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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2014 · Q56 Marks

Find the equation of the tangent to the curve y = x³ - ln x at the point on the curve where x = 1.

  1. (i)Find the equation of the tangent to the curve y = x³ - ln x at the point on the curve where x = 1.[4]
  2. (ii)Show that this tangent bisects the line joining the points (–2,16) and (12, 2).[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. [1] M1 for attempt to differentiate dy/dx = 3x² - 1/x
  2. [1] B1 for y = 1 When x = 1, y = 1 and dy/dx = 2
  3. [1] DM1 for attempt to find equation of tangent (y −1 = 2(x-1))
  4. [1] A1 allow equation unsimplified (y = 2x-1)
  5. [1] B1 for midpoint from given coordinates Mid-point (5, 9)
  6. [1] B1 for checking the mid-point lies on tangent 9 = 2(5)-1

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 5.

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