Solving Quadratic Inequalities (C) - satisfying two inequalities 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. Representing inequalities on a number line. Testing intervals and combining solution sets. Familiarity with sketching quadratic graphs.
Solving Quadratic Inequalities (C) - satisfying two inequalities WORKSHEET DESCRIPTION
This worksheet challenges students to solve quadratic inequalities where two conditions must be satisfied at the same time.
Section A begins with paired inequalities alongside their graphs. Students are guided to identify x-intercepts, solve each inequality separately, and then combine solutions by representing overlaps clearly on a number line. This visual and systematic approach helps them understand how solution sets interact.
Section B increases the difficulty, presenting a range of inequalities that require either sketching graphs or testing values through substitution. Here, students must carefully consider the intersection of solution sets, encouraging deeper reasoning about quadratic behaviour. The structured progression from guided graph-based examples to more open-ended problems ensures learners not only practise individual inequalities but also build the skills needed to handle multiple conditions simultaneously, a key step towards more advanced algebra.
Section A begins with paired inequalities alongside their graphs. Students are guided to identify x-intercepts, solve each inequality separately, and then combine solutions by representing overlaps clearly on a number line. This visual and systematic approach helps them understand how solution sets interact.
Section B increases the difficulty, presenting a range of inequalities that require either sketching graphs or testing values through substitution. Here, students must carefully consider the intersection of solution sets, encouraging deeper reasoning about quadratic behaviour. The structured progression from guided graph-based examples to more open-ended problems ensures learners not only practise individual inequalities but also build the skills needed to handle multiple conditions simultaneously, a key step towards more advanced algebra.
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