Magic or Madness -- Justine Larbalestier

Reason Cansino has never lived anywhere for longer than a few months.  For the last fifteen years, she and her mother have moved from one small village to the next, changing their names regularly and trusting no one but each other.  Staying one step ahead of Reason's evil grandmother, Esmeralda, is their first priority.  She caught up with them once, when Reason was ten, but they were able to escape.

Not this time.  When Sarafina suddenly (and terrifyingly) goes mad, the government sends Reason to her nearest known relation -- Esmeralda. 

Reason may not know her grandmother, but she knows plenty about her.  She knows that she's evil.  She knows that she's dangerous.  And she knows that Esmeralda believes herself to be a witch.

Although Sarafina raised Reason on a diet of logic and mathematics, she also taught her to protect herself from Esmeralda's spells -- because even though Reason knows that none of it is real, it will be a psychological defense against Esmeralda*.

It doesn't take long for Reason to realize that not everything her mother has brought her up to believe is true.

Set in Sydney and New York City, Magic or Madness focuses on three teens -- two Australian, one American.  And get this -- depending on who the focus is, the spelling and the vocabulary change.  So as the reader, you really feel the shift between cities.  Pretty rad, huh?  That alone probably would have made me rave.  But wait, there's more.  There's mystery and treachery and characters that you'll care about and more mystery and a very cool magic system.

Also a hell of a cliffhanger.  The last sentence made me feel all queasy and uncertain and DESPERATE for the sequel.  Good pick for fans of urban fantasy, of course, but I'd also try it on Libba Bray fans.

*You know.  Because Esmeralda believes in her own magic, and therefore has to believe in Reason's "magical" defenses, too.  Trust me.  JL describes it much more coherently.