Percentages (Copy)
O Level and IGCSE Mathematics Cheat Sheet – 1.13 Percentages
Key Percentage Formulas
- Percentage of a quantity:
(Percentage ÷ 100) × Quantity
Example: 20% of 150 = (20/100) × 150 = 30 - Express one quantity as % of another:
(Part ÷ Whole) × 100%
Example: 45 out of 60 = (45/60) × 100% = 75%
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Percentage Increase / Decrease
- Increase: New = Original × (1 + %/100)
- Decrease: New = Original × (1 − %/100)
- Example (Increase): £80 increased by 15% = 80 × 1.15 = £92
- Example (Decrease): $500 decreased by 12% = 500 × 0.88 = $440
Simple Interest (SI)
- Formula: SI = (Principal × Rate × Time) ÷ 100
- Example: $500 at 6% for 4 years → SI = (500 × 6 × 4) ÷ 100 = $120
Compound Interest (CI)
- Formula: New Amount = Principal × (1 + Rate/100)ᵗ
- Example: $1,000 at 5% for 3 years → 1000 × (1.05)³ = $1,157.63
Reverse Percentages
- If given final amount after increase/decrease, divide by multiplier.
- Example: Selling price = $138 after 15% profit → Cost price = 138 ÷ 1.15 = $120.
- Example: Price after 20% discount = $72 → Original = 72 ÷ 0.8 = $90.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Other Common Percentage Applications
| Term | Description | Example |
|---|---|---|
| Deposit | Upfront payment as % of total | 10% deposit on $800 = $80 |
| Discount | Price reduction as % | 25% off $60 = $45 |
| Profit | Selling price > Cost price | CP $200, SP $260 → Profit = 60, % = 30% |
| Loss | Cost price > Selling price | CP $150, SP $120 → Loss = 30, % = 20% |
| Over 100% | More than original | 250% of $40 = $100 |
Repeated Percentage Change
- Multiply by multiplier each time.
- Example: $500 increases by 10% then decreases by 5%:
Step 1: 500 × 1.10 = 550
Step 2: 550 × 0.95 = 522.50
Exam Special Tips
- Use multipliers for quick calculations (1.2 for +20%, 0.85 for −15%).
- Reverse % questions → divide, not subtract.
- For compound interest, don’t round until final answer.
- Be careful with over 100% situations — treat normally using multiplier.
Common Mistakes & Confusions
- Subtracting percentage points instead of using multiplier.
- Forgetting that reverse % needs division, not subtraction.
- Rounding too early in compound interest.
- Confusing % change with % of a quantity.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course