M2.2 Algebra, Equations and Linear Graphs
Expanding and factorising single-term expressions, linear equations, coordinate midpoint and distance, gradient and intercept in contexts.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
Expansion distributes a term across a bracket, while factorisation reverses the process.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
A linear equation remains balanced when the same valid operation is applied to both sides.
Exam cue: Keep algebraic equivalence visible and interpret gradient and intercept using the quantities and units on the axes.
Concept 3
Gradient and intercept encode a straight-line rate and starting value in a coordinate or real-life model.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Combining unlike terms or changing a sign incorrectly when moving between equivalent equations.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Expand
Multiply terms so that brackets are removed without changing the expression's value.
Factorise
Rewrite an expression as a product of factors.
Midpoint
The point whose coordinates are the averages of corresponding endpoint coordinates.
Intercept
A coordinate at which a graph crosses an axis.
Linear equation
An equation in which the highest power of the variable is 1.
Straight-line model
A relationship represented by a constant gradient and an intercept.
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
Expand 4(3x-5).
Factorise 15x+25.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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