Substitution and formulae · Grade 8

In Grade 8 you learn: formulas with powers; rearranging and using formulas.

Substitution means replacing the letters in an expression or formula with numbers and working out the value. It is how formulas get used in real life — a taxi fare, a cooking time, or how far a ball rolls.

Key facts

  • Replace each letter with its value, using brackets round negative numbers: if x = −3, 2x = 2 × (−3) = −6.
  • Then follow the order of operations: brackets, powers, × and ÷, then + and −.
  • 3x² means 3 × x²: square first, then multiply. It is not (3x)².
  • A negative number squared is positive: (−4)² = 16.
  • A fraction line acts like a bracket: work out the top and the bottom first.
  • A formula such as A = lw links quantities; substitute what you know to find the one you don’t.

Worked examples

Example 1

Find 5a − 2b when a = 4 and b = −3.

Answer: 26

Example 2

Find 2x² − 3x when x = −4.

Answer: 44

Example 3

Use s = ut + ½at² to find s when u = 3, a = 4 and t = 5.

Answer: s = 65

Other years