AP Calculus BC Unit 5 Progress Check MCQ Part B includes multiple-choice questions designed to assess students' understanding of calculus concepts. This assessment focuses on critical points, concavity, and absolute maximum values within various functions. Ideal for AP Calculus students preparing for the exam, it provides practice with real exam-style questions. The content aligns with the AP Calculus curriculum, ensuring comprehensive coverage of essential topics.

Key Points

  • Includes multiple-choice questions on concavity and critical points in calculus.
  • Covers absolute maximum and minimum values of functions on specified intervals.
  • Designed for AP Calculus BC students preparing for the exam.
  • Aligns with the AP Calculus curriculum for effective exam preparation.
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6 pages
AP® Calculus BC
newtopiccyclegrowin
6 pages
AP® Calculus BC
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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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FAQs

What types of questions are included in this AP Calculus assessment?
The assessment features multiple-choice questions that test students' understanding of calculus concepts such as critical points, concavity, and absolute maximum and minimum values. Each question is designed to reflect the style and rigor of the AP exam, providing students with a realistic practice experience. Topics include analyzing the second derivative, determining points of inflection, and evaluating functions over specified intervals.

How does this progress check help students prepare for the AP Calculus exam?
This progress check is tailored to reinforce key calculus concepts that are crucial for success on the AP exam. By working through the multiple-choice questions, students can identify areas where they need further review and practice. The questions are aligned with the AP curriculum, ensuring that students are familiar with the types of problems they will encounter during the actual exam.

What is the significance of critical points in calculus?
Critical points are where the derivative of a function is zero or undefined, indicating potential locations for local maxima, minima, or points of inflection. Understanding how to identify and analyze these points is essential for graphing functions and solving optimization problems. This knowledge is crucial for students as they prepare for the AP Calculus exam, where such concepts are frequently tested.

What role does the second derivative play in determining concavity?
The second derivative of a function provides information about its concavity. If the second derivative is positive, the graph is concave up, indicating that the function is increasing at an increasing rate. Conversely, if the second derivative is negative, the graph is concave down, suggesting that the function is increasing at a decreasing rate. This concept is vital for analyzing the behavior of functions and is a key topic in AP Calculus.