A-LevelMathematicsLogarithmic and exponential functions9709/22 · Oct/Nov 2022 · Q35 Marks

The variables x and y satisfy the equation y = Axk, where A and k are constants. The graph of In y against In x is a straight line passing through the points (0.56, 2.87) and (0.81, 3.47), as shown in the diagram. [Figure 3.1] Find the value of k, and the value of A correct to 2 significant figures.

(a)The variables x and y satisfy the equation y = Axk, where A and k are constants. The graph of In y against In x is a straight line passing through the points (0.56, 2.87) and (0.81, 3.47), as shown in the diagram. Find the value of k, and the value of A correct to 2 significant figures.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[B1] State or imply equation is ln y = ln A + k ln x
[M1] Equate k to gradient of line or eliminate ln A from simultaneous equations using appropriate values.
[A1] Obtain k = 2.4
[M1] Substitute appropriate values to find ln A
[A1] Obtain ln A = 1.526 and hence A = 4.6 AWRT

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About this question

Topic

Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.

Source

A-Level Mathematics, Oct/Nov 2022 Paper 2 Variant 2, question 3.

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