Fiction Magical Fantasy

I’ve been trying to remember a book from my childhood off and on for over a decade now. Read it approximately 12 years ago.
I do not remember the name of the story or the look of the book. I do remember several plot elements of it.

There is some kind of geometric based magic.
Magic books exist where you trace the symbols to move to the next pages.
MC passes a magic test with a book to go to special academy.
There’s an event where the MC uses magic symbols to make a leaf float on a river but intentionally flaws it so it’ll sink to not reveal his power.

Mc gets recruited by royalty to battle for crown in magic formation. Mc’s royal loses and he goes nuts breaking the formation.
Turns out the gold flaked rocks in the formation are transformed losing royals.
Turns out all magic books are magicians whose royals lost and got turned into magic books.

I know it seems a little chaotic but I’d appreciate any help.