

A worksheet on the discriminant of a quadratic equation. The exercises require to examine whether a given quadratic equation has a solution and the number of solutions if they exist using the discriminant.
Help your KS4 GCSE and A-Level Mathematics students master evaluating the discriminant with this structured, printable PDF practice worksheet. This activity provides targeted practice determining the nature of roots for any quadratic equation.
Whether you need a ready-to-use main lesson task, homework sheet, cover lesson, or revision assignment, this resource reduces teacher workload while building student problem-solving confidence.
What’s Included:
- Printable Student Worksheet: Carefully scaffolded questions covering discriminant calculations.
- Full Answer Key: Complete step-by-step worked solutions for easy marking or pupil self-assessment.Clean Layout: Generous workspace provided for clear working.
Skill Progression Covered:
- Calculating the Discriminant: Identify coefficients to evaluate numerical values accurately.
- Determining Nature of Roots: Classify equations as having two real roots, one repeated root, or no real roots based on positive, zero, or negative discriminants.
- Working with Various Quadratic Forms: Practice across standard forms, missing terms, and negative leading coefficients.
Ideal For:
- Key Stage 4 / GCSE Math: Evaluating the discriminant and analyzing nature of roots.
- Key Stage 5 / A-Level Math: Understanding quadratic functions and conditions for real/repeated roots.
- Lesson Uses: Independent practice, homework, revision/retrieval practice, cover work, or small-group intervention.
UK Curriculum Alignment:
- GCSE Maths: Evaluate the discriminant and analyze quadratic expressions algebraically.
- A-Level Maths: Understand and use the discriminant of a quadratic function, including conditions for real and repeated roots.
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