A worksheet on solving quadratic equations using the quadratic formula, leaving answers as integers, fractions or decimals. Detailed solutions are included.
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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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20 GCSE/IGCSE Algebra worksheets (with solutions)
Help your secondary students master the most challenging aspects of algebraic manipulation with this extensive, high-quality worksheet pack. Designed to build procedural fluency and conceptual confidence, this resource flows logically from foundational skills to advanced GCSE Higher tier topics.It is an ideal resource for **Key Stage 3 (Extension), Key Stage 4 (GCSE Foundation/Higher, IGCSE), and AS-Level bridging work.** **What’s Included?** This comprehensive PDF pack includes structured question sections covering three vital algebraic concepts: 📂 **1. Adding and Subtracting Algebraic Fractions (40 Questions)** * **Level 1**: Common numerical denominators and basic simplification. * **Level 2:** Different numerical denominators with linear expression numerators requiring expansion. * **Level 3**: Linear algebraic denominators requiring a common algebraic base (e.g. \(\frac{3}{x-2} - \frac{4}{x+3}\) ) (p. 2). * **Level 4 (Grade 7-9)**: Quadratic denominators requiring factoring first before finding the lowest common multiple. 📂 **2. Rearranging Formulae / Changing the Subject (18 Questions)** * **Level 1:** Formulae involving square roots, fractions, and multi-step inverse operations. * **Level 2 (Grade 8/9):** Complex manipulation where the subject appears multiple times, requiring expansion, grouping common terms, and factorising out the subject. 📂 **3. Equations with Algebraic Fractions (20 Questions)** * **Level 1:** Solving linear fractional equations by clearing the denominators. * **Level 2:** Solving advanced equations that simplify into quadratics, requiring either factorisation or the quadratic formula to solve. 📂 **4. Expanding & Factorising Quadratics** * Supplemental targeted practice on expanding double brackets and simplifying expressions. **Key Features** ✔️ **Full Worked Solutions Included:** Every question comes with a comprehensive, step-by-step written solution. Perfect for quick self-marking, peer assessment, or displaying on your interactive whiteboard. ✔️ **Highly Scaffolded:** Tasks naturally progress in difficulty, allowing students to build up to Grade 9/A* style questions seamlessly. ✔️ **Zero Preparation:** Simply download, select the pages you need, print, and teach! **Ideal For:** * **Main Lesson Practice**: Ideal for independent classwork following a teacher explanation. * **Homework & Revision:** Excellent for consolidation leading up to mock exams or final assessments. * **Cover Lessons:** Clear sequencing and comprehensive answer keys make this completely self-contained for supply or cover staff. * **Flipped Learning / Homework**: Perfect for independent study or remote learning tasks. **File Type**: PDF **Pages:** Complete bundle with question sheets and full answer keys.
£17.90
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Solving quadratic equations worksheets (with solutions)
A collection of four worksheets on solving quadratic equations using factorisation, the quadratic formula and the method of completing the square. Detailed solutions are provided.
£3.35
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Algebra for GCSE/IGCSE worksheets (with solutions)
A large collection of 24 worksheets (254 pages) on selected topics from algebra: Algebraic manipulation Substitution into formulae Simplifying expressions by collecting like terms Collecting like terms (expressions with different variables) Multiplying a single term over a bracket Expanding double brackets Factorisation Quadratic factorisation 9.Indices Rearranging formulae Inverse functions Composite functions Equation of a straight line Parallel and perpendicular lines Solving linear equations Solving quadratic equations by factorising Quadratic formula Completing the square and solving quadratic equations by com- pleting the square Simultaneous Equations -Elimination Simultaneous Equations -Substitution Simultaneous Equations One Linear, One Quadratic Linear inequalities Quadratic inequalities The nth term of linear and quadratic sequences Designed for the GCSE/IGCSE specification. Detailed solutions are included.
£19.90
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Solving quadratic equations Bundle
A collection of three worksheets on solving quadratic equations. The first is on solving quadratic equations by factorising. The second is on solving quadratic equations using the quadratic formula. The third is on completing the square and solving quadratic equations by completing the square. Detailed solutions are included.
£3.50
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Discriminant of a quadratic equation and quadratic formula worksheets (with solutions)
A collection of three worksheets. Two worksheets on the discriminant of a quadratic equation with exercises for evaluating the discriminant of given equations, determining the number of real solutions of given quadratic equations and deciding whether the discriminant of a quadratic equation is positive, negative or zero by the corresponding graph and one worksheet on solving quadratic equations using the quadratic formula. Solutions are provided.
£2.80
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11 GCSE math worksheets (with solutions)
11 maths worksheets on the following topics: factorisation, expanding brackets, quadratic formula. improper fractions and mixed numbers and simultaneous equations. Detailed solutions are included.
£10.90
Bundle
Linear and quadratic equations worksheets (with solutions)
Three worksheets on solving linear equations, and quadratic equations by factorising and using the quadratic formula. Solutions are included.
£3.35
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