A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2018 · Q46 Marks

The variables x and y satisfy the equation yⁿ = Ax³, where n and A are constants. It is given that y = 2.58 when x = 1.20, and y = 9.49 when x = 2.51.

(i)Explain why the graph of ln y against ln x is a straight line.[2]
(ii)Find the values of n and A, giving your answers correct to 2 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

[B1] State or imply n ln y = ln A + 3 ln x
[B1] State that the graph of ln y against ln x has an equation which is linear in ln y and ln x, or has equation of the form nY = ln A + 3X, where Y = ln y and X = ln x, and is thus a straight line.
[M1] Substitute x- and y-values in n ln y = ln A + 3 ln x or in the given equation and solve for one of the constants
[A1] Obtain a correct constant, e.g. n = 1.70
[M1] Solve for a second constant
[A1] Obtain the other constant, e.g. A = 2.90

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Feb/Mar 2018 Paper 3 Variant 2, question 4.

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