2.2 Equations and inequalities - algebraic method
Form and solve linear, simultaneous, quadratic, proportional and inequality models using valid algebraic or specified approximation methods.
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
Form, manipulate and solve equations and inequalities from words, diagrams and algebra.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Solve simultaneous and quadratic equations at the specified tier and unit.
Exam cue: Define the variable, construct the relationship, solve with a method valid for the unit and substitute back to verify the result.
Concept 3
Use trial and improvement, direct or inverse proportion and solution checking 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
Using trial and improvement when a full algebraic method is demanded, or failing to reverse an inequality after multiplication by a negative value.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
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
Solution
A solution is a value that makes an equation or inequality true.
Simultaneous equations
A simultaneous solution satisfies all equations in the system.
Quadratic equation
A quadratic equation has highest variable power two after simplification.
Trial and improvement
Trial and improvement brackets and refines an approximate solution systematically.
Constant of proportionality
The constant connects variables in a direct or inverse proportion model.
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
In the expansion of (x−2)(x+5)(x+1), what coefficient multiplies x²?
The sides of a rectangle are x+4 and x−1. Which expression represents its area?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”