Final answer:
The sentence with correct capitalization rules is 'Of my fall semester courses at Troy High School, probably geometry and physics were my favorites.'
Step-by-step explanation:
The correct sentence is C. Of my fall semester courses at Troy High School, probably geometry and physics were my favorites.
This sentence is correct because it follows the conventional rules for capitalization. The rules state that names of particular places, like schools, should be capitalized, hence 'Troy High School' is correct. Academic subjects are not capitalized unless they are languages, so 'geometry' and 'physics' should not be capitalized. Seasons such as 'fall' are also not capitalized unless they are part of a formal name.