Exercise 1 — Cambridge IGCSE 0580 Mar 2025 Paper 22 Q23
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Cambridge IGCSE·Mathematics 0580·Extended
Index Laws
Key knowledge — Algebra
Formulas & equations
Quadratic formula: x = (−b ± √(b²−4ac)) ÷ 2aDifference of two squares: a² − b² = (a+b)(a−b)Completing the square: ax² + bx + c = a(x + b/2a)² + (c − b²/4a)Sum of arithmetic sequence: Sₙ = n/2 × (first + last) = n/2 × (2a + (n−1)d)nth term of AP: aₙ = a + (n−1)dnth term of GP: aₙ = arⁿ⁻¹
Key facts & rules
- To solve a quadratic: factorise, complete the square, or use the formula.
- To solve simultaneous equations: elimination (add/subtract to remove one variable) or substitution.
- Inequalities: flip the sign when multiplying or dividing by a negative number.
- Algebraic fractions: find common denominator, then add/subtract numerators.
- Direct proportion: y = kx. Inverse proportion: y = k/x.
Laws & theorems
- Factor theorem: if (x − a) is a factor of f(x), then f(a) = 0.
IGCSE Algebra — Index laws Practice Extended
5 Cambridge IGCSE 0580 questions on index laws at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.
How to approach index laws — open the study guide
Index laws on IGCSE 0580
Key rules: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m-n), (a^m)^n = a^(mn), a^0 = 1, a^(-n) = 1/a^n. These apply to both numbers and variables.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Jun 2025 Paper 41 Q21
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Exercise 3 — Cambridge IGCSE 0580 Jun 2025 Paper 42 Q21
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Exercise 4 — Cambridge IGCSE 0580 Nov 2025 Paper 21 Q19
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Exercise 5 — Cambridge IGCSE 0580 Nov 2025 Paper 22 Q24
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