1997 AP Calculus AB: Section I, Part A

Size: px

Start display at page:

Download "1997 AP Calculus AB: Section I, Part A"

Drusilla Phillips
5 years ago
Views:

1 997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx= If f( x) = x x, thn f ( x) = x x x x x x + x 5x 6 x b. If f ( x ) dx= a+ b, thn ( ( ) 5) a f x + dx= a b a+ b+ 5 5b 5a 7b 4a 7b 5a 7b 6a 4. If f( x) = x + x+, thn f ( ) = x 5 AP Calculus Multipl-Choic Qustion Collction 00 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

2 997 AP Calculus AB: Sction I, Part A 5. Th graph of 4 y = x 6x + 4x + 48 is concav down for x < 0 x > 0 x < or x > x < or x > < x < 6. dt = t t t + C t + C + C t + C t + C 7. d cos ( x ) = dx 6 sin( )cos( ) x x x 6 cos( ) x x sin ( ) x 6x sin( x )cos( x ) sin( x )cos( x ) AP Calculus Multipl-Choic Qustion Collction 0 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

3 997 AP Calculus AB: Sction I, Part A Qustions 8-9 rfr to th following situation. A bug bgins to crawl up a vrtical wir at tim t = 0. Th vlocity v of th bug at tim t, 0 t 8, is givn by th function whos graph is shown abov. 8. At what valu of t dos th bug chang dirction? What is th total distanc th bug travld from t = 0 to t = 8? An quation of th lin tangnt to th graph of y = cos( x) at π x = is 4 π y = x 4 π y = x 4 π y = x 4 π y = x 4 π y = x 4 AP Calculus Multipl-Choic Qustion Collction 0 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

4 997 AP Calculus AB: Sction I, Part A. Th graph of th drivativ of f is shown in th figur abov. Which of th following could b th graph of f?. At what point on th graph of y = x is th tangnt lin paralll to th lin x 4y =?,, 8, 4, (, ) AP Calculus Multipl-Choic Qustion Collction 0 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

5 997 AP Calculus AB: Sction I, Part A. Lt f b a function dfind for all ral numbrs x. If intrval f ( x) = 4 x x, thn f is dcrasing on th (,) (, ) (, 4) (, ) (, ) 4. Lt f b a diffrntiabl function such that f () = and f () = 5. If th tangnt lin to th graph of f at x = is usd to find an approximation to a zro of f, that approximation is Th graph of th function f is shown in th figur abov. Which of th following statmnts about f is tru? lim f ( x) = lim f( x) x a x b lim f ( x ) = x a lim f ( x ) = x b lim f ( x ) = x b lim f ( x ) dos not xist. x a AP Calculus Multipl-Choic Qustion Collction 04 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

6 997 AP Calculus AB: Sction I, Part A 6. Th ara of th rgion nclosd by th graph of y = x + and th lin y = 5 is π 7. If x + y = 5, what is th valu of d y dx at th point ( 4, )? π 4 tan x 0 cos dx is x If f( x) = ln x, thn f ( x) = x x x x x x x x x AP Calculus Multipl-Choic Qustion Collction 05 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

7 997 AP Calculus AB: Sction I, Part A 0. Th avrag valu of cos x on th intrval [,5] is sin 5 sin 8 sin 5 sin sin sin 5 sin + sin 5 sin + sin 5 8. lim ln x xx is 0 nonxistnt. What ar all valus of x for which th function f dfind by f ( x) = ( x ) x is incrasing? Thr ar no such valus of x. x< and x> < x < < x < All valus of x. If th rgion nclosd by th y-axis, th lin y =, and th curv y = x is rvolvd about th y-axis, th volum of th solid gnratd is π 5 6π 6π 5 8π π AP Calculus Multipl-Choic Qustion Collction 06 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

8 997 AP Calculus AB: Sction I, Part A 4. Th xprssion is a Rimann sum approximation for x dx x dx x dx x dx x dx 5. xsin( x) dx= x cos( x) + sin( x) + C 4 x cos( x) sin( x) + C 4 x cos( x) sin( x) + C 4 x cos( x) + sin( x) + C x cos( x) 4sin( x) + C AP Calculus Multipl-Choic Qustion Collction 07 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

9 997 AP Calculus AB: Sction I, Part B 40 Minuts Graphing Calculator Rquird Nots: () Th xact numrical valu of th corrct answr dos not always appar among th choics givn. Whn this happns, slct from among th choics th numbr that bst approximats th xact numrical valu. () Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr. 76. If x f( x) =, thn f ( x) = x x x x x ( x) x (x+ ) x (x ) x 77. Th graph of th function y = x + 6x + 7x cosx changs concavity at x = Th graph of f is shown in th figur abov. If F() F(0) = f( x) dx=. and F ( x) f( x), = thn AP Calculus Multipl-Choic Qustion Collction 08 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

10 997 AP Calculus AB: Sction I, Part B 79. Lt f b a function such that f( + h) f() lim = 5. Which of th following must b tru? h h 0 I. f is continuous at x =. II. f is diffrntiabl at x =. III. Th drivativ of f is continuous at x =. I only II only I and II only I and III only II and III only 80. Lt f b th function givn by 4 ( ) x f x th graph of f at ( x, f( x )) qual to? =. For what valu of x is th slop of th lin tangnt to A railroad track and a road cross at right angls. An obsrvr stands on th road 70 mtrs south of th crossing and watchs an astbound train travling at 60 mtrs pr scond. At how many mtrs pr scond is th train moving away from th obsrvr 4 sconds aftr it passs through th intrsction? If y = x 8, what is th minimum valu of th product xy? What is th ara of th rgion in th first quadrant nclosd by th graphs of y = cos x, y = x, and th y-axis? Th bas of a solid S is th rgion nclosd by th graph of y = ln x, th lin x =, and th x-axis. If th cross sctions of S prpndicular to th x-axis ar squars, thn th volum of S is ( ) AP Calculus Multipl-Choic Qustion Collction 09 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

11 997 AP Calculus AB: Sction I, Part B 85. If th drivativ of f is givn by hav a rlativ maximum valu? x f ( x) = x, at which of th following valus of x dos f Lt f ( x) = x. If th rat of chang of f at x = c is twic its rat of chang at x =, thn c = At tim t 0, th acclration of a particl moving on th x-axis is at ( ) = t+ sin t. At t = 0, th vlocity of th particl is. For what valu t will th vlocity of th particl b zro? AP Calculus Multipl-Choic Qustion Collction 0 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

12 997 AP Calculus AB: Sction I, Part B x 88. Lt f ( x) = h( t) dt, whr h has th graph shown abov. Which of th following could b th graph of f? a AP Calculus Multipl-Choic Qustion Collction Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

13 997 AP Calculus AB: Sction I, Part B x f( x) A tabl of valus for a continuous function f is shown abov. If four qual subintrvals of [ 0, ] ar usd, which of th following is th trapzoidal approximation of 0 f ( xdx )? Which of th following ar antidrivativs of f ( x) = sinxcosx? I. II. III. sin x F( x ) = cos x F( x ) = cos( x) F( x) = 4 I only II only III only I and III only II and III only AP Calculus Multipl-Choic Qustion Collction Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

14 997 Calculus AB Solutions: Part A. C. A. C 4. D 5. E 6. C 7. D 8. C 9. B 0. E. E. B AP Calculus Multipl-Choic Qustion Collction 7 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

15 997 Calculus AB Solutions: Part A. A 4. C 5. B 6. D 7. A 8. C 9. D 0. E. E. D. A AP Calculus Multipl-Choic Qustion Collction 8 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

16 997 Calculus AB Solutions: Part A 4. B 5. A AP Calculus Multipl-Choic Qustion Collction 9 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

17 997 Calculus AB Solutions: Part B 76. E 77. D 78. D 79. C 80. A 8. A 8. B 8. C 84. C 85. C 86. A AP Calculus Multipl-Choic Qustion Collction 0 Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

18 997 Calculus AB Solutions: Part B 87. B 88. E 89. B 90. D AP Calculus Multipl-Choic Qustion Collction Copyright 005 by Collg Board. All rights rsrvd. Availabl at apcntral.collgboard.com.

1997 AP Calculus AB: Section I, Part A

1997 AP Calculus AB: Section I, Part A 997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs for which f () is a ral numbr.. (4 6 ) d= 4 6 6