Sheet № 03 · Foundation + Higher · AQA · Edexcel · OCR
Percentages –
Percentages crop up in almost every GCSE Maths paper and in everyday life — discounts, tax, interest rates, and data analysis all rely on them. Both Foundation and Higher tier students must handle percentage of an amount, percentage change, and converting between fractions, decimals, and percentages. Higher tier adds reverse percentages a
§Key definitions
Question:
A laptop costs £480. It is reduced by 15% in a sale. Work out the sale price.
Q1 (Foundation):
Find 35% of £260.
Q2 (Foundation):
A jumper originally costs £45. Its price increases by 8%. What is the new price?
Q3 (Higher):
£5,000 is invested at 3% compound interest per year. Work out the value of the investment after 4 years. Give your answer to the nearest penny.
§Formulas to memorise
Percentage of an amount = (percentage ÷ 100) × amount
Percentage change = (change ÷ original) × 100
Multiplier for an increase of r% = 1 + r/100
Multiplier for a decrease of r% = 1 − r/100
Compound change after n periods = original × (multiplier)^n
Reverse percentage — to find the original: original = final amount ÷ multiplier
Worked example
A laptop costs £480. It is reduced by 15% in a sale. Work out the sale price.
Working:
⚠ Common mistakes
- ✗Using the new value instead of the original when calculating percentage change. The denominator must always be the original amount, not the new one.
- ✗Confusing simple and compound interest. Simple interest is the same amount each period. Compound interest applies the percentage to the new total each period, so it grows faster.
- ✗Forgetting to state increase or decrease in percentage change questions. The examiner expects you to label the direction of change clearly.
✦ Exam tips
- →Learn the multiplier method. It is faster than finding the percentage and adding/subtracting separately, and it is essential for compound change questions.
- →On non-calculator papers, build percentages from 10% and 1%. This is reliable and quick — see our formulas guide for the key relationships to memorise.
- →Read the question carefully to see if it asks for the new amount or the change. These are different values and confusing them loses marks.
- →Use estimation to sense-check. A 15% decrease on £480 should give something a bit less than £480. If you get £552, you know you added instead of subtracting.
Bonus
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