Exempt(ed) from

Hello, I got a bit confused when I came across the necessity of using a phrase including the expression mentioned in the topic. I couldn't simply differentiate the two possible (are both indeed acceptable?) uses of 'exempt' and 'exempted from'. The question is - what is the difference, if any, between the two following sentences: "He was exempted from the exam" and "He was exempt from the exam". Is the latter correct? Maybe if the example of the sentences including the word had a more general meaning, both could be used, e.g. "Such people are exempt from the exam" vs "Such people are exempted from the exam". Please enlighten me on that vague (to me) matter. (I know that one is an adjective and the other passive form of the verb.)
mike