Of course, '~이다' is followed by a noun ends with a letter with a final consonant whereas '~다' is followed by a noun ends with a letter without final consonants. Let this rule be (*) for reference. For example, '이건 트럭이다' which is correct whereas '이건 트럭다' which is wrong. Another example is '이건 버스다' is correct whereas '이건 버스이다' which looks somewhat strange. The following is the first question.
Question 1: Is the sentence '이건 버스이다' wrong?
Especially, in academic writing, '~다' seems to be avoided. For example, in almost all mathematics textbooks in Korean, we see a sentence like '이것은 함수이다' but not '이것은 함수다'. The figure following is the final question of math type 가 of 대학수학능력시험(something like Korean SAT). We can see the phrase '극소이고' which should be '극소고' according to the rule (*).
So the next question is
Question 2 Is the rule () correct? If it is correct, should we write '극소고' in place with '극소이고'? If the rule () is not correct, is there any difference between '극소고' and '극소이고'? Can we say which one is recommanded?