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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2011 · Q88 Marks

The temperature, T° Celsius, of an object, t minutes after it is removed from a heat source, is given by T = 55e⁻⁰·¹ᵗ + 15.

  1. (i)Find the temperature of the object at the instant it is removed from the heat source.[1]
  2. (ii)Find the temperature of the object when t = 8.[1]
  3. (iii)Find the value of t when T = 25.[3]
  4. (iv)Find the rate of change of T when t = 16.[3]

Mark scheme

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

  1. [1] (i) 70
  2. [1] (ii) 39.7
  3. [1] (iii) 55e⁻⁰·¹ᵗ = 10 oe
  4. [1] (iii) 0.1t = ln(55/10) oe
  5. [1] (iii) 17(.0)
  6. [1] (iv) dT/dt = -5.5e⁻⁰·¹ᵗ
  7. [1] (iv) -5.5 (for k value)
  8. [1] (iv) -1.11

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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 8.

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