Direct and Inverse Proportion
Recognise, represent and solve direct and inverse proportion relationships.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Unitary method
Exam cue: Identify the invariant relationship, find the constant of proportionality and write an equation before substituting.
Concept 2
Direct proportion
Exam cue: Test whether multiplying one variable produces the expected change in the other.
Concept 3
Inverse proportion
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Foundation uses recipes, best buys, scale and simpler direct or inverse contexts. Higher formalises proportion with powers, roots, equations and graphs.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Assuming every increasing relationship is direct proportion.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Direct proportion
y = kx, or the appropriate stated power of x.
Inverse proportion
y = k/x, or the appropriate stated power of x.
Proportion constant
Find k from a known matching pair.
Direct and Inverse Proportion: method
Identify the invariant relationship, find the constant of proportionality and write an equation before substituting.
Direct and Inverse Proportion: check
Test whether multiplying one variable produces the expected change in the other.
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
Foundation · AO1 technique · Non-calculator — y is directly proportional to x. If y=18 when x=6, find y when x=11.
Shared F/H · AO1 technique · Non-calculator — p is directly proportional to q². If p=45 when q=3, find p when q=5.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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