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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2021 · Q108 Marks

The diagram shows the graph of the curve `y = 1/(x+2)² + 3/(x+2)` for `x > -2`. The points A and B lie on the curve such that the x-coordinates of A and of B are -1 and 2 respectively. [Figure 10.1]

  1. (a)Find the exact y-coordinates of A and of B.[2]
  2. (b)Find the area of the shaded region enclosed by the line AB and the curve, giving your answer in the form `p/q - ln r`, where p, q and r are integers.[6]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [B1] At A y = 4
  2. [B1] At B y = 13/16 or 0.8125
  3. [B1] Allow unsimplified
  4. [B1] for -1/(x+2)
  5. [B1] for 3ln(x+2)
  6. [M1] For correct use of limits in their integral, but must have at least one of the two preceding B marks
  7. [A1] for 207/32
  8. [A1] for -ln 64
  9. [(B1)] Or 17/32 x + 47/16
  10. [(B1)] for -1/(x+2)
  11. [(B1)] for 3ln(x+2)
  12. [(M1)] For correct use of limits in their integral, but must have at least one of the two preceding B marks
  13. [(A1)] for 207/32
  14. [(A1)] for -ln 64

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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 2021 Paper 1 Variant 2, question 10.

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