Quadratic Equations Worksheets — GCSE
Quadratic equations appear throughout the GCSE Maths specification and are essential for any student aiming for grade 5 and above. Our GCSE quadratic equations worksheets cover all the methods required: factorising (including the difference of two squares), completing the square, and the quadratic formula — as well as applying these methods to real-world problems and geometric contexts.
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Key Skills Covered
Methods for Solving Quadratic Equations
The three main methods are factorising (works best when the quadratic factorises neatly: x² + 5x + 6 = (x+2)(x+3)), completing the square (useful for finding the vertex of a parabola and solving non-factorisable quadratics), and the quadratic formula x = (−b ± √(b²−4ac)) / 2a (always works, examiners expect you to use it when asked). Our worksheets include all three methods with annotated worked examples.
Quadratics in Exam Questions
GCSE exam questions on quadratics range from straightforward "solve this equation" at Foundation tier to multi-step problems at Higher tier where the quadratic arises from a geometric context (e.g. area problems where a rectangle's dimensions involve unknowns). Our worksheets include exam-style questions at both tiers, with mark scheme guidance in the answer key.
Sample Questions
Solve by factorising: x² + 7x + 12 = 0
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x = −3 or x = −4
Solve using the quadratic formula: 2x² − 5x − 3 = 0
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x = 3 or x = −½
Complete the square: x² + 6x − 1 = 0
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(x+3)² − 10 = 0; x = −3 ± √10
A rectangle has length (x+5) and width (x+2). Its area is 40 cm². Find x.
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x² + 7x − 30 = 0; x = 3 (taking positive root)
Find the discriminant of 3x² − 4x + 2 = 0. What does it tell you about the roots?
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b²−4ac = 16−24 = −8. Negative, so no real roots.
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