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A-LevelMathematicsAlgebra9709/31 · Oct/Nov 2019 · Q810 Marks

Let f(x) = x² + x + 6 x²(x + 2) (i) Express f(x) in partial fractions. (ii) Hence, showing full working, show that the exact value of S 4 f(x) dx is 2. [5]

  1. (i)Express f(x) in partial fractions.[5]
  2. (ii)Hence, showing full working, show that the exact value of S 4 f(x) dx is 2.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

  1. [B1] State or imply the form A/x + B/x² + C/(x+2)
  2. [M1] Use a correct method for finding a constant
  3. [A1] Obtain one of A = − 1, B = 3, C = 2
  4. [A1] Obtain a second value
  5. [A1] Obtain the third value
  6. [B1] Integrate and obtain terms ln|x| - 3/x + 2ln|x+2|
  7. [M1] Substitute limits correctly in an integral with terms a ln x, b/x and c ln(x+2), where abc ≠ 0
  8. [A1] Obtain (9/4) following full and exact working AG

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2019 Paper 3 Variant 1, question 8.

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