I've seen the following examples in my textbook so far.
He said that his son would graduate from college next spring.
He said that he might come tomorrow.
I wonder that if a clause which indicates time or condition is added to these sentences, the new sentences become correct, like:
He said that his son would graduate from college if he [passes] the last examination next spring.
He said that he might come before he [goes] to school tomorrow.
Are these sentences correct? (I wonder the present tense can be used here, even though the other tenses in these sentences are all the past tense.) If not, how can we add clauses indicating time or condition to the former sentences?