If your version of "love/hate" is the same as my version, then you need to run for the hills.
For me, a "love/hate" relationship means that you and your partner oscillate between passion and utter loathing, with very little warning before the switch. You could be having a profound and beautiful conversation that suddenly devolves into a screaming match. You end every night either furious or in each other's arms. It's a concept straight from a movie, and it sounds a lot more romantic on big screen than it actually is.
If this is what you're experiencing, you need to leave. Being happy 50% of the time and being really unhappy the other 50% of the time is no way to live your life. There are men or women out there that can make you happy nearly all of the time. So don't compromise. Staying with the person you're with now represents compromise, and your willingness to let drama and anger into your life.
So, in short, is it normal? Yes. A "love/hate" relationship is perfectly normal, in the week before the break up.