Question

Is the use of "came" in the following sentences correct? If not please let me know the colloquial term, or what natives use to say such sentences:
- He came first in the race. (Here we mean that 'He' won the race, or the first one to cross the winning line).
- She came first in the class. (Here we mean that the 'She' hold the 1st position in exams among all the students in the class).

Answer 1

I think the first one is alright, I woul use "She's first in her class" for the second one, but that's just my opinion

Answer 2

In my humble opinion - as a sports fan - the first sentence would sound better as "He came in first in the race" or "He finished first in the race." As a sports reference, I always hear "she came in first." I know, that's using "in" twice" but "came first" sounds wrong, just to me. I agree with jalcantara that the second sentence sounds better as "She's first in her class."