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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2024 · Q27 Marks

Evaluate ∫(from π/4 to π/2) cos(x/2) dx. You must show all your working.

  1. (a)Evaluate ∫(from π/4 to π/2) cos(x/2) dx. You must show all your working.[4]
  2. (b)Find ∫(1/(4x-3) + 1/x²) dx.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B2] 4sin(x/4) π/2 π/4 π/3
  2. [B2] B1 for ksin(x/4) where k > 0 or k = -4
  3. [M1] FT provided at least B1 awarded
  4. [A1] dep on all previous marks awarded
  5. [A1] 0.495 or 0.4954[57...] rot to 4 or more sf
  6. [B3] (1/4)ln(4x-3) - (x^(-2)/(-2)) (+c) oe, isw
  7. [B3] B2 for (1/4)ln(4x-3) or (1/4)ln(x-0.75)
  8. [B3] or B1 for (1/4)ln4x-3 or (1/4)lnx-0.75
  9. [B3] or kln(4x-3)
  10. [B3] or kln(x-0.75) where k ≠ 1/4
  11. [B3] and B1 for x^(-2)/(-2) oe

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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, May/June 2024 Paper 2 Variant 2, question 2.

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