Changing the subject · Year 11

In Year 11 you learn: the subject on both sides.

Changing the subject means rearranging a formula so that a different letter is on its own. If you know A = πr² but want the radius from an area, you rearrange it to r = √(A/π). The moves are exactly the same as solving an equation.

Key facts

  • The subject is the letter on its own on one side: in v = u + at, v is the subject.
  • Undo the operations on the new subject in reverse order, doing the same to both sides.
  • To undo a square, take the square root; to undo a square root, square both sides.
  • If the new subject is on the bottom of a fraction, multiply both sides by it first.
  • If the new subject appears twice, collect those terms on one side and factorise it out.

Worked examples

Example 1

Make t the subject of v = u + at.

Answer: t = (v − u)/a

Example 2

Make r the subject of V = ⅓πr²h.

Answer: r = √((3V)/(πh))

Example 3

Make x the subject of y = (2x + 3)/(x − 1).

Answer: x = (y + 3)/(y − 2)

Other years