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The Chain Rule (continued) (Topic 3.1)

Unit 3 - Day 3

​Learning Objectives​
  • Calculate derivatives of compositions of differentiable functions

​Success Criteria
  • I can calculate derivatives of compositions of functions.

  • I can make sense of functions given in multiple representations.

Quick Lesson Plan
Activity: Free Response Practice

FRQ 1: 2012 AB 4, parts a, b, and c
Scoring Guidelines and Sample Responses

FRQ 2: 2017 AB 6, parts a, b, and c
Scoring Guidelines and Sample Responses


Today students will put their knowledge of the chain rule to the test with some AP-caliber questions. Exposure to old AP questions is an essential part of preparing students for the exam so students get used to the style and rigor of the AP test.

Teaching Tips

In the “Quick Lesson Plan” above, we have outlined a protocol for how we work on free response questions in our classroom. You may wish to change this protocol depending on the length of your classes or the needs of your students. Early in the year we often assign parts of AP questions to work on in groups. As we are progressing through the year, we transition to mostly individual work with some group input. Later in the year we will do free response questions that are done only as individuals. We believe that giving students the five minutes to discuss their answers in groups helps ease anxiety and makes for excellent discussion among students.

When looking at the scoring guidelines, be explicit with students about what counts as “justification”, especially when discussing continuity. Students may have many questions about their individual response and how many points it would earn. Be patient in answering these questions but you may also ask students to hold off on overly specific questions that pertain only to their own answer.

The College Board provides sample responses and an explanation of where points were earned for that response. Give students time to guess the score before revealing it. Our students tend to enjoy grading other people’s work and are more willing to discuss mistakes when they are not their own. If you run short on time and can only look at one year’s sample responses, we recommend the 2012 question. Seeing students’ answers to justification questions may be more valuable than seeing common calculation errors.

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