1.04 Changing the subject of a formula

Worksheet
Rearrange equations
1

Make x the subject of the following equations:

a

y = x + z

b

y = \dfrac{x}{4}

c
y = - 5 \left(9 + x\right)
d
kx = m + nx
e

\dfrac{x}{8} + \dfrac{n}{9} = 3

f

\dfrac{x}{- 2} + \dfrac{n}{- 5} = 5

2

Make R the subject in the equation D = R T.

3

Make m the subject of the following equations:

a
\dfrac{m}{y} = gh
b

y = 6 m x - 9

c

x = 8 k \left(n + m\right)

d

x = - 9 k \left(n + m\right)

4

Consider the Pythagoras formula: c^{2} = a^{2} + b^{2}.

a

Rearrange the formula to make a^{2} the subject.

b

Rearrange the formula to make b^{2} the subject.

5

Make R the subject of V = I R - E.

6

Make y the subject for the following:

a
15 x^{2} + 5 y = 20
b

8 x^{3} = 2 y - 6

c
\dfrac{x}{y} = h - k
7

Make k the subject of the following equations:

a

m = \dfrac{5 k x}{8} - 4

b

r = \dfrac{k}{k - 9}

8

Make r the subject of the equation L = \dfrac{E}{R + r}.

9

Make x the subject of the equation y = k \left(n - x\right).

10

Consider the equation R = c d - 5 c t^{2}.

a

Explain the first step in making c the subject of the equation.

b

Hence, make c the subject.

Applications
11

The formula that converts Celsius into Fahrenheit is F = \dfrac{9}{5} C + 32.

Describe the steps that must be taken to make C the subject of the formula.

12

Rearrange the formula for the area of a circle, A = \pi r^{2}, to make r^{2} the subject.

13

Rearrange the formula for kinetic energy: K = \dfrac{1}{2} m v^{2}, to make v^{2} the subject.

14

The volume of a cone is given by the formula V = \dfrac{1}{3} \pi r^{2} h. Rearrange the equation to make r^{2} the subject.

15

The area of a sector of a circle can be found using the formula A = \dfrac{S \pi r^{2}}{360}. Rearrange the equation to make r^{2} the subject.

16

The bend allowance for sheet metal is given by the formula B = 2 \pi \left(R + \dfrac{T}{2}\right) \times \dfrac{A}{360}.

Make T, the thickness of the sheet, the subject of the formula.

17

The life expectancy, y, of a person born in Japan is approximated by the equation \\ y = 0.27 x + 72, where x is the number of years since 1970.

a

Make x the subject of this equation.

b

Find the value of x for when the life expectancy is 95. Round your answer to three decimal places.

c

In what year will the life expectancy of a person born in Japan reach 95 years?

18

The amount of oil, y, imported to the United States from Canada, in millions of barrels per day, can be approximated by the equation y = 0.106 x + 1.37, where x is the number of years since 2000.

In what year will the approximate number of barrels imported from Canada be 3.5 million per day?