0606/21 Oct/Nov 2025, Question 6: Turning Curves into Straight Lines
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 4 marks
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The question, in short
A straight line through (1, ln 15) and (2, ln 75) is obtained when ln y is plotted against x. Show y = Abˣ and find integers A and b.
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Solution · 4 marks
- 1ln y = mx + c
- 2m = (ln 75 − ln 15)/(2 − 1) = ln 5
- 3ln 15 = ln 5 + c, so c = ln 3
- 4ln y = x ln 5 + ln 3 = ln(3 × 5ˣ)
- 5y = 3 × 5ˣ
Answery = 3 × 5ˣ (A = 3, b = 5)
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