"Exams in that class are easy."
Wouldn't クラスwork better than 授業? From my experience, 授業refers more to classes in general and the time you are in class, while クラス is more specific and refers to the course itself. Of course, they are almost interchangeable, but just because some are 外来語 doesn't make such words less Japanese
The English word "class" doesn't always mean a course either.
If the teachers write the tests for their own class, or if students are separated into different classes based on their previous year performance to which different ability level exam papers are then given, then it seems the translation could easily make sense with クラス. ^^
I see what you're saying and I think there's a possibility for that kind of usage, but for me in this specific case, since the English says "exams in that class are easy", I think the words "in that class" point to a class as in a course.
If I wanted to say "Ms. Tanaka's English class", it's 田中先生の英語の授業 (Tanaka-sensei no eigo no jugyou). Saying クラス in this case would be absolutely incorrect.