If you are truly tired and not simply procrastinating, then a short energizing nap before studying is the best thing to do. Coffee/espresso might be able to help you a bit, but the body has a way of taking what it needs in spite of your best efforts to deprive it of what it wants.
Just make sure you ask your room mate to wake you up or make sure to set an alarm clock. You just might sleep through the whole studying bit and wake up a few minutes before your exam.
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