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 piecewise functions. Students preparing for the AP exam will find detailed questions that challenge their grasp of calculus principles. The document serves as a valuable resource for high school students aiming to excel in AP Calculus AB.

Key Points

  • Includes multiple-choice questions covering limits and continuity.
  • Focuses on piecewise functions and their properties.
  • Designed for AP Calculus AB students preparing for the exam.
  • Offers a comprehensive review of key calculus concepts.
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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 topics are covered in the AP Calculus AB Unit 1 Progress Check?
The AP Calculus AB Unit 1 Progress Check covers essential topics such as limits, continuity, and the behavior of functions. It includes questions that require students to analyze piecewise functions and determine their limits at specific points. Additionally, the assessment challenges students to apply the squeeze theorem and understand the implications of discontinuities in functions. This comprehensive review prepares students for the types of questions they will encounter on the AP exam.
How does the document help students prepare for the AP Calculus AB exam?
The document provides a series of multiple-choice questions that simulate the format and difficulty of the AP Calculus AB exam. By working through these questions, students can identify areas of strength and weakness in their understanding of calculus concepts. The answers and explanations help clarify misunderstandings and reinforce learning. This targeted practice is essential for students aiming to achieve a high score on the AP exam.
What is the significance of understanding limits in calculus?
Understanding limits is fundamental in calculus as it lays the groundwork for concepts such as continuity, derivatives, and integrals. Limits help define how functions behave as they approach specific points or infinity, which is crucial for analyzing function behavior. Mastery of limits allows students to tackle more complex calculus problems and is a key focus in the AP Calculus AB curriculum. This foundational knowledge is essential for success in higher-level mathematics.
What are piecewise functions, and why are they important in calculus?
Piecewise functions are defined by different expressions based on the input value, making them essential for modeling real-world situations where a function's behavior changes. Understanding piecewise functions helps students analyze and interpret graphs that have discontinuities or different rules for different intervals. They are frequently encountered in calculus problems, especially when determining limits and continuity. Mastery of piecewise functions is crucial for success in AP Calculus AB.

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