AP Calculus BC: Unit 1 Progress Check: MCQ Part C

AP Calculus BC: Unit 1 Progress Check: MCQ Part C

AP Calculus BC Unit 1 Progress Check focuses on multiple-choice questions designed to assess students' understanding of calculus concepts. It includes questions on continuity, the Intermediate Value Theorem, and asymptotic behavior, essential for mastering the AP Calculus BC curriculum. This resource is ideal for students preparing for the AP exam, offering practice problems that mirror the format and rigor of the actual test. The document provides detailed rationales for each question, helping learners identify areas for improvement.

Key Points

  • Includes multiple-choice questions on calculus continuity and limits.
  • Covers key concepts such as the Intermediate Value Theorem and vertical asymptotes.
  • Offers rationales for answers to enhance understanding of calculus principles.
  • Designed for AP Calculus BC students preparing for the May exam.
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AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part C
Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or
in print beyond your school’s participation in the program is prohibited.
Page 1 of 10
1.
Let be the function given by . On which of the following open
intervals is continuous?
A
B
C
D
2.
Let be the function defined above. For what values of is continuous at ?
A
0.508 only
B
0.647 only
C
and 0.508
D
and 0.647
3.
Let be the function given by . The Intermediate Value
Theorem applied to on the closed interval guarantees a solution in to
which of the following equations?
AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part C
Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or
in print beyond your school’s participation in the program is prohibited.
Page 2 of 10
A
B
C
D
4.
The graph of the function is shown above. On which of the following intervals is
continuous?
AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part C
Copyright © 2017. The College Board. These materials are part of a College Board program. Use or distribution of these materials online or
in print beyond your school’s participation in the program is prohibited.
Page 3 of 10
A
B
C
D
5. The function is continuous on the interval and is not continuous on the
interval . Which of the following could not be an expression for ?
A
B
C
D
6.
Let be the function defined above, where is a constant. For what value of is
continuous at ?
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End of Document
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FAQs of AP Calculus BC: Unit 1 Progress Check: MCQ Part C

What topics are covered in the AP Calculus BC Unit 1 Progress Check?
The AP Calculus BC Unit 1 Progress Check covers essential topics such as continuity, the Intermediate Value Theorem, and limits. It includes multiple-choice questions that challenge students to apply these concepts in various scenarios. Additionally, the document addresses asymptotic behavior, providing insights into vertical and horizontal asymptotes. This comprehensive review is crucial for students aiming to solidify their understanding before the AP exam.
How does the Intermediate Value Theorem apply in this progress check?
The Intermediate Value Theorem is a fundamental concept in calculus that states if a function is continuous on a closed interval, it takes on every value between its endpoints. In this progress check, students encounter questions that require them to apply this theorem to determine the existence of solutions within specified intervals. Understanding this theorem is vital for solving problems related to continuity and function behavior, making it a key focus in the assessment.
What is the significance of vertical asymptotes in calculus?
Vertical asymptotes indicate points where a function approaches infinity, often corresponding to values that make the function undefined. In the context of the AP Calculus BC Unit 1 Progress Check, questions about vertical asymptotes help students analyze the behavior of rational functions and understand limits. Recognizing vertical asymptotes is essential for graphing functions accurately and solving calculus problems related to limits and continuity.

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