I read a book that I'm pretty sure is based on an anime. It's a card game based anime. All I remember is that the kids have a school to go to that is on an island, they have to battle a teacher to qualify, and they get sorted into houses. Monsters come out of the cards, and there's a variety of terrain-changing cards and stuff. There's some kind of polymerisation to combine monsters to form polymerisation monsters and stuff.
It does feature a duel academy situated on an island. Students are put into different dorms based on the Egyptian God Cards from the original series.
While some cards are "monsters", other cards such as spell cards affect the terrain or allow for polymerization. Monsters and spells "pop-up" from the cards thanks to the holographic duel disks that the players wear.
Hope that helps :)
This sounds like the Yu-Gi-Oh sequel series Yu-Gi-Oh! GX, which revolves around the Yu-Gi-Oh card game, but in a school/academy setting. Here's the description of the first episode, which matches your description
Jaden Yuki is on his way to the Duel Academy entrance exams when he bumps into Yugi Muto, who gives him a special card, the Winged Kuriboh. Jaden hurries off to the exams, but arrives late. He is given one last chance to get into the Academy, but must first beat Professor Crowler in a duel. Crowler plays his best monster, the powerful Ancient Gear Golem, but Jaden is able to prevail using his new partner, Winged Kuriboh, and the power of his Elemental Hero deck.
And Episode 2
Jaden arrives at Duel Academy and is placed in the Slifer Red dorm[...]
The rest of what you describe is part of the game (which all the series revolve around)
- Monsters come out of the cards
- a variety of terrain-changing cards
- polymerisation to combine monsters to form polymerisation monsters