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

What is the approximation of the value of sin 1

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Unformatted text preview: t; 5, f (c) = 3 . None I only I and II only I and III only I, II, and III 92. If 0 ≤ k < π π and the area under the curve y = cos x from x = k to x = is 0.1, then k = 2 2 (A) 1.471 (B) 1.414 (C) 1.277 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 1.120 (E) 0.436 137 1998 AP Calculus BC: Section I, Part A 55 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. 1. What are all values of x for which the function f defined by f ( x) = x3 + 3 x 2 − 9 x + 7 is increasing? (A) −3 < x < 1 (B) −1 < x < 1 (C) x < −3 or x > 1 (D) x < −1 or x > 3 (E) All real numbers 2. In the xy-plane, the graph of the parametric equations x = 5t + 2 and y = 3t , for −3 ≤ t ≤ 3 , is a line segment with slope 3 5 (A) 3. 5 3 (C) 3 (D) 5 (E) 13 The slope of the line tangent to the curve y 2 + ( xy + 1)3 = 0 at ( 2, − 1) is − (A) 4. (B) ∫ 3 2 1 2 x − 6x + 8 (B) − 3 4 (C) 0 (D) 3 4 (E) 3 2 dx = (A) 1 x−4 ln +C 2 x−2 (B) 1 x−2 ln +C 2 x−4 (C) 1 ln ( x − 2 )( x − 4 ) + C 2 (D) 1 ln ( x − 4 )( x + 2 ) + C 2 (E) ln ( x − 2 )( x − 4 ) + C AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 138 1998 AP Calculus BC: Section I, Part A 5. If f and g are twice differentiable and if h( x) = f ( g ( x) ) , then h′′( x) = (A) f ′′ ( g ( x) ) [ g ′( x) ] + f ′ ( g ( x) ) g ′′( x) (B) f ′′ ( g ( x) ) g ′( x) + f ′ ( g ( x) ) g ′′( x) (C) f ′′ ( g ( x) ) [ g ′( x) ] (D) f ′′ ( g ( x) ) g ′′( x) (E) f ′′ ( g ( x) ) 2 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 139 1998 AP Calculus BC: Section I, Part A 6. The graph of y = h( x) is shown above. Which of the following could be the graph of y = h′( x) ? AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 140 1998 AP Calculus BC: Section I, Part A e 7. ⌠ ⎮ ⌡1 (A) 8. If e− 1 e (B) e2 − e (C) e2 1 −e+ 2 2 (D) e2 − 2 (E) e2 3 − 22 dy π = sin x cos 2 x and if y = 0 when x = , what is the value of y when x = 0 ? dx 2 (A) 9. ⎛ x2 − 1 ⎞ dx = ⎜ ⎜x⎟ ⎟ ⎝ ⎠ −1 (B) − 1 3 (C) (D) 0 1 3 (E) 1 The 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) 4,800 10. A particle moves on a plane curve so that at any time t > 0 its x-coordinate is t 3 − t and its y-coordinate is ( 2t − 1) . The acceleration vector of the particle at t = 1 is 3 (A) ( 0,1) (B) ( 2,3) (C) 11. If f is a linear function and 0 < a < b, then (A) 0 (B) 1 (C) ( 2, 6 ) b ∫a (D) ( 6,12 ) (E) ( 6, 24 ) (D) b−a (E) b2 − a 2 2 f ′′( x) dx = ab 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 141 1998 AP Calculus BC: Section I, Part A ⎧ ln x for 0 < x ≤ 2 ⎪ 12. If f ( x) = ⎨ 2 then lim f ( x) is x →2 ⎪ x ln 2 for 2 < x ≤ 4, ⎩ (A) ln 2 (B) ln 8 (C) ln16 (D) 4 (E) nonexistent 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. What is the approximation of the value of sin 1 obtained by using the fifth-degree Taylor polynomial about x = 0 for sin x ? 11 (A) 1 − + 2 24 (B) 11 1− + 24 (C) 11 1− + 35 11 (D) 1 − + 48 (E) 11 1− + 6 120 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 142 1998 AP Calculus BC: Section I, Part A 15. ∫ x cos x dx = (A) x sin x − cos x + C (B) x sin x + cos x + C (C) − x sin x + cos x + C (D) x sin x + C (E) 12 x sin x + C 2 16. If f is the function defined by f ( x) = 3 x5 − 5 x 4 , what are all the x-coordinates of points of inflection for the graph of f ? (A) −1 (B) 0 (C) 1 (D) 0 and 1 (E) −1, 0, and 1 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) AP Calculus Multiple-Choice Question Coll...
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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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