1. The model UN will be on campus tomorrow, so no classes will be held in Upper Deneen. (correct)
2. Many young people don’t bother to register to vote. Because they don’t really care about the candidates.
The second sentence is a fragment. You can correct it by making it one sentence: Many young people don't bother to register to vote because they don't really care about the candidates.
3. Since she had high blood pressure, Carol’s doctor recommended that she try to start exercising. (correct)
4. While it may take a little longer to finish a paper. Professional writers recommend putting it aside for a few hours before doing final proofreading.
The first sentence is a fragment. To correct it, make it an introductory clause by putting a comma after "paper": While it may take a little longer to finish a paper, professional writers recommend putting it aside for a few hours before doing final proofreading.
5. John didn’t think he would like taking a college math class since he had always struggled in high school. (correct)
6. Newsweek recently ran an article about the new trend in television shows such as Real World, Big Brother, and Survivor. That allow viewers to be voyeurs.
The second sentence is a fragment and needs to be connected to the previous sentence:
Newsweek recently ran an article about the new trend in television shows such as Real World, Big Brother, and Survivor that allow viewers to be voyeurs.
7. Mission Impossible 2 was even better than the first film because the action sequences were so much more exciting. (correct)
8. Students who write down their assignments in a calendar tend to manage time better. Unless they forget to check their calendars everyday.
The last sentence is a fragment and needs to be connected with the previous sentence:
Students who write down their assignments in a calendar tend to manage time better unless they forget to check their calendars everyday.