The Secret Hour (Midnighters Book 1) by Scott Westerfeld
Jessica, a likable high-school student, moves with her family to the dreary small town of Bixby, Oklahoma. Unknown to her, she is one of the midnighters, kids born at the stroke of midnight who can enter a secret 25th hour past midnight where all phenomena and beings of the regular world freeze still in time and threatening night-creatures range freely.
Unaware of her powers, she starts waking up and blundering into the 25th hour and its assorted hazards. The four other midnighter kids (who are smug and eccentric) must find her and fill her in, especially since she seems to be a super-special midnighter that the night critters are anxious to kill.
The most intriguing part of the book is the teenagers’ defenses: math, metal, and elaborate names (with thirteen letters) that activate their weapons.