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Intermediate Value Theorem (Topic 1.16)

Unit 1 - Day 15

​Learning Objectives​
  • Explain the behavior of a function on an interval using the Intermediate Value Theorem

​Success Criteria
  • I can verify that the conditions for the IVT have been met

  • I can use the IVT to describe a function’s guaranteed outputs.

Quick Lesson Plan
Activity: Justifying with the IVT

Scoring guidelines for AB 2014 Question 4, part b
Scoring guidelines for AB 2007 Question 3, part a


After having initially learned the IVT yesterday, students today will use previous AP questions to practice writing justifications. Students can work individually or in pairs on answering AB 2014 Question 4 part b. Then we recommend showing the scoring guidelines and discussing what merits full points. As a class, we will discuss the sample student responses and predict the sample student’s score before actually revealing the student’s score (shown on last page of document). We will then repeat the process with AB 2007 Q3 part a. At then end, allow students to make revisions to their original justifications so that it would receive full points.

Teaching Tips

Students in AP calculus typically do not feel comfortable speaking openly about their own mistakes. Nevertheless, getting feedback on written responses is one of the best learning experiences for students. In this lesson we are using anonymous student samples, but we predict that later in the year students in our class will not feel embarrassed by showcasing their own work for critique. Establishing a culture of trust and community is going to be crucial for this kind of vulnerability we are asking of our students. As teachers, we want to model a growth mindset when it comes to making mistakes and seeking improvement.

Exam Insights

Did you know that you can search old AP exams by topic? If you’re looking for more IVT examples, or want AP examples for other topics you’re teaching this year, look here!

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