The AP Calculus AB Unit 1 Progress Check focuses on multiple-choice questions designed to assess understanding of calculus concepts. It includes questions on continuity, the Intermediate Value Theorem, and limits, providing a comprehensive review for students preparing for the AP exam. This resource is ideal for AP Calculus students looking to solidify their knowledge and practice problem-solving skills. The document features various scenarios and functions to analyze, ensuring a thorough grasp of essential calculus principles.

Key Points

  • Includes multiple-choice questions covering continuity and limits.
  • Focuses on the Intermediate Value Theorem and its applications.
  • Designed for AP Calculus AB students preparing for the exam.
  • Covers key calculus concepts essential for success in the course.
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10 pages
AP® Calculus AB
newtopiccyclegrowin
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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End of Document
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FAQs

What types of questions are included in the AP Calculus AB Unit 1 Progress Check?
The AP Calculus AB Unit 1 Progress Check includes multiple-choice questions that assess students' understanding of key calculus concepts such as continuity, limits, and the Intermediate Value Theorem. Each question is designed to challenge students' problem-solving skills and conceptual knowledge. The variety of scenarios presented helps students apply calculus principles in different contexts, which is crucial for mastering the subject.

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 the context of the AP Calculus AB Unit 1 Progress Check, students are asked to identify scenarios where this theorem guarantees the existence of solutions to equations. Understanding this theorem is essential for analyzing functions and their behaviors, making it a key focus in the assessment.

What is the significance of continuity in calculus?
Continuity is a critical concept in calculus that ensures a function behaves predictably without any breaks or jumps. In the AP Calculus AB Unit 1 Progress Check, questions related to continuity challenge students to determine where functions are continuous and where they may have discontinuities. Mastery of this concept is essential for understanding limits, derivatives, and integrals, which are foundational topics in calculus.

How can students use this progress check to prepare for the AP exam?
Students can use the AP Calculus AB Unit 1 Progress Check to identify their strengths and weaknesses in calculus concepts. By practicing with multiple-choice questions, they can familiarize themselves with the exam format and improve their problem-solving speed. Additionally, reviewing the explanations for each answer helps reinforce understanding and clarify any misconceptions, making this resource a valuable tool for effective exam preparation.