koreanfestivals1-3, Exercise 1: The name and the earliest records

Model answer:

Seol (설) in Middle Korean means "year of age", because it is also the date when Koreans grow a year older (the article notes this has changed in South Korea as of 2023). The modern word sal ("age") comes from the same origin.
Gujeong (구정, "old new year") is the lunar new year, the original Seollal; Sinjeong (신정, "new new year") is the Gregorian 1 January.

Two early records (any two): the Book of Wei in the Records of the Three Kingdoms (worshipping events with singing and dancing in Buyeo, in the 12th month); the Book of Sui and Old Book of Tang (7th century, national rituals in Silla); the Samguk Yusa (13th century, the oldest surviving Korean record, mentioning 488 AD); the Goryeosa (one of the nine major national festivals of Goryeo by the 13th century).

"Earliest attestation" is not "earliest custom" because it shows only what was written down and has survived. The custom may be older, and its timing may have differed (the Buyeo record is in the 12th month).

Source: Wikipedia, Korean New Year.