Help!

I'm sorry if you guys have heard this many times, but I need help in my class. I'm currectly taking AP U.S. History. I think my highest score on was test was a 72; I did well on my essays. I managed to pass with a B the first nine weeks. My teacher picks obscure questions, and questions like, "What was the name of George Washington's horse?". We are divided in groups, and we divide the chapter among our group. Finally we receive a summary from each member of your group. She lectures from time to time; her lectures only contain the title, then some subtiles, and then she starts explaning. I read the chapter, and I take quizzes online, but is not getting me anywhere. We can't write in our books. My friends and I have tried to make study groups, but it doesn't seem to help. I don't know how to study, or how to pass her test. I'm also worried about the AP exam; only two people pass the AP exam out of four classes.
Please give me hints, tips or whatever you think is neccesary to be successful in class as well as on the AP U.S. History exam.