0606/12 Oct/Nov 2025, Question 8: Exponentials, Logarithms, e and ln
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Sketch y = 5 ln(4x + 3) on the given axes, giving the axis intercepts and the equation of any asymptote.
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Solution · 4 marks
- 1Defined for 4x + 3 > 0, so x > −3/4; vertical asymptote x = −3/4
- 2y = 0 when 4x + 3 = 1 ⇒ x = −1/2
- 3x = 0: y = 5 ln 3
- 4Curve increases, going down towards the asymptote and rising slowly to the right
AnswerIncreasing log curve with vertical asymptote x = −3/4, crossing the x-axis at x = −1/2 and the y-axis at y = 5 ln 3, passing through the first, second and third quadrants
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