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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2018 · Q1110 Marks

The diagram shows part of the graph of y = 16x + 27/x², which has a minimum at A. [Figure 11.1]

  1. (i)Find the coordinates of A.[4]
  2. (ii)The points P and Q lie on the curve y = 16x + 27/x² and have x-coordinates 1 and 3 respectively. Find the area enclosed by the curve and the line PQ. You must show all your working.[6]

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Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [M1] for dy/dx = 16 - P/x³
  2. [M1dep] Equating to zero and obtaining x³
  3. [A2] A1 for each
  4. [B1] B1 for both
  5. [B1] FT from their P and their Q
  6. [M1] for [px² + q/x]
  7. [A1] Integration correct
  8. [M1dep] for application of limits
  9. [A1] 12

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, May/June 2018 Paper 1 Variant 1, question 11.

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