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Last updated

26 July 2026

A worksheet on factorising simple algebraic expressions and quadratic expressions involving trinomials with leading coefficient one or greater. Solutions are included. Good for GCSE/IGCSE students.

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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.

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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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Four worksheets on factoring polynomials covering different cases: extracting a common factor, difference of two squares, perfect squares, quadratic factorisation. Detailed solutions are provided. Master factorising quadratics and polynomials with this comprehensive 4-worksheet algebra practice bundle. Perfectly aligned with the UK National Curriculum for KS3 and KS4 (Years 9–11), this differentiated maths pack confidently guides students from basic common factors to advanced difference of squares and non-monic quadratics. ________________________________________ Are you looking for a high-quality, time-saving resource to teach, reinforce, or review factorising algebraic expressions and quadratic equations? This complete algebra practice bundle is sequentially designed to build student confidence, mathematical fluency, and absolute mastery over factorising polynomials. Featuring four extensive worksheets with a clear progression of difficulty, this resource makes classroom differentiation effortless for secondary school maths teachers working with mixed-ability groups. **What is Included in This Bumper Pack?** This download contains four separate practice packs, structured progressively to scaffold learning: • **Worksheet 1 (Foundational Factorisation):** Focuses on extracting highest common factors (HCF) from linear, quadratic, multivariate, and fractional algebraic expressions (e.g., pulling out common variables and integers). • **Worksheet 2 (Quadratic Factorisation Pack A):** Targets standard monic trinomials in the form x^2 + bx + c, exploring positive and negative coefficients, combined integers, and variable challenges. • **Worksheet 3 (Quadratic Factorisation Pack B):** Introduces specialized structures, including the Difference of Two Squares (DOTS), Perfect Square Trinomials, and multi-step factorising where a common factor must be extracted first. • **Worksheet 4 (Advanced Polynomial Factoring):** Stretches high-ability learners with non-monic quadratics (where a is greater than 1) and higher-degree expressions featuring cubic and quartic terms up to x^4. • **Full Teacher Solutions:** Complete, step-by-step written answers are provided for every single expansion and factorisation problem across all four worksheets to support quick peer-marking, student self-assessment, or to save you valuable grading time. **Versatile Classroom Applications** This versatile bundle is highly adaptable and can be seamlessly integrated into your maths planning as: • Structured homework assignments to consolidate weekly learning. • Independent main-lesson practice during algebra, quadratic, and polynomial units. • Target math intervention, catch-up work, or small-group revision sessions. • Cover lessons, low-stakes quizzes, or end-of-term GCSE exam preparation. **National Curriculum Alignment** This resource perfectly covers the fluency and reasoning proficiency requirements for Key Stage 3 and Key Stage 4 Mathematics, matching core algebra objectives within the GCSE Foundation and Higher specifications (AQA, Edexcel, and OCR modules): • **KS3/KS4 Maths:** Simplify and manipulate algebraic expressions by taking out common factors and factorising quadratic expressions into the product of two linear expressions. ________________________________________

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11 maths worksheets on the following topics: factorisation, expanding brackets, quadratic formula. improper fractions and mixed numbers and simultaneous equations. Detailed solutions are included. Master core maths concepts with this comprehensive, no-prep Algebra 1 / GCSE Math Worksheet Bundle | Algebra & Fractions Review! Aligned to Key Stage 3, Key Stage 4, and GCSE exam objectives, this extensive, ready-to-print resource packet covers expanding brackets, factorising quadratics, solving with the quadratic formula, rearranging formulas, and improper fraction conversions. Complete with detailed, step-by-step worked solutions, it is the ultimate time-saving tool for main lessons, homework, cover work, or revision sessions. ________________________________________ Are your secondary students struggling with equation manipulation, expanding expressions, or fractional operations? Simplify your mathematics lesson planning with this high-utility Algebra and Fractions Resource Pack. This bundle contains carefully structured worksheets designed to build computational confidence and arithmetic fluency across critical secondary maths benchmarks. Every single student problem page comes paired with a highly detailed, full-solution worked answer key that maps out the exact algebraic expansions, factorisations, rearrangements, or numeric conversions required to reach the correct answer. It is perfect for student self-assessment, small group intervention, homework packets, cover lessons, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Expanding Single Brackets:** Practice multiplying out terms over basic and complex bracketed variables, plus full expansions and simplifications. • **Expanding Double Brackets:** Multi-page progression practice focusing on multiplying two binomial expressions and combining like terms. • **Factorising Expressions:** Activities centred on finding highest common factors, factorising linear expressions, and factorising quadratic trinomials where the leading coefficient is equal to 1 or greater than 1. • **The Quadratic Formula:** Rigorous practice solving equations using the standard quadratic formula, including clean integer answers and problems requiring answers to two decimal places. • **Formulae and Equations:** Changing the subject of a formula, evaluating expressions given specific variable values, simplifying multi-term expressions, index laws, and solving linear equations. • **Improper Fractions & Mixed Numbers:** Matching matching sets, converting mixed numbers to improper fractions, and converting improper fractions to simplified mixed numbers to solidify number sense fluency. • **Teacher Answer Keys:** Complete, visual step-by-step worked solutions matching every single student worksheet page. **Why Teachers Love This Pack:** • **Zero Prep Required:** Just print out the PDF pages and you are ready to go! • **Scaffolded Progressions:** Skills move logically from basic numeric operations to complex multi-step algebraic rearrangements. • **Clean Layouts:** Generous workspace for students to neatly line up their math steps, columns, fractions, and working out. • **Detailed Worked Keys:** Perfect for leaving with cover teachers or distributing digitally for independent study guide use. **Curriculum Alignment:** • **UK National Curriculum (GCSE Maths):** Algebra Assessment Objectives A4 (Bracket Expansions/Factorising), A5 (Rearranging Formulae), and A18 (Quadratic Equations). • **International Frameworks:** Suitable for Year 8, Year 9, Year 10, and Year 11 mathematics classes, as well as foundation or higher-tier IGCSE revision.

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A bundle of 20 worksheets (with detailed solutions) on Number and Algebra topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * Operations with positive and negative numbers * Recurring decimals * Surds * Sequences * Percentage of a quantity * Reverse percentage * Compound interest * Simple interest * Percentage change * Percentage Increase Decrease * Simplifying expressions by collecting like terms * Expanding single brackets * Expanding double brackets * Factorising simple expressions * Factorising quadratic expressions * Solving linear equations * Solving quadratic equations * Operations with algebraic fractions * Linear inequalities * Quadratic inequalities The pack is ideal for use in revision sessions or for individual study. The solutions provided are very clear and explanatory.

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