AP® Calculus BC
叭的组词
2002 Free-Respon Questions
The materials included in the files are intended for u by AP teachers for cour and exam preparation in the classroom; permission for any other u 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 purpos but
may not mass distribute the materials, electronically or otherwi. The 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.
The materials were produced by Educational Testing Service® (ETS®), which develops and administers the examinations of the Advanced
三代旁系血亲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, rvices, and employment policies are guided by that principle.
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 compod of more than 4,200 schools, colleges, universities, and other educational organizations. Each year, the College Board rves over three million students and their parents, 22,000 high schools, and 3,500 colleges, through major programs and
rvices in college admission, guidance, asssment, 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 c
ommitted to the principles of equity and
excellence, and that commitment is embodied in all of its programs, rvices, activities, and concerns.
Copyright © 2002 by College Entrance Examination Board. All rights rerved. 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.
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.
1. Let f and g be the functions given by f （ x ）= e x and g （x ） = ln x .
(a) Find the area of the region enclod by the graphs of f and g between x = 12 and x = 1.
(b) Find the volume of the solid generated when the region enclod by the graphs of f and g between x = 12
and x = 1 is revolved about the line y = 4.
jky
(c) Let h be the function given by h （x ） = f （x ） - g （x ）. Find the absolute minimum value of h ( x ) on the clod interval 12 ˆ x ˆ 1, and find the absolute maximum value of h ( x ) on the clod interval 12 ˆ x ˆ 1. Show the analysis that leads to your answers.
Copyright © 2002 by College Entrance Examination Board. All rights rerved. 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 amument park on a given day is modeled by the function E defined by
E ( t ) = 15600 . 3 t 2 - 24 t + 160 8
The rate at which people leave the same amument park on the same day is modeled by the function L defined by
L ( t ) = 9890 （t 2 - 38t + 370） Both E （t ） and L （t ） are measured in people per hour and time t is measured in hours after midnight. The functions are valid for 9 ˆ t ˆ 23, the hours during which the park is open. At time t = 9, there are no people in the park.
(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 ) =
∫9t （E ( x ) - L ( x )） dx for 9 ˆ t ˆ 23. The value of H (17) to the nearest whole number is 3725. Find the value of H ‡(17), and explain the meaning of H (17) and H ‡(17) in the context of the amument park.
梦见被虫子咬(d) At what time t , for 9 ˆ t ˆ 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 rerved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.
3 GO ON TO THE NEXT PAGE.
2002 AP® CALCULUS BC FREE-RESPONSE QUESTIONS
3.The figure above shows the path traveled by a roller coaster car over the time interval 0 ˆtˆ 18 conds. The
position of the car at time t conds can be modeled parametrically by
x( t ) =10t +4 sin t
y ( t ) = (20- t )(1-cos t ),
where x and y are measured in meters. The derivatives of the functions are given by
调档函格式x ‡( t ) =10+4 cos t
y ‡( t ) = (20- t )sin t +cos t -1.
(a)Find the slope of the path at time t= 2. Show the computations that lead to your answer.
(b)Find the acceleration vector of the car at the time when the car’s horizontal position is x= 140.
(c)Find the time t at which the car is at its maximum height, and find the speed, in m/c, of the car at this
time.
(d) For 0<t<18, there are two times at which the car is at ground level （y=0）. Find the two times and
write an expression that gives the average speed, in m/c, of the car between the two times. Do not
evaluate the expression.
END OF PART A OF SECTION II
Copyright © 2002 by College Entrance Examination Board. All rights rerved.
Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.
4
2002 AP ®
CALCULUS BC FREE-RESPONSE QUESTIONS
CALCULUS BC
SECTION II, Part B
Time—45 minutes
Number of problems—3
No calculator is allowed for the problems.
4.The graph of the function f shown above consists of two line gments. Let g be the function given by
g （x）=∫0x f （t） dt.
(a)Find g( -1),g‡( -1), and g‡‡( -1).汽车查违章
中考励志的句子(b)For what values of x in the open interval （-2, 2） is g increasing? Explain your reasoning.
(c)For what values of x in the open interval （-2, 2） is the graph of g concave down? Explain your reasoning.
(d)On the axes provided, sketch the graph of g on the clod interval -2, 2 .
(Note: The axes are provided in the pink test booklet only.)
Copyright © 2002 by College Entrance Examination Board. All rights rerved.
6103Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board.
5GO ON TO THE NEXT PAGE.
