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A-LevelMathematicsLogarithmic and exponential functions9709/32 · May/June 2021 · Q35 Marks

The variables x and y satisfy the equation x = A(3⁻ʸ), where A is a constant.

  1. (a)Explain why the graph of y against lnx is a straight line and state the exact value of the gradient of the line.[3]
  2. (b)Calculate the value of A, giving your answer correct to 2 decimal places.[2]

Mark scheme

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

  1. [B1] State or imply ln x = ln A − y ln 3
  2. [B1] State that the graph of y against ln x has an equation that is linear in y and ln x, or has an equation of the standard form 'y = mx + c' and is thus a straight line
  3. [B1] State that the gradient is −1/ln 3
  4. [M1] Substitute ln x = 0, y = 1.3 and use correct method to solve for A
  5. [A1] Obtain answer A = 4.17 only

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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, May/June 2021 Paper 3 Variant 2, question 3.

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