Translation:Today at noon I have a Chinese exam.
The translation provided is actually wrong. The correct translation for this sentence should be "Today at noon I have an exam in Chinese" and not a "Chinese exam". Although it is grammatically correct, the semantics is wrong. The adjective "Chinese" implies ORIGIN as in Chinese food, language, tradition, etc., ...but "an exam in Chinese".
What about "a book? A Chinese book would be any book that originated from China!
For some reason "Today at midday I have a test in Chinese" is accepted but the same phrase with "exam" is not!
So why isn't 'At midday today' accepted, when 'Today at midday' is not??!! GRRR!
I think that would be a random exam in the Chinese language instead of an exam in the Chinese language.
Richard...Without specifying what the "same issue" actually is, given the number of comments pro and con above yours, it's hard to respond. My feeling about the question of whether it should be: Chinese exam or exam in Chinese is below. In brief, to me both phrases are synonymous and should be acceptable.
I wrote "Today at noon I have an exam in Chinese" and it was accepted. I agree with you that "...I have a Chinese exam" changes the meaning.
I think you're splitting hairs. An exam in Chinese and a Chinese exam would be taken by most students of Chinese to mean the exact same thing. You hear students all the time say I have a French test today or an exam in German. They're all saying the same thing essentially. To assert otherwise is nonsense.
Probably not correct because it sounds like the exam is about the Chinese people not the Chinese language.