0580/42 Feb/Mar 2025, Question 22: Simultaneous Equations with a Curve
Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks
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The question, in short
Find where the line y = 4x + 12 meets the curve y = 2x² − x − 3 at points P and Q, showing working and giving coordinates to 2 decimal places.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 14x + 12 = 2x² − x − 3
- 22x² − 5x − 15 = 0
- 3x = (5 ± √(25 + 120))/4 = (5 ± √145)/4
- 4x = 4.260… or x = −1.760…
- 5y = 4x + 12 = 29.04 or 4.96
- 6(4.26, 29.04) and (−1.76, 4.96)
Answer(4.26, 29.04) and (−1.76, 4.96)
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Also searched as: 0580/42/F/M/25 · 0580_m25_qp_42 · 0580 m25 42 · question 22.
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