Unit 2 Progress Check for AP Calculus AB includes multiple-choice questions designed to assess understanding of key calculus concepts. This resource provides answers to various questions covering derivatives, average rates of change, and the properties of functions. Ideal for AP Calculus students preparing for the exam, it helps reinforce learning and identify areas for improvement. The content aligns with the College Board's curriculum framework, ensuring relevance for exam preparation.

Key Points

  • Includes answers to multiple-choice questions from Unit 2 of AP Calculus AB.
  • Covers essential calculus topics such as derivatives and rates of change.
  • Designed for AP Calculus students to aid in exam preparation and concept reinforcement.
  • Aligns with the College Board's AP Calculus curriculum framework for effective study.
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9 pages
AP® Calculus AB
newtopiccyclegrowin
9 pages
AP® Calculus AB
141
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AP Calculus AB Scoring Guide
Unit 2 Progress Check: MCQ Part A
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 9
1. The derivative of a function is given by . At what value of for
does the line tangent to the graph of at have slope 2 ?
A
0.512
B
1.849
C
2.287
D
8.113
2.
Let be the function given by . Selected values of are given in the table
above. If the values in the table are used to approximate , what is the difference
between the approximation and the actual value of ?
A
0
B
0.433
C
0.567
D
1
3.
Let be the function given by . Which of the
following statements is true?
AP Calculus AB Scoring Guide
Unit 2 Progress Check: MCQ Part A
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 9
A
B
C
D
4.
Selected values of a function are shown in the table above. What is the average rate of
change of over the interval ?
A
B
C
D
AP Calculus AB Scoring Guide
Unit 2 Progress Check: MCQ Part A
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 9
5.
The graph of the function , shown above, consists of three line segments. What is the
average rate of change of over the interval ?
A
B
0
C
D
4
6. The function is given by . What is the average rate of change of
over the interval ?
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FAQs

What types of questions are included in the AP Calculus AB Unit 2 Progress Check?
The AP Calculus AB Unit 2 Progress Check features multiple-choice questions that assess students' understanding of derivatives, average rates of change, and the behavior of functions. These questions are designed to challenge students' comprehension and application of calculus concepts. Each question typically requires students to analyze graphs, interpret functions, and apply differentiation rules. This format prepares students for the types of questions they will encounter on the AP exam.

How can the answers from this progress check help AP Calculus students?
The answers provided in the Unit 2 Progress Check serve as a valuable resource for AP Calculus students to verify their understanding and performance. By reviewing the correct answers, students can identify areas where they may need further study or clarification. This self-assessment tool encourages active learning and helps students build confidence as they prepare for the AP exam. Additionally, understanding the rationale behind each answer can deepen their grasp of calculus concepts.

What is the significance of average rates of change in calculus?
Average rates of change are a fundamental concept in calculus that measures how a function's output changes relative to changes in its input over a specified interval. This concept is crucial for understanding the behavior of functions and is often used to analyze real-world scenarios. In the context of the AP Calculus exam, students must be able to calculate average rates of change and interpret their significance in various applications, including motion and growth models. Mastery of this topic is essential for success in calculus.

What role do derivatives play in AP Calculus AB?
Derivatives are a central topic in AP Calculus AB, representing the instantaneous rate of change of a function at a given point. Understanding derivatives is essential for analyzing the behavior of functions, including identifying critical points, determining concavity, and solving optimization problems. Students are expected to apply differentiation techniques to various types of functions and interpret the results in practical contexts. Mastery of derivatives is crucial for success on the AP exam and in higher-level mathematics.