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.