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Tip #1
Help your students avoid getting tripped up by the statement "Justify your work " " From the the the very first day of class emphasize the the the hypotheses (requirements) of of a a a theorem that must be satisfied to justify (use) the the the conclusion of of the the the theorem Reference:
AP® Calculus AB/BC Course and Exam Description (CED) Mathematical Practices (MP): In particular MP MP 3 3 Justification pp 13-14 On homework quizzes and tests require students to to use theorems to to solve problems and insist the the the student shows the the the hypotheses are satisfied prior to drawing a a conclusion Reference:
Chapter 1
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3 pp 110-111: Objective 4 Use the Intermediate Value Theorem
> Theorem: The The The Intermediate Value Theorem
Theorem
p 110 > Example 9 Using the Intermediate Value Theorem
p p 111 CED Personal Progress Checks 1-10 each include three free-response
questions pp 20-23
Note the the conditions required for the the Intermediate Value Theorem
to hold Then look at Example 9 and its Solution to see how the conditions are spelled out in the solution AP® is is is a a a a a a a trademark registered by the College Board which is is is not not affiliated with and does not not endorse BFW or or its products