0606/23 Oct/Nov 2025, Question 9: Turning Curves into Straight Lines
Cambridge IGCSE Additional Mathematics 0606 · Paper 23 (Calculator) · Calculator · 6 marks
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The question, in short
Given paired x and y values for a relationship y = Ax^b, plot ln y versus ln x on the provided axes and then determine the constants A and b from the line.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 2 marks
Using the table of x and y values, plot ln y against ln x on the given grid to produce a straight line.
- 1ln x: −0.5, 1.5, 2.5, 3.5
- 2ln y: 0.5, 1.5, 2, 2.5
- 3Plot the four points and draw a single ruled straight line through them
AnswerPoints (−0.5, 0.5), (1.5, 1.5), (2.5, 2), (3.5, 2.5) plotted with a single ruled straight line of best fit
Part (b) · 4 marks
From your plotted line, work out the numerical values of the constants A and b.
- 1ln y = b ln x + ln A
- 2Gradient b = (2.5 − 0.5)/(3.5 − (−0.5)) = 0.5
- 3Intercept: 2.5 = 0.5 × 3.5 + ln A, so ln A = 0.75
- 4A = e^0.75 ≈ 2.12
Answerb = 0.48 to 0.52, A = 2.01 to 2.23
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