Maths Resources GCSE Worksheets


Solving Quadratic Inequalities Worksheet

Solving Quadratic Inequalities Worksheet

Help your students prepare for their Maths GCSE with this free solving quadratic inequalities worksheet of 56 questions and answers

  • Section 1 of the solving quadratic inequalities worksheet contains 48 skills-based solving quadratic inequalities questions, in 3 groups to support differentiation
  • Section 2 contains 4 applied solving quadratic inequalities questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 4 foundation and higher level GCSE exam style solving quadratic inequalities questions 
  • Section 3 contains 3 foundation and higher level GCSE exam style questions on solving quadratic inequalities 
  • Answers and a mark scheme for all quadratic inequalities questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions created by fully qualified expert secondary maths teachers
  • Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Solving quadratic inequalities at a glance


Quadratic inequalities are inequalities that involve a squared term. As with linear inequalities, there are four types: greater than >, less than <, greater than or equal to ≥ and less than or equal to ≤. 


To solve a quadratic inequality, we first write it as a quadratic equation by changing the inequality sign to an equals sign. We can then solve the quadratic equation either by factorising or using the quadratic formula. This tells us the roots of the equation, i.e. the values for which the expression is equal to 0.


Once we have the roots of the equation, we can sketch the quadratic function – this will be a parabola. We need to look for the x values which satisfy the inequality – if the inequality is > 0 then we are looking for the x values for which the graph is above the x axis and if it is < 0 then we are looking for the x values where the graph is below the x axis.


Looking forward, students can progress with more inequalities worksheets, to additional algebra worksheets, for example a simplifying expressions worksheet, factorising worksheet or simultaneous equations worksheet.



For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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GCSE Maths Worksheets

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