# Algebra - Changing the Subject of a Formula

a - answer    s - solution    v - video    d - discussion

## Question 1

Make $x$ the subject

a) $y=x+2$a s v d
b) $h=x-5$a s v d
c) $x+b=a$a s v d
d) $g=x-h$a s v d
e) $a+b=x+c$a s v d
f) $x+w=yz$a s v d
g) $10m=x-4$a s v d
h) $\frac pq=x+5$a s v d
i) $x-s=\frac t5$a s v d
j) $2(a+b)=x-\frac cd$a s v d

## Question 2

Make $a$ the subject

a) $c=ab$a s v d
b) $3=at$a s v d
c) $r=4a$a s v d
d) $5t=ak$a s v d
e) $ax=9p$a s v d
f) $mn=ap$a s v d
g) $5+h=4a$a s v d
h) $ac=y+x$a s v d
i) $b=15ac$a s v d
j) $20abc=55-k$a s v d

## Question 3

Make $m$ the subject

a) $55=\frac mn$a s v d
b) $g=\frac mh$a s v d
c) $p=\frac m5$a s v d
d) $\frac m4=12h$a s v d
e) $\frac {m}{2a}=b$a s v d
f) $41p=\frac {m}{qt}$a s v d
g) $10x+y=\frac {m}{z}$a s v d
h) $\frac {m}{8g}=6t-7p$a s v d
i) $\frac {m}{4p^2}=\frac12$a s v d
j) $22a^2-b=\frac {m}{7u+v^3}$a s v d

## Question 4

Make $p$ the subject

a) $k=p^2$a s v d
b) $p^2=9$a s v d
c) $p^2=5$a s v d
d) $3q=p^2$a s v d
e) $p^2=r^2$a s v d
f) $4t^2=p^2$a s v d
g) $p^3=8$a s v d
h) $p^3=4$a s v d
i) $s=p^n$a s v d
j) $4x-y=p^z$a s v d

## Question 5

Make $d$ the subject

a) $4=\sqrt d$a s v d
b) $e=\sqrt d$a s v d
c) $\sqrt d=2f$a s v d
d) $10g^2=\sqrt d$a s v d
e) $\sqrt[3] d=1$a s v d
f) $3h=\sqrt[3] d$a s v d
g) $k=\sqrt[5] d$a s v d
h) $\sqrt[n] d=y$a s v d
i) $\sqrt[x] d=pq$a s v d
j) $\sqrt[4] d=h+y$a s v d

## Question 6

Make $g$ the subject

a) $h=\frac4g$a s v d
b) $\frac8g=2$a s v d
c) $5a=\frac{15}{g}$a s v d
d) $\frac mg=k$a s v d
e) $20a=\frac {bc}{g}$a s v d
f) $30k=\frac {50k}{g}$a s v d
g) $4+e^2=\frac {16cd}{g}$a s v d
h) $\frac {1-5t}{g}=5u+w$a s v d
i) $\frac {5h^3}{g}=h$a s v d
j) $4x^3y^2z=\frac {12xy^2z^3}{g}$a s v d

## Question 7

Make the highlighted letter the subject

a) $A={\bf s}^2$a s v d
b) $P=m{\bf g}h$a s v d
c) $C=2\pi{\bf r}$a s v d
d) $A=\frac12b{\bf h}$a s v d
e) $E=m{\bf c}^2$a s v d
f) $A=\frac12{\bf r}^2\theta$a s v d
g) $a^2+{\bf b}^2=c^2$a s v d
h) $A=\frac{h({\bf a}+b)}{2}$a s v d
i) $a=\frac{v^2}{\bf r}$a s v d
j) $v=u+a{\bf t}$a s v d
k) $w=\sqrt{\frac{\bf g}{l}}$a s v d
l) $V=\frac43\pi {\bf r}^3$a s v d
m) $v=u+\frac12a{\bf t}^2$a s v d
n) $T=\frac{1}{2\pi}\sqrt{\frac m{\bf k}}$a s v d
o) $T^2=\frac{4\pi^2}{GM}{\bf r}^3$a s v d
p) $ax^2+{\bf b}x+c=0$a s v d
q) $x=\frac{-b+\sqrt{b^2-4a{\bf c}}}{2a}$a s v d
r) $S_{\infty}=\frac{a}{1-r}$a s v d
s) $S_n=\frac{{\bf a}(1-r^n)}{1-r}$a s v d
t) $u=a{\bf r}^{n-1}$a s v d

## Question 8

Make $x$ the subject
##### (You must be able to factorise before attempting these questions}

a) $ax+bx=2$a s v d
b) $cx-dx=e$a s v d
c) $2x+mx=3n$a s v d
d) $7st=px-qx$a s v d
e) $5+g=2hx-kx$a s v d
f) $y-z=xy+xz$a s v d
g) $3+2x-ax=b$a s v d
h) $6-kx+x-b=0$a s v d
i) $0=20-x-m+mx+6$a s v d
j) $2x+5=kx+p$a s v d
k) $3x-2+y=x+6-rx-px$a s v d

## Question 9

Make the highlighted letter the subject

a) $\frac1a=\frac1{\bf b}-\frac1c$a s v d
b) $\frac1x=\frac1y+\frac1{\bf z}$a s v d
c) $\frac3p=\frac2q-\frac5{\bf r}$a s v d
d) $\frac ab=\frac c{\bf d}+\frac ef$a s v d