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

A 8 1 5 b if 1 1 a 1 4 b 2 0 e x dx

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Unformatted text preview: n y = dx (A) 1 − cos ( 2 x ) + C 2 1 (B) − cos 2 ( 2 x ) + C 2 (D) 5. 3 8 4 (A) 4. 3 4 If f ( x) = ( 2 x + 1) , then the 4th derivative of f ( x) at x = 0 is (A) 0 3. − (B) 12 sin ( 2 x ) + C 2 (E) lim n→∞ 4n 2 n 2 + 10, 000n (A) 0 (C) 1 sin ( 2 x ) + C 2 1 − sin ( 2 x ) + C 2 is (B) 1 2,500 (C) 1 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 4 (E) nonexistent 38 1985 AP Calculus AB: Section I 6. If f ( x) = x, then f ′(5) = (A) 0 7. ln 3 + ln1 1 (D) 5 (E) 25 2 ln 8 ln 2 (B) (C) 4 ∫1 et dt (D) 4 ∫1 ln x dx (E) 4 ∫1 1 dt t ⎛ x⎞ The slope of the line tangent to the graph of y = ln ⎜ ⎟ at x = 4 is ⎝2⎠ 1 8 (A) 9. (C) Which of the following is equal to ln 4 ? (A) 8. 1 5 (B) If 1 ∫ −1 (A) 1 4 (B) 2 0 e − x dx = k , then ∫ −1 −2k −k (B) ( x −1) , then 2 10. If y = 10 (A) ( ln10 )10( (D) 2 x ( ln10 )10 (C) 1 2 (C) − (D) 1 (E) 4 2 e − x dx = k 2 (D) k 2 (E) 2k dy = dx ) (B) ( 2 x )10( ( x −1) (E) x 2 ( ln10 )10 x 2 −1 ) x 2 −1 (C) ( ) ( x −2) x 2 − 1 10 2 ( x −1) 2 2 11. The position of a particle moving along a straight line at any time t is given by s (t ) = t 2 + 4t + 4 . What is the acceleration of the particle when t = 4 ? (A) 0 (B) 2 ( (C) ) 4 (D) 8 (E) 12 () 12. If f ( g ( x) ) = ln x 2 + 4 , f ( x) = ln x 2 , and g ( x) > 0 for all real x, then g (x) = (A) 1 2 x +4 (B) 1 2 x +4 (C) x2 + 4 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) x2 + 4 (E) x+2 39 1985 AP Calculus AB: Section I 13. If x 2 + xy + y 3 = 0 , then, in terms of x and y, (A) − 2x + y x + 3y 2 (B) x + 3y2 − 2x + y (C) dy = dx −2 x 1+ 3y (D) 2 14. The velocity of a particle moving on a line at time t is v meters did the particle travel from t = 0 to t = 4 ? (A) 32 (B) 40 (C) 1 = 3t 2 64 −2 x x + 3y 3 2 + 5t 2 − 2x + y x + 3 y2 −1 meters per second. How many (D) 80 ( (E) (E) 184 ) 15. The domain of the function defined by f ( x) = ln x 2 − 4 is the set of all real numbers x such that (A) x <2 x ≤2 (B) x >2 (C) (D) x ≥2 (E) x is a real number 16. The function defined by f ( x) = x3 − 3 x 2 for all real numbers x has a relative maximum at x = (A) 17. 1 ∫ 0 xe −2 −x (B) 0 (C) 1 (D) 2 (E) 4 (C) 1 − 2e −1 (D) 1 (E) dx = (A) 1 − 2e (B) −1 2e − 1 18. If y = cos 2 x − sin 2 x , then y′ = (A) −1 (B) (C) −2sin ( 2 x ) 0 −2 ( cos x + sin x ) (D) (E) 2 ( cos x − sin x ) 19. If f ( x1 ) + f ( x2 ) = f ( x1 + x2 ) for all real numbers x1 and x2 , which of the following could define f ? (A) f ( x) = x + 1 (B) f ( x) = 2 x (C) f ( x) = 1 x AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) f ( x) = e x (E) f ( x) = x 2 40 1985 AP Calculus AB: Section I 20. If y = arctan ( cos x ) , then dy = dx − sin x (A) (B) − ( arcsec ( cos x ) ) sin x 2 2 1 + cos x 1 (D) ( arccos x ) 2 (E) +1 1 + cos 2 x 1 1 − x2 is { x : x > 1} , what is the range of f ? (A) { x : −∞ < x < −1} (B) { x : −∞ < x < 0} (D) { x : −1 < x < ∞} (E) { x : 0 < x < ∞} 2 ∫1 (C) { x : −∞ < x < 1} x2 −1 dx = x +1 1 2 (A) 23. ( arcsec ( cos x ) )2 1 21. If the domain of the function f given by f ( x) = 22. (C) (B) 1 5 2 (C) 2 (D) (E) (C) 0 (D) 2 (E) 6 (C) 0 (D) 4 (E) 12 ln 3 d⎛1 1 2⎞ ⎜ 3 − x + x ⎟ at x = −1 is dx ⎝ x ⎠ −6 (A) 24. If ∫ −2 ( x (A) 2 (B) 7 −4 ) + k dx = 16, then k = −12 (B) −4 25. If f ( x) = e x , which of the following is equal to f ′(e)? (A) lim e x+h h →0 h (B) lim (D) e x+h − 1 h →0 h (E) lim lim e x + h − ee h →0 h ee + h − e h →0 h (C) lim ee + h − ee h →0 h AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 41 1985 AP Calculus AB: Section I 26. The graph of y 2 = x 2 + 9 is symmetric to which of the following? I. II. III. The x-axis The y-axis The origin (A) I only 27. 3 ∫0 (B) II only (C) III only (D) I and II only (E) I, II, and III x − 1 dx = (A) 0 (B) 3 2 (C) 2 (D) 5 2 (E) 6 28. If the position of a particle on the x-axis at time t is −5t 2 , then the average velocity of the particle for 0 ≤ t ≤ 3 is (A) − 45 (B) − 30 (C) − 15 (D) − 10 (E) −5 29. Which of the following functions are continuous for all real numbers x ? I. II. III. y= 2 x3 y = ex y = tan x (A) None 30. (B) I only (C) II only (D) I and II (E) I and III ∫ tan ( 2 x ) dx = (A) −2 ln cos(2 x) + C (B) 1 − ln cos(2 x) + C 2 (D) 2 ln cos(2 x) + C (E) 1 sec(2 x) tan(2 x) + C 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (C) 1 ln cos(2 x) + C 2 42 1985 AP Calculus AB: Section I 1 31. The volume of a cone of radius r and heigh...
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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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