A-LevelMathematicsLogarithmic and exponential functions9709/32 · Feb/Mar 2022 · Q35 Marks

The variables x and y satisfy the equation xⁿy² = C, where n and C are constants. The graph of ln y against ln x is a straight line passing through the points (0.31, 1.21) and (1.06, 0.91), as shown in the diagram. [Figure 3.1]

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Mark scheme

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

[1] State or imply n ln x + 2 ln y = ln C
[1] Substitute values of ln y and ln x, or equate gradient of line to ±½n, but not ± n, and solve for n
[1] Obtain n = 0.8[0] or 0.8[00] or 4/5
[1] Solve for C
[1] Obtain C = 14.41
[1] Obtain two correct equations in n and C by substituting x and y values in the given equation
[1] Solve for n
[1] Obtain n = 0.8[0] or 0.8[00] or 4/5
[1] Solve for C
[1] Obtain C = 14.41

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Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Feb/Mar 2022 Paper 3 Variant 2, question 3.

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