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A-LevelMathematicsSeries9709/12 · Feb/Mar 2023 · Q45 Marks

The circumference round the trunk of a large tree is measured and found to be 5.00m. After one year the circumference is measured again and found to be 5.02 m.

  1. (a)Given that the circumferences at yearly intervals form an arithmetic progression, find the circumference 20 years after the first measurement.[2]
  2. (b)Given instead that the circumferences at yearly intervals form a geometric progression, find the circumference 20 years after the first measurement.[3]

Mark scheme

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

  1. [M1] 5.00+20×0.02 or 5.02 +19×0.02 Allow for a = 5, n = 20 with d = 0.02 only. a = 5, n = 21(OE) with d = 0.2 gets M1 only.
  2. [A1] 5.40
  3. [B1] r = 5.02/5 = 1.004 or 251/250
  4. [M1] 5.00×(their1.004)20 or 5.02×(their1.004)19 Allow a = 5, n = 20.
  5. [A1] 5.42 Any correct rounding of 5.41557108 .

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About this question

Topic
Series, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2023 Paper 1 Variant 2, question 4.

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