Sheet № 77 · Foundation + Higher · AQA · Edexcel · OCR
Percentage Change –
Percentage change questions are among the most common on GCSE Maths exams. Instead of being given a percentage and asked to apply it, you are given two values and must calculate what percentage one has changed relative to the other. This skill is essential for topics ranging from profit and loss to population growth.
§Key definitions
Question:
A shirt was priced at £40. In a sale, the price is reduced to £34. Find the percentage decrease.
Answer:
15% decrease
Q1 (Foundation):
A games console was £300. Its price rises to £345. Find the percentage increase.
Q2 (Foundation):
A car depreciates from £12,000 to £9,600. Find the percentage decrease.
Q3 (Higher):
Last year 480 students passed an exam. This year 552 passed. Work out the percentage increase to 1 decimal place.
§Formulas to memorise
Percentage change = (change / original value) × 100
Change = new value − original value
If the result is positive the value has increased; if negative it has decreased
Worked example
A shirt was priced at £40. In a sale, the price is reduced to £34. Find the percentage decrease.
Working:
⚠ Common mistakes
- ✗Dividing by the new value instead of the original. The formula requires you to divide by the original. In the shirt example, dividing £6 by £34 gives the wrong answer.
- ✗Forgetting to multiply by 100. The division gives a decimal (e.g. 0.15). You must multiply by 100 to express it as a percentage.
- ✗Confusing percentage change with the actual change. The actual change is in the same units as the values (e.g. £6). The percentage change is a relative measure (e.g. 15%).
✦ Exam tips
- →Always identify which value is the original. In profit/loss questions, the original is the cost price. In growth questions, the original is the starting value.
- →Write the formula first, then substitute. This earns you a method mark on AQA, Edexcel, and OCR papers.
- →If the question asks for an answer to a specific number of decimal places, do not round early — only round your final answer.