Key Terms
- Variable: A letter representing an unknown number (e.g. x, y)
- Term: A number, letter, or combination (e.g. 3x, −7, 5y²)
- Expression: A group of terms with no equals sign (e.g. 3x + 2y)
- Coefficient: The number multiplying a variable (e.g. 5 in 5x)
- Constant: A term with no variable (e.g. −7 in 3x − 7)
- Equation: Two expressions set equal (e.g. 2x + 1 = 9)
- Formula: A rule connecting variables (e.g. A = lw)
Must-Know Facts
- 3y means 3 × y (the × sign is omitted in algebra)
- y² means y × y (not 2 × y)
- An invisible coefficient of 1: y means 1y
- ab means a × b; a²b means a × a × b
- The sign (+ or −) belongs to the term that follows it
- Squaring and multiplying by 2 are different: x² ≠ 2x
Key Methods
- Identifying terms: separate at + or − signs (keep the sign with the term)
- Reading powers: x³ = x × x × x (three lots of x multiplied)
- Writing products: write letters in alphabetical order (ab, not ba)
- Substitution: replace each letter with its value using brackets for negatives
Common Mistakes
- Confusing 2x and x²: 2x means 2 × x (multiply by 2); x² means x × x (square it) — these are completely different
- Dropping negative signs in substitution: If x = −3, write (−3)² = 9 with brackets — writing −3² gives −9 instead
- Treating 3ab and 3ba as different: Multiplication is commutative — always write letters in alphabetical order so 3ba becomes 3ab
- Forgetting the invisible coefficient: y means 1y — when collecting like terms, remember to count this 1
This topic summary covers Knowledge Organiser: Algebraic Notation within Algebraic Notation for GCSE Mathematics. Revise Algebraic Notation in Algebra for GCSE Mathematics with 13 exam-style questions and 4 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Algebraic Notation
In the expression 7x, what is the coefficient?
Explain the difference between an equation and an identity. Give one example of each.
Quick recall flashcards
Term
A single part of an expression: 3x is one term
Variable
A letter representing an unknown value