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0606/23 May/Jun 2026, Question 1: Modulus Equations and Inequalities

Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 5 marks

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The question, in short

On a grid spanning x from −3 to 3 and y from −6 to 8, plot y = |2x + 1| for −3 ≤ x ≤ 3, then use a second graph to solve |2x + 1| > x + 2.

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

Part (a) · 2 marks

Draw the graph of y = |2x + 1| on the grid for values of x from −3 to 3.

  1. 12x + 1 = 0 at x = −0.5, so the vertex is (−0.5, 0)
  2. 2x = −3: y = |−5| = 5; x = 0: y = 1; x = 3: y = 7
  3. 3Draw straight lines from (−3, 5) to (−0.5, 0) and from (−0.5, 0) to (3, 7)

AnswerV-shaped graph with vertex at (−0.5, 0), passing through (−3, 5), (0, 1) and (3, 7)

Part (b) · 3 marks

Draw a suitable line on the grid and use it to find the x values where |2x + 1| exceeds x + 2.

  1. 1Draw the line y = x + 2
  2. 2Intersections: 2x + 1 = x + 2 ⇒ x = 1; −(2x + 1) = x + 2 ⇒ x = −1
  3. 3The V-graph is above the line to the left of x = −1 and to the right of x = 1
  4. 4x < −1 or x > 1

Answerx < −1, x > 1

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Also searched as: 0606/23/M/J/26 · 0606_s26_qp_23 · 0606 s26 23 · question 1.
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