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Topic: [ap-calculus] Rational Zero Theorem Test
Replies: 2   Last Post: Sep 17, 2012 10:25 AM

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Michael Penigian

Posts: 6
Registered: 9/2/12
Re: [ap-calculus] Rational Zero Theorem Test
Posted: Sep 16, 2012 6:28 PM
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Bob, thank you. I'm trying to gather up and make sense of all of these resources. There haven't been enough released multiple choice sections from the last few years, and there was an overhaul to the MC back in the late 90s I believe so some resources are outdated. Other resources such as 5 Steps to a 5 have difficult continuity questions involving the Rational Zero Test. I haven't seen it other than there, but would like to be safe. I see what you're saying about the main focus being on the Calculus and will try to keep that in mind throughout the year.

Thanks again,

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-----Original Message-----
From: Wilder Bob <>
To: Michael Penigian <>; AP Calculus <>
Sent: Sun, Sep 16, 2012 5:06 pm
Subject: RE: [ap-calculus] Rational Zero Theorem Test

Hi Michael - the short answer is no.

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

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

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

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 []
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.

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