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Mathematical Definitions 02 (F)

Boost your GCSE Maths vocabulary. Learn what equations, identities, and expressions mean, and how to spot them in questions, so you can choose the right method quickly.

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Fascinating Fact:

In a balance puzzle, an equation shows two sides are equal, such as 3x + 5 = 20, which you solve by undoing operations to keep both sides balanced.

In GCSE Maths, precise language matters. Clear definitions of equation, identity, and expression help you understand what a question is asking, choose valid algebraic steps, and explain your reasoning confidently.

Key Terms

Equation: A statement with an equals sign that is true for specific values, e.g., 3x + 5 = 20.
Identity: An equality that is true for all allowed values, e.g., 2(x + 3) ≡ 2x + 6.
Expression: A combination of numbers, variables, and operations with no equals sign, e.g., 4y − 7.

Frequently Asked Questions (Click to see answers)

What is the difference between an equation and an identity?

An equation is true for particular values (you solve it). An identity is true for all valid values (no solving needed), often shown with the symbol ≡.

What does “expression” mean in GCSE Maths?

An expression has no equals sign. It represents a value, like 5a − 2. You simplify expressions; you do not solve them.

How can I test if a statement is an identity?

Expand and simplify both sides. If they match for all values (or for many test values you substitute), it’s an identity; otherwise it’s just an equation.