I LOVED these books, so I may be a bit biased. In my opinion the reading of violence is much better (for a developing child) than the reading of vivid sex scenes or anything like that. I was relieved that these books have VERY little romance in them. There's a bit of a love story that occasionally involves kissing, but it is all very tame and fits the story (it's actually their love story that saves them... not the love itself... that would be cheesy). To me, that feels appropriate for the age group and I would definitely let an 11 year old read it. The violence portion is quite violent. BUT I don't think it's the type of violence that would keep a kid up at night. Almost everything was about supernatural things that attack. It was scary, but I think it was manageable, even for an 11 year old. As a teacher, this is probably NOT something I'm supposed to say, but something I plan to teach my kids. When you have a GOOD book, and you're loving the story, go ahead and skip a bit if it's getting to scary. I've done that and how is it different than closing your eyes during a scary movie?
I'll try to summarize the "death match" so you'll know what that's all about. It takes place in the future, in an alternate reality in which most of the US (presumably) is destroyed. Only small sections of the population are still alive in suffering districts. The Capital is the district that "won" the war that destroyed the rest. The Capital is full of wealth and power and each year the President stages "The Hunger Games" in which two young people from each district are pitted against each other to fight to the death. The whole thing is broadcast live to all the districts (who, all except for the Capital, think it's atrocious) as entertainment and to "teach a lesson" to the other districts about who's in charge. It's dreadful. So the storyline follows one girl from one district as she fights in the Hunger Games. Etc, etc... it's a page-turner. And leaves you wanting SO badly to fix their whole society, because everything is rigged against all the "normal people" in the districts.
Long story short, go ahead and let her read it. If she finds it too scary, she'll stop reading it. You could read it ahead, if you have time (ha!). But it IS a quick read and, like I said, REALLY enjoyable. Or read it together! Good luck!
L.
PS. The movie is coming out soon and will ruin the books forever (like all movies based on books do).