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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2023 · Q710 Marks

The diagram shows the curve y = 6x-x² for 0 ≤ x ≤ 5 and the line y = x. Find the area of the shaded region.

  1. (a)The diagram shows the curve y = 6x-x² for 0 ≤ x ≤ 5 and the line y = x. Find the area of the shaded region.[4]
  2. (b)(i)Find ∫((1/(2x-6)³) + cosx)dx.[3]
  3. (b)(ii)Find ∫(x²+1)²/(2x) dx.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

  1. [B1] (6x²/2 - x³/3)|_0^5
  2. [B1] Area under line: 0.5×5×5 oe
  3. [M1] Fully actioned correct plan: 3(25) - 5³/3 - 0.5×5×5 oe
  4. [A1] 125/6 oe isw
  5. [B1] + sinx
  6. [B2] (2x-6)^(-2) / (-2×2)
  7. [B1] for any two correct

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, May/June 2023 Paper 2 Variant 1, question 7.

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