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

A f is continuous for all real numbers b f has a

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Unformatted text preview: ollege Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 5.6 pounds (E) 6.5 pounds 87 1993 AP Calculus AB: Section I 43. ∫ x f ( x) dx = (A) x f ( x) − ∫ x f ′( x) dx (B) x2 x2 f ( x) − ∫ f ′( x)dx 2 2 (C) x f ( x) − (D) x f ( x) − ∫ f ′( x) dx (E) x2 2 ∫ x2 f ( x) + C 2 f ( x) dx 44. What is the minimum value of f ( x) = x ln x ? (A) −e (B) −1 (C) − 1 e (D) 0 (E) f ( x) has no minimum value. 45. If Newton’s method is used to approximate the real root of x3 + x − 1 = 0 , then a first approximation x1 = 1 would lead to a third approximation of x3 = (A) 0.682 (B) 0.686 (C) 0.694 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 0.750 (E) 1.637 88 1993 AP Calculus BC: Section I 90 Minutes—Scientific Calculator 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. 1. The area of the region enclosed by the graphs of y = x 2 and y = x is (A) 2. 1 6 (B) If f ( x) = 2 x 2 + 1, then lim f ( x) − f (0) x2 (B) 1 1 2 (D) 5 6 (E) 1 is (C) 2 (D) 4 (E) nonexistent x If p is a polynomial of degree n, n > 0 , what is the degree of the polynomial Q( x) = ∫ p(t )dt ? 0 (A) 0 4. (C) x →0 (A) 0 3. 1 3 (B) 1 (C) n −1 A particle moves along the curve xy = 10. If x = 2 and (A) − 5 2 (B) − 6 5 (D) n n +1 (E) dx dy ? = 3, what is the value of dt dt (C) 0 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 4 5 (E) 6 5 89 1993 AP Calculus BC: Section I 5. 6. Which of the following represents the graph of the polar curve r = 2 sec θ ? 2 If x = t + 1 and y = t , then (A) 7. ∫ 3 4t 1 3 x4 x e dx 0 (A) 8. 3 d2y dx 2 = (B) 3 2t (C) 3t (B) 1 e 4 (C) (C) 3 2 (D) 6t (E) e −1 (D) e (E) 4(e − 1) 2x (D) e−2 x (E) 2e−2 x = 1 (e − 1) 4 If f ( x) = ln(e 2 x ) , then f ′( x) = (A) 1 (B) 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 90 1993 AP Calculus BC: Section I 9. If f ( x) = 1 + 2 x3 , which of the following is NOT true? (A) f is continuous for all real numbers. (B) f has a minimum at x = 0 . (C) f is increasing for x > 0 . (D) f ′( x) exists for all x. (E) f ′′( x) is negative for x > 0 . 10. Which of the following functions are continuous at x = 1 ? I. ln x II. ex ln(e x − 1) III. (A) I only 11. −2 x ∞ ∫4 3 9 − x2 (B) II only (C) I and II only (D) II and III only (E) I, II, and III dx is 2 (A) 7 3 (B) 3⎛ 2 ⎞ ⎜73 ⎟ 2⎝ ⎠ 2 2 (C) 9 3 + 7 3 (D) 2 3⎛ 2 ⎞ ⎜ 93 + 73 ⎟ 2⎝ ⎠ (E) nonexistent 12. The position of a particle moving along the x-axis is x(t ) = sin(2t ) − cos(3t ) for time t ≥ 0 . When t = π , the acceleration of the particle is (A) 9 13. If (B) 1 9 (C) 0 (D) − 1 9 (E) –9 dy = x 2 y , then y could be dx ⎛ x⎞ (A) 3 ln ⎜ ⎟ ⎝3⎠ (B) x3 e3 +7 (C) x3 2e 3 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 3e2 x (E) x3 +1 3 91 1993 AP Calculus BC: Section I 14. The derivative of f is x 4 ( x − 2)( x + 3) . At how many points will the graph of f have a relative maximum? (A) None (B) One (C) Two (D) Three (E) Four (C) III only (D) I and III (E) II and III 2 15. If f ( x) = e tan x , then f ′( x) = 2 (A) e tan (B) sec2 x e tan (C) tan 2 x e tan (D) 2 tan x sec 2 x e tan (E) 2 tan x e tan x 2 x 2 x −1 2 2 x x 16. Which of the following series diverge? ∞ ∑ I. k =3 ∞ ∑ II. k =1 ∞ ∑ III. k =2 (A) None 2 2 k +1 ⎛6⎞ ⎜⎟ ⎝7⎠ k (−1) k k (B) II only 17. The slope of the line tangent to the graph of ln( xy ) = x at the point where x = 1 is (A) 0 (B) 1 (C) e (D) e2 (E) 1− e (E) 2 x ln(1 + x 2 ) 18. If e f ( x ) = 1 + x 2 , then f ′( x) = (A) 1 1+ x 2 (B) 2x 1+ x 2 (C) 2 x(1 + x 2 ) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) () 2 x e1+ x 2 92 1993 AP Calculus BC: Section I 19. The shaded region R, shown in the figure above, is rotated about the y -axis to form a solid whose volume is 10 cubic units. Of the following, which best approximates k ? (A) 1.51 (B) 2.09 (C) 2.49 (D) 4.18 (E) 4.77 20. A particle moves along the x-axis so that at any time t ≥ 0 the acceleration of the particle is 5 17 a (t ) = e−2t . If at t = 0 the velocity of the particle is and its position is , then its position at 2 4 any time t > 0 is x(t ) = e−2t +3 2 (A) − (B) e−2t +4 4 (C) 91 4e−2t + t + 24 (D) e−2t 15...
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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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