Unit 2 Progress Check FRQ Part A AP Calculus AB

Unit 2 Progress Check FRQ Part A AP Calculus AB

Unit 2 Progress Check for AP Calculus AB focuses on Free Response Questions (FRQs) designed to assess students' understanding of calculus concepts. This assessment includes problems related to derivatives, integrals, and the application of calculus in real-world scenarios. It is essential for AP Calculus AB students preparing for the exam, providing practice with the types of questions they will encounter. The document features a graph of a continuous function and requires students to demonstrate their problem-solving skills through detailed calculations and justifications.

Key Points

  • Includes Free Response Questions aligned with AP Calculus AB curriculum.
  • Covers topics such as derivatives, integrals, and function analysis.
  • Features a continuous function graph for practical application problems.
  • Designed for AP Calculus AB students preparing for the May exam.
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AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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 5
1.
A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION.
You are permitted to use your calculator to solve an equation, find the derivative of a function
at a point, or calculate the value of a definite integral. However, you must clearly indicate the
setup of your question, namely the equation, function, or integral you are using. If you use
other built-in features or programs, you must show the mathematical steps necessary to
produce your results. Your work must be expressed in standard mathematical notation rather
than calculator syntax.
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.
AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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 5
Let be the continuous function defined on whose graph, consisting of two line
segments, is shown above. Let and be the functions defined by and
.
(a) The function is defined by . Find .
Please respond on separate paper, following directions from your teacher.
(b) The function is defined by . Find .
Please respond on separate paper, following directions from your teacher.
(c) Find the value of for such that .
AP Calculus AB Scoring Guide
Unit 2 Progress Check: FRQ 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 5
Please respond on separate paper, following directions from your teacher.
Part A
The third point is earned for a correct product rule expression that substitutes all 4 correct numerical
values. The expression does not need to be simplified. The third point can also be earned if a student
imports an incorrect value for either or
Select a point value to view scoring criteria, solutions, and/or examples and to score the response.
0
1 2 3
The student response accurately includes all three of the criteria below.
Solution:
from the graph.
Part B
The third point is earned for a correct quotient rule expression that substitutes all 4 correct numerical
values. The expression does not need to be simplified.
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End of Document
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Faqs of Unit 2 Progress Check FRQ Part A 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 that focus on key calculus concepts such as derivatives, integrals, and the analysis of functions. Students are required to solve problems that involve finding derivatives at specific points, calculating definite integrals, and applying calculus principles to real-world scenarios. Each question is designed to test students' understanding and ability to justify their solutions mathematically.
How does the Unit 2 Progress Check help students prepare for the AP exam?
The Unit 2 Progress Check serves as a valuable tool for AP Calculus AB students by providing practice with the format and types of questions they will encounter on the AP exam. It encourages students to apply their knowledge in a structured manner, reinforcing their understanding of calculus concepts. Additionally, the emphasis on justifying answers helps students develop the critical thinking skills necessary for success on the exam.
What is the significance of the continuous function graph in the assessment?
The continuous function graph included in the Unit 2 Progress Check is significant as it provides a visual representation of the concepts being tested. It allows students to engage with the material in a practical context, enhancing their understanding of how calculus applies to real-world situations. Analyzing the graph helps students develop skills in interpreting graphical data, which is crucial for solving calculus problems effectively.
What skills are assessed in the Free Response Questions?
The Free Response Questions in the Unit 2 Progress Check assess a range of skills including problem-solving, analytical thinking, and mathematical justification. Students must demonstrate their ability to compute derivatives and integrals accurately, as well as articulate their reasoning clearly. This assessment format encourages a deeper understanding of calculus concepts and prepares students for the rigorous expectations of the AP exam.
How should students approach solving the Free Response Questions?
Students should approach the Free Response Questions by carefully reading each problem and identifying the key concepts involved. It is important to show all steps in the solution process, including any calculations and justifications for their answers. Utilizing a graphing calculator can aid in finding derivatives and evaluating integrals, but students must also express their work in standard mathematical notation to demonstrate their understanding fully.