Exercise 1 — Cambridge IGCSE 0580 Mar 2024 Paper 22 Q24
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Cambridge IGCSE·Mathematics 0580·Extended
Completing Squares
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 — Completing squares Practice Extended
2 Cambridge IGCSE 0580 questions on completing squares at the Extended tier — each with its full mark scheme. For the Core tier on the same skill, click here.
How to approach completing squares — open the study guide
Completing squares on IGCSE 0580
Practice with past paper questions on completing squares at the Extended tier.
Practice exercises
Exercise 2 — Cambridge IGCSE 0580 Jun 2025 Paper 41 Q18
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