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```# 25
1. If π₯ + π₯ + π₯ = π₯ 2 , what are the possible values of x?
(A) 0 only
(B) 3 only
(C) 0 and 3 only
(D) β3 and 3 only
(E) β3, 0, and 3
2. If 52π₯+1 = 96, then x =
(A) 0.1417
(B) 0.4795
(C) 0.9180
(D) 1.2833
(E) 2.3360
3. Which of the following is an equation of a line that
has an x-intercept of 2?
1
(A) π¦ = 2 π₯ β 1
(B) π¦ = π₯ + 2
(C) π¦ = 2π₯ β 2
(D) π¦ = 2π₯
(E) π¦ = 2π₯ + 1
4. There were b boy and g girls in a classroom. After 10
girls left the room, the number of boys was twice the
number of girls. Which of the following equations
represents the relationship between b and g?
(A) π =
(B) π
(C) π
(D) π
(E) π
πβ20
2
πβ10
= 2
= 2(π β 10)
= 2π β 10
= 2π
1
# 25
5. If π₯ = β2 + β2, then (π₯ 2 β2)2=
(A) 16
(B) 8
(C) 4
(D) 2
(E) 1
6. The radius of a machine shaft is specified to be 0.75
inch, but errors up to and including 0.001 inch are
allowed. The allowable values for the radius r of the
shaft can be described by which of the following?
(A) r β€ 0.751
(B) 0.749 β€ r β€ 0.75
(C) 0.741 β€ r β€ 0.751
(D) 0.749 β€ r β€ 0.751
(E) 0.74 β€ r β€ 0.75
7.If π(π₯) =
π₯ 3 β7
π₯
, what is the product of f(3) and f(4)?
(A) 0.5
(B) 11.9
(C) 20.9
(D) 48
(E) 95
8. In the figure above, how many line segments are
there whose endpoints are any two of the five labeled
points?
(A) 4
(B) 5
(C) 10
(D) 15
(E) 25
2
# 25
9. If 4π₯ β 8 = 2(2π₯ β π) for all x, then c =
(A) β4
(B) β2
(C) 2
(D) 4
(E) 8
10. If a > 0 and (π3 )2 = 123.1, then a =
(A) 0.8
(B) 1.0
(C) 1.7
(D) 2.2
(E) 2.6
11. What is the least positive even integer n for which
3n β 1 is NOT a prime?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 20
12. If π(π₯) = π₯ 3 β π₯ β π and if f(0) = β3, then k =
(A) β30
(B) β24
(C) β3
(D) 0
(E) 3
1, 3, 4.6, 6.5, 9.2, 7.4, 6, 11.4
13. What number must be added to the list above so that
the mean of the new list is 6.5?
(A) 6.1
(B) 6.5
(C) 6.7
(D) 7.9
(E) 9.4
3
# 25
14. If π(π₯) = π₯ 2 + 1 and π(π₯) = π₯ 3 + 1,
then π(π(π₯)) =
(A) π₯ 6 + 1
(B) π₯ 6 + 2π₯ 3 + 2
(C) π₯ 6 + 3π₯ 4 + 3π₯ 2 + 2
(D) π₯ 5 + π₯ 3 + π₯ 2 + 1
(E) π₯ 3 + π₯ 2 + 2
1
15. A salesperson earns \$275 per week plus 5 2 percent
she sells. To the nearest dollar, how much must her
product sales total for her to earn \$500 per week?
(A) \$4,091
(B) \$4,263
(C) \$8,816
(D) \$9,366
(E) \$14,091
16. The cube shown above has edges of length 7. What
is the perimeter of triangle ACF?
(A) 26.8
(B) 29.7
(C) 33.8
(D) 42.4
(E) 49.0
4
# 25
17. If π₯ > 0, what does π₯ π₯ approach as x approaches 0?
(A) 0
(B) 0.5
(C) 0.8
(D) 1
(E) e
18. In β³ π΄π΅πΆ, the measure of β A is 50º, and the
measure of β C is 30º. If AB = 10.2, what is the length
of side BC?
(A) 6.7
(B) 7.6
(C) 15.6
(D) 17.0
(E) 20.1
19. Line segment AB shown above is extended beyond
point B to a point C (not shown). If AB:BC = 1:2, what
are the coordinates of point C?
(A) (6,8)
(B) (6,9)
(C) (8,12)
(D) (8,18)
(E) (12,18)
5
# 25
20. If ππ = π(π + 1)(π + 2), which of the following
statements must be true for all positive integers n?
I. ππ is divisible by 2
II. ππ is divisible by 3
III. ππ is divisible by 4
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
21. If π¦ = ππ₯ + 3 and π¦ = ππ₯ β 1 are equations of
perpendicular lines, then mp =
(A) β1
(B) 0
(C) 1
(D) π2
(E) π2
22. In the xy-plane, the point (0,0) is on the graph of
π¦ = π(π₯). Which of the following points must be on
the graph of π¦ = π(π₯ β 2) + 3 ?
(A) (2, β3)
(B) (2, 2)
(C) (2, 3)
(D) (β2, β3)
(E) (β2, 3)
23. If 2 + 3i is a zero of a polynomial function with real
coefficients, which of the following must be another
zero of the function?
(A) 3 β 2i
(B) 2 β 3i
(C) β2 + 3i
(D) β2 β 3i
(E) It cannot be determined from the information
given.
6
# 25
24. If x is an integer greater than 2, which of the
following CANNOT be an integer?
π₯
(A) π₯β1
(B)
(C)
(D)
(E)
π₯ 2 +5π₯+6
π₯
π₯ 2 β1
5
π₯ 2 +1
π₯+2
π₯3
π₯β2
25. On a test, 5 true-false questions are asked. If a
person taking the test knows nothing about the material
and guesses randomly at the answers, what is the
probability that this person will answer all 5 correctly?
(A)
(B)
(C)
(D)
(E)
1
20
1
25
1
32
1
50
1
120
26. In the xy-plane, what is the perimeter of an
equilateral triangle with one vertex at (0, 3) and a
second at (4, 0)?
(A) 9
(B) 12
(C) 15
(D) 21
(E) It cannot be determined from the information
given
7
# 25
27. Triangle OPR in the figure above is revolved about
the x-axis. What is the volume of the solid generated?
(A) 3.0
(B) 6.0
(C) 12.6
(D) 18.8
(E) 56.5
π‘
28. If π(π‘) = 2 cos π‘ and π(π‘) = sin 2, what is the slope
of the line joining (0, π(0)) and (π, π(π))?
2
(A) β π
1
(B) β π
(C) 0
1
(D) π
(E)
2
π
29. In the xy-plane, the points (2, 2) and (β2, β2) are
symmetric with respect to which of the following?
I.
II.
III.
The origin
The x-axis
The line y = βx
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
8
# 25
30. The scores for each of 5 people in a contest were
125, 125, 126, 128, and 131. For these 5 scores, which
of the following is true?
(A) Mode < median < mean
(B) Mode < mean < median
(C) Median < mode < mean
(D) Median < mean < mode
(E) Mean < median < mode
31. Which of the following degree measures is
approximately equal to a radian measure of 1.5?
(A) 0.026º
(B) 0.052º
(C) 21.5º
(D) 43.0º
(E) 85.9º
32. If 0 < x < y and a < 0, which of the following
inequalities are true?
I.
II.
III.
ax < ay
1
π¦
π
π₯
1
<π₯
π
<π¦
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
9
# 25
33. Which of the following is the equation of the circle
graphed in the figure above?
(A) (π₯ β 1)2 + (π¦ + 2)2
(B) (π₯ + 1)2 β (π¦ β 2)2
(C) (π₯ + 1)2 + (π¦ + 2)2
(D) (π₯ + 1)2 + (π¦ β 2)2
(E) (π₯ + 1)2 + (π¦ β 2)2
=4
=2
=4
=2
=4
1
34. If f(x) = sin x and g(x) has a period that is 2 that of
f(x), which of the following could be g(x)?
1
(A) 2 sin π₯
(B) sin 2π₯
π₯
(C) sin 2
(D) 2sin π₯
1
(E) sin(π₯ + 2)
10
# 25
35. The graph of f is shown above. If π(π₯) =
1
, for
π(π₯)
which of the following values of x in [β10, 10] could
π(π₯) = 0?
(A) β10
(B) 0
(C) 2
(D) 3
(E) 5
π
36. If sinπ = x 2 and 0 < π < 2 , then sin(2π) =
(A) 2π₯ 2
(B) 2π₯ 2 β1 β π₯ 4
(C) π₯ 2 β1 β π₯ 4
1
(D) 2
4
(E)
π₯ β1βπ₯
1
2π₯ 2 β1βπ₯ 4
11
# 25
37. If f is a function whose graph is shown above,
which of the following is the graph of the inverse of f?
(A)
(B)
(C)
(D)
(E)
12
# 25
38. If the domain of a function f is {1,2}, which of the
following CANNOT be the range of f?
(A) {1}
(B) {3}
(C) {1,2}
(D) {3,4}
(E) {1,2,3}
39. In the figure above, ππ΄ and ππ΅ are radii of the unit
circle with the center O. Which of the following
represents the length of chord AB?
(A) 2sin π
(B) sin (2π)
(C) cos (2π)
(D) 2cos (2π)
(E) 2
40. In a contest, each of n judges assigns a wholenumber score between 1 and 10, inclusive, to a
performer. The performerβs final score is the arithmetic
mean of the n ratings. If two performers have final
scores of exactly 5.4 and 6.0, respectively, what is the
least possible number of judges?
(A) 3
(B) 5
(C) 6
(D) 10
(E) 15
13
# 25
41. If ππ = 1.05ππβ1 and π1 = 100, what is π10 ?
(A) 148
(B) 155
(C) 163
(D) 1,103
(E) 1,258
42. What is the y-intercept of the line defined by the
parametric equations π₯(π‘) = β3π‘ + 7 and
π¦(π‘) = 2π‘ β 5?
(A) β5
7
(B) β 5
1
(C) β 2
1
(D) β 3
(E) 7
43. If a > 1 and b < 0, then
|π|β|ππ|
|π|β1
=
(A) β1
(B) 1
(C) βb
(D) b
π(π+1)
(E) πβ1
44. A car travels from point X to point Y at 60 miles per
hour (mph), and then back to point X along the same
route at 40 mph. Which of the following is true of the
carβs round trip?
(A) The distance traveled at 60 mph is greater than
the distance traveled at 40 mph.
(B) The car travels the same amount of time at 60
mph as at 40 mph.
(C) The car travels a longer time at 60 mph than at
40 mph.
(D) The average speed of the car is 50 mph.
(E) The average speed of the car is less than 50
mph.
14
# 25
45. What is the value of ln x when ln x = π βπ₯ ?
(A) 0
(B) 0.27
(C) 0.37
(D) 1.00
(E) 2.72
46. If n is an integer greater than 4, then
1
1 1
1
1
1 + (1 β ) + ( β ) + β― + (
β )=
2
2 3
πβ1 π
(A) 1 β
1
π
1
(B) 1 + π
1
(C) 2 + π
1
(D) 2 β π
1
(E) 2 + (πβ1)π
2
3
47. If the slope of line β is 5 and the slope of line m is 5,
what is the degree measure of the smaller angle formed
at the intersection of β and m?
(A) 9.16º
(B) 11.31º
(C) 13.29º
(D) 21.80º
(E) 30.96º
π(π₯+1)
48. If π(π₯) =
π(3) β π(1) =
2
and π(2) = 4, then
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
15
# 25
If t < 3x, then 0 < y < 4
49. If the above statement is true and y = 5, which of the
following statements must be true?
(A) t < 3x
(B) t β€ 3x
(C) t = 3x
(D) t > 3x
(E) t β₯ 3x
50. A laser operator is aiming a laser at the center of a
circular disk in space. The disk has a radius of 50 feet
and is situated 225 miles directly above the surface of
the Earth where the laser is located. If the operator
makes a 0.05º error in aiming the laser, by how many
feet will the laser beam miss the edge of the disk?
(5,280 feet = 1 mile)
(A) 937
(B) 987
(C) 1,012
(D) 1,037
(E) The laser beam will not miss the disk.
16
# 25
1. C
2. C
3. A
4. C
5. D
6. D
7. E
8. C
9. D
10.D
11.C
12.E
13.E
14.B
15.A
16.B
17.D
18.C
19.C
20.C
21.A
22.C
23.B
24.A
25.C
26.C
27.D
28.B
29.D
30.A
31.E
32.D
33.E
34.B
35.D
36.B
37.D
38.E
39.A
40.B
41.B
42.D
43.D
44.D
45.B
46.D
47.A
48.D
49.E
50.B
17
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