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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2011 · Q1010 Marks

The diagram shows part of the curve y = x³ – 9x² + 24x + 2 cutting the y-axis at the point P. The curve has a minimum point at Q. [Figure 10.1]

  1. (i)Find the coordinates of the point Q.[4]
  2. (ii)Find the area of the region enclosed by the curve and the line PQ.[6]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [B1] (i) 3x² - 18x + 24
  2. [M1] (i) Solves 3 term quadratic equals zero
  3. [A1 cso] (i) x = 4 (and x = 2)
  4. [A1] (i) Q(4, 18)
  5. [B2, 1, 0] (ii) x⁴/4 - 3x³ + 12x² + 2x
  6. [M1] (ii) Uses limits of 0 and xQ in integral (area under curve = 72)
  7. [B1] (ii) Area under PQ = (32 + 8)
  8. [M1] (ii) Plan for area including use of limits
  9. [A1] (ii) 32

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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, Oct/Nov 2011 Paper 2 Variant 2, question 10.

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