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0580/12 Feb/Mar 2025, Question 19: Linear Inequalities

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Non-calculator · 3 marks

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The question, in short

Find odd values of n with 7 < n ≤ 15, then explain why the inequality −1 < x < 8 does not match the given number line.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

List all odd integers n greater than 7 and at most 15.

  1. 1n > 7 so 7 is not included; n ≤ 15 so 15 is included
  2. 2Odd numbers: 9, 11, 13, 15

Answer9, 11, 13, 15

Part (b) · 1 mark

State why Pip's inequality −1 < x < 8 fails to describe the number line shown.

  1. 1Filled circles mean the end values are included
  2. 2The inequality should be −1 ≤ x ≤ 8
  3. 3So Pip needed ≤ signs, not <

AnswerPip needed to use two ≤ signs (the circles are filled, so −1 and 8 are included)

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