0606/22 Oct/Nov 2025, Question 4: Turning Curves into Straight Lines
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 6 marks
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The question, in short
A straight line through (1, 13.5) and (7.5, 0.5) comes from plotting eʸ against x³. Use this to express y in terms of x and state where the equation holds.
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Part (a) · 4 marks
Using the two points, find the linear relation between eʸ and x³, then take logs to give y in terms of x.
- 1eʸ = mx³ + c
- 2m = (13.5 − 0.5)/(1 − 7.5) = −2
- 313.5 = −2(1) + c, so c = 15.5
- 4eʸ = 15.5 − 2x³
- 5y = ln(15.5 − 2x³)
Answery = ln(15.5 − 2x³)
Part (b) · 2 marks
Determine the range of x values for which your equation is valid.
- 1ln is defined only for positive values: 15.5 − 2x³ > 0
- 2x³ < 7.75, so x < ∛7.75 (≈ 1.98)
Answerx < ∛7.75
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