1969, 1973, 1985, 1993, 1997, 1998 AP Multiple Choice Sections, AB and BC, Solutions (620)

Sin 2 x x3 x5 1 n 1 x 2 n1 3 5 2n 1 a x b 2

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Unformatted text preview: ues of x is f NOT continuous? (A) 0 only 6. If y 2 − 2 xy = 16, then (A) 7. +∞ ∫2 (A) 8. (B) 1 only x y−x dx x2 1 2 (C) 2 only (D) 0 and 2 only (E) 0, 1, and 2 dy = dx (B) y x− y (C) y y−x (D) y 2y − x (E) 2y x− y is (B) ln 2 (C) 1 (D) 2 (E) nonexistent If f ( x) = e x , then ln ( f ′(2) ) = (A) 2 (B) 0 (C) 1 e 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 2e (E) e2 68 1988 AP Calculus BC: Section I 9. Which of the following pairs of graphs could represent the graph of a function and the graph of its derivative? (A) I only 10. (B) II only (C) III only (D) I and III sin x (D) cos x (E) II and III sin ( x + h ) − sin x is h →0 h lim (A) 0 (B) 1 (C) (E) nonexistent 11. If x + 7 y = 29 is an equation of the line normal to the graph of f at the point (1, 4 ) , then f ′(1) = (A) 7 (B) 1 7 (C) − 1 7 (D) − 7 29 (E) −7 12. A particle travels in a straight line with a constant acceleration of 3 meters per second per second. If the velocity of the particle is 10 meters per second at time 2 seconds, how far does the particle travel during the time interval when its velocity increases from 4 meters per second to 10 meters per second? (A) 20 m (B) 14 m (C) 7 m AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 6 m (E) 3m 69 1988 AP Calculus BC: Section I 13. sin ( 2 x ) = x3 x5 (−1) n −1 x 2 n−1 + −… + +… 3! 5! ( 2n − 1)! (A) x− (B) (2 x)3 (2 x)5 (−1) n −1 (2 x) 2 n−1 2x − + −… + +… 3! 5! ( 2n − 1)! (C) − (D) x 2 x 4 x6 x 2n + + +… + +… 2! 4! 6! ( 2n ) ! (E) 2x + (2 x) 2 (2 x) 4 (−1) n (2 x) 2 n + −… + +… 2! 4! ( 2n ) ! 14. If F ( x) = ∫ (2 x)3 (2 x)5 (2 x) 2 n −1 + +… + +… 3! 5! ( 2n − 1)! x2 1 1 + t 3 dt , then F ′( x) = (A) 2 x 1 + x 6 (D) 1 + x3 (B) 2 x 1 + x3 (E) x2 ∫1 (C) 3t 2 2 1+ t 3 1 + x6 dt 15. For any time t ≥ 0 , if the position of a particle in the xy-plane is given by x = t 2 + 1 and y = ln ( 2t + 3) , then the acceleration vector is ⎛ 2⎞ (A) ⎜ 2t , ⎟ ⎝ (2t + 3) ⎠ (B) ⎛ −4 ⎞ ⎜ 2t , ⎜ (2t + 3) 2 ⎟ ⎟ ⎝ ⎠ ⎛ ⎞ 2 (D) ⎜ 2, ⎜ (2t + 3)2 ⎟ ⎟ ⎝ ⎠ (E) ⎛ −4 ⎞ ⎜ 2, ⎜ (2t + 3)2 ⎟ ⎟ ⎝ ⎠ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (C) ⎛ ⎞ 4 ⎜ 2, ⎜ (2t + 3)2 ⎟ ⎟ ⎝ ⎠ 70 1988 AP Calculus BC: Section I 16. ∫ xe2 x dx = xe 2 x e 2 x − +C (A) 2 4 (B) (E) xe 2 x e2 x + +C (D) 2 2 17. 3 ∫2 (A) xe 2 x e 2 x − +C 2 2 x 2e2 x +C 4 (C) xe 2 x e 2 x + +C 2 4 3 dx = ( x − 1)( x + 2) − 33 20 − (B) 9 20 (C) ⎛5⎞ ln ⎜ ⎟ ⎝2⎠ ⎛8⎞ (D) ln ⎜ ⎟ ⎝5⎠ (E) ⎛2⎞ ln ⎜ ⎟ ⎝5⎠ 18. If three equal subdivisions of [ −4, 2] are used, what is the trapezoidal approximation of 2 ∫ −4 e− x dx ? 2 (A) e 2 + e0 + e−2 (D) ( (B) 1 4 2 0 −2 e +e +e +e 2 (E) ) e 4 + e 2 + e0 14 e + 2e2 + 2e0 + e −2 2 ( (C) e 4 + 2e2 + 2e0 + e −2 ) 19. A polynomial p( x) has a relative maximum at ( −2, 4 ) , a relative minimum at (1,1) , a relative maximum at ( 5, 7 ) and no other critical points. How many zeros does p ( x) have? (A) One (B) Two (C) Three (D) Four (E) Five 20. The statement “ lim f ( x) = L ” means that for each ε > 0 , there exists a δ > 0 such that x →a (A) if 0 < x − a < ε , then f ( x) − L < δ (B) if 0 < f ( x) − L < ε , then x−a <δ (C) if f ( x) − L < δ , then 0 < x − a < ε (D) 0 < x − a < δ and (E) if 0 < x − a < δ , then f ( x) − L < ε f ( x) − L < ε AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 71 1988 AP Calculus BC: Section I 21. The average value of (A) 1 2 1 on the closed interval [1,3] is x (B) ( ) 2 3 (C) ln 2 2 (D) ln 3 2 (E) ln 3 x 22. If f ( x) = x 2 + 1 , then f ′( x) = ( ) x −1 (A) x x2 + 1 (B) 2 x2 x2 + 1 (C) x ln x 2 + 1 (D) ln x 2 + 1 + (E) ( ) ( ) ( ( ) x −1 2 x2 x2 + 1 x⎡ 2 x2 ⎤ x 2 + 1 ⎢ ln x 2 + 1 + 2 ⎥ x + 1⎥ ⎢ ⎣ ⎦ ) ( ) 23. Which of the following gives the area of the region enclosed by the loop of the graph of the polar curve r = 4 cos(3θ) shown in the figure above? (A) 16 ∫ π 3 π − 3 (D) 16 ∫ π 6 π − 6 cos(3θ) d θ 2 cos (3θ) d θ (B) (E) 8∫ π 6 π − 6 cos(3θ) d θ 8∫ π 6 π − 6 cos 2 (3θ) d θ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (C) 8 ∫ π 3 π − 3 cos 2 (3θ) d θ 72 1988 AP Calculus BC: Section I 24. If c is the number that satisfies the conclusion of the Mean Value Theorem for f ( x) = x3 − 2 x 2 on the interval 0 ≤ x ≤ 2, then c = (A) 0 1 2 (B) (C) 1 (D) 4 3 (E) 2 25. The...
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This note was uploaded on 12/29/2010 for the course MATH 214 taught by Professor Smith during the Fall '10 term at Oregon Tech.

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