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

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Unformatted text preview: , how many people are infected 12 days after the epidemic is first discovered? (A) 343 39. If (B) 1,343 (C) 1,367 (D) 1,400 (E) 2,057 dy 1 = , then the average rate of change of y with respect to x on the closed interval [1, 4] is dx x (A) − 1 4 (B) 1 ln 2 2 (C) 2 ln 2 3 (D) 2 5 (E) 2 40. Let R be the region in the first quadrant enclosed by the x-axis and the graph of y = ln(1 + 2 x − x 2 ) . If Simpson’s Rule with 2 subintervals is used to approximate the area of R, the approximation is (A) 0.462 41. Let f ( x) = ∫ (B) 0.693 x 2 −3 x t 2 e dt −2 (D) 0.986 (E) 1.850 (D) 2 (E) 3 (D) e (E) e2 . At what value of x is f ( x) a minimum? (A) For no value of x 42. (C) 0.924 (B) 1 2 (C) 3 2 lim (1 + 2 x)csc x = x→0 (A) 0 (B) 1 (C) 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 98 1993 AP Calculus BC: Section I () 43. The coefficient of x 6 in the Taylor series expansion about x = 0 for f ( x) = sin x 2 is (A) − 1 6 (B) 0 (C) 1 120 (D) 1 6 (E) 44. If f is continuous on the interval [ a, b ] , then there exists c such that a < c < b and (A) f (c ) b−a ∞ ( k =1 f (b) − f (a ) b−a (B) ) (C) f (b) − f (a) (D) f ′(c)(b − a ) 1 b ∫a (E) f ( x)dx = f (c)(b − a) k 45. If f ( x) = ∑ sin 2 x , then f (1) is (A) 0.369 (B) 0.585 (C) 2.400 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 2.426 (E) 3.426 99 1997 AP Calculus AB: Section I, Part A 50 Minutes—No Calculator Note: 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. 2. 2 3 (A) (B) (C) (D) (E) 1. 2 4 6 36 42 ∫ 1 (4 x If f ( x) = x 2 x − 3, then f ′( x) = 3x − 3 (A) 2x − 3 x (B) 2x − 3 1 (C) 2x − 3 −x + 3 (D) 2x − 3 5x − 6 (E) 3. If 2 2x − 3 b ∫a (A) 4. − 6 x) dx = f ( x) dx = a + 2b, then a + 2b + 5 (B) b ∫ a ( f ( x) + 5) dx = 5b − 5a (C) 7b − 4 a (D) 7b − 5a (C) –1 (D) –3 (E) 7b − 6 a 1 If f ( x) = − x3 + x + , then f ′(−1) = x (A) 3 (B) 1 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) –5 100 1997 AP Calculus AB: Section I, Part A 5. The graph of y = 3 x 4 − 16 x3 + 24 x 2 + 48 is concave down for (A) x<0 (B) x>0 (C) x < −2 or x > − (D) x< (E) 2 <x<2 3 2 3 2 or x > 2 3 t 6. 12 e dt = 2∫ (A) 7. −t e +C (B) e − t 2 +C (C) t 2 e +C (D) t 2 2e +C (E) et + C d cos 2 ( x3 ) = dx (A) 6 x 2 sin( x3 ) cos( x3 ) (B) 6 x 2 cos( x3 ) (C) sin 2 ( x3 ) (D) −6 x 2 sin( x3 ) cos( x3 ) (E) −2sin( x3 ) cos( x3 ) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 101 1997 AP Calculus AB: Section I, Part A Questions 8-9 refer to the following situation. A bug begins to crawl up a vertical wire at time t = 0 . The velocity v of the bug at time t, 0 ≤ t ≤ 8 , is given by the function whose graph is shown above. 8. At what value of t does the bug change direction? (A) 2 9. (B) 4 (C) 6 (D) 7 (E) 8 What is the total distance the bug traveled from t = 0 to t = 8 ? (A) 14 (B) 13 (C) 11 (D) 8 10. An equation of the line tangent to the graph of y = cos(2 x) at x = (A) π⎞ ⎛ y − 1 = −2 ⎜ x − ⎟ 4⎠ ⎝ (C) π⎞ ⎛ y = 2⎜ x − ⎟ 4⎠ ⎝ (D) π⎞ ⎛ y = −⎜ x − ⎟ 4⎠ ⎝ (E) π is 4 π⎞ ⎛ y −1 = − ⎜ x − ⎟ 4⎠ ⎝ (B) (E) 6 π⎞ ⎛ y = −2 ⎜ x − ⎟ 4⎠ ⎝ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 102 1997 AP Calculus AB: Section I, Part A 11. The graph of the derivative of f is shown in the figure above. Which of the following could be the graph of f ? 12. At what point on the graph of y = (A) ⎛1 1⎞ ⎜ ,− ⎟ ⎝2 2⎠ ⎛1 1⎞ (B) ⎜ , ⎟ ⎝ 2 8⎠ 12 x is the tangent line parallel to the line 2 x − 4 y = 3 ? 2 (C) 1⎞ ⎛ ⎜1, − ⎟ 4⎠ ⎝ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) ⎛ 1⎞ ⎜1, ⎟ ⎝ 2⎠ (E) ( 2, 2 ) 103 1997 AP Calculus AB: Section I, Part A 13. Let f be a function defined for all real numbers x. If f ′( x) = 4 − x2 x−2 , then f is decreasing on the interval (A) ( −∞, 2 ) (B) ( −∞, ∞ ) (C) ( −2, 4 ) (D) ( −2, ∞ ) (E) ( 2, ∞ ) 14. Let f be a differentiable function such that f (3) = 2 and f ′(3) = 5 . If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is (A) 0.4 (B) 0.5 (C) 2.6 (D) 3.4 (E) 5.5 15. The graph of the function f is shown in the figure above. Which of the following statements about f is true? (A) (B) (C) (D) (E) lim f ( x) = li...
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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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