Substitution and formulae

Substitution means putting numbers in place of letters, then working out the answer. Use brackets when you substitute a negative number, and follow BIDMAS.

Key facts

  • Replace each letter with its number.
  • Put negative numbers in brackets: x = −3 gives (−3)².
  • 3a means 3 × a, so if a = 4, 3a = 12.

Worked examples

Example 1

Find 4a − 2b when a = 5 and b = 3.

  1. Put the numbers in. 4 × 5 − 2 × 3
  2. Multiply first. 20 − 6
  3. Subtract. 14

Answer: 14

Example 2

Use v = u + at to find v when u = 4, a = 3 and t = 5.

  1. Put the numbers in. v = 4 + 3 × 5
  2. Multiply first. v = 4 + 15
  3. Add. v = 19

Answer: v = 19

Example 3

Find x² − 3x when x = −2.

  1. Use brackets. (−2)² − 3 × (−2)
  2. Square, then multiply. 4 − (−6)
  3. Subtracting a negative is adding. 4 + 6 = 10

Answer: 10