IGCSE Maths Number Notes
Number is the foundation of IGCSE Maths, covering standard form, percentages, ratio, indices and bounds used throughout every other topic.
Key concepts
- Standard form
- Numbers written as A × 10ⁿ with 1 ≤ A < 10, for very large or very small values.
- Percentage change
- Use multipliers: increase by 15% is × 1.15; reverse percentages divide by the multiplier.
- Indices & surds
- Index laws and simplifying roots such as √50 = 5√2 appear on the extended tier.
- IGCSE lets you use a calculator on both papers, but standard-form input still needs care.
- Reverse percentage problems are a common source of lost marks.
- Ratio questions often combine with fractions of an amount.
Key formulas
Percentage multiplier
new = original × (1 ± rate)
+ for increase, − for decrease.
Standard form
A × 10ⁿ, 1 ≤ A < 10
Worked example
Write 0.00042 in standard form.
- 1Move the decimal point to just after the first non-zero digit: 4.2.
- 2Count the places moved: 4 to the right, so the power is −4.
- 3Write in standard form.
Answer: 4.2 × 10⁻⁴
Common mistakes
✗ Standard form with A outside 1 ≤ A < 10, e.g. 42 × 10³.
✓ Adjust to 4.2 × 10⁴.
✗ Adding percentages instead of using multipliers.
✓ Use × 1.15 for a 15% rise, not + 15.
✗ Dividing the ratio total incorrectly.
✓ Add the ratio parts, divide the amount by the total, then multiply by each part.
Quick check
Try these, then reveal the answers.
Write 34 000 in standard form.Reveal answer
3.4 × 10⁴
Increase £80 by 25%.Reveal answer
£100
Share £60 in the ratio 2 : 3.Reveal answer
£24 and £36
Exam tips
- Enter standard form using your calculator's ×10ˣ key, not the letter E, when writing final answers.
- For reverse percentages, identify the multiplier and divide by it.
- Keep exact surd form until the final line unless a decimal is requested.
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Frequently asked questions
Is a calculator allowed for IGCSE number questions?+
Yes — both Edexcel IGCSE Maths papers allow a calculator, but you must still show clear method.
What is a reverse percentage?+
Finding the original amount before a percentage change, done by dividing by the percentage multiplier.
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