A-LevelMathematicsLogarithmic and exponential functions9709/22 · Oct/Nov 2019 · Q35 Marks

The variables x and y satisfy the equation y = kxᵃ, where k and a are constants. The graph of ln y against ln x is a straight line passing through the points (0.22, 3.96) and (1.32, 2.43), as shown in the diagram. Find the values of k and a correct to 3 significant figures.

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[B1] ln y = ln k + a ln x (SOI)
[M1] Equate gradient of line to a
[A1] Obtain a = -1.39 (OE)
[M1] Substitute appropriate values into a correct equation to find ln k
[A1] Obtain ln k = 4.266... and k = 71.2 (SC1 for gradient = -1.39 and no other relevant working)

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2019 Paper 2 Variant 2, question 3.

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