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Solving quadratic equations by factorising worksheet no 3 (with solutions)

Solving quadratic equations by factorising worksheet no 3 (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

27 July 2026

pdf, 73.61 KB
pdf, 73.61 KB

A worksheet on solving simple and harder quadratic equations using factorisation. Detailed solutions are included.

Get this resource as part of a bundle and save up to 42%

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

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Solving Quadratic Equations Pack Factoring, Formula, Completing the Square

Three worksheets on solving quadratic equations by: using the quadratic formula, factorising and completing the square. Detailed solutions are included.<br /> <br /> Master quadratic equations with this comprehensive algebra revision pack! Featuring 3 distinct worksheet sets with over 60 structured problems, students will practice solving quadratics by factorising, rewriting expressions by completing the square, and using the quadratic formula. Full, step-by-step worked solution keys are included for every question to save you hours of marking time!<br /> ________________________________________<br /> Are your students struggling to remember the different methods for solving quadratic equations? Do they need targeted, scaffolded practice to master factorising, completing the square, or applying the quadratic formula?<br /> This GCSE / IGCSE Maths Solving Quadratics Pack provides massive, comprehensive practice across three core algebraic methods. Designed to build deep conceptual mastery and strong procedural fluency, this resource takes students from basic common factor identification all the way to advanced quadratic formula calculations with decimal rounding.<br /> Perfect for Key Stage 4, GCSE/IGCSE Maths preparation, or international algebra curricula!<br /> ________________________________________<br /> ⚡ What’s Included in This 3-Worksheet Resource?<br /> This resource features three standalone student worksheets complete with matching, fully worked step-by-step answer keys:<br /> • Worksheet 1: Solving Quadratic Equations by Factorising (22 Problems)<br /> o Progresses systematically from basic single variable common factorisation (such as x^2 + 4x = 0) and difference of two squares (such as x^2 - 16 = 0) to standard trinomials where a = 1.<br /> o Includes non-standard configurations and challenging trinomials where the leading coefficient is greater than 1, such as 3x^2 + 14x + 8 = 0.<br /> • Worksheet 2: Completing the Square Expressions (16 Problems)<br /> o Section 1 features 8 specialized drills focused strictly on rewriting expressions into completed square form where a = 1, including fractional configurations.<br /> o Section 2 provides 8 advanced expressions where the leading coefficient is greater than 1, requiring students to factor out a common coefficient first, such as 2x^2 + 16x + 3.<br /> • Worksheet 3: Mixed Quadratic Equations & Formula Practice (18 Problems)<br /> o A comprehensive review sheet combining multiple methods of solving.<br /> o Features fundamental integer solutions alongside high-tier equations requiring the quadratic formula, resulting in roots where students must round their answers to two decimal places.<br /> • Complete Step-by-Step Worked Solution Keys<br /> o Includes the full algebraic layouts showing the exact substitution steps, radical simplifications, and solution paths. Ideal for quick marking or independent student self-correction!<br /> ________________________________________<br /> 🎯 Why Teachers Love This Pack:<br /> • No Prep Required: Simply choose your target skill page, print, photocopy, and you are ready to teach!<br /> • Scaffolded Progressions: Problems are organized logically, gradually advancing from fundamental drills to high-tier algebraic challenges.<br /> • Flexible Class Application: Perfect for direct independent practice, homework assignments, exam preparation, cover lessons, or revision sheets.<br /> • Generous Student Formatting: Clean layouts leave students plenty of physical white space to write out their formulas, brackets, and calculations neatly.<br /> ________________________________________<br /> 📐 Curriculum & Topics Covered:<br /> • Key Stage 4 National Curriculum: Algebraic proficiency, manipulating expressions, and finding exact or approximate solutions to quadratics.<br /> • GCSE & IGCSE Maths (Foundation & Higher Tier): Factorise quadratic expressions, find exact or decimal roots, and use completing the square to rewrite expressions.<br /> • Target Keywords: Solving quadratics worksheets, quadratic formula, factorising quadratics, completing the square, algebra revision, difference of two squares, expanding brackets, maths exam practice pack.<br /> ________________________________________

£3.45
Bundle

Solving quadratic equations by factorising worksheets (with solutions)

Three worksheets on solving simple and harder quadratic equations using factorisation. Detailed solutions are included.

£2.90
Bundle

Factoring Quadratics & Solving Polynomial Equations Worksheets BUNDLE | Algebra

Master factoring polynomials and solving quadratic equations with this comprehensive, zero-prep 10-worksheet bundle! Designed for Key Stage 3, Key Stage 4, GCSE Maths, and A-Level revision, this bundle guides students step-by-step from foundational factoring concepts all the way to solving complex equations using factoring and the Quadratic Formula. Every worksheet set includes clear, structured practice problems alongside a full, step-by-step answer key to make marking fast and student self-checking effortless! WHAT IS INCLUDED IN THIS 10-WORKSHEET BUNDLE: * **Worksheet 1: Factorization (Common Factor and Grouping)** Practice with GCF extraction, multi-variable terms, binomial common factors, and factoring by grouping four-term polynomials. * **Worksheet 2: Factoring the Difference of Two Squares** Single-variable, multi-variable, fractional coefficients, and multi-step difference of squares factoring. * **Worksheet 3: Factoring Perfect Squares** Perfect square trinomial identification, expanding perfect squares, and factoring out common numerical factors first. * **Worksheet 4: Quadratic Factorisation (Basic - leading coefficient of 1)** Comprehensive practice factoring simple trinomials with positive and negative middle and last terms. * **Worksheet 5: Quadratic Factorisation (Advanced - leading coefficient greater than 1)** Factoring complex trinomials using decomposition or grouping methods. * **Worksheet 6: Quadratic Factorisation Review & Mixed Practice** Comprehensive mixed review combining simple quadratics, difference of squares, perfect squares, and leading coefficients greater than 1. * **Worksheet 7: Solving Quadratic Equations by Factorising** Applying the Zero Product Property to solve equations in factored form, standard form, and equations requiring initial rearrangement. * **Worksheet 8: Solving Equations Using the Quadratic Formula** Step-by-Step practice applying the quadratic formula, identifying double roots, handling rational/irrational solutions, and rounding to two decimal places. * **Complete Step-by-Step Answer Keys:** Worked-out solutions included for all 10 worksheet sets. **SKILLS COVERED:** * Extracting Greatest Common Factors (GCF) * Factoring by Grouping * Difference of Two Squares * Perfect Square Trinomials * Factoring Quadratics * Zero Product Property * Solving Quadratic Equations by Factoring * Applying the Quadratic Formula * Rearranging Equations into Standard Form **PERFECT FOR:** * Whole Unit Practice & Lesson Supplements * Independent Classwork & Daily Homework * Key Stage 3, Key Stage 4, GCSE & A-Level Algebra Revision * Emergency Cover Lessons & Sub Plans * Small Group Intervention & Tutoring

£9.90

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