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IGCSE Maths · Edexcel 4XMA1 · Unit 2 Higher · Algebra

Quadratic Inequalities — Practice Questions

12 exam-style questions (37 marks), building from warm-up to grade 8–9. Show full working: Edexcel gives method marks even when the final answer is wrong.

Section A — Warm-up (grades 5–6)
  1. (2 marks)Solve x² − 9 < 0.
  2. (3 marks)Solve x² − 7x + 10 ≤ 0.
  3. (3 marks)Solve x² + 2x − 15 > 0.
  4. (3 marks)List all the integers that satisfy x² − 4x − 12 < 0.
Section B — Core (grades 6–7)
  1. (3 marks)Solve 2x² − 5x − 3 ≥ 0.
  2. (3 marks)Solve x² < 3x + 10.
  3. (3 marks)Solve 12 + x − x² > 0.
  4. (3 marks)Solve x(x − 6) ≥ 16. Show your answer on a number line.
Section C — Stretch (grades 8–9)
  1. (3 marks)Solve x² + 2x − 4 < 0. Give your answer in surd form.
  2. (4 marks)Find all the integers that satisfy both x² < 20 and 3x − 2 > 1.
  3. (4 marks)A rectangle has width x cm and length (x + 4) cm. Its area is less than 60 cm². Find the range of possible values of x.
  4. (3 marks)Solve 3x² ≤ 7x + 6. Write your answer using set notation.
When you’re doneRevise the method in the notes, then mark your answers with the worked solutions.
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