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A-LevelMathematicsAlgebra9709/33 · Oct/Nov 2018 · Q910 Marks

Let f(x) = (6x² + 8x + 9) / ((2 - x)(3 + 2x)²).

  1. (i)Express f(x) in partial fractions.[5]
  2. (ii)Hence, showing all necessary working, show that ∫₋₁⁰ f(x) dx = 1 + ½ ln(2/7).[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

  1. [B1] State or imply the form A/(2-x) + B/(3+2x) + C/((3+2x)²)
  2. [M1] Use a correct method to find a constant
  3. [A1] Obtain one of A = 1, B = -1, C = 3
  4. [A1] Obtain a second value
  5. [A1] Obtain the third value
  6. [B3ft] Integrate and obtain terms -ln(2-x) - 1/2 ln(3+2x) - 3/(2(3+2x))
  7. [M1] Substitute correctly in an integral with terms a ln (2 – x), b ln (3 + 2x) and c / (3 + 2x) where abc ≠ 0
  8. [A1] Obtain the given answer after full and correct working

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About this question

Topic
Algebra, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2018 Paper 3 Variant 3, question 9.

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