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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2012 · Q77 Marks

Find d/dx (tan 4x).

  1. (i)Find d/dx (tan 4x).[2]
  2. (ii)Hence find ∫(1 + sec² 4x) dx.[3]
  3. (iii)Hence show that ∫[0 to π/16] (1 + sec² 4x) dx = k(π + 4), where k is a constant to be found.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [M1] One term only
  2. [A1] 4 sec² 4x
  3. [B1] x +
  4. [M1] tan 4x / 4
  5. [A1] isw
  6. [M1] Correct use of limits
  7. [A1] k = 1/8 Rounds to 0.125. Accept π/8 or 0.125π

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 2 Variant 2, question 7.

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