Substitution and formulae · Year 8
In Year 8 you learn: 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