Cambridge International AS and A Level Mathematics Pure Mathematics 1

Changing the subject of a formula

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1

EXAMPLE 1.16 Make a the subject in A = 12 (a + b)h.

SOLUTION

It is usually easiest if you start by arranging the equation so that the variable you

want to be its subject is on the left-hand side.

(^12) (a + b)h = A
Multiply both sides by 2 ⇒ (a + b)h = 2 A
Divide both sides by h ⇒ a + b = (^2) hA
Subtract b from both sides ⇒ a = (^2) hA − b
EXAMPLE 1.17 Make T the subject in the simple interest formula I = PR 100 T.
SOLUTION
Arrange with T on the left-hand side PR 100 T = I
Multiply both sides by 100 ⇒ PRT = 100 I
Divide both sides by P and R ⇒ T = (^100) PRI
EXAMPLE 1.18 Make x the subject in the formula v = ω ax^22 –. (This formula gives the speed
of an oscillating point.)
SOLUTION
Square both sides ⇒ v^2 = ω^2 (a^2 − x^2 )
Divide both sides by ω^2 ⇒ v
2
ω^2 =^ a
(^2) − x 2
Add x^2 to both sides ⇒ v
2
ω^2 +^ x
(^2) = a 2
Subtract v
2
ω^2 from both sides^ ⇒^ x^2 =^ a^2 −
v^2
ω^2
Take the square root of both sides ⇒ x = ± a^2 v
2

• ω 2

EXAMPLE 1.19 Make m the subject of the formula mv = I + mu. (This formula gives the
momentum after an impulse.)

SOLUTION

Collect terms in m on the left-hand side

and terms without m on the other. ⇒ mv − mu = I

Factorise the left-hand side ⇒ m(v − u) = I

Divide both sides by (v − u) ⇒ m I

vu

=

–