napamet

1. by heart; from memory
   Deca moraju da nauče pesmu napamet. — The kids have to learn the poem by heart.
   Znam njegov broj telefona napamet. — I know his phone number by heart.
2. at random; off the top of one's head
   Nije znao odgovor, pa je zaokružio napamet. — He didn't know the answer, so he circled one at random.
   Ne pričaj napamet, prvo proveri. — Don't just say things off the top of your head, check first.

Don't confuse it with the two-word "na pamet" in "pasti na pamet" — to occur to someone.