The final exam is cumulative, but with a stronger emphasis on the material after the midterm. It is a closed-book exam. Just as for the midterm, I am not going to expect detailed memorization of formulas or algorithms. The ideas are more important than the memorization of things you could look up, so if you need a definition, formula, or algorithm, I'll give it to you. However, I'll expect you to understand the formulas, definitions, and algorithms covered in the readings, with a heavy emphasis on things we discussed in class. Also, I will not totally blindside you with lots of questions from the readings that are completely unrelated to what we covered in class, to test whether or not you did/studied the readings. On the other hand, if you study only what we discussed in class, ignoring everything else in the readings, I can't promise you won't get bitten on some question.
Again, especially on algorithms, but also with issues in general, the understanding is what's important. Knowing how to walk through algorithms we discussed: good. Being able to demonstrate you understand the ideas behind algorithms rather than just doing it by rote, e.g. pros and cons: better. Understanding an algorithm well enough to modify it for some purpose: even better.
That said, here are some specific things you can safely ignore in your studying. (Section numbers from Manning and Schuetze.)
With a higher proportion of articles and papers in the readings in the second half, all of which have "related work" discussions, let me also say that I do not expect you to be responsible for memorizing the historical facts in discussions of who did what work. For example, from Jurafsky (2003), you could be asked a question about Corley and Crocker's use of HMMs to model human syntactic category preferences, but you wouldn't have to remember it was Corley and Crocker who did that work. And, analogous to my attitude with respect to algorithms and formulas as expressed above, I might test your understanding of what they did, but I'd be very unlikely to ask you to re-generate details of their model or experimentation from memory.
I hope that this provides you with some useful guidance. My goal is to write an exam that is interesting (to you), informative (to me), and fair (to all).