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A-LevelMathematicsLogarithmic and exponential functions9709/22 · Feb/Mar 2022 · Q35 Marks

The variables x and y satisfy the equation y = 3^(2a)a^x, where a is a constant. The graph of ln y against x is a straight line with gradient 0.239.

  1. (a)Find the value of a correct to 3 significant figures.[3]
  2. (b)Hence find the value of x when y = 36. Give your answer correct to 3 significant figures.[2]

Mark scheme

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

  1. [B1] State or imply equation is ln y = ln 3^(2a) + x ln a
  2. [M1] Equate gradient of line involving a to 0.239
  3. [A1] Obtain ln a = 0.239 and hence a = 1.27
  4. [M1] Substitute y = 36 in ln y = ... equation and solve for x [Or substitute in original equation with necessary manipulation]
  5. [A1] Obtain 3.32

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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, Feb/Mar 2022 Paper 2 Variant 2, question 3.

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