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0606/13 May/Jun 2026, Question 1: The Quadratic Formula and Completing the Square

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 6 marks

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The question, in short

Rewrite the quadratic 2x² − 6x + 5 in completed-square form a(x + b)² + c, then use it to solve the inequality 2x² − 6x + 5 > 13.

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Part (a) · 3 marks

Express 2x² − 6x + 5 as a(x + b)² + c and state the constants a, b and c.

  1. 12x² − 6x + 5 = 2(x² − 3x) + 5
  2. 2= 2[(x − 3/2)² − 9/4] + 5
  3. 3= 2(x − 3/2)² + 1/2

Answer2(x − 3/2)² + 1/2

Part (b) · 3 marks

Using your completed square or another method, find the range of x satisfying 2x² − 6x + 5 > 13.

  1. 12(x − 3/2)² + 1/2 > 13
  2. 2(x − 3/2)² > 25/4
  3. 3x − 3/2 > 5/2 or x − 3/2 < −5/2
  4. 4Critical values 4 and −1
  5. 5x > 4, x < −1

Answerx > 4, x < −1

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Also searched as: 0606/13/M/J/26 · 0606_s26_qp_13 · 0606 s26 13 · question 1.
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