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Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 24 2 (E) 36 77 1993 AP Calculus AB: Section I
90 Minutes—Scientific Calculator 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 assumed to be the set of all real
numbers x for which f (x) is a real number.
1. If f ( x) = 3
x2 , then f ′(4) = (A) –6 2. (B) –3 3 (D) 6 (E) 8 Which of the following represents the area of the shaded region in the figure above?
d ∫c (D) (b − a ) [ f (b) − f (a) ] lim f ( y )dy 3n3 − 5n n→∞ n3 − 2n 2 + 1 (A) –5 b (B) (A) 3. (C) ∫ a ( d − f ( x) ) dx (E) (d − c) [ f (b) − f (a) ] (C) 1 (C) f ′(b) − f ′(a) is
(B) –2 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (D) 3 (E) nonexistent 78 1993 AP Calculus AB: Section I
4. If x3 + 3 xy + 2 y 3 = 17 , then in terms of x and y,
(A) − (B) − (C) − (D) − (E) 5. dy
=
dx x2 + y
x + 2 y2
x2 + y
x + y2 x2 + y
x + 2y
x2 + y
2 y2
− x2 1+ 2 y2 If the function f is continuous for all real numbers and if f ( x) =
then f (−2) =
(A) –4 6. (C) –1 The area of the region enclosed by the curve y = (A) 7. (B) –2 5
36 (B) ln 2
3 (C) ln (D) 0 (D) x + 13 y = 66 4
3 (D) ln 2 3
2 (E) ln 6 2x + 3
at the point (1,5 ) is
3x − 2 (B) 13x + y = 18
(E) (E) 1
, the xaxis, and the lines x = 3 and x = 4 is
x −1 An equation of the line tangent to the graph of y =
(A) 13 x − y = 8 x2 − 4
when x ≠ −2 ,
x+2 (C) x − 13 y = 64 −2 x + 3 y = 13 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 79 1993 AP Calculus AB: Section I
8. If y = tan x − cot x, then
(A) sec x csc x 9. dy
=
dx (B) sec x − csc x (C) sec x + csc x (D) sec2 x − csc2 x (E) sec2 x + csc2 x If h is the function given by h( x) = f ( g ( x)), where f ( x) = 3 x 2 − 1 and g ( x) = x , then h( x) =
(A) 3x3 − x (B) 3x 2 − 1 (C) (D) 3 x − 1 (E) 3x 2 − 1 (D) 1 3x 2 x − 1 (E) 2 10. If f ( x) = ( x − 1) 2 sin x, then f ′(0) =
(A) –2 (B) –1 (C) 0 11. The acceleration of a particle moving along the xaxis at time t is given by a (t ) = 6t − 2 . If the
velocity is 25 when t = 3 and the position is 10 when t = 1 , then the position x(t ) =
(A) 9t 2 + 1 (B) 3t 2 − 2t + 4 (C) t 3 − t 2 + 4t + 6 (D) t 3 − t 2 + 9t − 20 (E) 36t 3 − 4t 2 − 77t + 55 12. If f and g are continuous functions, and if f ( x) ≥ 0 for all real numbers x , which of the
following must be true?
I. II. III. b ∫a b
b
f ( x) g ( x)dx = ⎛ ∫ f ( x)dx ⎞ ⎛ ∫ g ( x)dx ⎞
⎜a
⎟⎜ a
⎟
⎝
⎠⎝
⎠ b b ∫ a ( f ( x) + g ( x) ) dx = ∫ a
b ∫a f ( x) dx = (A) I only b ∫a b f ( x)dx + ∫ g ( x)dx
a f ( x)dx (B) II only (C) III only (D) II and III only AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. (E) I, II, and III
80 1993 AP Calculus AB: Section I
13. The fundamental period of 2 cos(3x) is
(A) 14. ∫ 2π
3
3x 2
x3 + 1 (B) 2π (C) 6π (D) 2 (E) 3 dx = (A) 2 x3 + 1 + C (B) 33
x +1 + C
2 (C) x3 + 1 + C (D) ln x3 + 1 + C (E) ln( x3 + 1) + C 15. For what value of x does the function f ( x) = ( x − 2)( x − 3) 2 have a relative maximum?
(A) –3 (B) − 7
3 (C) − 5
2 (D) 16. The slope of the line normal to the graph of y = 2 ln(sec x) at x =
(A) 7
3 (E) 5
2 π
is
4 −2 (B) − 1
2 (C) 1
2 (D) 2 (E) nonexistent AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 81 1993 AP Calculus AB: Section I
17. ∫ (x 2 + 1) 2 dx = (A) ( x 2 + 1)3
+C
3 (B) ( x 2 + 1)3
+C
6x (C) ⎛ x3
⎞
⎜ + x⎟ + C
⎜3
⎟
⎝
⎠ (D) 2 x( x 2 + 1)3
+C
3 (E) x5 2 x3
+
+ x+C
5
3 2 π
3π
⎛ x⎞
that satisfies the
18. If f ( x) = sin ⎜ ⎟ , then there exists a number c in the interval < x <
2
2
⎝2⎠
conclusion of the Mean Value Theorem. Which of the following could be c ?
(A) 2π
3 (B) 3π
4 (C) ⎧
⎪ x3
19. Let f be the function defined by f ( x) = ⎨
⎪x
⎩
about f is true?
(A) 3π
2 for x ≤ 0,
Which of the following statements
for x > 0. f ′(0) = 0 (E) (E) f has a relative maximum. (D) π f is discontinuous at x = 0 . (C) (D) f is an odd function. (B) 5π
6 f ′( x) > 0 for x ≠ 0 AP Calculus MultipleChoice Question Collection
Copyright © 2005 by College Board. All rights reserved. Available at apcentral.collegeboard.com. 82 1993 AP Calculus AB: Section I
1
= ( x + 1) 3 20. Let R be the region in the first quadrant enclosed by the graph of y
, the line x = 7 ,
the xaxis, and the yaxis. The volume of the solid generated when R is revolv...
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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.
 Fall '10
 smith
 Calculus

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