Does her school use an online system where teachers can post assignments? Ours does (it's called Blackboard and is used in many areas around the country and there are other similar systems as well). Her school is frankly going to slip behind if teachers don't use some kind of online system to post assignments....If the school uses such a site, it's past time for her to check it every single day including weekends (one of my seventh grade daughter's teachers posts things for the week on Sunday afternoons so if she wants to know what's coming, in case she wants to work ahead, she does check in on Sundays). You should have your daughter's password and student ID number or whatever you need to see her assignments on the system, and until she is consistently and reliably checking her own assignments, you need to check them daily too as a backup. If the school does not use any online assignment system, see below....
Does the school give all students a planner notebook they use to write down every assignment, every day? Planners are in common use in every MS around here and students are given a few minutes in each class to ensure they write down that day's assignments. (This is done in addition to the online assignments listings. Our school system works pretty hard to help middle schoolers stay organized.) If the school does not provide these and insist on their use, you and she will need to buy one and you will need to work with her on USING it consistently and bringing it back and forth to school. Then at the end of the day as she stands at her locker she must get into the habit of taking that planner, opening it and using it to help her remember what to bring home.
Does she ride the bus home? That makes it easier for her to forget stuff as she bolts for the bus, and then once she's home there's no way to get back to retrieve a worksheet or textbook she needs. A planner could help ensure she doesn't leave things behind. If you pick her up after school, park, walk up to meet her in the lobby and do not leave school until she has checked her bag and ensured she has everything she needs. Yes, this is micromanaging for now, and some are going to say, no, just let her fail and take her lumps and learn from her errors. But kids do not learn to be organized by taking lumps - they learn by an adult teaching them how to be more organized!
She may indeed be hitting the difficult period of "Elementary was easy and I'm smart but now it's all so different and tough." That is very, very typical. Does the school have a counselor who specializes in teaching kids organization? Many schools do, and I would contact that person right away.
Also, be sure that she has a good space for doing homework; that she is away from TV, iPod or whatever; that if she goes online for homework she is not going onto other sites to read personal e-mail etc.(having the computer in a "public area" at home like your kitchen can help); that she has good light and all her supplies at hand so there's no getting up and down to retrieve things; and that any after-school activities get second place to homework, at least until she is organized enough she can get it done after any activities without a fuss or slacking off.
This may not be laziness -- it may be that she feels overwhelmed and doesn't know how to organize the many assignments she's got. Help her list what her assignments are for each week, while also looking past the current week (as in, there's a math text next Wednesday and a history short answer essay question due next Friday....). Help her decide: What must be done tonight because it's due tomorrow; what must I study for now that is in two days' time or whatever; can I work ahead on that assignment due next week?....Teach her to set priorities. That does require you to know, day to day, what she is doing. Again -- some parents squeal that it's "helicopter parenting" but it is actually called teaching your child to set priorities; kids are not born knowing how to do it, and kids who did fine without much or any oversight in elementary often do need this kind of help in early middle school, which has much more going on and many more assignments and deadlines to juggle.
I know you've "offered to teach her study skills and to quiz her" and she has refused. She is trying to show she can do it herself and she is capable, and she IS going to be capable soon. But you may have to sit down with her, talk to her like she's a grown girl and say, "We need to work together for a time to set priorities and then you will take that over for yourself, but for now, we're a team. We are not saying you can't do it yourself. But this is middle school, and what came easily in elementary just requires some different and new organizational skills you didn't need then. It's OK that you don't know this stuff. Very soon you will, but meanwhile, your teachers, you and we are a team."
Give her a lot of praise not just for improving grades but for working in advance on longer-term projects and studying in advance for tests and being organized when she brings home all the assignments.
Also, check in with her a lot on how things are going. Is the history an era that just does not interest her much? Is the science boring compared to last year when (for example) the teacher did a lot more hands-on experiments but this year the teacher just assigns stuff from the textbook? Communicate with her a lot about specifics and see how she feels about the actual content. Kids at this age start to get more resistant, I think, if they are bored; however, the curriculum won't change just because a kid doesn't happen to like Imperialism this year as much as he liked the Civil War last year...Discussing things with her, if she is bored by the content, could help her be more interested, or you could find ways to supplement with museum trips or other things to keep her interest up.