AP Calculus AB Unit 1 Progress Check MCQ Part C provides a comprehensive assessment tool for students preparing for the AP Calculus AB exam. This resource includes multiple-choice questions focused on key calculus concepts such as continuity, the Intermediate Value Theorem, and asymptotic behavior. Designed for high school students, it covers essential topics that are critical for mastering the AP curriculum. The questions are structured to reflect the style and rigor of the actual exam, helping students gauge their understanding and readiness for the May exam.

Key Points

  • Includes multiple-choice questions on continuity and limits.
  • Covers the Intermediate Value Theorem and its applications.
  • Features questions on vertical and horizontal asymptotes.
  • Designed for AP Calculus AB students preparing for the exam.
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AP® Calculus AB
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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 focuses on essential topics such as continuity, limits, and the Intermediate Value Theorem. It includes multiple-choice questions that assess students' understanding of these concepts, helping them prepare for the AP exam. Additionally, the questions address vertical and horizontal asymptotes, which are crucial for analyzing function behavior. This resource is tailored to align with the AP curriculum, ensuring that students are well-prepared for the exam.

How does the Intermediate Value Theorem apply in this progress check?
The Intermediate Value Theorem is a key concept assessed in the AP Calculus AB Unit 1 Progress Check. It states that if a function is continuous on a closed interval, then it takes on every value between its endpoints. The questions in this progress check require students to apply this theorem to determine the existence of solutions to equations within specified intervals. Understanding this theorem is vital for students as it reinforces the relationship between continuity and the values a function can achieve.

What is the significance of continuity in calculus?
Continuity is a fundamental concept in calculus that ensures a function behaves predictably without any breaks or jumps. In the context of the AP Calculus AB Unit 1 Progress Check, students are tested on their ability to identify intervals of continuity for various functions. This understanding is crucial for analyzing limits and applying theorems like the Intermediate Value Theorem. Mastery of continuity helps students develop a deeper comprehension of function behavior, which is essential for solving more complex calculus problems.

What types of asymptotes are discussed in this progress check?
The AP Calculus AB Unit 1 Progress Check addresses both vertical and horizontal asymptotes, which are critical for understanding the behavior of functions at extreme values. Vertical asymptotes indicate where a function approaches infinity, while horizontal asymptotes describe the behavior of a function as it approaches a specific value. Questions related to these concepts help students analyze function graphs and predict their behavior, which is essential for mastering calculus.

How can students use this progress check to prepare for the AP exam?
Students can utilize the AP Calculus AB Unit 1 Progress Check as a valuable study tool to assess their understanding of key calculus concepts. By working through the multiple-choice questions, students can identify areas of strength and weakness, allowing them to focus their study efforts effectively. Additionally, the format of the questions mirrors that of the actual AP exam, providing students with a realistic practice experience. This resource is an essential part of a comprehensive study plan for success on the AP exam.