Does my teacher have any right to do this?

It is normal for that to happen. I had college algebra last semester, and my professor would introduce a new section at the class period before the test. I always hated that, though, because if the section was completely new to me and difficult, then I would be a nervous wreck trying to learn the new stuff while studying the old stuff at the same time. Time is essential in college, and because most classes only meet on certain days instead of everyday like in high school, instructors cannot afford to fit in “review days” and stuff like that. Most of the time you learn a new section everyday, take the exam, and then repeat.