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.
- (a)Given that the circumferences at yearly intervals form an arithmetic progression, find the circumference 20 years after the first measurement.[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.
- [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.
- [A1] 5.40
- [B1] r = 5.02/5 = 1.004 or 251/250
- [M1] 5.00×(their1.004)20 or 5.02×(their1.004)19 Allow a = 5, n = 20.
- [A1] 5.42 Any correct rounding of 5.41557108 .
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