Reverse Percentages, Appreciation and Depreciation
Use multiplier reasoning to recover originals and model repeated percentage increase or decrease.
How to study National 5 Mathematics
Secure one operational skill at a time, connect it to neighbouring techniques, then apply it in unfamiliar contexts with complete working and a checked conclusion.
Core concepts
Concept 1
A reverse-percentage problem divides the final amount by the multiplier that produced it.
Exam cue: Identify whether the given value is before or after the percentage change.
Concept 2
Appreciation and compound interest apply a multiplier greater than 1 for each period.
Exam cue: Convert the percentage to a multiplier and raise it to the number of periods.
Concept 3
Depreciation applies a multiplier between 0 and 1 repeatedly, so percentage changes compound rather than add.
Exam cue: Interpret the time interval and round money or quantities only at the end.
Risk pitfalls and guardrails
Subtracting a percentage of the final value to find the original.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Adding repeated percentage changes instead of compounding.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Using 0.08 rather than 1.08 for an 8% increase.
Guardrail: Check signs, brackets, restrictions, units, accuracy and whether the answer needs a reason.
Memory anchors
Increase multiplier
1 + rate as a decimal.
Decrease multiplier
1 − rate as a decimal.
Reverse percentage
Original = final ÷ multiplier.
Repeated change
Final = original × multiplier^number of periods.
Compound interest
Interest is applied to the updated balance each period.
Depreciation
Repeated multiplication by a value between 0 and 1.
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
Increase 240 by 15%.
A bicycle priced at £850 is reduced by 12%. What is the sale price?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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