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

5n1 4 n100 1 5 a 32 if b a b 1 f xdx

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Unformatted text preview: + 3t + 2 4 (E) e−2t + 3t + 4 4 21. The value of the derivative of y = (A) –1 (B) − 1 2 32 x +8 4 2x +1 at x = 0 is (C) 0 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 1 2 (E) 1 93 1993 AP Calculus BC: Section I 22. If f ( x) = x 2e x , then the graph of f is decreasing for all x such that (A) x < −2 (B) −2 < x < 0 (C) x > −2 (D) x<0 (E) x>0 23. The length of the curve determined by the equations x = t 2 and y = t from t = 0 to t = 4 is 4 (A) ∫0 (B) 2∫ (C) (D) (E) 4t + 1 dt 4 t 2 + 1 dt 0 4 ∫0 2t 2 + 1 dt ∫0 4 4t 2 + 1 dt 2π ∫ 4 0 4t 2 + 1 dt 24. Let f and g be functions that are differentiable for all real numbers, with g ( x) ≠ 0 for x ≠ 0. f ′( x) f ( x) exists, then lim is If lim f ( x) = lim g ( x) = 0 and lim x→0 x →0 x→0 g ′( x ) x→0 g ( x ) (A) 0 (B) f ′( x) g ′( x) (C) f ′( x) x→0 g ′( x ) (D) (E) lim f ′( x) g ( x) − f ( x) g ′( x) ( f ( x) )2 nonexistent 25. Consider the curve in the xy-plane represented by x = et and y = te −t for t ≥ 0 . The slope of the line tangent to the curve at the point where x = 3 is (A) 20.086 (B) 0.342 (C) –0.005 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) –0.011 (E) –0.033 94 1993 AP Calculus BC: Section I 26. If y = arctan(e 2 x ), then 2e2 x (A) 1 − e4 x (B) dy = dx 2e 2 x 1+ e 27. The interval of convergence of (C) 4x ∞ ∑ n =0 ( x − 1) n 3n e2 x 1+ e 4x (D) 1 (E) 1 − e4 x 1 1 + e4 x is (A) −3 < x ≤ 3 (B) −3 ≤ x ≤ 3 (D) −2 ≤ x < 4 (C) −2 < x < 4 (E) 0 ≤ x ≤ 2 ( ) 28. If a particle moves in the xy-plane so that at time t > 0 its position vector is ln(t 2 + 2t ), 2t 2 , then at time t = 2 , its velocity vector is (A) 29. ⎛3 ⎞ ⎜ ,8 ⎟ ⎝4 ⎠ ∫ x sec 2 (B) ⎛3 ⎞ ⎜ ,4⎟ ⎝4 ⎠ (C) ⎛1 ⎞ ⎜ ,8 ⎟ ⎝8 ⎠ ⎛1 ⎞ (D) ⎜ , 4 ⎟ ⎝8 ⎠ (E) ⎛5⎞ ⎜ − ,4⎟ ⎝ 16 ⎠ x dx = (A) x tan x + C (B) x2 tan x + C 2 (D) x tan x − ln cos x + C (E) x tan x + ln cos x + C (C) sec2 x + 2sec 2 x tan x + C 30. What is the volume of the solid generated by rotating about the x-axis the region enclosed by the π curve y = sec x and the lines x = 0, y = 0, and x = ? 3 (A) π 3 (B) π (C) π3 (D) 8π 3 (E) ⎛1 ⎞ π ln ⎜ + 3 ⎟ ⎝2 ⎠ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 95 1993 AP Calculus BC: Section I ⎛ (5 + n)100 ⎞⎛ ⎞ 5n 31. If sn = ⎜ , to what number does the sequence {sn } converge? ⎟⎜ ⎜ 5n+1 ⎟⎜ (4 + n)100 ⎟ ⎟ ⎝ ⎠⎝ ⎠ 1 5 (A) 32. If b ∫a (B) 1 f ( x)dx = 5 and (C) 100 ⎛5⎞ (D) ⎜ ⎟ ⎝4⎠ 5 4 (E) The sequence does not converge. b ∫ a g ( x)dx = −1 , which of the following must be true? f ( x) > g ( x) for a ≤ x ≤ b I. b II. ∫ a ( f ( x) + g ( x) ) dx = 4 III. ∫ a ( f ( x) g ( x) ) dx = −5 b (A) I only (B) II only 33. Which of the following is equal to (A) ∫ (D) ∫ π 2 π − 2 π 2 π − 2 (C) III only (D) II and III only (E) I, II, and III π ∫ 0 sin x dx ? π cos x dx (B) ∫ 0 cos x dx sin x dx (E) ∫π 2π (C) 0 ∫ −π sin x dx sin x dx AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 96 1993 AP Calculus BC: Section I 34. In the figure above, PQ represents a 40-foot ladder with end P against a vertical wall and end Q on level ground. If the ladder is slipping down the wall, what is the distance RQ at the instant when Q 3 is moving along the ground as fast as P is moving down the wall? 4 (A) 6 10 5 (B) 8 10 5 (C) 80 7 35. If F and f are differentiable functions such that F ( x) = ∫ (D) 24 x 0 (E) 32 f (t )dt , and if F (a) = −2 and F (b) = −2 where a < b , which of the following must be true? (A) f ( x) = 0 for some x such that a < x < b. (B) f ( x) > 0 for all x such that a < x < b. (C) f ( x) < 0 for all x such that a < x < b. (D) F ( x) ≤ 0 for all x such that a < x < b. (E) F ( x) = 0 for some x such that a < x < b. 36. Consider all right circular cylinders for which the sum of the height and circumference is 30 centimeters. What is the radius of the one with maximum volume? (A) 3 cm (B) 10 cm (C) 20 cm AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 30 π 2 cm (E) 10 cm π 97 1993 AP Calculus BC: Section I ⎧x ⎪ 37. If f ( x) = ⎨ 1 ⎪ ⎩x for x ≤ 1 then for x > 1, (A) 0 (B) e ∫ 0 f ( x)dx = 3 2 (C) 2 (D) e (E) e+ 1 2 38. During a certain epidemic, the number of people that are infected at any time increases at a rate proportional to the number of people that are infected at that time. If 1,000 people are infected when the epidemic is first discovered, and 1,200 are infected 7 days later...
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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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