Quadratic Formula & Discriminant Worksheet Bundle - Algebra 1

Three worksheets on the discriminant of a quadratic equation and the quadratic formula. In the first worksheet the exercises require to evaluate the discriminant of given equations. In the second worksheet the exercises require to examine whether a given quadratic equation has a solution and the number of solutions if they exist and solve quadratic equations (in standard form or not) using the quadratic formula. In the third worksheet the exercises require to solve quadratic equations using the quadratic formula, leaving answers as integers, fractions or decimals.
Detailed solutions to all worksheets are included.

Help your KS4 GCSE and A-Level Mathematics students master quadratic equations with this structured, 3-worksheet practice bundle. This comprehensive resource guides pupils through a complete, step-by-step skill progression: calculating discriminants, applying the quadratic formula, and solving multi-step quadratic equations requiring algebraic manipulation.

Whether you need a ready-to-use main lesson task, homework packet, cover work, or revision assignment, this resource reduces teacher workload while building student fluency in algebra.

What’s Included in This Bundle:

• Worksheet 1: Discriminant of Quadratic Equations: Practice evaluating the discriminant to determine if an equation has two real roots, one repeated root, or no real roots.
• Worksheet 2: Quadratic Formula Practice: Solve quadratic equations with integer solutions, fractional answers, and rounded decimals.
• Worksheet 3: Discriminant & Quadratic Formula (Combined & Multi-Step): Practice expanding brackets, rearranging terms into standard quadratic form, evaluating roots, and solving.
• Full Step-by-Step Answer Keys: Complete worked solutions included for effortless marking or pupil self-assessment.

Skill Progression Covered:

• Evaluating the Discriminant: Calculate numerical values to classify the nature of real roots.
• Applying the Quadratic Formula: Use the formula to find exact integer, simplified fraction, and rounded decimal answers.
• Multi-Step Equation Rearrangement: Expand brackets, collect like terms, and set equations to zero before solving.

Ideal For:

• Key Stage 4 / GCSE Math: Solving quadratics, working with surds, and evaluating the discriminant.
• Key Stage 5 / A-Level Math: Understanding quadratic functions, nature of roots, and algebraic manipulation.
• Lesson Uses: Independent practice, homework, revision/retrieval practice, cover work, or small-group intervention.

UK Curriculum Alignment:

• GCSE Maths: Solve quadratic equations algebraically by using the quadratic formula, work with surds, and evaluate the discriminant.
• A-Level Maths: Understand and use the discriminant of a quadratic function, including conditions for real and repeated roots.