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

Let f x cos arctan x what is the range of f a d 25 x

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y f ( x) = 3 x5 − 20 x3 , find all values of x for which the graph of f is concave up. (A) x>0 (B) − 2 < x < 0 or x > 2 (C) −2 < x < 0 or x > 2 (D) x> 2 (E) −2 < x < 2 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 23 1973 AP Calculus AB: Section I 23. 1 ⎛ 2+h⎞ ln ⎜ ⎟ is h→0 h ⎝ 2 ⎠ lim (A) e2 (B) 1 (C) 1 2 (D) 0 (E) nonexistent 24. Let f ( x) = cos ( arctan x ) . What is the range of f ? (A) (D) 25. ⎧ π ⎨x − < x < 2 ⎩ {x π4 ∫0 (A) π⎫ ⎬ 2⎭ (B) 0 < x ≤ 1} (E) − 1 < x < 1} {x (C) {x − 1 ≤ x ≤ 1} (C) 1 3 {x 0 ≤ x ≤ 1} (E) π +1 4 tan 2 x dx = π −1 4 (B) 1 − π 4 2 −1 (D) 26. The radius r of a sphere is increasing at the uniform rate of 0.3 inches per second. At the instant when the surface area S becomes 100π square inches, what is the rate of increase, in cubic inches 4 ⎛ ⎞ per second, in the volume V ? ⎜ S = 4π r 2 and V = π r 3 ⎟ 3 ⎝ ⎠ (A) 10π 27. 2x 12 ∫0 (B) 12π 1− x (A) 1 − 2 3 2 (C) 22.5 π (D) 25 π (E) 30 π (C) π 6 (D) π −1 6 (E) 2− 3 dx = (B) 13 ln 24 28. A point moves in a straight line so that its distance at time t from a fixed point of the line is 8t − 3t 2 . What is the total distance covered by the point between t = 1 and t = 2? (A) 1 (B) 4 3 (C) 5 3 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 2 (E) 5 24 1973 AP Calculus AB: Section I 1 . The maximum value attained by f is 2 29. Let f ( x) = sin x − 1 2 (A) (B) 1 ∫1 x−4 (A) 30. − 2 x2 3 2 (D) π 2 (E) 3π 2 (C) ln 2 (D) 2 (E) ln 2 + 2 (C) 8 (D) 16 (E) 32 ) 5 (C) 5 x − + C x dx = 1 2 (B) () ln 2 − 2 a , then a = 4 31. If log a 2a = (A) 2 32. (C) (B) 4 5 ∫ 1 + x 2 dx = −10 x ( (A) (1 + x2 ) +C (B) 5 ln 1 + x 2 + C 2x (D) 5arctan x + C (E) 5ln 1 + x 2 + C 2 ( ) 33. Suppose that f is an odd function; i.e., f (− x) = − f ( x) for all x. Suppose that f ′ ( x0 ) exists. Which of the following must necessarily be equal to f ′ ( − x0 ) ? (A) f ′ ( x0 ) (B) − f ′ ( x0 ) (C) 1 f ′ ( x0 ) (D) −1 f ′ ( x0 ) (E) None of the above AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 25 1973 AP Calculus AB: Section I x over the interval 0 ≤ x ≤ 2 is 34. The average value of 1 2 3 (A) (B) 1 2 2 (C) 2 2 3 (D) 1 35. The region in the first quadrant bounded by the graph of y = sec x, x = (E) 4 2 3 π , and the axes is rotated 4 about the x-axis. What is the volume of the solid generated? π2 4 (A) 36. If y = enx , then dx n π −1 (C) π (D) 2π (E) 8π 3 n !e nx (C) n e nx (D) nn e x (E) n !e x 3 + e4 x (D) 4 + e4 x (E) 2 x2 + 4 (E) –5 ) (E) ( 4,8) (C) cos 2 ( xy ) = (B) dy = 4 y and if y = 4 when x = 0, then y = dx 4e4 x (A) 38. If dny n n enx (A) 37. If (B) 2 ∫1 (A) (B) e4 x (C) f ( x − c ) dx = 5 where c is a constant, then 5+c (B) 5 (C) 2−c ∫ 1−c f ( x ) dx = 5−c (D) c − 5 39. The point on the curve 2 y = x 2 nearest to ( 4,1) is (A) ( 0, 0 ) 40. If tan( xy ) = x , then (B) ( 2, 2 ) (C) ( ) 2,1 (D) (2 2, 4 dy = dx (A) 1 − y tan( xy ) sec( xy ) x tan( xy ) sec( xy ) (D) cos 2 ( xy ) x (B) sec 2 ( xy ) − y x (E) cos 2 ( xy ) − y x AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 26 1973 AP Calculus AB: Section I ⎧ x + 1 for x < 0, 41. Given f ( x) = ⎨ ⎩cos π x for x ≥ 0, (A) 11 + 2π (B) − 1 ∫ −1 f ( x) dx = 1 2 (C) 11 − 2π (D) 1 2 (E) 1 − +π 2 42. Calculate the approximate area of the shaded region in the figure by the trapezoidal rule, using 4 5 divisions at x = and x = . 3 3 (A) 50 27 (B) 251 108 (C) 7 3 (D) 127 54 (E) 77 27 (C) − ⎛ x⎞ 43. If the solutions of f ( x) = 0 are –1 and 2, then the solutions of f ⎜ ⎟ = 0 are ⎝2⎠ (A) (D) − 4 − (E) 1 and 1 2 44. For small values of h, the function 1 5 and 2 2 (B) −1 and 2 3 3 and 2 2 −2 and 4 16 + h is best approximated by which of the following? (A) 4+ h 32 (B) 2+ h 32 (D) 4− h 32 (E) 2− h 32 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (C) h 32 27 1973 AP Calculus AB: Section I 45. If f is a continuous function on [ a, b ] , which of the following is necessarily true? (A) f ′ exists on ( a , b ) . (B) If f ( x0 ) is a maximum of f, then f ′ ( x0 ) = 0 . (C) ⎛ ⎞ lim f ( x) = f ⎜ lim x ⎟ for x0 ∈ ( a , b ) x→ x0 ⎝ x→ x0 ⎠ (D) f ′( x) = 0 for some x ∈ [ a , b ] (E) The graph of f ′ is a straight line. AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 28 1973 AP Calculus BC: Section I 90 Minutes—No Calculator N...
View Full Document

Ask a homework question - tutors are online