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A-LevelMathematicsIntegration9709/12 · May/June 2019 · Q35 Marks

A curve is such that dy/dx = x^3 - 4/x^2. The point P (2, 9) lies on the curve.

  1. (i)A point moves on the curve in such a way that the x-coordinate is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the y-coordinate when the point is at P.[2]
  2. (ii)Find the equation of the curve.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [M1] Multiply numerical gradient at x = 2 by ±0.05.
  2. [A1] -0.35 (units/s) or Decreasing at a rate of (+) 0.35
  3. [B1] (y =) x^4/4 + 4/x (+c) oe
  4. [M1] The power of at least one term increase by 1.
  5. [A1] c = 3 or (y =) x^4/4 + 4/x + 3 oe

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2019 Paper 1 Variant 2, question 3.

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