A-LevelMathematicsLogarithmic and exponential functions9709/21 · Oct/Nov 2021 · Q35 Marks

The variables x and y satisfy the equation aʸ = kx, where a and k are constants. The graph of y against In x is a straight line passing through the points (1.03, 6.36) and (2.58, 9.00), as shown in the diagram. [Figure 3.1] Find the values of a and k, giving each value correct to 2 significant figures.

Find the values of a and k, giving each value correct to 2 significant figures.[5]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[B1] State or imply equation is y ln a = ln k + ln x
[M1] Equate gradient of line to 1/(ln a)
[A1] Obtain 1/(ln a) = (9.00 - 6.36)/(2.58 - 1.03) or equivalent and hence a=1.8
[M1] Substitute appropriate values to find ln k
[A1] Obtain ln k = 2.7... and hence k=15

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2021 Paper 2 Variant 1, question 3.

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