O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2015 · Q76 Marks

Two variables, x and y, are such that y = Axᵇ, where A and b are constants. When lny is plotted against lnx, a straight line graph is obtained which passes through the points (1.4, 5.8) and (2.2, 6.0).

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[M1] for attempt to find the gradient
[A1] b = 0.25
[M1] for a correct substitution of values from either point and attempt to obtain c or solution by simultaneous equations dealing with c = ln A
[A1] leading to A = 233 or e^5.45
[M1] for correct use of either equation in attempt to obtain y using their value of A and of b found in (i)
[A1] leading to y = 348

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, Oct/Nov 2015 Paper 1 Variant 2, question 7.

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