Notation, vocabulary and manipulation: understand and use the concepts and vocabulary of expressions, equations, formulae, inequalities, terms and factors

The idea

This row requires you to recognise and name six algebraic objects. An expression is a collection of terms with operations but no equals or inequality sign, like 3x² + 5y. An equation states two expressions are equal, like 4x + 1 = 13, and can be solved. A formula is a rule connecting quantities, like A = πr², used for substitution. An inequality compares expressions using <, >, ≤ or ≥, like 2x − 3 ≥ 7. A term is a single part separated by + or − signs; 3x² and 5y are terms. A factor is a number or expression that divides another exactly, so 3 and x are factors of 3x².

What earns the marks

• Identifies an expression as terms combined by operations with no equals or inequality sign, for example 3x² + 5y.
• Identifies an equation as a statement of equality between two expressions, for example 4x + 1 = 13, and recognises that it can be solved.
• Identifies a formula as a rule linking quantities, for example A = πr², and recognises that it is used by substitution or rearrangement.
• Identifies an inequality as a comparison using <, >, ≤ or ≥, for example 2x − 3 ≥ 7.
• Identifies a term as a part of an expression separated by + or − signs, for example 3x² and 5y in 3x² + 5y.
• Identifies a factor as a number or expression that divides another exactly, for example 3 and x as factors of 3x².

Common mistakes and how to put them right

• Calling any algebraic string an equation.

  Put it right: An equation must contain an equals sign, so 5x + 2 is an expression, not an equation.

• Treating a formula as just another equation.

  Put it right: A formula is a general rule linking quantities, such as A = πr², and is used by substitution or rearrangement rather than solved for one unknown value.

• Counting terms by the number of symbols.

  Put it right: Terms are separated by + or − signs, so 3x² + 5y has two terms even though it contains several symbols.

• Confusing factors with terms.

  Put it right: In 3x², the factors are 3 and x (with x used twice), while 3x² itself is one term of the expression.

Exam tips

• Underline the key sign in each option: an equals sign points to an equation or formula, and an inequality sign points to an inequality.
• Say the definition quietly to yourself before selecting: expression, equation, formula, inequality, term or factor.
• Eliminate options that use the wrong label for a correct example, because MCQs often test vocabulary rather than calculation.