AP Calculus BC Unit 5 Progress Check MCQ Part B

AP Calculus BC Unit 5 Progress Check focuses on multiple-choice questions designed to assess understanding of key calculus concepts. This assessment includes topics such as concavity, critical points, and absolute maxima and minima, providing a comprehensive review for students preparing for the AP exam. The questions challenge students to apply their knowledge of derivatives and second derivatives in various contexts. Ideal for AP Calculus BC students, this resource enhances exam readiness through practice and application of calculus principles.

Key Points

  • Includes multiple-choice questions on concavity and critical points.
  • Covers absolute maxima and minima relevant to AP Calculus BC.
  • Designed to enhance understanding of derivatives and second derivatives.
  • Provides a comprehensive review for students preparing for the AP exam.
MR ALi
6 pages
AP® Calculus BC
169
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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) 2.467 only
(B) 1 and 2.467
(C) 1.443 and 2.734
(D) 1 and 1.962
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 local minima 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 local maxima at and at .
3.
Let
be the function given by . What is the absolute maximum value of on the
closed interval
?
(A)
(B) 36
(C) 80
(D) 180
4.
Let
be the function defined by . What is the absolute maximum value of on the
interval ?
(A)
(B)
(C)
(D) 3
5.
Let
be the function defined by . What is the absolute maximum value of on the
interval ?
(A)
(B)
(C) 0
(D) 1
AP CALCULUS BC Scoring Guide
Unit 5 Progress Check: MCQ Part B
AP Calculus BC
Page 1 of 6
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?
(A)
and
(B)
and
(C)
only
(D)
Scoring Guide
Unit 5 Progress Check: MCQ Part B
Page 2 of 6
AP Calculus BC
7.
Let be the function defined by . The graph of , the derivative of , is shown above.
On which of the following intervals is the graph of
concave up?
(A)
and
(B) and
(C)
and
(D)
8.
The Second Derivative Test cannot be used to conclude that is the location of a relative minimum or relative
maximum for which of the following functions?
(A)
, where and
(B)
, where and
(C)
, where and
(D)
, where and
Scoring Guide
Unit 5 Progress Check: MCQ Part B
AP Calculus BC
Page 3 of 6
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End of Document
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FAQs

What types of questions are included in the AP Calculus BC Unit 5 Progress Check?
The AP Calculus BC Unit 5 Progress Check includes multiple-choice questions that assess students' understanding of calculus concepts such as concavity, critical points, and absolute extrema. Each question is designed to challenge students to apply their knowledge of derivatives and second derivatives in various scenarios. This format helps students practice for the AP exam by simulating the types of questions they will encounter. Additionally, the questions often require analytical thinking and problem-solving skills, making them an effective study tool.

How does the Unit 5 Progress Check help students prepare for the AP exam?
The Unit 5 Progress Check serves as a valuable resource for AP Calculus BC students by providing targeted practice on essential topics. By working through the multiple-choice questions, students can identify areas where they need further review and solidify their understanding of calculus principles. The questions are aligned with the AP exam format, allowing students to become familiar with the style and complexity of the questions they will face. This practice not only boosts confidence but also enhances problem-solving skills critical for success on the exam.

What key calculus concepts are emphasized in this progress check?
Key concepts emphasized in the AP Calculus BC Unit 5 Progress Check include the analysis of concavity, identification of critical points, and determination of absolute maxima and minima. Students are encouraged to apply their knowledge of the first and second derivatives to solve problems effectively. Understanding these concepts is crucial for mastering calculus and performing well on the AP exam. The progress check reinforces these ideas through practical application, ensuring that students are well-prepared for their assessments.

What is the significance of understanding concavity in calculus?
Understanding concavity is significant in calculus as it helps determine the behavior of functions. Concavity indicates whether a function is curving upwards or downwards, which is essential for identifying local maxima and minima. By analyzing the second derivative, students can ascertain the concavity of a function and make informed conclusions about its graph. This knowledge is crucial not only for solving calculus problems but also for understanding the underlying principles of function behavior, which is a key component of the AP Calculus curriculum.

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