Solving Quadratic Inequalities (A) - without sketching WORKSHEET
Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher Plus
Targeting grades: 8-9
Prerequisite knowledge: Solving quadratic equations by factorisation or formula. Substituting values into expressions. Understanding inequality symbols and solution sets.
Solving Quadratic Inequalities (A) - without sketching WORKSHEET DESCRIPTION
This worksheet introduces solving quadratic inequalities, guiding students step by step through logical reasoning.
In Section A, students start with the roots of a quadratic equation and use substitution to test values within and outside these roots. This helps them decide which intervals make the quadratic inequality true. This approach builds intuition and helps learners see how different intervals between roots behave.
Section B moves on to structured problems that encourage following a clear sequence of solving the quadratic equation, testing intervals, and writing the final solution in inequality form.
Finally, Section C provides more challenging problems that require students to apply the full process independently, consolidating their skills and deepening understanding. The progression from guided substitution to independent reasoning ensures learners develop confidence in handling inequalities systematically while reinforcing links between equations and inequalities.
In Section A, students start with the roots of a quadratic equation and use substitution to test values within and outside these roots. This helps them decide which intervals make the quadratic inequality true. This approach builds intuition and helps learners see how different intervals between roots behave.
Section B moves on to structured problems that encourage following a clear sequence of solving the quadratic equation, testing intervals, and writing the final solution in inequality form.
Finally, Section C provides more challenging problems that require students to apply the full process independently, consolidating their skills and deepening understanding. The progression from guided substitution to independent reasoning ensures learners develop confidence in handling inequalities systematically while reinforcing links between equations and inequalities.
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