Use a multiplier for any percentage change
To increase by multiply by ; to decrease by multiply by . So a rise is and a fall is .
Reverse percentage: divide by the multiplier
If a price already includes a change, the stated value is NOT . Work backwards: . After a discount, original .
Compound change uses powers of the multiplier
For repeated yearly change over years, . Growth (interest) uses ; depreciation uses . This is NOT the same as simple interest.
Drawn from real examiner reports.
Reverse % treated as a simple decrease
After a discount students apply the percentage to the sale price instead of the original — e.g. increasing the sale price by , or finding of it and subtracting, or using as the multiplier instead of dividing by .
The most common error on Nov 2024 Paper 1H (Q7): students increased the sale price by 15% or used 1.15 rather than dividing by 0.85.
Simple interest used for compound
Working out of the start once and multiplying by the number of years (simple interest) instead of applying the multiplier to the running total each year. Each year of compound interest is bigger than the last, so simple interest undercounts.
On Nov 2024 Paper 2H (Q9) students who used simple interest scored only 1 mark.
Wrong decimal: 0.035 not 0.35
Converting the rate wrongly: is , so the multiplier is — not (that is ). Then you raise to the power, never the bare .
On Nov 2024 Paper 2H (Q9) the biggest cause of 0 marks was using 0.35 instead of 0.035, and some cubed 0.035 instead of 1.035.
Change divided by new value, not original
For a percentage increase or profit, dividing the change by the NEW value instead of the ORIGINAL, so the percentage comes out wrong.
On Nov 2024 Paper 2H (Q4b) the most common error was dividing the difference by the new value (806) instead of the original value (650).
Finding the % but forgetting to subtract
Finding of a value is only half of a decrease: of is , but the reduced value is , not . The single multiplier does both steps at once.
Using the change rate as the multiplier
For depreciation of a year the multiplier is , not ; multiplying by would wipe out each year. Likewise a profit gives multiplier , not .
Decide first: multiply or divide
If you are told the original amount, multiply by the multiplier. If you are told the amount AFTER a change and asked for the original, divide by the multiplier. Writing the multiplier down first prevents the classic reverse-% slip.
Check a reverse % by going forwards
Test any reverse-percentage answer by applying the stated change FORWARDS: you must land back on the given value. If a reduction gave you , check , the sale price you started from.
Raise the multiplier, not the bare rate
For compound interest convert the rate to a decimal (), add to , then raise THAT to the power of the years: . Never raise the bare rate () or multiply the rate by the years.
Round money only at the very end
Money answers are usually wanted to the nearest penny ( d.p.). Keep the full unrounded figure through the calculation and round only at the end — rounding early can shift the final pounds-and-pence answer.
Every percentage change is a single multiplier:
Example. A coat costs and is increased by :
What is the multiplier for a 15% increase? For a 15% decrease?
A laptop costs . In a sale its price is reduced by . Work out the sale price.
