If you finish UMTYMP before finishing high school, we highly encourage you to continue taking math courses until you graduate. There are many books you can buy with AP practice exams, but the College Board provides actual past exams that you can use as well: Also, be sure to take multiple practice exams, and then compare you work agains the sample scoring rubrics. How should you prepare for this? Read as much information as you can about the AP exams and grading, such as the links at the end of the FAQ posted above. AP exams are more likely to have problems with real-world interpretations and units - and including the units can be worth a point. In UMTYMP we tend to focus a bit more on "pure" math problems, in part because our Calc 1 students range from 8th through 10th grades and have not all taken the same science courses. See this PDF about justifying extrema, for example. On a 5 point problem it's easy to lose a point or two because of units, or whether you included the correct words next to a table of values or sign chart. On AP exams, the graders are dealing with hundreds of thousands of exams for consistency have to use rigid grading rubrics which don't allow for a lot of interpretation of your work or knowledge. In UMTYMP we know what we've taught you, we know your work well, and we can make subjective judgements to give you (say) 8/10 points. Normally we have an in-person session to talk about the differences between UMTYMP exams and AP exams. Alternatively, they could wait until they're in Calculus 2, at which point they'll have seen almost all of the BC curriculum (and a good deal more), but will have to go back and study topics they haven't seen in a while. (The flip side is that there are things in UMTYMP which don't appear in the AP curriculum.) A student could take the BC exam while in our Calculus 1 course, but will have to study a few topics on their own. The short summary: the list of topics in UMTYMP Calculus 1 is very similar to the AP Calculus BC exam, but there are a few things that we cover in different orders, or don't cover until a later class.
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