It is easy to think of the AP Calculus test as a comprehensive 'we are going to test you on everything anyone should have covered up to this point ....', but it is not. In fact, it is possible for students who are absolutely horrid at algebra to score fairly well.
The reason for this is that the goal of the exam is to test a student on their calculus knowledge and understanding. It is really interesting to see how they are able to construct questions to assess ONLY that. There is, of course, some algebra required, but it is not as extensive as many of our class tests probably are.
Now - that said - a goal of many of our classes is also to prepare our students for success in whatever STEM courses follow in college, and some colleges may expect students to remember such details from a precalculus class, but I have never asked questions that aim to review that. One of the calculator capabilities AP Calc students are expected to be familiar with is finding roots, and any question that asks for roots I would expect to be a calculator question.....
It is possible that a question could expect a student to use the IVT to assess the guarantee of a root in a particular interval..... but not the rational root theorem.
Another thing to remember - polynomials are very specialized functions, and the goal of AP Calculus is, in some respects, to show how calculus is used to analyze various properties of functions that are NOT polynomials. So - the students' prior knowledge is loaded with properties and behavior of nice smooth continuous polynomial things, but calculus questions often ask about similar properties of more unusual functions (think about the use of limits to define/identify horizontal and vertical asymptotes and continuity; or the use of derivatives to identify points of inflection and so on ....)
Hope this helps some ....
Bob Wilder Middletown High School
________________________________________ From: Michael Penigian [ray973@AOL.com] Sent: Sunday, September 16, 2012 2:48 PM To: AP Calculus Subject: [ap-calculus] Rational Zero Theorem Test
Good Afternoon everyone,
Thank you for your feedback on the greatest integer function. I have another question about how far the AB test may go for certain questions. Would they ever have a function whose highest power is greater than 2 where students would have to use the Rational Zero Theorem and list all of the root candidates for say finding zeros or vertical asymptotes? Thanks.