O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2025 · Q84 Marks

On the axes, sketch the graph of y = 5 ln(4x+3). State the intercepts with the axes. State the equation of any asymptote.

On the axes, sketch the graph of y = 5 ln(4x+3). State the intercepts with the axes. State the equation of any asymptote.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[4] B1 for correct shape in first three quadrants tending towards a vertical asymptote in the second and third quadrants.
Dep B1 for curve passing through x = -0.5 oe on the x-axis, or stated and no other points on the x-axis
Dep B1 for curve passing through y = 5ln3 oe on the y-axis, or stated and no other points on the y-axis
B1 for x = -3/4 oe shown on graph or stated as the equation of the asymptote. May be implied by a dotted or straight vertical line through x = -3/4. This is not a dependent mark.

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2025 Paper 1 Variant 2, question 8.

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