I take propranolol during exams too - I take one tablet about forty five minutes before the exam is due to start, to allow it time to kick in (I have to be at the exam hall twenty minutes ahead of the scheduled start time, and if I don't feel it working by then, I panic and can't then stop myself having a panic attack). One tablet is normally enough for a shortish exam, occasionally I'll have a long exam (3 hours +) and although the medication should last that long, I can feel the effects wearing off towards the end, so I bring an extra tablet in with me and sit it on my desk, just in case. I've never had to take the supplementary tablet, but knowing that it's there if I need it calms me down.
One thing I would suggest doing beforehand is having a dry run with the tablets ahead of the exams. They have some side effects, and although your doctor is probably sure you won't experience the really severe ones (breathing difficulties, anaphylaxis etc) it's best to make sure of that before you go into the exam hall! In my opinion, it also takes a bit of getting used to - it helps with the physical effects of anxiety but not the mental ones, which means your head will still be panicky and racing, but you shouldn't be shaking on the outside. Personally, I also get a feeling of floating/like the world has slowed down, which you might get too.
I hope the propranolol does help you, because it has greatly changed my exam experiences -I've only taken it for two exam sittings so far, but beforehand I'd had panic attacks and shakes so bad during exams that I couldn't do as well as I knew I could. It takes a bit of experimentation, getting to know how much works for you, and when to take it, but it is worth it in the end