I would encourage him to follow self calming techniques and also see if you can distract him a little in the off hours. Let him know that doing well on a test isn't just about what you know, but also about mindset going in. While you might not be able to make sure he knows all the right info, you CAN make sure he brings his best self to the test. What sorts of routines and activities really help him be his best self?
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).