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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2018 · Q66 Marks

Find d/dx (5x²-125)³.

  1. (i)Find d/dx (5x²-125)³.[2]
  2. (ii)Using your answer to part (i), find ∫ x(5x² - 125)^(-2/3) dx.[2]
  3. (iii)Hence find ∫¹⁰_₅ x (5x² - 125)^(-2/3) dx.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [M1] For kx(5x-125)^(-1/3)
  2. [A1] Allow unsimplified
  3. [M1] For m(5x²-125)^(2/3) (+c)
  4. [A1] FT on their k from part (i)
  5. [M1] Dep on previous M1 For use of limits in their answer to part (ii), must be in the form m(5x²-125)^(2/3) (+c),
  6. [A1] Allow greater accuracy

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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 2018 Paper 1 Variant 2, question 6.

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