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(A)
(B)
(C) 200 + t
(D) 200 – 2t
(E) 2t – 100
8. In the above figure, if AC is a diameter of the
circle, B is a point on the circle, and sin 
θ = 1/2,
then sin 
φ =
(A)
(B)
(C)
(D)
(E)
9. If an equilateral triangle is rotated 360
° around
one of its altitudes, the resulting solid is a
(A) cone
(B) cube
(C) cylinder
(D) sphere
(E) right prism
10. How many integers are in the solution set of
|3x – 2| < 1?
(A) None
(B) One
(C) Two
(D) Three
(E) Infinitely many
11. If f(x,y) = x
2
– xy + y
2
, for all real numbers,
then which of the following must be true?
(A) f(x,y) = f(x,–y)
(B) f(x,y) = f(–x,y)
(C) f(x,y) = f(–x, –y)
(D) f(x,y) = f(x,1/y)
(E) f(x,y) = f(x, –1/y)
12. If 
, for what value of x is
f(x) undefined?
(A) –4
(B) –2
(C) 0
(D) 2
(E) 4
13. An angle measure of 45
° is equivalent to an
angle measure of
(A)
1
4
radians
(B)
1
π
radians
(C)
π
4
radians
(D)
π
2
radians
(E)
π radians
14. If cos x = 0.2586 and 0 < x < 
π
2
, what is the
value of x?
(A) 8.254
(B) 1.309
(C) 0.999
(D) 0.688
(E) 0.005
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15. If log
3
2 = x, then x =
(A) 0.27
(B) 0.63
(C) 0.89
(D) 1.2
(E) 1.7
16. If f(x) = 3x – 6, and if g(f(x)) = x, then g(x) =
(A)
(B)
(C) 6 – 3x
(D)  
(E)  
17. Where defined, 
(A) sin x
(B) cos x
(C) tan x
(D) sin x csc x
(E)
18. What is the area of a right triangle with an
angle of 58
° and with a shorter leg of 5?
(A) 8
(B) 15
(C) 20
(D) 27
(E) 33
19. The diameter and the height of a right circular
cylinder are equal. If the volume of the cylin-
der is 6, what is the height of the cylinder?
(A) 1.5
(B) 2.0
(C) 2.2
(D) 2.5
(E) 2.8
20. If x
1/4
= 20, then x =
(A)
(B) 5
(C) 80
(D) 2,000
(E) 160,000
21. In the coordinate plane, the graph of which of
the following lines is perpendicular to the
graph of line 
(A)
(B)
(C)
(D)
(E)
22. If 
, then x =
(A) 6
(B) 9
(C) 12
(D) 15
(E) 16
23. If the probability that an event, e, will occur is
represented by the expression 
, then which
of the following expressions represents the
probability that event e will not occur?
(A)
(B)
(C)
(D) x + 1
(E) x – 1

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24. A student’s final grade in a certain course is
the average of his scores on ten tests graded
on a scale of 0 to 100, inclusive. For the first
six tests, the student’s scores averaged 83. If x
is the student’s final grade for the course, then
which of the following is true?
(A) 8.3 
≤ x ≤ 83.0
(B) 49.8 
≤ x ≤ 83.0
(C) 49.8 
≤ x ≤ 89.8
(D) 54.7 
≤ x ≤ 89.8
(E) 83.0 
≤ x ≤ 89.8
25. Which of the following represents the multi-
plicative inverse of the complex number 2 – i?
(A) 2 + i
(B) i – 2
(C)
(D)
(E)
26.
(A) –1
(B)
(C)
(D)
(E) 2
27. If 
, what is f 
–1
(2.5)?
(A) 0.4
(B) 0.9
(C) 1.3
(D) 1.7
(E) 2.3
28. If 
, then which of the following must
be true?
I.
sin x < cos x
II. tan x < cot x
III. sec x < cos x
(A) I only
(B) II only
(C) III only
(D) I, II, and III
(E) None
29. In the above figure, if Arcsin s = 2 Arcsin d,
then x =
(A) 15
°
(B) 30
°
(C) 45
°
(D) 60
°
(E) 75
°
30. If, for all n, 2
n
+ 2 
n
+ 2 
n
+ 2 
n
= x(2 
n+1
), then x =
(A) 2
(B) 4
(C) 2 
n
(D) 2 
2n
(E) 2 
n+1
31. If i 
x
= 1, then x could equal
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
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32. The formula for the area enclosed by an
ellipse is A = 
πab, where a and b are one–half
the lengths of the major and minor axes,
respectively. In the figure above, the equation
of the circle is x 
2
+ y 
2
= 12, then what is the
area enclosed by the ellipse?
(A) 62
(B) 87
(C) 103
(D) 117
(E) 131
33. The above figure is a possible graph for which
of the following equations?
(A) y = 2 sin x
(B) y = sin x + 2
(C) y = csc x + 1
(D) y = csc x – 1
(E) y = sec x + 1
34. What is 
?
(A) –1
(B) 0
(C) 1
(D) 2
(E) The limit does not exist.
35. If 0 
≤ x ≤ π and cos x = –1, then cos =
(A)
(B)  
(C) 0
(D)
(E)
36. Which of the following defines the range of
the function 
?
(A) All real numbers
(B) All real numbers except –1
(C) All real numbers except 0
(D) All real numbers except 1
(E) All real numbers greater than –1

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37. Which of the following figures represents the
graph of
x = 3 sin 
θ
y = 2 cos 
θ
(A)
(B)
(C)
(D)
(E)
38. If 5
x
= 2, what does 3
x
equal?
(A) 2.8
(B) 2.3
(C) 2.1
(D) 1.9
(E) 1.6
39. If 4 cos x = sin x and if x is in radian measure,
what is the least positive value of x?
(A) 6.452
(B) 2.133
(C) 1.326
(D) 1.021
(E) 0.933
40. Triangle ABC has coordinates A(–1, –2),
B(0,4), and C(3, –1). Which of the following
provides the coordinates of triangle A’B’C’,
respectively, the image of triangle ABC after
a reflection in the line y = –x?
(A) (–2, –1), (4,0), (–3, –1)
(B) (1,2), (0, –4), (–3,1)
(C) (2,1), (–4,0), (1, –3)
(D) (3,2), (5,1), (2, –2)
(E) (4,0), (3, –1), (–1, –2)
41. If sin x = cos x, then x could terminate only in
the
(A) first quadrant
(B) second quadrant
(C) first or third quadrants
(D) second or third quadrants
(E) second or fourth quadrants
42. If the line x = k is tangent to the circle
(x – 2) 
2
+ (y + 1) 
2
= 4, then the point of tan-
gency is
(A) (–6, –1) or (2, –1)
(B) (–2, –1) or (6, –1)
(C) (0, –1) or (4, –1)
(D) (0,1) or (4,1)
(E) (2,1) or (6,1)
43. The graph of y = 2 cos 2x + 2 intersects the y–
axis where y =
(A) 0
(B) 2
(C) 3
(D) 4
(E) 5
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44. What is the last term in the expansion
(2x + 3y)
4
?
(A) y
4
(B) 9y
4
(C) 27y
4
(D) 81y
4
(E) (xy)
4
45. If two unbiased dice are rolled, what is the
probability that the number of dots on the two
exposed faces will total 4?
(A)
(B)
(C)
(D)
(E)
46. Which of the following could be a graph of the
equation y = ax
2
+ bx + c, where b
2
– 4ac = 0?
(A)
(B)
(C)
(D)
(E)

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47. A plane cuts through a cube in such a way that
the plane passes through three of the cube’s
vertices, no two of which lie on the same edge.
If the edge of the cube has a length of 1, what
is the surface area of the smaller fragment of
the cube?
(A) 2.4
(B) 2.7
(C) 3.1
(D) 3.7
(E) 4.3
48. Which of the following equations describes a
parabola with focus (2,3) and directrix y = 0?
(A) (x + 2)
2
+ (y + 3)
2
= 2
(B) (x – 2)
2
+ (y – 3)
2
= 4
(C) (x – 2)
2
= – (y – 3)
2
(D) (x – 2)
2
= 2(y + 3)
(E) (x – 2)
2
= 3(2y – 3)
49. A student taking a true–false test guesses ran-
domly on three items. What is the probability
that exactly two of the guesses will be cor-
rect?
(A)
1
16
(B)
1
8
(C)
1
4
(D)
3
8
(E)
1
2
50. (1) Given any individual x, if x is a C, then x is
also a Q.
(2) There exists at least one individual x such
that x is not a Q.
Which of the following conclusions can be
logically deduced from the two statements
above?
(A) There exists at least one x such that x is
not a C.