Cambridge IGCSE·Mathematics 0580·Extended Linear Equations

📋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 — Linear equations Practice Extended

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

How to approach linear equations — open the study guide

Linear equations on IGCSE 0580

Solve equations with one unknown by performing the same operation on both sides. Expand brackets first, then collect like terms, then isolate the variable. Check your answer by substituting back.