AP Calculus AB Unit 1 Progress Check focuses on multiple-choice questions designed to assess students' understanding of calculus concepts. This scoring guide provides detailed answers and explanations for each question, helping students prepare for the AP exam. Topics include continuity, the Intermediate Value Theorem, and function behavior across specified intervals. Ideal for AP Calculus students looking to enhance their problem-solving skills and exam readiness.

Key Points

  • Includes multiple-choice questions covering key calculus concepts for AP Calculus AB.
  • Provides detailed answer explanations to enhance understanding of continuity and the Intermediate Value Theorem.
  • Covers function behavior and guarantees solutions within specified intervals.
  • Designed to assist students in preparing effectively for the AP Calculus exam.
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9 pages
AP® Calculus AB
newtopiccyclegrowin
9 pages
AP® Calculus AB
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AP Calculus AB Scoring Guide
Unit 1 Progress Check: MCQ Part C
Copyright © 2021. 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 9
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 © 2021. 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 9
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 © 2021. 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 9
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 essential topics such as continuity of functions, the Intermediate Value Theorem, and the behavior of functions over specified intervals. Students will encounter multiple-choice questions that assess their understanding of these concepts. The guide also emphasizes problem-solving strategies and the application of calculus principles in various scenarios.

How does the Intermediate Value Theorem apply in this scoring guide?
The Intermediate Value Theorem is a crucial concept in calculus that states if a function is continuous on a closed interval, then it takes on every value between its endpoints. In this scoring guide, students will find questions that require them to apply this theorem to determine the existence of solutions within given intervals. Understanding this theorem is vital for solving problems related to function behavior and continuity.

What is the significance of continuity in calculus?
Continuity is a fundamental concept in calculus that ensures a function behaves predictably without breaks or jumps. In the context of the AP Calculus AB Unit 1 Progress Check, continuity is explored through various questions that test students' ability to identify continuous functions over specified intervals. Mastery of this concept is essential for understanding limits, derivatives, and integrals.

What types of questions can students expect in the AP Calculus AB exam?
Students can expect a variety of question types in the AP Calculus AB exam, including multiple-choice questions that assess their understanding of calculus concepts like limits, derivatives, integrals, and the application of theorems such as the Intermediate Value Theorem. The scoring guide provides practice questions that mirror the format and content of the actual exam, helping students familiarize themselves with the types of problems they will encounter.

How can this scoring guide help students prepare for the AP exam?
This scoring guide is designed to assist students in their preparation for the AP Calculus AB exam by providing a comprehensive review of key concepts and problem-solving techniques. The detailed answer explanations help clarify misunderstandings and reinforce learning. By practicing with the multiple-choice questions included in the guide, students can build their confidence and improve their performance on the exam.