AP Calculus BC Unit 5 Progress Check focuses on multiple-choice questions designed to assess understanding of key calculus concepts. Topics include the second derivative test, concavity, critical points, and absolute maximum values on specified intervals. This resource is ideal for AP Calculus students preparing for the exam, providing practice with various calculus problems. The assessment includes a range of questions that challenge students' comprehension and application of calculus principles.

Key Points

  • Includes multiple-choice questions on second derivatives and concavity.
  • Covers critical points and their implications for local maxima and minima.
  • Focuses on absolute maximum values within specified intervals.
  • Designed for AP Calculus BC students preparing for the exam.
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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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End of Document
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FAQs

What topics are covered in the AP Calculus BC Unit 5 Progress Check?
The AP Calculus BC Unit 5 Progress Check covers essential topics such as the second derivative test, concavity, and critical points. Students will encounter questions that require them to analyze functions for local maxima and minima, as well as determine absolute maximum values over specified intervals. The assessment is structured to reinforce understanding of calculus concepts and prepare students for the AP exam.

How does the second derivative test apply to critical points?
The second derivative test is a method used to determine whether a critical point is a local maximum, local minimum, or neither. If the second derivative at a critical point is positive, the function is concave up, indicating a local minimum. Conversely, if the second derivative is negative, the function is concave down, suggesting a local maximum. This test is crucial for analyzing the behavior of functions in calculus.

What is the significance of absolute maximum values in calculus?
Absolute maximum values represent the highest point of a function over a given interval. Identifying these values is essential for understanding the overall behavior of functions and their applications in real-world scenarios. In the context of the AP Calculus BC exam, students must be able to find these values using various methods, including evaluating endpoints and critical points. Mastery of this concept is vital for success in calculus.

What types of problems can students expect in this progress check?
Students can expect a variety of problems that test their understanding of calculus concepts, including determining points of inflection, analyzing concavity, and applying the second derivative test. The questions are designed to mimic the style of AP exam questions, providing practice in a timed setting. This progress check serves as a valuable tool for students to gauge their readiness for the AP Calculus BC exam.

How can the results of the progress check be used for exam preparation?
Results from the progress check can help students identify areas of strength and weakness in their understanding of calculus concepts. By reviewing the questions they struggled with, students can focus their study efforts on specific topics, such as the second derivative test or finding absolute maximum values. This targeted approach to studying can enhance their overall performance on the AP exam.