AP Calculus AB Unit 1 Progress Check focuses on multiple-choice questions assessing students' understanding of calculus concepts. It includes questions on continuity, the Intermediate Value Theorem, and function behavior across various intervals. Designed for AP Calculus students preparing for the exam, this resource provides detailed answers to help reinforce learning. The content aligns with the College Board's curriculum framework, ensuring relevance for exam preparation.

Key Points

  • Includes answers to multiple-choice questions from Unit 1 of AP Calculus AB.
  • Covers key calculus concepts such as continuity and the Intermediate Value Theorem.
  • Designed for AP Calculus students to aid in exam preparation and understanding.
  • Aligns with the College Board's curriculum framework for AP Calculus.
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10 pages
AP® Calculus AB
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10 pages
AP® Calculus AB
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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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FAQs

What topics are covered in the AP Calculus AB Unit 1 Progress Check?
The AP Calculus AB Unit 1 Progress Check covers fundamental topics such as limits, continuity, and the behavior of functions. It includes multiple-choice questions that assess students' understanding of these concepts through practical applications. The questions are designed to reflect the types of problems students may encounter on the AP exam, making it a valuable resource for review.

How does the Intermediate Value Theorem apply in the context of this progress check?
The Intermediate Value Theorem states that if a function is continuous on a closed interval, then it takes on every value between its endpoints. In the context of this progress check, students must identify situations where this theorem guarantees the existence of solutions to equations. Understanding this theorem is crucial for solving problems related to function behavior and continuity.

What is the significance of continuity in calculus as discussed in this document?
Continuity is a fundamental concept in calculus that ensures a function behaves predictably without breaks or jumps. The document emphasizes the importance of identifying intervals where functions are continuous, which is essential for applying various calculus principles, including the Intermediate Value Theorem. Mastery of continuity helps students analyze and graph functions effectively.

What types of questions can students expect in the AP Calculus AB Unit 1 Progress Check?
Students can expect multiple-choice questions that test their knowledge of calculus concepts such as limits, derivatives, and integrals. The questions are structured to challenge students' understanding and application of these concepts in different scenarios. This format helps prepare students for the style and rigor of the AP exam.

How can students use the answers provided in this progress check to improve their calculus skills?
Students can use the answers to the multiple-choice questions as a guide to identify areas of strength and weakness in their understanding of calculus. By reviewing the explanations for each answer, students can gain insights into the reasoning behind correct solutions, which can enhance their problem-solving skills and deepen their comprehension of calculus concepts.