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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2012 · Q87 Marks

The variables x and y are related in such a way that when lg y is plotted against lg x a straight line graph is obtained as shown in the diagram. The line passes through the points (2, 4) and (8, 7).

  1. (i)Express y in terms of x, giving your answer in the form y = axᵇ, where a and b are constants.[5]
  2. (ii)the gradient,[1]
  3. (iii)the intercept on the vertical axis?[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] Finding gradient
  2. [M1] Finding y intercept
  3. [M1] lgy = c + mlgx is sufficient
  4. [A1] a = 1000 or 10³
  5. [A1] y = 1000x⁰.⁵ or 1000√x
  6. [B1] m = 1
  7. [B1] c = 6

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 2 Variant 2, question 8.

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