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0580/21 May/Jun 2026, Question 8: Substitution

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 8 marks

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The question, in short

Given P(0, 4) and Q(1, 8), find the midpoint of PQ, the vector QP, and c where y = x² + ax + b passes through P, Q and (−2, c).

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

Part (a) · 2 marks

Find the coordinates of the midpoint of the line segment joining P(0, 4) and Q(1, 8).

  1. 1x: (0 + 1) ÷ 2 = 0.5
  2. 2y: (4 + 8) ÷ 2 = 6
  3. 3Midpoint = (0.5, 6)

Answer(0.5, 6)

Part (b) · 2 marks

Find the vector QP, where P is (0, 4) and Q is (1, 8).

  1. 1→QP = P − Q
  2. 2x: 0 − 1 = −1, y: 4 − 8 = −4
  3. 3→QP = column vector (−1, −4)

Answercolumn vector (−1, −4)

Part (c) · 4 marks

Given y = x² + ax + b passes through P and Q and also (−2, c), find the value of c.

  1. 1At P(0, 4): 4 = 0 + 0 + b, so b = 4
  2. 2At Q(1, 8): 8 = 1 + a + 4, so a = 3
  3. 3y = x² + 3x + 4
  4. 4c = (−2)² + 3(−2) + 4 = 4 − 6 + 4 = 2

Answer2

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Also searched as: 0580/21/M/J/26 · 0580_s26_qp_21 · 0580 s26 21 · question 8.
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