One of the three mathematical practices of the AP Precalculus course is communication and reasoning. Part of this strand is being able to justify conclusions with appropriate rationales.
Since the AP Precalculus Free Response Questions are all based on task models, we have a pretty good understanding of the kinds of things students will be asked to justify on the exam. So we created the Calc Medic Ultimate Justification Guide to prepare students for these questions. The left column of the document gives the statement or conclusion, while the right column gives the justification. Some variance is expected of course: we don't need students to memorize these verbatim, but there is a level of formality and precision required in students' responses in order to receive full points, and we need to prepare students for this!
Justifications aren't just restricted to the free response section though. We've seen multiple choice questions on several practice exams with the following structure:
[Set-up of question]
Which of the following statements gives the correct answer and rationale to ____?
(A) Right answer, wrong rationale
(B) Right answer, right rationale
(C) Wrong answer, wrong rationale
(D) Wrong answer, right rationale
These questions often have to do with justifying a function type or regression model, or supporting the existence of a particular function feature, like a hole or asymptote. We've added these kinds of justifications to the Ultimate Justification Guide as well!
You can download the blank version where students fill in the second column or the completed version with all justifications already given.
Blank version:
Completed version:
How to Use the Calc Medic Ultimate Justification Guide
Fill it out throughout the course: Give the blank version of the guide to students at the beginning of the year. Have them complete the right column as they encounter each of the statements throughout the course.
Use it as an AP Exam review activity: Use one of your review days before the AP Exam to have students complete the right column of the blank version. Have students work individually first, then in pairs, then in small groups.