Cambridge IGCSE·Mathematics 0580·Extended Indices

📋Key knowledge — Numbers

Formulas & equations

Percentage change = (change ÷ original) × 100
Simple interest = P × R × T ÷ 100
Compound interest: A = P(1 + r/100)ⁿ
Speed = Distance ÷ Time
Density = Mass ÷ Volume
Upper bound = measured value + ½ × precision
Lower bound = measured value − ½ × precision

Key facts & rules

A prime number has exactly 2 factors: 1 and itself. 1 is NOT prime.
HCF: highest common factor — use a Venn diagram of prime factors.
LCM: lowest common multiple — product of all prime factors, using highest powers.
Standard form: A × 10ⁿ where 1 ≤ A < 10.
Rational numbers can be written as fractions p/q (q ≠ 0). Irrational numbers cannot (e.g. π, √2).
To convert a recurring decimal to a fraction: multiply by 10ⁿ to eliminate the recurring part, then subtract.
Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1; a⁻ⁿ = 1/aⁿ; a^(1/n) = ⁿ√a.

Laws & theorems

Order of operations: Brackets → Indices → Multiply/Divide → Add/Subtract (BIDMAS).
Significant figures: count from the first non-zero digit.

IGCSE Numbers — Indices Practice Extended

7 Cambridge IGCSE 0580 questions on indices at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.

How to approach indices — open the study guide