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

Available at apcentralcollegeboardcom d 6 e 9 33 1973

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: ver x − 2 < δ ? (A) π4 ε 4 ∫0 π −1 4 ε 2 (C) ε ε +1 (D) (C) 1 3 ε +1 ε (D) (E) 3ε (E) π +1 4 tan 2 x dx = (A) 25. (B) (B) 1 − π 4 2 −1 26. Which of the following is true about the graph of y = ln x 2 − 1 in the interval ( −1,1) ? (A) (B) (C) (D) (E) It is increasing. It attains a relative minimum at ( 0, 0 ) . It has a range of all real numbers. It is concave down. It has an asymptote of x = 0 . 13 x − 4 x 2 + 12 x − 5 and the domain is the set of all x such that 0 ≤ x ≤ 9 , then the 3 absolute maximum value of the function f occurs when x is 27. If f ( x) = (A) 0 (B) 2 (C) 4 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 6 (E) 9 33 1973 AP Calculus BC: Section I x = sin y is made in the integrand of 28. If the substitution 12 (A) ∫0 (D) ∫0 π4 12 sin y dy (B) 2∫ 0 sin 2 y dy (E) 2∫ 0 2 π6 x 12 ∫0 sin 2 y dy cos y 1− x dx , the resulting integral is 2∫ (C) π4 0 sin 2 y dy sin 2 y dy 29. If y′′ = 2 y′ and if y = y′ = e when x = 0, then when x = 1, y = (A) ( ∫1 x−4 (A) 30. ) e2 e +1 2 − 2 ( e3 − e ) (B) e (C) e3 2 (B) ln 2 − 2 (C) ln 2 (D) 2 (E) ln 2 + 2 (C) ln x x (D) (E) 1 x ln x (D) e 2 (E) 2 dx x2 1 2 31. If f ( x) = ln ( ln x ) , then f ′( x) = (A) 1 x (B) 1 ln x x 32. If y = x ln x , then y′ is (A) x ln x ln x x2 (B) x1 x ln x (C) 2 x ln x ln x x (D) x ln x ln x x (E) None of the above AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 34 1973 AP Calculus BC: Section I 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) − (E) None of the above 1 f ′ ( x0 ) x over the interval 0 ≤ x ≤ 2 is 34. The average (mean) 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) (B) x +1 1 37. ∫0 x2 + 2 x − 3 (A) 36. (B) − ln 3 lim x2 (A) –2 38. If − (D) 2π (E) 8π 3 (D) ln 3 (E) divergent (D) 2 (C) π (E) 4 (E) –5 dx is 1 − cos 2 (2 x) x →0 π −1 ln 3 2 (C) 1 − ln 3 2 = (B) 0 (C) 1 2−c 2 ∫ 1 f ( x − c ) dx = 5 where c is a constant, then ∫ 1−c f ( x ) dx = (A) 5+c (B) 5 (C) 5−c AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) c − 5 35 1973 AP Calculus BC: Section I 39. Let f and g be differentiable functions such that f (1) = 2 , f ′(1) = 3 , f ′(2) = −4 , g (1) = 2 , g ′(1) = −3 , g ′(2) = 5. If h( x) = f ( g ( x) ) , then h′(1) = (A) –9 (B) –4 (C) 0 (D) 12 (E) 15 40. The area of the region enclosed by the polar curve r = 1 − cos θ is (A) 3 π 4 (B) π (C) ⎧ x + 1 for x < 0, 41. Given f ( x) = ⎨ ⎩cos π x for x ≥ 0, (A) 11 + 2π (B) − 1 2 3 π 2 (D) 2π (E) 3π (D) 1 2 (E) 1 − +π 2 1 ∫ −1 f ( x) dx = (C) 11 − 2π 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 AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 127 54 (E) 77 27 36 1973 AP Calculus BC: Section I 43. ∫ arcsin x dx = x dx (A) sin x − ∫ (B) ( arcsin x )2 + C (C) arcsin x + ∫ (D) x arccos x − ∫ (E) x arcsin x − ∫ 1 − x2 2 dx 1 − x2 x dx 1 − x2 x dx 1 − x2 () 44. If f is the solution of x f ′( x) − f ( x) = x such that f (−1) = 1, then f e −1 = (A) −2e −1 (B) 0 e −1 C) (D) −e−1 (E) 2e −2 x 45. Suppose g ′( x) < 0 for all x ≥ 0 and F ( x) = ∫ t g ′(t ) dt for all x ≥ 0 . Which of the following 0 statements is FALSE? (A) F takes on negative values. (B) F is continuous for all x > 0. (C) F ( x) = x g ( x) − ∫ (D) F ′( x) exists for all x > 0. (E) F is an increasing function. x 0 g (t ) dt AP Calculus Multiple-Choice Question Collection Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 37 1985 AP Calculus AB: Section I 90 Minutes—No Calculator Notes: (1) In this examination, ln x denotes the natural logarithm of x (that is, logarithm to the base e). (2) 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. 2 ∫1 x −3 dx = − (A) 2. 7 8 (C) 15 64 (D) If y = If (B) 24 3 4+ x 2 (E) 15 16 ( 4 + x2 ) 2 48 (D) 240 (E) 384 dy = dx , then −6 x (C) (B) 3x ( 4 + x2 ) 2 (C) 6x ( 4 + x2 ) 2 (D) −3 ( 4 + x2 ) 2 (E) 3 2x dy = cos ( 2 x ) , the...
View Full Document

Ask a homework question - tutors are online