Algebra vocabulary
OCR mark schemes treat algebra vocabulary as an examinable topic in its own right. Foundation Paper 1 routinely awards 1–2 marks on "is this an expression, equation, identity, formula, or inequality?".
📖Definition— Definitions
- Expression: a combination of letters and numbers, e.g. 3x + 5. No equals sign. Cannot be solved.
- Equation: two expressions joined by =, true only for specific values of the variable. e.g. 3x + 5 = 11. Has solution(s).
- Identity: an equation that is true for ALL values of the variable, e.g. 2(x + 3) ≡ 2x + 6. Use ≡ symbol.
- Formula: an equation expressing a relationship between variables, used to compute one quantity from others, e.g. A = πr² (area of a circle).
- Inequality: like an equation but uses <, >, ≤, or ≥ instead of =, e.g. 2x + 3 > 7.
Terms, coefficients, factors
- A term is a single number, letter, or product, separated by + or − within an expression.
- In 3x² − 5xy + 7, the terms are 3x², −5xy, and 7.
- The coefficient of a term is the numerical part.
- In 3x², the coefficient is 3.
- In −5xy, the coefficient is −5.
- A constant term has no variable (the 7 above).
- A factor is a number or expression that multiplies into another. Factors of 6x² are 1, 2, 3, 6, x, 2x, 3x, 6x, x², 2x², 3x², 6x².
Like and unlike terms
Like terms have the same letter parts (same letters AND same powers).
- 3x and 5x — like (collect: 8x).
- 3x and 5x² — unlike (different powers).
- 3xy and 5yx — like (multiplication is commutative; xy = yx).
Only like terms can be added/subtracted to simplify.
Linear vs quadratic
- Linear expressions/equations have variable to power 1: 3x + 5, 2y = 7.
- Quadratic has highest power 2: x² − 5x + 6.
- Cubic has highest power 3.
- Exponential has variable in the exponent: 2^x.
OCR mark scheme conventions
- "What is the coefficient of x in…?" — B1 for the correct number (with sign).
- "Is this an equation or identity?" — B1 for the correct classification.
- "How many terms are in…" — B1 for counting correctly.
- The use of ≡ for identity is preferred but = is usually accepted with full credit.
⚠Common mistakes
- Confusing equation and identity (3x = 12 is an equation; 3x ≡ 3x is an identity).
- Missing the sign of the coefficient (in 3x − 5y, the coefficient of y is −5, not 5).
- Combining unlike terms (3x + 5x² ≠ 8x³).
- Forgetting that "factors" can be expressions (in 2x²(3x − 1), the factors are 2, x², and (3x − 1)).
AI-generated · claude-opus-4-7 · v3-ocr-maths-leaves