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Discriminant and Quadratic Formula Worksheet - Algebra 1 Practice

Discriminant and Quadratic Formula Worksheet - Algebra 1 Practice

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

7 July 2026

pdf, 89.79 KB
pdf, 89.79 KB

A worksheet on the discriminant of a quadratic equation and the quadratic formula. 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. Detailed solutions included.

Help your KS4 GCSE and A-Level Mathematics students master the discriminant and quadratic formula with this structured, printable PDF practice worksheet. This activity moves systematically from evaluating the nature of roots to solving multi-step quadratic equations requiring algebraic manipulation.

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 evaluation and formula solving.
  • 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:

  • Determining the Number of Real Roots: Use the discriminant to determine if an equation has two real roots, one repeated root, or no real roots.
  • Solving Standard Quadratic Equations: Apply the quadratic formula to solve equations yielding integer, fractional, or simplified surd answers.
  • Equation Rearrangement: Expand brackets, simplify terms, and rearrange into standard quadratic form 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.

Get this resource as part of a bundle and save up to 30%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Solving Quadratics Worksheets Bundle | Factoring Completing Square Formula

Three worksheets on solving quadratic (and higher order equations) by: * factoring * completing the square * using the quadratic formula Detailed solutions to all worksheets are included. Mastering quadratic equations requires students to know multiple pathways to a solution. This comprehensive, print-and-go bundle includes three distinct multi-page worksheets that guide students step-by-step through the three most essential methods: factoring, completing the square, and using the quadratic formula. Whether you need a cohesive unit plan, targeted independent practice, or stress-free cover plans, this bundle saves you hours of planning time. **What is Included in This 3-Worksheet Bundle?** * **Worksheet 1: Solving Polynomial Equations by Factoring** Features single variables, multi-factor polynomials, trinomials, differences of squares, and equations requiring reorganization before factoring. * **Worksheet 2: Quadratics - Completing the Square** Builds confidence systematically, moving from simple equations to challenging quadratics featuring leading coefficients. * **Worksheet 3: Discriminant and the Quadratic Formula** Walks students through evaluating the discriminant to identify the number of solutions before solving equations completely using the formula. * **Complete Answer Keys:** Fully worked-out, step-by-step solutions for every problem across all three worksheets, making marking easy and enabling student self-checking. **Why Teachers Love This Bundle** * **No-Prep Printables:** Simply choose your page, hit print, and your lesson is ready to go! * **Generous Student Workspace:** Every single problem is laid out inside a clean, spacious grid box, giving your students plenty of room to write down all their algebraic steps neatly. * **Perfect for Scaffolding:** Seamlessly transitions from introductory calculations to advanced algebraic problem-solving. **Educational Curriculum Alignment** * **UK National Curriculum:** Perfect for GCSE Maths Higher Tier (Algebra - Quadratic Equations) and AS-Level Maths pure mathematics revision. * **International Curricula:** Aligns seamlessly with IGCSE Maths and IB Math standard level tracks focusing on solving quadratic functions using different algebraic methods.

£3.00
Bundle

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.

£3.35

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