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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2018 · Q99 Marks

y [Figure: Graph showing y = 2√x curve from O, a tangent/normal line AB. Point A(4,4) is on the curve. Point B is on the x-axis.] The diagram shows part of the curve y = 2√x. The normal to the curve at the point A (4, 4) meets the x-axis at the point B.

  1. (i)Find the equation of the line AB.[4]
  2. (ii)Find the coordinates of B.[1]
  3. (iii)Showing all your working, find the area of the shaded region.[4]

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Mark scheme

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

  1. [B1] dy/dx = x⁻¹/²
  2. [B1] x=4 → dy/dx = 1/2
  3. [M1] grad of normal = -2
  4. [A1] (y-4) = -2(x-4) → [y=-2x+12]
  5. [B1] (6, 0) FT
  6. [B1] Area of triangle = 1/2 × 2 × 4 = 4 FT
  7. [M1] Area under curve = ∫ 2√x dx
  8. [A1] = (4/3)x³/²
  9. [A1] Total area = 14⅔ [14.7] FT

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2018 Paper 2 Variant 2, question 9.

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