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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2020 · Q107 Marks

The diagram shows part of the graphs of y = 4x^(1/2) and y = (x-3)². The graph of y = (x-3)² meets the x-axis at the point A(a, 0) and the two graphs intersect at the point B(b, 4). [Figure 10.1]

  1. (a)Find the value of a and of b.[2]
  2. (b)Find the area of the shaded region.[5]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [B2] B1 for each a=3, b=1
  2. [M1] ∫ (their b to 0) 4x^(1/2) dx + ∫ (their b to their a) (x-3)² dx
  3. [M2] M1 for each, soi [3/5 * 4x^(5/3)] (their b to 0) + [(x-3)³/3] (their b to their a)
  4. [M1] (12/5 (their b))-(0) + ( (their a-3)³/3 - (their b-3)³/3 )
  5. [A1] 76/15 or 5 1/15 or 5.07 or 5.06 rot to four or more figs; cao

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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 2020 Paper 2 Variant 1, question 10.

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