M6.2 Inequalities, Formulae, Sequences and Graphs
Linear inequalities, changing the subject, linear nth terms, graphical simultaneous equations and simple quadratic graphs.
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
An inequality describes a set of values and its number-line endpoints depend on whether equality is included.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Changing the subject uses inverse operations while preserving the formula's equality.
Exam cue: Use correct open or closed endpoints, label axes and read graphical solutions at an accuracy supported by the graph.
Concept 3
Graph intersections represent simultaneous solutions, while quadratic graphs may provide approximate roots.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Treating an inequality solution as one value or forgetting to reverse its sign after multiplying or dividing by a negative.
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
Inequality
A comparison describing values greater than, less than or possibly equal to a boundary.
Solution set
All values that satisfy an equation or inequality.
Subject of a formula
The variable isolated on one side of the formula.
Nth term
A position-to-term formula for a sequence.
Quadratic graph
A parabolic graph produced by a degree-2 expression.
Intersection
A point whose coordinates satisfy both graph relationships.
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
Solve 3x+4<19.
Which inequality is equivalent to -2x≤8 after dividing by -2?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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