Cambridge IGCSE·Mathematics 0580·Core Simplification

📋Key knowledge — Algebra

Formulas & equations

Quadratic formula: x = (−b ± √(b²−4ac)) ÷ 2a
Difference 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)d
nth 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 — Simplification Practice Core

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

How to approach simplification — open the study guide

Simplification on IGCSE 0580

Collect like terms (same variable and power). Cancel common factors in fractions. For algebraic fractions, find a common denominator before adding or subtracting.