2.1 Algebraic conventions and manipulation of expressions and formulae
Translate, substitute, simplify, expand, factorise and rearrange algebra using correct notation and structural reasoning.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Use algebraic vocabulary and conventions and substitute into expressions and formulae.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Collect terms, expand brackets, multiply algebraic terms and factorise at the specified tier.
Exam cue: Preserve equivalence at every step and make the algebraic structure visible rather than relying on unsupported mental manipulation.
Concept 3
Manipulate algebraic fractions, identities, proofs and formula subjects where required.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 1, Unit 2, Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Treating an expression as an equation or changing one side of a formula without applying the same inverse operation consistently.
Guardrail: The Unit 1 and Unit 3 lists are limited and Unit 2 supplies none; preserve exact values and know all other required relationships.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Expression
An expression combines numbers, variables and operations without an equals sign.
Equation
An equation states that two expressions are equal.
Identity
An identity is true for every permissible value of its variables.
Factorisation
Factorisation rewrites an expression as a product.
Subject of formula
The subject is the variable isolated on one side of a formula.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Substitute a=−2 and b=5 into 3a²−2b.
What is 4p−3q when p=2.5 and q=−2?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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