To me, this should be translated as “My exams took place last week,” while the test results show “My exams took place in the last week,” which sounds strange in English. I'm really confused!
Mes exams ont lieu la dernière semaine
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Mes exams ont lieu la dernière semaine

Bonjour Aria,
The expression for 'to take place' is 'avoir lieu'.
You have to conjugate the verb avoir to indicate the tense.
ont lieu
is the present of this expression and not the past tense, as you suggest, in which case it would be:
Mes examens ont eu lieu...
So the accepted translation is correct.
My exams take place in the last week of term
Bonne Continuation !
Aria,
it may be easier if you read the translation as ‘ … in the final week. ‘ Same meaning as ‘ in the last week ‘ - both are correct. The sentence is a fragment of a conversation and in context ‘ the last/final week ( of something eg the course/semester/ month etc ) ‘ would be clear.
“ … last week “ would be ‘ la semaine dernière’.
The difference in meaning of the adjective dernier/e when it precedes or follows the noun is the point of the lesson.
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