A-LevelMathematicsLogarithmic and exponential functions9709/32 · May/June 2020 · Q25 Marks

The variables x and y satisfy the equation y² = Aekx, where A and k are constants. The graph of In y against x is a straight line passing through the points (1.5, 1.2) and (5.24, 2.7) as shown in the diagram. [Figure 2.1] Find the values of A and k correct to 2 decimal places.

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B1] State or imply 2 ln y = ln A + kx
[M1] Substitute values of ln y and x, or equate gradient of line to k, and solve for k
[A1] Obtain k = 0.80
[M1] Solve for ln A
[A1] Obtain A = 3.31

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, May/June 2020 Paper 3 Variant 2, question 2.

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