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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2024 · Q98 Marks

The diagram shows part of the curve y = 4/(2x+1) and the straight line 2y = 6x+1. Find the area of the shaded region, giving your answer in the form lna+b, where a is an integer and b is a rational number. [Figure X.X]

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Mark scheme

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

  1. [M1] 8/(2x+1) = 6x+1
  2. [M1] 12x²+8x-7=0
  3. [A1] x = 1/2
  4. [M1] kln(2x+1)
  5. [M1] Area under curve = [kln(2x+1)]^(their x) _(1/2)
  6. [A1] Area under curve = 2ln 2
  7. [B1] Area under straight line = 5/8 or 0.625 oe
  8. [A1] Shaded area = ln4 - 5/8

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2024 Paper 1 Variant 2, question 9.

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