The blood test will probably be to see if your blood type is positive or negative , most OBs will do it in the beginning , but some wait until you're 36 weeks .
Strep b test and i got checked for dialation. Then the normal stuff, blood pressure, listen to the heart beat, check your weight.
I didn't get blood work at 36 weeks though.
I didn't get a vaginal exam but I had the strep b test and a pee test, and an ultrasound to see how far down bub was in my pelvis and that she was measuring right, then the normal like blood pressure and babies heartbeat
(I live in Australia so could be different where you are)
If you haven't had the group B strep test yet, you need to, it killed my friend's baby because she wasn't tested for it. Blood work I'm not sure but the vaginal exam will be done every week now because you're considered full term even though you're not a 40 weeks yet. They just check for dilation and such