O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2025 · Q66 Marks

When ln y is plotted against x³, a straight line passing through the points (2,5) and (-8,25) is obtained.

Mark scheme

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

[B1] ln y = mx³ + c_soi (c may be shown as a log term)
[M1] Form simultaneous equations using points (2,5) and (-8,25): 25 = -8m + c, 5 = 2m + c (For at least one equation, may be used with gradient of -2)
[A1] Solve for m and c: m = -2, c = 9 (y=-2x+9 seen implies M1A1)
[A1] Express y in terms of x: y = e⁹⁻²ˣ³ oe
[M1] Substitute y = e²⁵ into the equation from part (a): 25 = 9 - 2x³ (For equating exponential indices and obtaining x = ... or use of x = (25-their 9)/(their - 2))
[A1] Solve for x: x = -2 only

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2025 Paper 1 Variant 2, question 6.

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