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

12 c 01 c 2 ap calculus multiple choice question

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Unformatted text preview: ection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 143 1998 AP Calculus BC: Section I, Part A 18. Which of the following series converge? I. ∞ n ∑ n+2 II. n =1 (A) (B) (C) (D) (E) ∞ ∑ n =1 cos(nπ) n III. ∞ 1 ∑n n =1 None II only III only I and II only I and III only 19. The area of the region inside the polar curve r = 4 sin θ and outside the polar curve r = 2 is given by 3π 1π 2 (A) ∫ 0 ( 4sin θ − 2 ) d θ 2 5π ( 14 2 (B) ∫ π ( 4sin θ − 2 ) d θ 2 4 ) 16 16sin 2 θ − 4 d θ (D) 2∫π (E) 6 20. When x = 8 , the rate at which 3 ( 5π 16 2 (C) ∫ π ( 4sin θ − 2 ) d θ 2 6 ) 1π 16sin 2 θ − 4 d θ 2 ∫0 x is increasing is 1 times the rate at which x is increasing. What k is the value of k ? (A) 3 (B) 4 (C) 6 (D) 8 (E) 12 1 1 21. The length of the path described by the parametric equations x = t 3 and y = t 2 , where 3 2 0 ≤ t ≤ 1 , is given by 1 ∫0 t 2 + 1 dt 1 t 2 + t dt 1 t 4 + t 2 dt (A) (B) ∫0 (C) ∫0 (D) 11 4 ∫ 0 4 + t dt 2 (E) 1 12 t 4t 2 + 9 dt 6 ∫0 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 144 1998 AP Calculus BC: Section I, Part A b ∫ b→∞ 1 22. If lim (A) ∞ ∑ n =1 ∞ (B) ∑ n =1 (C) xp 1 np 1 np ∞ ∑ n =1 (D) dx 1 n ∞ ∑ n =1 1 n p −1 ∞ (E) ∑ n =1 p−2 1 n p +1 is finite, then which of the following must be true? converges diverges converges converges diverges 23. Let f be a function defined and continuous on the closed interval [ a, b ] . If f has a relative maximum at c and a < c < b , which of the following statements must be true? I. f ′(c) exists. II. If f ′(c) exists, then f ′(c) = 0 . III. If f ′′(c) exists, then f ′′(c) ≤ 0 . (A) II only (B) III only (C) I and II only (D) I and III only AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) II and III only 145 1998 AP Calculus BC: Section I, Part A 24. Shown above is a slope field for which of the following differential equations? 25. (B) dy = x2 dx (C) dy = x+ y dx (D) (B) dy = 1+ x dx (A) dy x = dx y 0 (C) 1 3 (D) 1 (E) dy = ln y dx ∞ 2 − x3 x e dx is ∫0 − (A) 1 3 (E) divergent dP P⎞ ⎛ = P⎜2− ⎟, dt 5000 ⎠ ⎝ where the initial population P (0) = 3, 000 and t is the time in years. What is lim P(t ) ? 26. The population P (t ) of a species satisfies the logistic differential equation t →∞ (A) 2,500 ∞ 27. If ∑ an x n (B) 3, 000 (C) 4, 200 (D) 5, 000 (E) 10, 000 is a Taylor series that converges to f ( x) for all real x, then f ′(1) = n =0 ∞ (A) x t2 28. lim (B) 0 ∫1 e a1 (C) ∞ ∑ an (D) e 2 (D) n =0 ∞ ∑ nan (E) e (E) nonexistent n =1 ∑ nan n−1 n =1 dt x→1 x2 − 1 (A) 0 is (B) 1 (C) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 146 1998 AP Calculus BC: Section I, Part B 50 Minutes—Graphing Calculator Required Notes: (1) The exact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among the choices the number that best approximates the exact numerical value. (2) Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f (x) is a real number. 76. For what integer k, k > 1 , will both ∞ ∑ n =1 (A) 6 (B) 5 ( −1)kn n (C) ∞ n ⎛k⎞ and ∑ ⎜ ⎟ converge? n =1 ⎝ 4 ⎠ 4 (D) 3 ( (E) 2 ) 77. If f is a vector-valued function defined by f (t ) = e −t , cos t , then f ′′(t ) = (A) −e−t + sin t (B) e −t − cos t (D) ( e−t , cos t ) (E) ( e−t , − cos t ) (C) ( −e−t , − sin t ) 78. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second? (A) − ( 0.2 ) π C (B) − ( 0.1) C (C) − (D) ( 0.1)2 C (E) ( 0.1)2 π C ( 0.1) C 2π AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 147 1998 AP Calculus BC: Section I, Part B 79. Let f be the function given by f ( x) = ( x − 1)( x 2 − 4) x2 − a continuous for all real numbers x? (A) (B) (C) (D) (E) . For what positive values of a is f None 1 only 2 only 4 only 1 and 4 only ( ) 80. Let R be the region enclosed by the graph of y = 1 + ln cos 4 x , the x-axis, and the lines x = − 2 . The closest integer approximation of the area of R is 3 and x = (A) 2 3 (B) 1 0 (C) 2 (D) 3 (E) 4 (D) (E) dy d2y 2 81. If = 1 − y , then = dx dx 2 (A) −2 y (B) −y 82. If f ( x) = g ( x) + 7 for 3 ≤ x ≤ 5, then (A) 2∫ (B) 2∫ (C) 2∫ (D) ∫3 (E) ∫3 5 3 5 3 5 3 5 5 (C) −y 1− y2 y 1 2 5 ∫ 3 [ f ( x) + g ( x)] dx = g ( x) dx + 7 g...
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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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