AP Calculus BC
Scoring Guide
Unit 4 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 depth of water in a zoo aquarium at a certain point is modeled by the function
defined
above, where
is measured in feet and time is measured in hours.
(a)
Find
. Using correct units, explain the meaning of
in the context of the
problem.
Please respond on separate paper, following directions from your teacher.
(b)
The graph of
is concave up for
. Use the line tangent to the graph of
at
to show that
.
Please respond on separate paper, following directions from your teacher.
(c)
Find
.

AP Calculus BC
Scoring Guide
Unit 4 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
Please respond on separate paper, following directions from your teacher.
Part A
The first 2 points may be earned with the presence of a correct numerical answer.
The second point may be earned with a maximum of one sign error in
The third point requires a time reference, rate, and units. The response is eligible for the third point if the
second point is earned AND provided the behavior described is consistent with the sign of the