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Quadratic inequalities worksheet (with detailed solutions)

Quadratic inequalities worksheet (with detailed solutions)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

13 August 2026

pdf, 163.1 KB
pdf, 163.1 KB

A worksheet on quadratic inequalities. Detailed solutions are provided.

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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 Review Worksheets Bundle | GCSE Maths & Algebra 1 | 91t Prep Packet

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. Looking for a comprehensive, no-prep collection to help your secondary students master algebra? This 20-page Algebra Revision Worksheets Bundle is the ultimate resource pack for Key Stage 3 and GCSE Maths revision, smoothly guiding students from basic linear equations through to complex algebraic fractions and quadratic inequalities. ________________________________________ Master GCSE Algebra with This Comprehensive, Scaffolded Revision Worksheet Pack! Take the stress out of lesson planning and exam preparation with this complete, high-quality algebra resource collection. This pack contains structured, progressive worksheets that systematically isolate core algebraic skills before challenging students with multi-step, higher-tier examination problems. Whether you need a comprehensive end-of-term revision booklet, targeted homework tasks, cover lesson resources, or structured classroom booklets, this print-and-go bundle saves you hours of preparation time. **Why Mathematics Teachers Value This Bundle:** • Scaffolded Learning Progression: Every single topic starts with accessible, baseline questions to build learner confidence before gradually advancing to include fractional coefficients, multiple variables, and complex negative distributions. • Full Step-by-Step Solutions Included: Every question features completely worked-out mathematical workflows. This makes tracking answers effortless for teachers and allows for meaningful student self-assessment. • Spacious, Clear Layout: The clean aesthetic avoids over-crowding the page, giving secondary pupils plenty of room to write out their operations systematically and reduce calculation errors. • Perfect for Revision & Cover: Highly structured for independent work, making it an ideal choice for GCSE exam countdowns, targeted intervention groups, or robust cover work. **Detailed Module Breakdown:** • Solving Linear Equations: Core practices involving balancing equations, expanding brackets, distributing negative signs, and manipulating variables on both sides. • Solving Quadratic Equations: Comprehensive coverage including factorising quadratics, taking square roots, and applying the Quadratic Formula to two decimal places. • Operations with Algebraic Fractions: Simplification and manipulation of complex rational expressions using addition, subtraction, division, and factor cancellation. • Quadratic Inequalities: Comprehensive mastery of inequality intervals using structural quadratic factorisation and numerical number-line test values. **UK Curriculum and Exam Board Alignment:** • Key Stage 3 (KS3) Maths: Perfect stretching material for upper-band Year 9 classes moving toward higher curriculum tiers. • GCSE Maths (Foundation & Higher Tier): Fully aligned with the National Curriculum "Algebra" strand requirements for AQA, Edexcel, and OCR exam board specifications. ________________________________________

£18.90
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Solving Quadratic Inequalities Bundle: Graphs & Equations | Algebra 2 & PreCalc

A collection of three worksheets on determining the sign of trinomials given the trinomials or their graphs and solving quadratic inequalities using sign tables. Detailed solutions are included. Comprehensive quadratics revision bundle covering quadratic inequalities, sign tables, and interval analysis from graphs and equations. Perfect for GCSE Higher Tier and A-Level Maths students, complete with massive step-by-step mark schemes. ________________________________________ Give your secondary maths students a complete, scaffolded pathway to mastering quadratic inequalities! Save hours of lesson preparation with this all-in-one resource bundle. This package is specifically designed to target the two distinct ways quadratic inequalities are tested: graphical analysis and algebraic interval testing. Students will learn how to confidently determine the sign of a quadratic expression, solve inequalities using given parabolas, construct formal sign tables, and write final solution sets using formal interval notation. **What is Included in This Massive Bundle?** **Packet 1: Analyzing the Sign of Quadratic Expressions (Visual & Algebraic)** • Visual Graph Analysis: Students inspect 6 different given parabola graphs to determine intervals where the function is positive, negative, or exactly zero. • Algebraic Sign Tables: Students factor quadratic equations to find critical roots, build formal sign charts (tables), and identify where the expression satisfies positive or negative conditions. **Packet 2: Solving Inequalities From Graphs & Factoring** • Graphical Solution Sets: Challenge problems where students look at a parabola on a coordinate grid and write the exact interval for where the function satisfies the inequality. • Pure Algebraic Inequalities: Practice solving factored and un-factored quadratic trinomial equations by determining positive and negative intervals. **Packet 3: Advanced Quadratic Inequalities & Interval Number Lines** • Variable Practice: Extra drill worksheets featuring multi-step inequalities using assorted variables (x, y, p, a). • 91t Interval Number Lines: Problems where students find boundary points, plot them on a number line, test values within each region, and write final answers using union symbols. **Packet 4: Massive Step-by-Step Mark Schemes & Worked Solutions** • Incredibly detailed, fully worked solutions guides! • Every single problem includes fully drawn sign tables, shaded interval number lines, and step-by-step algebraic breakdown pathways to save you marking time or to allow for seamless student self-assessment. **Key Skills Covered:** • Visually determining the sign of a function directly from a graph • Solving quadratic inequalities algebraically by factoring • Building and interpreting algebraic sign tables • Executing the test point method on a number line interval • Writing final solution sets using formal interval notation and union symbols **Why Teachers Love This Bundle:** • Print-and-Go Convenience: No extra preparation, formatting, or drawing graphs on whiteboards required. • Scaffolded Rigor: Seamlessly transitions from foundational visual properties (GCSE Higher Tier) to complex algebraic interval evaluation (AS and A-Level Pure Maths). • Perfect for Multiple Settings: Use these packets for structured classwork, independent homework, revision booklets, or highly comprehensive cover lessons! ________________________________________

£3.65
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Linear and Quadratic Inequalities Worksheets Bundle | Algebra 1 & 2 Practice

Three worksheets on the following topics: solving linear inequalities, solving quadratic inequalities and finding the integers that satisfy a double inequality. Solutions are included. Master solving linear inequalities, factorising quadratic inequalities and identifying integer values with this complete KS3 and GCSE maths resource pack with full answers. ________________________________________ Are your student groups struggling to solve multi-step linear inequalities or keep track of when to flip the inequality sign? Do they get confused when factorising quadratic expressions into binomial boundary points or when testing intervals to identify the correct solution set? Take the stress out of your lesson planning with this comprehensive linear and quadratic inequalities practice pack! This collection is meticulously designed to build numerical fluency, moving students smoothly from foundational balance calculations to advanced secondary school interval analysis. ________________________________________ **What’s Included in This Resource Pack?** This all-in-one packet delivers distinct, targeted worksheet units. Each section features a clear, progressive problem set followed by a matching teacher answer manual showing exact setups and calculation transformations: **Section: Solving Linear Inequalities** Core fluency practice covering one-step, two-step, and multi-step inequalities. Includes problems with variables on both sides, fractional terms, and distributive bracket expansions that require students to flip signs across negative multipliers. **Section: Solving Quadratic Inequalities** oAdvanced sheets where students set quadratic terms to zero, factorise quadratics into binomial pairs to locate critical boundaries, and run interval test calculations to establish precise solution ranges. **Section: Identifying Satisfying Integers** Targeted reasoning exercises challenging students to evaluate open and closed boundary conditions to systematically list all real whole numbers that mathematically satisfy the given constraint. **Full Teacher Answer Keys** Every section includes fully worked-out solutions showing the line-by-line algebraic transformations, boundary interval diagrams, and substitution testing checks. It is perfectly ready for quick marking, projectable self-assessment, or independent study checks! ________________________________________ **Ideal For Curriculum Delivery:** * KS3 Maths: Perfect for introducing inequality notation, number line rules, and simple single-variable rearrangements in Years 7, 8, and 9. • KS4 / GCSE Maths (Foundation & Higher Tier): Excellent as a comprehensive unit review covering multi-step operations, algebraic expansions, and non-linear quadratic intervals. • Remedial Support / Revision: High-utility worksheets for intervention groups, GCSE Higher revision packages, or independent learning centers. ________________________________________ ⭐ Why Teachers Choose Our Resources: * **Ready to Print:** No-prep layout saves valuable preparation time—simply print and copy. * **Scaffolded Progress:** The problem sets intentionally scale in difficulty to build student confidence. * **Spacious Design:** Clean layout gives learners plenty of room to write out their working directly on the sheet. *If you find this maths resource helpful, please leave a review! Your feedback helps create better classroom tools.* ________________________________________

£3.50
Bundle

GCSE Maths-Algebra Revision Pack

A bundle of 10 worksheets (with detailed solutions) on Algebra topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * 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.

£8.90
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Linear and Quadratic Inequalities (5 worksheets with solutions)

A collection of five worksheets on solving linear and quadratic inequalities. Detailed solutions are provided.

£3.90
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Linear, quadratic and compound inequalities Bundle

A collection of three worksheets on inequalities. The first is on linear inequalities. The second is on quadratic inequalities. The third is on solving simultaneously two linear inequalities in one variable using the real number line. Detailed solutions are included.

£3.35
Bundle

Linear and quadratic inequalities worksheets (with solutions)

Three worksheets on inequalities. One on on linear inequalities and two on quadratic inequalities. Detailed solutions are provided. Good practice for GCSE students.

£3.35

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