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

The maximum acceleration attained on the interval 0 t

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Unformatted text preview: flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of barrels of oil that passed through the pipeline that day? (A) 500 (B) 600 (C) 2, 400 (D) 3, 000 (E) 10. What is the instantaneous rate of change at x = 2 of the function f given by f ( x) = (A) −2 (B) 1 6 11. If f is a linear function and 0 < a < b, then (A) 0 (B) 1 1 2 (C) (C) b ∫a (D) 2 4,800 x2 − 2 ? x −1 (E) 6 f ′′( x) dx = ab 2 (D) b−a (E) b2 − a 2 2 ⎧ ln x for 0 < x ≤ 2 ⎪ then lim f ( x) is 12. If f ( x) = ⎨ 2 x →2 ⎪ x ln 2 for 2 < x ≤ 4, ⎩ (A) ln 2 (B) ln 8 (C) ln16 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 4 (E) nonexistent 127 1998 AP Calculus AB: Section I, Part A 13. The graph of the function f shown in the figure above has a vertical tangent at the point ( 2, 0 ) and horizontal tangents at the points (1, − 1) and ( 3,1) . For what values of x, −2 < x < 4 , is f not differentiable? (A) 0 only (B) 0 and 2 only (C) 1 and 3 only (D) 0, 1, and 3 only (E) 0, 1, 2, and 3 14. A particle moves along the x-axis so that its position at time t is given by x(t ) = t 2 − 6t + 5 . For what value of t is the velocity of the particle zero? (A) 1 15. If F ( x) = ∫ (A) (B) 2 x 0 (C) 3 (D) 4 (E) 5 (C) 2 (D) 3 (E) 18 t 3 + 1 dt , then F ′(2) = −3 (B) −2 () 16. If f ( x) = sin e − x , then f ′(x) = (A) − cos(e − x ) (B) cos(e − x ) + e − x (C) cos(e − x ) − e − x (D) e − x cos(e− x ) (E) −e − x cos(e− x ) AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 128 1998 AP Calculus AB: Section I, Part A 17. The graph of a twice-differentiable function f is shown in the figure above. Which of the following is true? (A) f (1) < f ′ (1) < f ′′ (1) (B) f (1) < f ′′ (1) < f ′ (1) (C) f ′ (1) < f (1) < f ′′ (1) (D) f ′′ (1) < f (1) < f ′ (1) (E) f ′′ (1) < f ′ (1) < f (1) 18. An equation of the line tangent to the graph of y = x + cos x at the point ( 0,1) is (A) y = 2x +1 y = x +1 (B) (C) y=x (D) y = x −1 (E) y=0 19. If f ′′( x) = x ( x + 1)( x − 2 ) , then the graph of f has inflection points when x = 2 (A) –1 only (B) 2 only (C) –1 and 0 only 20. What are all values of k for which (A) –3 21. If (B) 0 k ∫ −3 x 2 (D) –1 and 2 only (E) –1, 0, and 2 only dx = 0 ? (C) 3 (D) –3 and 3 (E) –3, 0, and 3 dy = ky and k is a nonzero constant, then y could be dt (A) 2e kty (B) 2e kt (C) e kt + 3 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) kty + 5 (E) 121 ky + 2 2 129 1998 AP Calculus AB: Section I, Part A 22. The function f is given by f ( x) = x 4 + x 2 − 2 . On which of the following intervals is f increasing? (A) ⎛1 ⎞ , ∞⎟ ⎜− 2 ⎝ ⎠ (B) 1⎞ ⎛1 , ⎜− ⎟ 2 2⎠ ⎝ (C) ( 0, ∞ ) (D) ( −∞, 0 ) (E) 1⎞ ⎛ ⎜ −∞, − ⎟ 2⎠ ⎝ AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 130 1998 AP Calculus AB: Section I, Part A 23. The graph of f is shown in the figure above. Which of the following could be the graph of the derivative of f ? AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 131 1998 AP Calculus AB: Section I, Part A 24. The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given by v(t ) = t 3 − 3t 2 + 12t + 4 is (A) 9 (B) 12 (C) 14 (D) 21 (E) 40 25. What is the area of the region between the graphs of y = x 2 and y = − x from x = 0 to x = 2? 2 3 (B) 8 3 (C) 4 x 0 1 (D) 1 k 14 3 (E) 16 3 2 f ( x) (A) 2 26. The function f is continuous on the closed interval [ 0, 2] and has values that are given in the table above. The equation f ( x) = (A) (B) 0 1 must have at least two solutions in the interval [ 0, 2] if k = 2 1 2 (C) 1 (D) 2 (E) 3 27. What is the average value of y = x 2 x3 + 1 on the interval [ 0, 2] ? (A) 26 9 (B) 52 9 (C) 26 3 (D) 52 3 (E) 24 (C) 4 (D) 43 (E) 8 ⎛π⎞ 28. If f ( x) = tan(2 x), then f ′ ⎜ ⎟ = ⎝6⎠ (A) 3 (B) 23 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 132 1998 AP Calculus AB: 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 ass...
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