AP Calculus AB Unit 5 Progress Check focuses on multiple-choice questions designed to assess understanding of calculus concepts. This assessment includes topics such as critical points, concavity, and points of inflection, essential for mastering AP Calculus. Students will encounter various problems that align with the AP exam format, providing practice for the May exam. The document serves as a valuable resource for AP Calculus students aiming to enhance their problem-solving skills and conceptual understanding.

Key Points

  • Includes multiple-choice questions on critical points and concavity
  • Covers essential calculus concepts for AP exam preparation
  • Provides practice aligned with the AP Calculus exam format
  • Focuses on identifying points of inflection and absolute extrema
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AP® Calculus AB
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8 pages
AP® Calculus AB
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AP Calculus AB Scoring Guide
Unit 5 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 8
1.
The second derivative of the function is given by . At what values of in
the interval does the graph of have a point of inflection?
A
2.229 only
B
0 and 2.229
C
and 0.987
D
, 0, and 1.603
2.
The second derivative of the function is given by . The function has
many critical points, two of which are at and . Which of the following statements is
true?
A
has a local minimum at and at .
B
has a local minimum at and a local maximum at .
C
has a local maximum at and a local minimum at .
D
has a local maximum at and at .
3. Let be the function given by . What is the absolute maximum value of on
the closed interval ?
AP Calculus AB Scoring Guide
Unit 5 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 8
A
1
B
2
C
6
D
26
4. Let be the function defined by . What is the absolute minimum value of on
the interval ?
A
B
C
D
0
5. Let be the function defined by . What is the absolute maximum value of
on the interval ?
AP Calculus AB Scoring Guide
Unit 5 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 8
A
1
B
C
D
6.
The graph of , the derivative of the function , is shown above. On which of the following open
intervals is the graph of concave down?
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End of Document
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FAQs

What types of questions are included in the AP Calculus AB Unit 5 Progress Check?
The AP Calculus AB Unit 5 Progress Check includes multiple-choice questions that assess students' understanding of critical points, concavity, and points of inflection. Each question is designed to challenge students' problem-solving abilities and conceptual knowledge of calculus. The questions reflect the style and rigor of the AP exam, making them an effective tool for exam preparation. Students can expect to encounter a variety of scenarios requiring them to apply calculus principles in different contexts.

How does the Unit 5 Progress Check help students prepare for the AP Calculus exam?
The Unit 5 Progress Check is specifically designed to mirror the types of questions students will face on the AP Calculus exam. By practicing with these multiple-choice questions, students can identify their strengths and weaknesses in calculus concepts. This targeted practice helps reinforce understanding and builds confidence in problem-solving skills. Additionally, the questions cover critical topics such as concavity and extrema, which are essential for success on the exam.

What is the significance of points of inflection in calculus?
Points of inflection are significant in calculus as they indicate where a function changes its concavity. Understanding these points helps in analyzing the behavior of functions and determining local maxima and minima. In the context of the AP Calculus exam, identifying points of inflection is crucial for solving problems related to graphing and optimization. Mastery of this concept allows students to interpret and predict the behavior of functions accurately.

What topics are emphasized in the AP Calculus AB Unit 5 Progress Check?
The AP Calculus AB Unit 5 Progress Check emphasizes critical calculus topics such as critical points, concavity, and absolute extrema. These concepts are fundamental for understanding the overall behavior of functions. The assessment challenges students to apply their knowledge in various scenarios, enhancing their analytical skills. By focusing on these key areas, the progress check prepares students for the complexities of the AP exam.

How can students effectively use the Unit 5 Progress Check for study?
Students can effectively use the Unit 5 Progress Check by treating it as a diagnostic tool to assess their understanding of calculus concepts. After completing the questions, reviewing the answers and rationales helps reinforce learning and clarify misconceptions. Additionally, students can track their progress over time, identifying areas that require further study. Incorporating this practice into their study routine can significantly enhance their readiness for the AP exam.