Unit 2 Progress Check FRQ Part B AP Calculus AB

Unit 2 Progress Check FRQ Part B AP Calculus AB

Unit 2 Progress Check for AP Calculus AB focuses on Free Response Questions (FRQs) that assess students' understanding of calculus concepts. This assessment includes problems related to average rates of change, tangent lines, and differentiability. Designed for AP Calculus AB students preparing for the exam, it offers opportunities to practice and demonstrate mastery of calculus principles. The questions require students to show their work and justify their answers, aligning with the rigorous standards of the AP curriculum.

Key Points

  • Assesses understanding of average rates of change in calculus.
  • Includes problems on tangent lines and their equations.
  • Focuses on differentiability and its implications for functions.
  • Designed for AP Calculus AB students preparing for the exam.
, ,
  • Aliusa
127
/ 8
AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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.
NO CALCULATOR IS ALLOWED FOR THIS QUESTION.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly
label any functions, graphs, tables, or other objects that you use. Justifications require that you
give mathematical reasons, and that you verify the needed conditions under which relevant
theorems, properties, definitions, or tests are applied. Your work will be scored on the
correctness and completeness of your methods as well as your answers. Answers without
supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your
answer is given as a decimal approximation, it should be correct to three places after the
decimal point.
Unless otherwise specified, the domain of a function is assumed to be the set of all real
numbers for which is a real number.
The graphs of the function and its derivative are shown above for .
(a) Find the average rate of change of over the interval . For how many values
of in the interval does the instantaneous rate of change of equal the average
rate of change of over that interval?
Please respond on separate paper, following directions from your teacher.
AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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
(b) Write an equation for the line tangent to the graph of at .
Please respond on separate paper, following directions from your teacher.
(c) For each of and , find the value or give a reason why it does not
exist.
Please respond on separate paper, following directions from your teacher.
(d) Let be the function defined by . Find .
Please respond on separate paper, following directions from your teacher.
Part A
If the average rate of change has a maximum of one sign error, the response is eligible for the second
point based on a correct interpretation of the graph of with the presented average rate of change.
Select a point value to view scoring criteria, solutions, and/or examples and to score the response.
0
1 2
The student response accurately includes both of the criteria below.
average rate of change
answer
Solution:
AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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
The average rate of change of over the interval is
the instantaneous rate of change of at equals for two values of in the interval
Part B
Select a point value to view scoring criteria, solutions, and/or examples and to score the response.
0
1
The student response accurately includes a correct tangent line equation.
Solution:
An equation of the line tangent to the graph of at is
Part C
The second point is earned for “does not exist” with a reason that indicates is not differentiable at that
point (e.g., indicates graph has a corner point or sharp point).
Select a point value to view scoring criteria, solutions, and/or examples and to score the response.
0
1 2
The student response accurately includes both of the criteria below.
/ 8
End of Document
127
You May Also Like
Faqs of Unit 2 Progress Check FRQ Part B AP Calculus AB
What types of problems are included in the Unit 2 Progress Check?
The Unit 2 Progress Check includes various Free Response Questions (FRQs) that focus on key calculus concepts. Students are tasked with calculating average rates of change, finding equations for tangent lines, and analyzing the differentiability of functions. Each question is designed to test students' understanding of calculus principles and their ability to apply these concepts in problem-solving scenarios.
How does the assessment evaluate students' understanding of calculus?
The assessment evaluates students' understanding by requiring them to solve problems that demonstrate their grasp of calculus concepts. Students must show their work, providing justifications for their answers, which reflects their analytical thinking and comprehension of the material. This method of assessment aligns with the expectations of the AP Calculus AB exam, ensuring that students are prepared for the types of questions they will encounter.
What is the significance of showing work in AP Calculus FRQs?
Showing work in AP Calculus Free Response Questions is crucial as it demonstrates a student's understanding of the problem-solving process. It allows students to earn partial credit for their reasoning, even if the final answer is incorrect. This practice encourages a deeper engagement with the material, as students must articulate their thought processes and apply calculus principles systematically.
What skills are emphasized in the Unit 2 Progress Check for AP Calculus AB?
The Unit 2 Progress Check emphasizes critical skills such as analytical reasoning, problem-solving, and mathematical justification. Students are encouraged to think critically about calculus concepts, apply appropriate methods to solve problems, and clearly communicate their reasoning. These skills are essential not only for success on the AP exam but also for future studies in mathematics and related fields.