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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2012 · Q86 Marks

An open rectangular cardboard box with a square base is to have a volume of 256 cm³. Find the dimensions of the box if the area of cardboard used is as small as possible.

Mark scheme

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

  1. [B1] x²h = 256
  2. [M1] A = x² + 4xh
  3. [A1] A = x² + 1024/x
  4. [A1√] dA/dx = 2x - 1024/x² oe
  5. [M1] Equate to 0 and solve
  6. [A1] x = 8
  7. [A1] h = 4
  8. OR
  9. [B1] A = (256/h) + 64√h
  10. [M1] dA/dh = -256/h² + 32/√h
  11. [A1]
  12. [A1√]
  13. [M1]
  14. [A1] h = 4
  15. [A1] x = 8

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 2, question 8.

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