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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2019 · Q98 Marks

A solid circular cylinder has a base radius of r cm and a height of h cm. The cylinder has a volume of 1200π cm³ and a total surface area of S cm².

  1. (i)Show that S = 2πr² + 2400π/r.[3]
  2. (ii)Given that h and r can vary, find the stationary value of S and determine its nature.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [1] B1 πr²h = 1200π
  2. [1] B1 h = 1200/r² or πrh = 1200π/r and substitution into their S
  3. [1] B1 S = 2πr² + (2πr * 1200/r²) leading to given answer
  4. [1] M1 Must obtain the form Ar + B/r²
  5. [1] M1 Dep for equating to zero and attempt to solve to obtain r = ...
  6. [1] A1 For correct r
  7. [1] A1 Smin = 1340 or 1341
  8. [1] B1 For a correct method to reach a correct conclusion

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2019 Paper 1 Variant 2, question 9.

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