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A-LevelMathematicsIntegration9709/32 · Feb/Mar 2022 · Q88 Marks

Find the quotient and remainder when 8x³ + 4x² + 2x + 7 is divided by 4x² + 1.

  1. (a)Find the quotient and remainder when 8x³ + 4x² + 2x + 7 is divided by 4x² + 1.[3]
  2. (b)Hence find the exact value of ∫(from 0 to ½) (8x³ + 4x² + 2x + 7) / (4x² + 1) dx.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

  1. [1] Commence division and reach quotient of the form 2x + 1
  2. [1] Obtain (quotient) 2x + 1
  3. [1] Obtain (remainder) 6
  4. [1] Obtain terms x² + x
  5. [1] Obtain term of the form a tan⁻¹ 2x
  6. [1] Obtain term 3 tan⁻¹ 2x
  7. [1] Use x = 0 and x = ½ as limits in a solution containing a term of the form a tan⁻¹ 2x
  8. [1] Obtain final answer ¾(1 + π), or exact equivalent

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Feb/Mar 2022 Paper 3 Variant 2, question 8.

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