Exercises: Changing the subject of a formula

Make $x$ the subject of the formula $y = 3x + 7$.

The perimeter of a rectangle is $P = 2l + 2w$. Make $l$ the subject of the formula.

The formula $v = u + at$ is used in physics. Make $a$ the subject, then find $a$ when $v = 20$, $u = 5$ and $t = 3$.

The volume of a cylindrical water tank is $V = \pi r^2 h$.

1. a) Make $h$ the subject of the formula.
2. b) Make $r$ the subject of the formula.
3. c) A tank has volume $12\text{ m}^3$ and radius $1.5\text{ m}$. Find its height correct to two decimal places.

The formula to convert degrees Celsius to degrees Fahrenheit is $F = \frac{9}{5}C + 32$.

1. a) Make $C$ the subject.
2. b) Find the temperature in degrees Celsius when it is $68^\circ$F in Dublin.

The formula $s = ut + \frac{1}{2}at^2$ gives the distance travelled.

1. a) Make $a$ the subject of the formula.
2. b) Find $a$ when $s = 50$, $u = 4$ and $t = 5$.

The formula $T = 2\pi\sqrt{\dfrac{l}{g}}$ gives the period of a pendulum.

1. a) Make $l$ the subject of the formula.
2. b) A pendulum in the Science Gallery has period $T = 4$ seconds. Using $g = 9.8\text{ m/s}^2$, find $l$ correct to two decimal places.
3. c) By what factor does $l$ change if $T$ is doubled?

The formula for the final amount in a compound interest account is $F = P(1+i)^t$.

1. a) Make $P$ the subject of the formula.
2. b) Make $i$ the subject of the formula.
3. c) An investment grows to €5,000 after 4 years at an annual rate $i$. If the initial sum was €4,200, find $i$ as a percentage correct to two decimal places.

Given $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$:

1. a) Make $v$ the subject of the formula and write it as a single fraction.
2. b) Find $v$ when $f = 12$ and $u = 20$.
3. c) Explain what happens to $v$ as $u$ approaches $f$ from above.