Foundation November 2022 Paper 1 Q18
18 In 2019, comet A and comet B were both seen from Earth.
Comet A is seen from Earth every 84 years.
Comet B is seen from Earth every 105 years.
Find the next year when both comets will be seen from Earth. [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2439 | 4 | B3 for [LCM=] 420 or answer \(2439 + 420n\) OR B2 for listing the next 3 multiples for both comets 168, 252, 336 and 210, 315, 420 or [84 =] \(2^2 \times 3 \times 7\) and [105=] \(3 \times 5 \times 7\) or [LCM=] \(420k\) OR B1 for listing the next 3 multiples for one comet or [84 =] \(2^2 \times 3 \times 7\) or [105=] \(3 \times 5 \times 7\) allow in a factor tree or table Alternative method 1 B2 for listing the next 3 years for both comets 2103, 2187, 2271 and 2124, 2229, 2334 or B1 for listing the next 3 years for one comet Alternative method 2 B2 for Venn diagram with 3, 7 in the intersection 2, 2 in set 84 and 5 in set 105 or B1 for the diagram with one error | \(n = 1, 2, 3 \ldots\) |