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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2024 · Q88 Marks

The tangent to the curve y = e^(2x+5)^(1/2) at the point where x = 2 meets the x-axis at the point X and the y-axis at the point Y. Find the coordinates of the mid-point of XY, giving your answer in exact form.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1] dy/dx = e^((2x+5)^(1/2)) * (1/2)(2x+5)^(-1/2) * 2 (or chain rule)
  2. [A1] dy/dx = e^((2x+5)^(1/2)) * (2x+5)^(-1/2)
  3. [M1] Dep allow unsimplified (for substituting x=2 into dy/dx)
  4. [B1] When x=2, y = 3e²
  5. [M1] Tangent: y-3e² = (10e²/3)(x-2) (Allow for using their dy/dx and their y)
  6. [A1] When y=0, x = 11/10
  7. [A1] When x=0, y = 11e²/3
  8. [A1] (11/20, 11e²/6)

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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 2024 Paper 1 Variant 2, question 8.

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