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A-LevelMathematicsDifferentiation9709/12 · May/June 2010 · Q109 Marks

The equation of a curve is y = ½(2x – 3)³ – 4x. (i) Find dy/dx. (ii) Find the equation of the tangent to the curve at the point where the curve intersects the y-axis. (iii) Find the set of values of x for which ½(2x – 3)³ – 4x is an increasing function of x.

  1. (i)Find dy/dx.[3]
  2. (ii)Find the equation of the tangent to the curve at the point where the curve intersects the y-axis.[3]
  3. (iii)Find the set of values of x for which ½(2x – 3)³ – 4x is an increasing function of x.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

  1. [B2,1] Everything but the "×2"
  2. [B1] For the "×2", even if B0 given above.
  3. [B1] For correct y value
  4. [M1 A1] Must be using calculus for m. co. (ok unsimplified)
  5. [M1] Links dy/dx with 0
  6. [DM1] Method for quadratic – lead to 2 answers
  7. [A1] Correct set of values.

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source
A-Level Mathematics, May/June 2010 Paper 1 Variant 2, question 10.

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