Percentages, Change and Reverse Percentages
Find percentages, express change, use multipliers and recover original values.
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
Percentage of an amount
Exam cue: Translate a percentage change into a multiplier; divide the final value by that multiplier to find the original.
Concept 2
Percentage change and multipliers
Exam cue: Reapply the stated change to the recovered original and check that the final value returns.
Concept 3
Reverse percentages
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 and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar multi-step contexts.
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
Using the final value rather than the original value as the denominator for percentage change.
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
Increase by r%
Multiply by 1 + r/100.
Decrease by r%
Multiply by 1 - r/100.
Reverse percentage
Divide the changed value by the change multiplier.
Percentages, Change and Reverse Percentages: method
Translate a percentage change into a multiplier; divide the final value by that multiplier to find the original.
Percentages, Change and Reverse Percentages: check
Reapply the stated change to the recovered original and check that the final value returns.
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 — Find 17% of £240.
Foundation · AO1 technique · Non-calculator — Increase 360 by 12%.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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