-
AP
Calculus BC
2002 Free-Response Questions
?
The
materials included in these files are intended for
use by AP teachers for course
and exam
preparation in the classroom; permission for any
other use must be
?
sought
from the Advanced Placement Program
.
Teachers may reproduce them,
in whole
or in part, in limited quantities, for face-to-
face teaching purposes but
may not mass
distribute the materials, electronically or
otherwise. These materials
and any
copies made of them may not be resold, and the
copyright notices must be
retained as
they appear here. This permission does not apply
to any third-party
copyrights contained
herein.
These materials were
produced by Educational Testing Service
(ETS
), which develops and administers
the examinations of the Advanced
Placement Program for the College
Board. The College Board and Educational Testing
Service (ETS) are dedicated to the principle of
equal
opportunity, and their programs,
services, and employment policies are guided by
that principle.
?
?
Copyright ? 2002 by College Entrance
Examination Board. All rights reserved. College
Board, Advanced Placement Program, AP, SAT, and
the acorn logo
are registered trademarks of the
College Entrance Examination Board. APIEL is a
trademark owned by the College Entrance
Examination Board. PSAT/NMSQT is a
registered trademark jointly owned by
the College Entrance Examination Board and the
National Merit Scholarship Corporation.
Educational Testing Service
and ETS are registered trademarks of Educational
Testing Service.
The College
Board is a national nonprofit membership
association dedicated to preparing, inspiring, and
connecting students to college and
opportunity. Founded in 1900, the
association is composed of more than 4,200
schools, colleges, universities, and other
educational organizations. Each
year,
the College Board serves over three million
students and their parents, 22,000 high schools,
and 3,500 colleges, through major programs and
services in college admission,
guidance, assessment, financial aid, enrollment,
and teaching and learning. Among its best-known
programs are the
?
?
?
?
SAT
, the
PSAT/NMSQT
, and the Advanced Placement
Program
(AP
). The College
Board is committed to the principles of equity
and
excellence, and that commitment is
embodied in all of its programs, services,
activities, and concerns.
2002 AP
CALCULUS
BC FREE-RESPONSE QUESTIONS
CALCULUS BC
SECTION II, Part A
Time
—
45
minutes
Number of
problems
—
3
A graphing calculator is required for
some problems or parts of problems.
?
x
1. Let
f
and
g
be the functions given by
f
（
x
）
=
e
and
g
（
x
）
=
ln
x
.
(a)
Find the area of the region enclosed by the graphs
of
f
and
g
between
x
=
1
2
and
x
=
1.
1
(b)
Find the volume of the solid generated
when the region enclosed by the graphs of
f
and
g
between
x
=
2
and
x
=
1
is revolved about the line
y
=
4.
(c)
Let
h
be the function given by <
/p>
h
（
x
）
=
f
（
x
）
-
g
（
x
）
.
Find the absolute minimum value of
h
(
x
)
on
the closed interval
2
?
x
?
1,
and find the absolute maximum value of
h
(
x
)
on the closed
interval
1. Show the analysis that
leads to your answers.
1
1
2
?
x
?
Copyright ? 2002 by College
Entrance Examination Board. All rights
reserved.
Advanced Placement
Program and AP are registered trademarks of the
College Entrance Examination Board.
2
GO
ON TO THE NEXT PAGE.
2002 AP
CALCULUS
BC FREE-RESPONSE QUESTIONS
?
2. The rate at which people
enter an amusement park on a given day is modeled
by the function
E
defined
by
2
15600
E
(
t
) =
3
t
-
24
t
+
160
8
.
The rate at which people leave the same
amusement park on the same day is modeled by the
function
L
defined by
（
t
-
38
t
+
370
）
Both
E
（
t
）
and
L
（
t
）
are measured in people per hour and
time
t
is measured in hours
after midnight.
These functions are
valid for
9
?
t
?
23,
the hours during which the park is open. At time
t
=
9,
there are no
people in the park.
2
L
(
t
) =
9890
(a)
How many people have entered the park
by 5:00
P
.
M
.
(
t
=
17)? Round your answer to the nearest whole
number.
(b)
The price of admission to the park is
$$15 until 5:00
P
.
M
. (
t
=
17
). After 5:00
P
.
M
.,
the price of admission to
the park is
$$11. How many dollars are collected from
admissions to the park on the given day? Round
your
answer to the nearest whole
number.
(c)
Let
H
(
t
) =
∫
（
9
t
E
(
x
) -
L
(
x
)
）
dx
for 9
?
t
?
23. The value of
H
(
17
)
to the nearest whole number is
3725.
Find the value of
H
< br>?(
17
)
,
< br> and explain the meaning of
H
(
17
)
and
H
?(
17
)
in the context of the amusement
park.
(d)
At what time
t
,
for
9
?
t
?
23,
does the model predict that the number of people
in the park is a maximum?
Copyright ?
2002 by College Entrance Examination Board. All
rights reserved.
Advanced
Placement Program and AP are registered trademarks
of the College Entrance Examination
Board.
3
GO ON TO THE
NEXT PAGE.
-
-
-
-
-
-
-
-
-
上一篇：三年级小兔过桥看图写话范文_作文
下一篇：洋桃课堂AP微积分2005真题