Substitution and formulae · Grade 8

In Grade 8 you learn: substituting negative numbers and formulas with powers.

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