Unit 8 Progress Check: FRQ Part A

AP Calculus BC

Unit 8 Progress Check: FRQ Part A

Scoring Guide

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.

Gwen runs back and forth along a straight track. During the time interval Gwen's velocity, in feet per second, is modeled by the function given by

seconds, .

(a) What is the first time, , that Gwen changes direction? Find Gwen's average velocity over

the time interval

.

Please respond on separate paper, following directions from your teacher.

(b) At time

, how far is Gwen from her position at time

?

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

AP Calculus BC

Unit 8 Progress Check: FRQ Part A

Please respond on separate paper, following directions from your teacher.

Scoring Guide

(c) Find the total distance that Gwen runs during the 45 seconds from time .

to time

Please respond on separate paper, following directions from your teacher.

(d) Let represent Gwen's acceleration during the time interval

the value of

. Using correct units, explain the meaning of

of the problem.

seconds. Find

in the context

Please respond on separate paper, following directions from your teacher.

Part A

For the first point, supporting work stating that changes sign is required.

For the second point, supporting work that includes the average value expression with an appropriate definite integral is required. To be eligible for the second point, the presented value of may be incorrect but must be positive.

The third point requires the first two points to have been earned.

Select a point value to view scoring criteria, solutions, and/or examples to score the response.

0

1

2

3

The student response accurately includes all three of the criteria below.

average value integral

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

AP Calculus BC

Unit 8 Progress Check: FRQ Part A

answer

Solution: Gwen changes direction when

changes sign. The first time this happens is at

Scoring Guide

Gwen's average velocity over the time interval

is 7.264 feet per second.

Part B 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. definite integral answer

Solution:

At time

Gwen is 116.538 (or 116.537) feet from her position at time

Part C Select a point value to view scoring criteria, solutions, and/or examples and to score the response.

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

AP Calculus BC

Unit 8 Progress Check: FRQ Part A

0

1

The student response accurately includes both of the criteria below.

definite integral answer

Solution:

Scoring Guide

2

During the 45 seconds from time

to time

the total distance that Gwen runs is 250.099 feet.

Part D

The second point requires 3 things: (1) net change in Gwen's velocity, (2) units of feet per second, and (3)

reference to time interval from

to

Select a point value to view scoring criteria, solutions, and/or examples to score the response.

0

1

2

The student response accurately includes both of the criteria below. answer interpretation with units

Solution:

feet per second

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 4 of 9

AP Calculus BC

Unit 8 Progress Check: FRQ Part A

Scoring Guide

Since acceleration is the rate of change of velocity, feet per second, during the 15 seconds from time

is the net change in Gwen's velocity, in to time

2. 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.

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 5 of 9

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