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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2011 · Q78 Marks

The variables x and y are related so that when lgy is plotted against lgx a straight line passing through the points (4, 12) and (6, 17) is obtained. [Figure 7.1]

  1. (i)Express y in terms of x, giving your answer in the form y = axᵇ.[6]
  2. (ii)Find the value of x when y = 300.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.

  1. [1] (i) m = 2.5
  2. [1] (i) c = 2
  3. [1] (i) lgy = 2.5lgx + 2
  4. [1] (i) 2 = lg100 or lg10²
  5. [1] (i) 2.5lgx = lg x^2.5
  6. [1] (i) y = 100 x^2.5
  7. [1] (ii) Solve 2.5lgx = lg3 or x^2.5 = 3 correctly
  8. [1] (ii) 1.55

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About this question

Topic
Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2011 Paper 2 Variant 1, question 7.

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