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Completing the square and solving quadratic equations by completing the square worksheet

Completing the square and solving quadratic equations by completing the square worksheet

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

27 July 2026

pdf, 91.34 KB
pdf, 91.34 KB
A worksheet on completing the square and solving quadratic equations by completing the square. Detailed solutions are included.

Get this resource as part of a bundle and save up to 39%

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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Algebra Solving Quadratics Bundle | Factoring, Formula & Completing the Square

Three worksheets on solving quadratic equations. In the first worksheet equations are solved by using the quadratic formula, in the second worksheet equations are solved by by factorising and and in the third worksheet equations are solved by completing the square. Detailed solutions are included. Master quadratic equations with this comprehensive algebra revision pack! Featuring 3 distinct worksheet sets with 72 total problems, students will practice solving quadratics by factorising, using the quadratic formula, and completing the square. Full, step-by-step worked solution keys are included for every question to save you hours of marking time! ________________________________________ 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? 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. Perfect for Key Stage 4, GCSE/IGCSE Maths preparation, or international algebra curricula! ________________________________________ ⚡ **What’s Included in This 3-Worksheet Resource?** This resource features three standalone student worksheets complete with matching, fully worked step-by-step answer keys: • **Worksheet 1: The Quadratic Formula (14 Problems**) o Section A focuses on equations written in standard form with clean integer results. o Section B introduces equations requiring algebraic rearrangement before applying the formula, such as 4x^2 = 12x - 9. o Section C features advanced equations resulting in irrational roots where students must round their answers to two decimal places. • **Worksheet 2: Solving Quadratics by Factorising (30 Problems)** o Progresses systematically from basic single variable common factorisation and difference of two squares (such as x^2 - 36 = 0) to standard trinomials where a = 1. o Includes non-standard configurations and challenging trinomials where the leading coefficient is greater than 1, such as 3x^2 - 14x - 5 = 0. • **Worksheet 3: Completing the Square (22 Problems total)** o Section 1 features 8 specialized drills focused strictly on rewriting expressions into completed square form, including fractional expressions. o Section 2 provides 14 full quadratic equations for students to solve entirely using the completing the square method. • **Complete Step-by-Step Worked Solution Keys** 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! ________________________________________ 🎯 **Why Teachers Love This Pack:** • **No Prep Required:** Simply choose your target skill page, print, photocopy, and you are ready to teach! • **Scaffolded Progressions:** Problems are organized logically, gradually advancing from fundamental drills to high-tier algebraic challenges. • **Flexible Class Application:** Perfect for direct independent practice, homework assignments, exam preparation, cover lessons, or revision sheets. • **Generous Student Formatting:** Clean layouts leave students plenty of physical white space to write out their formulas, brackets, and calculations neatly. ________________________________________ 📐 **Curriculum & Topics Covered:** • **Key Stage 4 National Curriculum:** Algebraic proficiency, manipulating expressions, and finding exact or approximate solutions to quadratics. • **GCSE & IGCSE Maths (Foundation & Higher Tier):** Factorise quadratic expressions, find exact or decimal roots, and use completing the square to solve equations algebraically. • **Target Keywords:** Solving quadratics worksheets, quadratic formula, factorising quadratics, completing the square, algebra revision, difference of two squares, expanding brackets, maths exam practice pack. ________________________________________

£3.45
Bundle

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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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
Bundle

Algebra 1 Completing the Square & Solving Quadratic Equations Bundle

Three worksheets on completing the square and solving quadratic equations by completing the square. Detailed solutions are included.<br /> <br /> Master completing the square with this comprehensive Completing the Square & Solving Quadratic Equations Worksheets Bundle! Perfectly tailored for KS4 (GCSE Year 10 and Year 11), this multi-page worksheet pack covers everything from expanding expressions into vertex form to solving quadratics with fractional coefficients and surd solutions. Complete with clear step-by-step teacher answer keys, it is ideal for independent practice, homework, or exam revision.<br /> ________________________________________<br /> Are your students struggling to master the steps for completing the square or solving complex quadratic equations?<br /> This no-prep maths worksheet bundle simplifies the process. It offers progressive, scaffolded practice to build true confidence with transforming quadratic expressions, handling leading coefficients, and solving equations that yield whole numbers, fractions, and surds. Whether you need an introductory resource for Year 10 or rigorous revision for Year 11 GCSE exam preparation, these clean, distraction-free layouts keep students focused on the mathematics.<br /> What’s Included in This Bundle?<br /> • Part 1: Completing the Square Practice – Focuses on transforming standard quadratic expressions. Includes progressive difficulty from simple even b-coefficients to fractional b-coefficients and leading coefficients greater than 1 (e.g. 2x^2 + 10x + 3).<br /> • Part 2: Solving Quadratic Equations – Steps students through solving full equations set to zero. Practice covers basic integer roots, fractions, and simplifying radical/surd roots (such as -3 ± the square root of 3).<br /> • Full Step-by-Step Answer Keys – Every single worksheet features a matching solutions page showing the exact algebraic workflow for fast marking or student self-checking.<br /> <br /> Perfect For:<br /> • Main lesson tasks or independent seatwork<br /> • No-prep supply teacher lesson plans<br /> • Homework assignments or starter activities<br /> • Small group maths intervention or GCSE remediation<br /> • End of unit assessments and exam revision

£3.90
Bundle

Solving quadratic equations using square roots and by completing the square worksheets (with solutions)

Three worksheet on solving quadratic equations using the method of square root and by completing the square. Detailed solutions are included.

£3.35

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