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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2016 · Q910 Marks

A curve passes through the point (2, -4/3) and is such that dy/dx = (3x + 10)^(-1/2).

  1. (i)Find the equation of the curve.[4]
  2. (ii)The normal to the curve, at the point where x = 5, meets the line y = -5/3 at the point P. Find the x-coordinate of P.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

  1. [1] B1 for p(3x+10)^(1/2) where p is a constant
  2. [1] B1 for (2/3)(3x+10)^(1/2) oe unsimplified
  3. [1] M1 for attempt to find c, must have attempt to integrate, must have the first B1
  4. [1] A1
  5. [1] B1 When x = 5, y = -2/3
  6. [1] B1 perpendicular gradient = -5
  7. [1] M1 for attempt at the normal using their perpendicular gradient and their y value (but not y=-4/3 or y=-5/3)
  8. [1] A1
  9. [1] DM1 for use of y = -5/3 in their normal equation to get as far as x = ...
  10. [1] A1

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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, May/June 2016 Paper 1 Variant 2, question 9.

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