## In The Classroom, Integration Review for Semester Exam.doc - Section 4: Investigation

*In The Classroom, Integration Review for Semester Exam.doc*

# Integration Review for Semester Exam

Lesson 9 of 9

## Objective: SWBAT compute indefinite and definite integrals with u-substitution and other inverses of derivative rules. SWBAT use integration to compute area under functions and average value on an interval.

## Big Idea: Heading into the semester exam, we take a day to recap the various integration techniques and applications we have learned so far.

*60 minutes*

#### Setting the Stage

*5 min*

If you have not done so already, students are always eager to gain any insight or advantage for the exam that we are willing to provide. You might spend a small amount of time attending to this interest, without revealing specifics or otherwise compromising the validity of the exam.

In prior classes my students have been given study guides that in my opinion reveal way too much about the exam, to the point where students have learned to depend exclusively on the study guide in preparing for the exam. Part of the shift in focus to a college level course is in developing and following one’s own plan for preparing for exams. Yet, this is a study skill that many students need to be taught, because merely abandoning students in this endeavor and hoping they will somehow figure it out themselves is not the best instructional approach either.

I share some broad suggestions for how students might prepare:

- Using prior homework assignments and assessments to identify questions that students missed
- Looking up the content of questions in the textbook and our class notes to review and relearn that content
- Re-solve the questions correctly that were initially missed; then, look up additional practice problems on that content in their textbook or online to reinforce their learning

When students ask content-specific questions like “Which types of questions will be emphasized on the exam?” my answer is “I don’t know, ‘ya better prepare for everything we’ve learned this semester.”

I do verbalize a brief summary of the whole semester to help students sequence and put the course content in perspective (below). I encourage students to try to make connections and to look for coherence among the topics. I also ask students to recall and identify topics that they feel they need to study more, without being too helpful or compromising the validity of the exam.

Topics Covered on the Semester Exam

1) A graphical approach to limits

2) Modeling slope graphically with the difference quotient

3) Multiple derivative relationships graphically

4) The difference quotient as the derivative algebraically

5) Computing derivatives algebraically

6) Applying derivatives, especially optimization and related rates

7) Integration as differentiation in reverse

8) Properties and basic applications of integration

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#### Investigation

*38 min*

Pages 2-4 of the In The Classroom file contains 10 integration review questions ranging from computing indefinite and definite integrals, RAM, areas under functions, solving for the constant of integration given a point, and average value.

**DIFFERENTIATING THE LESSON**: You might customize these questions to address known student weaknesses, or vary the level of difficulty to challenge a wider range of students in your class. There is no way we will finish all of these questions in class today, so **you might post the unanswered questions online for students to complete on their own if they choose,** **and suggest that students discuss and post their answers on the class’s Facebook page.**

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- UNIT 1: Back to School
- UNIT 2: Limits and Derivatives
- UNIT 3: Formalizing Derivatives and Techniques for Differentiation
- UNIT 4: Applications of Differentiation, Part 1
- UNIT 5: Applications of Differentiation, Part 2
- UNIT 6: The Integral
- UNIT 7: Applications of Integration
- UNIT 8: Differential Equations
- UNIT 9: Full Course Review via Motion
- UNIT 10: The Final Stretch - Preparing for the AP Exam

- LESSON 1: Introducing the Integral
- LESSON 2: u-Substitution (Part 1 of 2)
- LESSON 3: u-Substitution (Part 2 of 2)
- LESSON 4: Rectangular Approximation Methods
- LESSON 5: RAM and the Definite Integral
- LESSON 6: In-Depth with Definite Integrals
- LESSON 7: Connections and Applications of Definite Integrals
- LESSON 8: Approximating Definite Integrals from Tables
- LESSON 9: Integration Review for Semester Exam