....Do you think it's worth asking this teacher for a LOR even though the trend is obviously downward counting the final exam?
While it may be a little late for you in this case, it brings up an interesting point. Part of you "job" as a premed is to get good letters of recommendation. It really is mostly a formailty, but it can be harder than you think, and often takes a lot longer than you could ever imagine. Some professors take forever and ever, even with you hasseling them, to get these things done. So... you really have to plan ahead.
What do you do then? You have to play this thing like it is a game. You know that you will need letters from non-science and science professors, so you need to actually start "cultivating" them from the beginning of class.
1) You need to be active and participate in class.
2) You need to ask questions on the way out the door or ake comments so that they get familiar with you.
3) You need to drop by during office hours to talk about projects and assignments.
4) You need to email them with questions or problems, even if you don't have any.
5) You need to show up on time, every day, and pay attention.
6) You need to do well in the class.
I've talked to a quite a few professors who laughed about people that made B's and C's in their classes and asked for recommendations. They also comment about students who they never even knew who asked for recommedations. This part of your application can be a formaity but it really does count-- and one negative recommedation could keep you out of any school. Geting LORs is like a job and you've got to spend a fair amount of time to get good ones.