Joseph Rao, from Massachusetts, writes in:
I had a grading questions regarding the AP. I noticed on the scoring keys that usually a response is given full credit if it is using the correct approach, but with an answer that was calculated incorrectly. I had a student on my recent exam who asked if she should receive points if she used the wrong approach on the first part, then calculated the second part of the question with another approach that was wrong, but made sense for the initial approach used. When in doubt should I just following the scoring key for if they specify to use the answer from the previous question? I chose to not award points because neither approach helped get any closer to an answer.
Joseph, you chose... wisely.
Now, before I even start answering this question, remember there's no such thing as a "typical" or general rubric. You've gotta follow each one independently. And the understanding among readers about how to deal with difficult responses will change on every problem, every year. Teachers get themselves tied into all sorts of conundrums repeating memes like "Oh, the AP awards points for substitution, but not for the answer." That may have been true on one or two rubrics, but neither that nor anything else is a universal rule for AP rubrics. Each rubric is designed independently. You cannot game the test.
But to answer your question as best as I can: If a calculation from part (a) must be used to answer part (b), usually credit is awarded just for the recognition that the answer from part (a) is used, whether that answer is right or wrong. I call it "wrong but consistent" -- a calculation that leads to an incorrect answer, but which is consistent with previous work, I mark as "WBC."
Don't let students lawyer up, though. Exceptions exist. The most obvious exception is when a previous answer renders a future answer ridiculous (as in a car moving 1500 m/s, or the mass of a proton being 500 kg). Or, if a previous answer renders future work trivial (i.e. calculating a force of zero newtons in part (a), meaning parts (b) and (c) would also answer zero somethings).
Sometimes, credit is awarded for a correct (not consistent, CORRECT) answer -- in this case, WBC work might earn partial credit, but not full credit.
When in doubt, follow the rubric and use your physicist's spidey sense. If you feel like you're awarding credit for bad physics, DON'T, regardless of how your student argues the rubric. If you feel like you're not awarding credit for good physics, DO. (And your student probably won't complain.)
In the case you describe, I can't imagine this student earning credit. "Wrong but consistent" doesn't mean compounding error upon error. It means, someone did everything right in one part of a problem, but not the other; we're going to credit the correct physics, and dock the incorrect physics. If it's all incorrect, there's no room for credit.
And as a final note, one that I have to give every year to multiple students: They are not allowed to go to Kansas City with the AP readers in order to serve as counsel for their test. Grade the test, give it back, and don't accept any arguments about the rubric. If you need me to serve as a final arbiter, you know where to reach me.