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(A) (5,0)
(B) (5,1)
(C) (4,2)
(D) (4,3)
(E) (3,4)
Figure 2
10. If 4 < x < 12 and 6 < y < 8, then which of the
following must be true?
(A)
(B) 2 < xy < 4
(C) 6 < xy < 12
(D) 24 < xy < 96
(E) 32 < xy < 72
11. In Figure 3, three equilateral triangles have a
common vertex. x + y + z =
(A) 270
(B) 180
(C) 120
(D) 90
(E) 60
Figure 3
12. If the operation 
φ is defined for all real num-
bers x and y by the equation x 
φ y = xy – y – x,
then –2 
φ – 1 =
(A) –3
(B) –2
(C) 1
(D) 3
(E) 5
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13. In Figure 4, if the circle has a radius of 3, what
is the length of minor arc PR?
(A)
(B)
(C)
π
(D)
(E) 3
π
Figure 4
14. What is the slope of the line perpendicular to
the line whose equation is
?
(A) 1.41
(B) 1.18
(C) .85
(D) .53
(E) .21
15. The number (73)
36
has how many digits when
multiplied out?
(A) 12
(B) 36
(C) 37
(D) 67
(E) 68
16. What is the least positive integer x for which
12 – x and 15 – x will be non–zero and have
opposite signs?
(A) 3
(B) 4
(C) 7
(D) 11
(E) 13
17. The solution set to the pair of equations:
mx + ny = 15
nx + my = 13
is x = 3 and y = 1. What are the values of m
and n?
(A) m = 5
n = 3
(B) m = 4
n = 3
(C) m = 3
n = 4
(D) m = 3
n = 5
(E) m = 2
n = 6
18. The lengths of the sides of quadrilateral Q are
all integers. If three of the sides have lengths
of 3, 4, and 5, then the maximum length of the
fourth side is
(A) 13
(B) 12
(C) 11
(D) 7
(E) 2
19. In Figure 5, if ABD is a right isosceles triangle,
then x =
(A) 25
(B) 30
(C)
(D) 45
(E) 60
Figure 5

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20. If xyz 
≠ 0, then 
(A) 4xyz
(B)
(C)
(D)
(E)
21. If f(x) = –x
2
– 3 and g(x) = 3 – x
2
, what is the
value of f(f(g(7)))?
(A) –46
(B) –2119
(C) –73207
(D) –4490164
(E) –7295398
22. A polygon Q with a certain perimeter P will
have its greatest area when all of its sides have
the same length. What is the maximum area
of a rectangle with a perimeter of P units?
(A)
(B)
(C) P
2
(D) 2P
2
(E) 4P
2
23. Which of the following graphs is NOT the
graph of a function?
(A)
(B)
(C)
(D)
(E)
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24. In the figure above, if sin
, then JL =
(A) 26.83
(B) 13.42
(C) 6.71
(D) 1.12
(E) 0.37
25. An equation for the circle with its center at the
origin and passing through the point (1,2) is
(A)
(B) x
2
+ y
2
= 3
(C) x
2
+ y
2
= 5
(D) x
2
+ y
2
= 9
(E) x
2
+ y
2
= 25
26. How many integers are in the solution set of
|1 – 3x| < 5?
(A) None
(B) One
(C) Two
(D) Three
(E) Infinitely many
27. If x, y, and z are positive integers such that
4x + 6y = z, then z must be divisible by
(A) 2
(B) 4
(C) 6
(D) 10
(E) 24
28. If the points (–2,4), (3,4), and (3, –2) are
connected to form a triangle, the area of the
triangle is
(A)
(B) 6
(C) 12
(D) 15
(E) 24
29. If i
2
= –1 and if k = 2 + i, then k
2
=
(A) 1
(B) 3 + 4i
(C) 4 + 3i
(D) 6 + 7i
(E) 9 + 12i
30. If a line contains the points (–2, 1) and (4,4),
then the x–intercept is
(A) –4
(B)
(C) 0
(D)
(E)
31. In Figure 7, if the radius of the circle is r, then
the ratio 
=
(A)
(B)
(C)
(D)
(E)
Figure 7
32. f(
θ) = sin
2
4 
θ + cos
2
4 
θ, find f(72°)
(A) –.71
(B) –.22
(C) 1.0
(D) 1.26
(E) 4.0

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33. If f(x) = 3x – 2 and g(f(x)) = x, then g(x) =
(A) 3x + 2
(B) 2 – 3x
(C)
(D)
(E)
34. In Figure 8, if AC // GE and GF = x and FE = y,
then the ratio 
=
(A)
(B)
(C)
(D)
(E)
Figure 8
35. If 
, then c =
(A)
(B) ab
(C)
(D)
(E)
36. If x
3
y
2
z < 0, then it must be true that
(A) x
3
< 0
(B) z < 0
(C) xy < 0
(D) xz < 0
(E) yz < 0
37. If the slope of a line is 3 and the y–intercept is
2, then the x–intercept of the line is
(A)
(B)
(C) –1
(D)
(E)
38. For the right triangle in Figure 9, all of the
following statements are true EXCEPT:
(A) sin 
θ 
(B) tan 
σ 
(C) cos 
θ
(D) sin 
θ = cos σ
(E) cot 
σ = tan θ
Figure 9
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39. Three candidates for president of the Student
Council—Ashley, José, and Kim—must each
be scheduled for a single 10–minute address
to the entire student body. If the order of the
presentations is determined randomly, how
many different orders are possible?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 27
40. If x 
≠ 0 then
=
(A) 2
2x
(B) 4
–x
(C) 4
2x
(D) 4
1–x
(E) 8
–x
All S are M.
No P are M.
41. Which of the following conclusions can be
logically deduced from the two statements
above?
(A) All S are P.
(B) All M are S.
(C) Some S are not M.
(D) Some M are P.
(E) No P are S.
42. Cube Q has volume V. In terms of V, a cube
with edges only one–fourth the length of those
of Q will have a volume of
(A)
(B)
(C)
(D)
(E)
43. If 
θ is an acute angle and cos θ = , b > 0 and
c > 0 and b
≠ c, then sin θ =
(A)
(B)
(C)
(D)
(E)
44. If a cube has an edge of length 2, what is
the distance from any vertex to the center of
the cube?
(A)
(B)
(C)
(D)
(E)
45. If x
2
+ ax + bx + ab = 0, and x + b = 2, then
x + a =
(A) –8
(B) –4
(C) –2
(D) 0
(E) 2

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46. Figure 10 shows two right circular cylinders,
C and C
′. If r = kr′ and h = kh′, then what is
the ratio of: 
?
(A)
(B)
π
(C) k
π
(D)
(E) k
3
Figure 10
47. If the circumference of a circle is 1, what is its
area?
(A) .08
(B) .79
(C) 1.27
(D) 3.14
(E) 6.28
48. What are the coordinates of the point of in-
tersection of the lines having the following
equations:
(A)
(B)
(C)
(D)
(E)
49. In Figure 12, the radius of the circles is 1.
What is the perimeter of the shaded part of
the figure?
(A)
(B)
π
(C)
(D)
(E)
Figure 12
50. If 
, for what value of x is
f(x) undefined?
(A) –4
(B) –2
(C) 0
(D)
(E) 2
STOP
IF YOU FINISH BEFORE TIME IS CALLED,
YOU MAY CHECK YOUR WORK ON THIS
TEST ONLY. DO NOT WORK ON ANY
OTHER TEST IN THIS BOOK.

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ANSWER KEY
1.
D
2.
B
3.
D
4.
E
5.
B
6.
C
7.
D
8.
D
9.
E
10.
D
11.
B
12.
E
13.
C
14.
C
15.
E
16.
E
17.
B
18.
C
19.
A
20.
E
21.
D
22.
A
23.
A
24.
B
25.
C
26.
D
27.
A
28.
D
29.
B
30.
A
31.
B
32.
C
33.
E
34.
D
35.
D
36.
D
37.
B
38.
C
39.
B
40.
A
41.
E
42.
C
43.
E
44.
B
45.
D
46.
E
47.
A
48.
E
49.
A