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A-LevelMathematicsIntegration9709/12 · Oct/Nov 2020 · Q1010 Marks

The diagram shows part of the curve y = 2/(3-2x)² - x and its minimum point M, which lies on the x-axis. [Figure 10.1]

  1. (a)Find expressions for dy/dx, d²y/dx² and ∫y dx.[6]
  2. (b)Find, by calculation, the x-coordinate of M.[2]
  3. (c)Find the area of the shaded region bounded by the curve and the coordinate axes.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

  1. [B2, 1, 0] B2 for all three elements correct, B1 for two elements correct, B0 for only one or no elements correct.
  2. [B1FT] FT providing their bracket is to a negative power
  3. [B1] 1/(3-2x)
  4. [B1] -x²/2
  5. [B1] + c
  6. [M1] Setting their 2-term differential to 0 and attempts to solve as far as x =
  7. [A1] x = ½
  8. [M1] Using their integral, their positive x limit from part (b) and 0 correctly.
  9. [A1] 1/24

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2020 Paper 1 Variant 2, question 10.

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