Algebraic vocabulary
Edexcel mark schemes are precise about terminology. A "formula" is not the same as an "equation"; an "expression" has no equals sign at all. Lose this and you lose easy marks on definitions and reasoning questions.
📖Definition— Key terms
- Term: a single algebraic part separated by + or − signs. In 3x² − 5x + 2: terms are 3x², −5x, +2.
- Coefficient: the number multiplying a variable. In 3x², coefficient of x² is 3.
- Constant: a term without a variable. In 3x² − 5x + 2, the constant is 2.
- Expression: a collection of terms with no equals sign. e.g. 3x + 5.
- Equation: contains an equals sign and can be solved for specific value(s) of the variable. e.g. 3x + 5 = 17 has solution x = 4.
- Formula (plural: formulae): a relationship between two or more variables, often used to calculate one from the others. e.g. A = πr² (a formula for circle area).
- Identity: an equation true for all values of the variable. e.g. 2(x + 3) ≡ 2x + 6. Use ≡ (three-bar equality) for identities.
- Inequality: uses <, >, ≤, ≥. e.g. 3x − 1 ≥ 8 has solution x ≥ 3.
- Factor (algebraic): an expression that divides another exactly. e.g. (x + 2) is a factor of x² + 5x + 6 because (x + 2)(x + 3) = x² + 5x + 6.
Edexcel exam tip
The question "is this an expression, equation, formula, or identity?" appears regularly on Foundation. Test:
- Does it have an = sign? No → expression.
- Yes, and it represents a definition like "y = mx + c" → formula.
- Yes, and it can be solved for a specific x → equation.
- Yes, and it is true for all x → identity (use ≡).
Forming algebraic expressions
"Twice a number plus three" → 2x + 3. "The sum of three consecutive integers" → n + (n+1) + (n+2) = 3n + 3.
⚠Common mistakes— Common errors
- Calling 2x + 3 = 7 an "expression" — it has an equals sign, so it's an equation.
- Confusing factor with multiple. (x + 2) is a factor of (x + 2)(x + 3); (x + 2)(x + 3) is a multiple of (x + 2).
- Using "=" where "≡" is required for identities.
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