=3\frac{1}{4}$
$x=25$
$x=9$
$x=27$
$x=18$
Question 3:   Rearrange the formula $y=\frac{x-1}{5}+1$ to make $x$ a subject
$x=4y+5$
$x=\frac{y}{5}+1$
$x=5y-4$
$x=\frac{y-1}{5}+1$
Question 4:   Rearrange the formula $y=\frac{x-2}{3}+\frac{x-1}{4}$ to make $x$ a subject
$x=1\frac{5}{7}y+1\frac{4}{7}$
$x=\frac{7}{12}y-\frac{7}{11}$
$x=\frac{3}{7}y+\frac{4}{7}$
$x=12y-11$
Question 5:   Rearrange the formula $p=\frac{q-r}{q+s}-1$ to make $q$ a subject
$q=\frac{s-r-1}{p}$
$q=-\frac{r}{p}-\frac{s}{p}-1$
$q=\frac{-r-s-1}{p}$
$q=\frac{-\left(r+s\right)}{p}-s$
Question 6:   Rearrange the formula $n=\frac{2m+s}{t}$ to make $m$ a subject
$m=\frac{nt-s}{2}$
$m=\frac{s-nt}{2}$
$m=\frac{2n-t}{s}$
$m=\frac{2n-s}{t}$
Question 7:   Transpose the following formula for $V$: $u=\sqrt{\frac{V-2}{V+3}}$
$V=\frac{-3{u}^{2}-2}{{u}^{2}-1}$
$V=\sqrt{3\frac{{u}^{2}+1}{{u}^{2}-1}}$
$V=\frac{3{u}^{2}+2}{{u}^{2}-2}$
$V=-\frac{3{u}^{2}}{{u}^{2}-3}$
Question 8:   Transpose the following formula for $x$: $y=\frac{1}{2}\sqrt[3]{\frac{{x}^{2}-{z}^{2}}{v}}$
$x=2\sqrt{{y}^{3}{v}^{2}+{z}^{2}}$
$x=\sqrt{8{y}^{3}v+{z}^{2}}$
$x=2\sqrt[3]{\frac{{y}^{2}-{z}^{2}}{v}}$
$x=\frac{1}{2}\sqrt{{y}^{2}v\frac{3}{}-{z}^{2}}$
Question 9:   Rearrange the formula $\frac{1}{3}px+\frac{2}{3}qy=3qx-py$ to make $x$ a subject
$x=\frac{-y\left(3p+2q\right)}{p-9q}$
$x=\frac{y\left(2p-3q\right)}{3p-6q}$
$x=-y\left(3p-2q\right)\left(2p+3q\right)$
$x=-y\left(3p+2q\right)\left(p-3q\right)$
Question 10:   Rearrange the formula $ax-p=2xp-a$ to make $a$ a subject
$a=p\left(x-1\right)\left(x+1\right)$
$a=p\left(2x-1\right)\left(x-1\right)$
$a=\frac{2xp+1}{x+1}$
$a=\frac{p\left(2x+1\right)}{x+1}$