Unit 8 Progress Check: FRQ Part A

AP Calculus BC

Scoring Guide

Unit 8 Progress Check: FRQ Part A

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

numbers

for which

is assumed to be the set of all real

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

(a) What is the first time,

the time interval

seconds,

given by

.

, that Gwen changes direction? Find Gwen¡¯s average velocity over

.

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

Scoring Guide

Unit 8 Progress Check: FRQ Part A

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

(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

seconds. Find

? . Using correct units, explain the meaning of

? in the context

the value of

of the problem.

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

Scoring Guide

Unit 8 Progress Check: FRQ Part A

answer

Solution:

Gwen changes direction when

changes sign. The first time this happens is at

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

Scoring Guide

Unit 8 Progress Check: FRQ Part A

0

1

2

The student response accurately includes both of the criteria below.

definite integral

answer

Solution:

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

Scoring Guide

Unit 8 Progress Check: FRQ Part A

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

numbers

for which

is assumed to be the set of all real

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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download