Equations, identities, formulae and expressions
WJEC tests this conceptually on Foundation/Intermediate and uses it to set up algebraic-proof Higher questions.
πDefinitionβ Definitions
- Expression β a string of mathematical symbols with no equals sign. e.g. 3x + 2.
- Equation β a statement that two expressions are equal for SOME values of the variable. e.g. 3x + 2 = 11 has solution x = 3.
- Identity β a statement true for ALL values of the variable. Often written with β‘. e.g. (x + 1)^2 β‘ x^2 + 2x + 1.
- Formula β a rule connecting two or more variables. e.g. A = Ο r^2.
How to tell them apart
| Question | Answer |
|---|---|
| Is there an = sign? No β expression. | |
| Is there an β‘ sign? Yes β identity. | |
| Does only specific value(s) of the variable make it true? Yes β equation. | |
| Is it a rule connecting variables? Yes β formula. |
Algebraic equivalence β proving identities
To prove A β‘ B, manipulate ONE side until it equals the other. Don't move terms across the β‘ β that's an equation move, not an identity proof.
Example: prove (n + 1)^2 β n^2 β‘ 2n + 1
- LHS = (n + 1)^2 β n^2
- = n^2 + 2n + 1 β n^2
- = 2n + 1
- = RHS β
Example: prove 3(x β 2) + 2(x + 5) β‘ 5x + 4
- LHS = 3x β 6 + 2x + 10
- = 5x + 4
- = RHS β
"Show that" / "Prove" structure
Each line must follow logically from the previous. Set out as:
- LHS = β¦ (factorise / expand / simplify)
- = β¦
- = RHS β
The final tick or "as required" is part of the WJEC mark scheme.
WJEC exam tip
When the question uses "β‘" or "show that β¦", do NOT solve for x β that misreads the task. Manipulate one side step-by-step. Solving an identity is the most common mistake on Higher Unit 1.
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