AP Calculus AB Unit 1 Progress Check focuses on multiple-choice questions designed to assess understanding of calculus concepts. This assessment includes various topics such as limits, continuity, and the squeeze theorem, providing a comprehensive review for students preparing for the AP exam. Ideal for AP Calculus students, it features a range of questions that challenge critical thinking and problem-solving skills. The document serves as an essential resource for reinforcing knowledge and preparing for the May exam.

Key Points

  • Includes multiple-choice questions on limits and continuity concepts.
  • Features questions that utilize the squeeze theorem for problem-solving.
  • Designed for AP Calculus AB students preparing for the AP exam.
  • Covers essential calculus topics to enhance understanding and application.
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15 pages
AP® Calculus AB
newtopiccyclegrowin
15 pages
AP® Calculus AB
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AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part B
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 15
1.
If is the function defined by , then is equivalent to which of the
following?
A
B
C
D
2.
Let and be functions such that and . What is ?
A
B
C
D
The limit cannot be determined from the information given.
3.
If is the function defined above, then is
AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part B
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 15
A
B
0
C
1
D
nonexistent
4. The function is defined for all in the interval . Which of the following
statements, if true, implies that ?
A
There exists a function with for , and .
B
There exists a function with for , and .
C
There exist functions and with for , and
.
D
There exist functions and with for , and
.
5.
The function is given by . The function is given by . If is a
function that satisfies for , what is ?
AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part B
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 15
A
B
4
C
7
D
The limit cannot be determined from the information given.
6.
Let be a function of . The value of can be found using the squeeze theorem
with the functions and . Which of the following could be graphs of , , and ?
A
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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. Topics covered include limits, continuity, and the application of the squeeze theorem. Each question is designed to challenge students' critical thinking and problem-solving abilities, ensuring they are well-prepared for the AP exam. This assessment serves as a valuable tool for reinforcing knowledge and identifying areas for improvement.
How does the squeeze theorem apply in calculus problems?
The squeeze theorem is a fundamental concept in calculus used to find limits of functions that are difficult to evaluate directly. It states that if a function is 'squeezed' between two other functions that have the same limit at a certain point, then the squeezed function must also approach that limit. This theorem is particularly useful in cases where direct substitution leads to indeterminate forms. Understanding how to apply the squeeze theorem is crucial for solving complex limit problems in calculus.
What is the significance of continuity in calculus?
Continuity is a key concept in calculus that ensures a function behaves predictably without any breaks, jumps, or holes. A function is continuous at a point if the limit as it approaches that point equals the function's value at that point. This concept is essential for understanding the behavior of functions and is foundational for theorems such as the Intermediate Value Theorem. Mastery of continuity helps students analyze and graph functions effectively.
What skills are assessed in the AP Calculus AB Unit 1 Progress Check?
The AP Calculus AB Unit 1 Progress Check assesses a variety of skills essential for mastering calculus. These include the ability to evaluate limits, analyze continuity, and apply theorems such as the squeeze theorem. Students are challenged to think critically and apply their knowledge to solve complex problems. This assessment is designed to prepare students for the types of questions they will encounter on the AP exam, reinforcing their understanding of calculus concepts.

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