Changing the subject
- To make a letter the subject, get it on its own using inverse operations, doing the same to both sides.
- Undo operations in the reverse order: y = 3x + 2 → y − 2 = 3x → x = (y − 2)/3.
- v = u + at → v − u = at → t = (v − u)/a.
More examples
- P = 2l + 2w → l = (P − 2w)/2.
- y = x/4 − 1 → y + 1 = x/4 → x = 4(y + 1).
- E = mc² → m = E/c². V = lwh → h = V/(lw).
Powers and roots
- If the subject is squared, square root at the end: A = πr² → r² = A/π → r = √(A/π).
- If the subject is under a root, square both sides.
Subject appearing twice (Higher)
- Collect the terms containing the subject on one side, then factorise and divide.
- ax + 3 = bx + 7 → ax − bx = 4 → x(a − b) = 4 → x = 4/(a − b).
Key terms
- Subject
- The letter on its own on one side of a formula.
- Rearrange
- Change a formula so that a different letter is the subject.
- Inverse operation
- The operation that undoes another, such as subtraction for addition.
- Factorise
- Take out a common factor, such as x(a − b).