Rearranging equations
A LEVEL LINKS
Scheme of work: 6a. Definition, differentiating polynomials, second derivatives
Textbook: Pure Year 1, 12.1 Gradients of curves
Key points
To change the subject of a formula, get the terms containing the subject on one side and
everything else on the other side.
You may need to factorise the terms containing the new subject.
Examples
Example 1 Make t the subject of the formula v = u + at.
v = u + at
v − u = at
vu
ta
1 Get the terms containing t on one
side and everything else on the other
side.
2 Divide throughout by a.
Example 2 Make t the subject of the formula r = 2t − πt.
r = 2t − πt
r = t(2 − π)
2
r
t
1 All the terms containing t are
already on one side and everything
else is on the other side.
2 Factorise as t is a common factor.
3 Divide throughout by 2 − π.
Example 3 Make t the subject of the formula
3
52
t r t
.
3
52
t r t
2t + 2r = 15t
2r = 13t
2
13
r
t
1 Remove the fractions first by
multiplying throughout by 10.
2 Get the terms containing t on one
side and everything else on the other
side and simplify.
3 Divide throughout by 13.
