Substitution
- Substitution means replacing letters with numbers: if a = 3 and b = 5, then 2a + b = 6 + 5 = 11.
- Use brackets for negative numbers: if x = −2, then x² = (−2)² = 4, and 3x² = 3 × 4 = 12.
- Follow BIDMAS: 3x² means square x first, then multiply by 3.
Using formulae
- Write the formula, substitute, then calculate: v = u + at with u = 5, a = 2, t = 3 gives v = 5 + 6 = 11.
- A = ½bh with b = 8 and h = 5 gives A = 20.
- F = 9C/5 + 32 with C = 20 gives F = 36 + 32 = 68.
Writing formulae
- Turn words into a formula: a taxi charges £3 plus £2 per mile, so C = 3 + 2m.
- A plumber charges £35 plus £28 per hour: C = 35 + 28h.
- The perimeter of a square with side s is P = 4s.
Key terms
- Substitute
- Replace a letter with a number.
- Formula
- A rule that shows how to work out one quantity from others.
- Variable
- A letter that stands for a quantity that can change.
- Subject
- The letter on its own on one side of a formula, such as v in v = u + at.
- Evaluate
- Work out the value.