# Algebra - Using Formulas

a - answer    s - solution    v - video

## Question 1

For the formula $x=y+10$

a) Find $x$ when $y=5$a s v
b) Find $x$ when $y=14$a s v
c) Find $x$ when $y=0$a s v
d) Find $x$ when $y=-5$a s v
e) Find $y$ when $x=12$a s v
f) Find $y$ when $x=43$a s v
g) Find $y$ when $x=6$a s v
h) Find $y$ when $x=8\frac12$a s v

## Question 2

For the formula $c=100d$

a) Find $c$ when $d=2$a s v
b) Find $c$ when $d=8$a s v
c) Find $c$ when $d=\frac14$a s v
d) Find $c$ when $d=-3$a s v
e) Find $d$ when $c=500$a s v
f) Find $d$ when $c=1200$a s v
g) Find $d$ when $c=20$a s v
h) Find $d$ when $c=-80$a s v

## Question 3

For the formula $g=h^2$

a) Find $g$ when $h=3$a s v
b) Find $g$ when $h=11$a s v
c) Find $g$ when $h=-4$a s v
d) Find $g$ when $h=\frac13$a s v
e) Find $h$ when $g=25$a s v
f) Find $h$ when $g=81$a s v
g) Find $h$ when $g=\frac{1}{36}$a s v
h) Find $h$ when $g=0.25$a s v

## Question 4

For the formula $x=2y+7$

a) Find $x$ when $y=4$a s v
b) Find $x$ when $y=10$a s v
c) Find $x$ when $y=-3$a s v
d) Find $x$ when $y=\frac12$a s v
e) Find $y$ when $x=13$a s v
f) Find $y$ when $x=25$a s v
g) Find $y$ when $x=7$a s v
h) Find $y$ when $x=-2$a s v

## Question 5

For the formula $A=lw$

a) Find $A$ when $l=2$ and $w=3$a s v
b) Find $A$ when $l=8$ and $w=6$a s v
c) Find $A$ when $l=-7$ and $w=-5$a s v
d) Find $A$ when $l=\frac14$ and $w=12$a s v
e) Find $l$ when $A=25$ and $w=5$a s v
f) Find $l$ when $A=72$ and $w=9$a s v
g) Find $w$ when $A=6$ and $l=\frac13$a s v
h) Find $w$ when $A=-12$ and $l=-0.5$a s v

## Question 6

For the formula $m=2p-q$

a) Find $m$ when $p=3$ and $q=2$a s v
b) Find $m$ when $p=7$ and $q=1$a s v
c) Find $m$ when $p=2$ and $q=5$a s v
d) Find $m$ when $p=\frac12$ and $q=1$a s v
e) Find $q$ when $m=4$ and $p=15$a s v
f) Find $q$ when $m=-1$ and $p=11$a s v
g) Find $p$ when $m=13$ and $q=7$a s v
h) Find $p$ when $m=25$ and $q=2$a s v

## Question 7

For the formula $v=u+at$

a) Find $v$ when $u=2$, $a=10$ and $t=5$a s v
b) Find $v$ when $u=18$, $a=15$ and $t=0$a s v
c) Find $v$ when $u=3$, $a=21$ and $t=\frac13$a s v
d) Find $u$ when $v=10$, $a=3$ and $t=2$a s v
e) Find $u$ when $v=3$, $a=-8$ and $t=5$a s v
f) Find $a$ when $v=17$, $u=5$ and $t=4$a s v
g) Find $a$ when $v=0$, $u=50$ and $t=10$a s v
h) Find $t$ when $v=40$, $u=10$ and $a=3$a s v

## Question 8

For the formula $K=\frac12mv^2$

a) Find $K$ when $m=5$ and $v=2$a s v
b) Find $K$ when $m=4$ and $v=3$a s v
c) Find $K$ when $m=1$ and $v=-3$a s v
d) Find $m$ when $K=16$ and $v=4$a s v
e) Find $m$ when $K=50$ and $v=4$a s v
f) Find $v$ when $K=54$ and $m=3$a s v
g) Find $v$ when $K=150$ and $m=12$a s v
h) Find $v$ when $K=1$ and $m=8$a s v

## Question 9

For the formula $E=mc^2$

a) Find $E$ when $m=2$ and $c=300$a s v
b) Find $E$ when $m=0.0001$ and $c=600$a s v
c) Find $E$ when $m=\frac12$ and $c=12$a s v
d) Find $m$ when $E=4500$ and $c=30$a s v
e) Find $m$ when $E=2025$ and $c=180$a s v
f) Find $c$ when $E=405$ and $m=6$a s v
g) Find $c$ when $E=900$ and $m=\frac{1}{100}$a s v
h) Find $c$ when $E=562500$ and $m=\frac{1}{160000}$a s v

## Question 10

For the formula $v=\sqrt{\frac{3RT}{M}}$

a) Find $v$ when $R=3$, $T=4$ and $M=1$a s v
b) Find $v$ when $R=6$, $T=9$ and $M=2$a s v
c) Find $v$ when $R=12$, $T=20$ and $M=5$a s v
d) Find $R$ when $v=3$, $T=6$ and $M=6$a s v
e) Find $R$ when $v=6$, $T=24$ and $M=8$a s v
f) Find $T$ when $v=1$, $R=1$ and $M=9$a s v
g) Find $M$ when $v=9$, $R=5$ and $T=27$a s v
h) Find $M$ when $v=4$, $R=4$ and $T=8$a s v

## Question 11

For the formula $x=\frac{m\lambda L}{d}$

a) Find $x$ when $m=5$, $\lambda=4$, $L=15$ and $d=2$a s v
b) Find $x$ when $m=3$, $\lambda=6$, $L=4$ and $d=9$a s v
c) Find $m$ when $x=12$, $\lambda=5$, $L=8$ and $d=10$a s v
d) Find $m$ when $x=7$, $\lambda=4$, $L=7$ and $d=2$a s v
e) Find $\lambda$ when $x=0.01$, $m=0.4$, $L=5$ and $d=10$a s v
f) Find $\lambda$ when $x=-5$, $m=-5$, $L=-2$ and $d=14$a s v
g) Find $d$ when $x=36$, $m=12$, $\lambda=3$ and $L=5$a s v
h) Find $d$ when $x=1$, $m=\frac14$, $\lambda=-20$ and $L=0.1$a s v

## Question 12

For the formula $T=2\pi\sqrt{\frac Lg}$

a) Find the exact value of $T$ when $L=150$ and $g=6$a s v
b) Find the value of $T$ when $L=6$ and $g=\frac32\pi^2$a s v
c) Find the value of $T$ when $L=\frac{9}{\pi^2}$ and $g=25$a s v
d) Find the value of $L$ when $T=6\pi$ and $g=5$a s v
e) Find the exact value of $L$ when $T=10$ and $g=4$a s v
f) Find the value of $g$ when $T=2\pi$ and $L=19$a s v
g) Find the value of $g$ when $T=20\pi$ and $L=150$a s v
h) Find the exact value of $g$ when $T=3$ and $L=9$a s v

## Question 13

For the formula $1-Q=\frac{1}{1-T}$

a) Find $Q$ when $T=-4$a s v
b) Find $Q$ when $T=\frac12$a s v
c) Find $Q$ when $T=19$a s v
d) Find $Q$ when $T=\frac83$a s v
e) Find $T$ when $Q=0$a s v
f) Find $T$ when $Q=\frac34$a s v
g) Find $T$ when $Q=2$a s v
h) Find $T$ when $Q=\frac97$a s v

## Question 14

For the formula $\frac1a=\frac1b+\frac1c$

a) Find $a$ when $b=\frac12$ and $c=\frac13$a s v
b) Find $a$ when $b=2$ and $c=3$a s v
c) Find $a$ when $b=\frac15$ and $c=2$a s v
d) Find $b$ when $a=\frac19$ and $c=\frac15$a s v
e) Find $b$ when $a=\frac{24}{7}$ and $c=8$a s v
f) Find $c$ when $a=\frac{1}{12}$ and $b=\frac15$a s v
g) Find $c$ when $a=\frac27$ and $b=\frac23$a s v
h) Find $c$ when $a=-4$ and $b=-\frac89$a s v