194 PRACTICE TEST 3 MATHEMATICS TEST

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MATHEMATICS TEST
60 Minutes—60 Questions

DIRECTIONS: Solve each of the problems in the time You may use a calculator on this test. For this test
allowed, then fill in the corresponding bubble on your you should assume that figures are NOT necessarily
answer sheet. Do not spend too much time on any one drawn to scale, that all geometric figures lie in a plane,
problem; skip the more difficult problems and go back and that the word line is used to indicate a straight
to them later. line.

1. The minimum fine for driving in excess of the speed DO YOUR FIGURING HERE.
limit is $25. An additional $6 is added to the minimum
fine for each mile per hour (mph) in excess of the speed
limit. Rachel was issued a $103 fine for speeding in a
55-mph speed limit zone. For driving at what speed, in
mph, was Rachel fined?
A. 48
B. 52
C. 62
D. 68
E. 78
2. 5x 3 × 2xy × 3xy2 is equivalent to:
F. 10x 3 y2
G. 10x 5 y3
H. 30x 3 y3
J. 30x 5 y3
K. 30x 5 y2
3. What is the fourth term in the arithmetic sequence
13, 10, 7, …?
A. 14
B. 9
C. 4
D. 0
E. −7
4. When written in symbols, “the product of r and s, raised
to the fourth power,” is represented as:
F. r 4 s4
G. (r + s)4
H. (rs)4
r4
J.
s4
K. rs4

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PRACTICE TEST 3 MATHEMATICS TEST 195

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5. Which of the following numbers has the digit 5 in the DO YOUR FIGURING HERE.
thousandths place?
A. 5,000.00
B. 50.0
C. 0.05
D. 0.005
E. 0.0005
6. Mandy and Jordan each bought some of the same note-
books and the same three-ring binder. Mandy paid $5.85
for 3 notebooks and 1 binder. Jordan paid $4.65 for
2 notebooks and 1 binder. What is the price of one of
the notebooks?
F. $2.70
G. $2.25
H. $1.80
J. $1.20
K. $0.75
7. If mn = k and k = x 2 n, and nk ,= 0, which of the
following is equal to m?
A. 1
B. 1/x
√
C. x
D. x
E. x 2

8. If 7x + 5 = 2x + 9, then x = ?
4
F.
5
4
G. 1
5
4
H.
9
4
J. 1
9
K. 2
9. What percent of 5 is 7?
A. 14%
B. 35%
C. 71%
D. 140%
E. 157%

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196 PRACTICE TEST 3 MATHEMATICS TEST

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10. If x is a positive real number such that x 2 = 16, then
√
DO YOUR FIGURING HERE.
x3 + x = ?
F. 18
G. 20
H. 66
J. 68
K. 74
11. −|−16| − (−16) = ?
A. −16
B. 0
C. 4
D. 16
E. 32

12. A partial deck of cards was found sitting out on a table.

If the partial deck consists of 6 spades, 3 hearts, and
7 diamonds, what is the probability of randomly select-
ing a red card from this partial deck? (Note: diamonds
and hearts are considered “red,” while spades and clubs
are considered “black.”)
9
F.
16
13
G.
16
7
H.
16
3
J.
8
5
K.
8
13. Which of the following is a simplified form of
4x − 4y + 3x?
A. x(7 − 4y)
B. x − y + 3x
C. −8xy + 3x
D. 7x − 4y
E. −4y − x

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PRACTICE TEST 3 MATHEMATICS TEST 197

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14. Gary has turtles, cats, and birds for pets. The number DO YOUR FIGURING HERE.
of birds he has is 4 more than the number of turtles,
and the number of cats is 2 times the number of birds.
Of the following, which could be the total number of
Gary’s pets?
F. 14
G. 18
H. 20
J. 22
K. 26
15. On a map, 1/4 inch represents 12 miles. If a road is
66 miles long, what is its length, in inches, on the map?
A. 5 1/2
B. 5 1/8
C. 1 1/2
D. 1 3/8
E. 7/8
16. If b = a − 4, then (a − b)3 = ?
F. 64
G. 16
H. −4
J. −16
K. −64
17. If g is an integer, which of the following could NOT
equal g2 ?
A. 0
B. 1
C. 4
D. 8
E. 9
18. Justin owns 6 different dress shirts, 3 different pairs of
pants, and 5 different ties. How many distinct outfits,
each consisting of a shirt, a pair of pants, and a tie,
can Justin make?
F. 14
G. 42
H. 90
J. 120
K. 144
19. An oil refinery produces gasoline from crude oil. For
every 10,000 barrels of crude oil supplied, the refinery
can produce 6,500 barrels of gasoline. How many bar-
rels of gasoline can be produced from 3,500 barrels of
crude oil?
A. 1,265
B. 1,750
C. 2,125
D. 2,275
E. 5,385

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198 PRACTICE TEST 3 MATHEMATICS TEST

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20. What is the slope of a line that passes through the origin DO YOUR FIGURING HERE.
and the point (−6, 2) ?
F. 3
G. 1/3
H. −1/3
J. −3
K. −6
21. If nx · n8 = n24 and (n6 )y = n18 , what is the value of
x + y?
A. 7
B. 9
C. 12
D. 19
E. 27
22. What is the slope-intercept form of 9x + 3y − 6 = 0?
F. y = 9x − 6
G. y = 3x + 2
H. y = 3x − 2
J. y = −3x + 2
K. y = −9x + 6
23. If the volume of a cube is 64, what is the shortest dis-
tance from the center of the cube to the base of the
cube?
A. 2
B. 4√
C. √2 4
D. 32
E. 16
24. For the right triangle !ABC shown below, what is
sin C?

a
F.
b
a
G.
c
b
H.
a
c
J.
b
c
K.
a

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PRACTICE TEST 3 MATHEMATICS TEST 199

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25. What is the area, in coordinate units, of the triangle in DO YOUR FIGURING HERE.
the figure below?
y

(0,4)

x
(5,0)

A. 4.5
B. 9.0
C. 10.0
D. 12.5
E. 20.0
26. A shoe store charges $39 for a certain type of sneaker.
This price is 30% more than the amount it costs the shoe
store to buy one pair of these sneakers. At an end-of-the-
year sale, sales associates can purchase any remaining
sneakers at 20% off the shoe store’s cost. How much
would it cost an employee to purchase a pair of sneakers
of this type during the sale (excluding sales tax)?
F. $31.20
G. $25.00
H. $24.00
J. $21.84
K. $19.50
27. After excavating a lot, workers removed an estimated
7,000 cubic yards of dirt from the area. If this dirt were
spread in an even layer over an empty lot with dimen-
sions 30 yards by 64 yards, about how deep, in yards,
would the layer of dirt be?
A. Less than 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
E. More than 4

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200 PRACTICE TEST 3 MATHEMATICS TEST

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28. The hypotenuse of the right triangle !ABC shown below DO YOUR FIGURING HERE.
3
is 17 feet long. The cosine of angle C is . How many
5
feet long is the segment AC?

F. 6
G. 10.2
H. 12
J. 15
K. 28.3
29. When the choir is arranged in rows of 5 people each, the
last row is one person short. When the choir is arranged
in rows of 6 people each, the last row is still one person
short. What is the least possible number of people in the
choir?
A. 29
B. 30
C. 56
D. 60
E. 99
30. What is the y-coordinate of the point in the standard
x
(x,y) coordinate plane at which the 2 lines y = + 3
2
and y = 3x − 2 intersect?
F. 5
G. 4
H. 3
J. 2
K. 1
31. Points B and C lie on segment AD as shown below.
Segment AD is 32 units long, segment AC is 23 units
long, and segment BD is 27 units long. How many units
long, if it can be determined, is segment BC?

A. 21
B. 18
C. 9
D. 4
E. Cannot be determined from the given information.

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PRACTICE TEST 3 MATHEMATICS TEST 201

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32. For all pairs of real numbers M and N where DO YOUR FIGURING HERE.
M = 6N + 5, N = ?
M
F. −5
6
M
G. +6
5
H. 6M + 5
M −5
J.
6
M +5
K.
6
33. In√the figure below, the perimeter of the triangle is 12 +
4 3 inches. What is the value of x, in inches?

A. 2
B. 4
C. 6
D. 8
E. 12
34. In the figure below, XY = YZ. If a = 40◦ , than XY =?

F. 9.50
G. 8.75
H. 7.75
J. 6.25
K. 5.50

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202 PRACTICE TEST 3 MATHEMATICS TEST

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35. In the (x, y) coordinate plane, what is the y-intercept of DO YOUR FIGURING HERE.
the line −9x − 3y = 15?
A. −9
B. −5
C. −3
D. 3
E. 15
36. The product of two integers is between 137 and 149.
Which of the following CANNOT be one of the inte-
gers?
F. 15
G. 13
H. 11
J. 10
K. 7
37. When x is divided by 7, the remainder is 4. What is the
remainder when 2x is divided by 7?
A. 1
B. 4
C. 5
D. 7
E. 8
38. A circle is circumscribed within a square with sides of
12 feet, as shown below. What is the area of the circle,
to the nearest square foot?

F. 144
G. 113
H. 72
J. 12π
K. 3π
39. The average of 7 consecutive numbers is 16. What is
the sum of the least and greatest of the 7 integers?
A. 13
B. 14
C. 16
D. 19
E. 32

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PRACTICE TEST 3 MATHEMATICS TEST 203

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40. In the figure below, ABCD is a trapezoid. Point E lies DO YOUR FIGURING HERE.
on line AD, and angle measures are as marked. What is
the measure of angle BDC?

F. 25◦
G. 30◦
H. 45◦
J. 55◦
K. 100◦

41. For which of the following functions is f (−5) > f (5)?

A. f (x) = 6x 2
B. f (x) = 6
C. f (x) = 6/x
D. f (x) = 6 − x 3
E. f (x) = x 6 + 6

42. For what value of n would the following system of

equations have an infinite number of solutions?
3a + b = 12
12a + 4b = 3n
F. 4
G. 9
H. 16
J. 36
K. 48
43. If x and y are positive integers such that the greatest
common factor of x 2 y2 and xy3 is 27, then which of the
following could y equal?
A. 81
B. 27
C. 18
D. 9
E. 3

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204 PRACTICE TEST 3 MATHEMATICS TEST

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44. What is the smallest possible integer for which 15% of DO YOUR FIGURING HERE.
that integer is greater than 2.3?
F. 3
G. 12
H. 15
J. 16
K. 18
45. What is the distance in the standard (x,y) coordinate
plane
√ between the points (0,1) and (4,4)?
A. 7
B. 3
C. 4
D. √
5
E. 27
46. The sides of a triangle are 9, 12, and 15 centimeters
long. What is the angle between the 2 shortest sides?
F. 180◦
G. 90◦
H. 60◦
J. 45◦
K. 30◦
47. In the pentagon, shown below, one interior angle
measures 40◦ . What is the total measure of the other
4 interior angles?

A. 120◦
B. 160◦
C. 320◦
D. 500◦
E. 680◦
48. For real numbers r and s, when is the equation |r − s| =
|r + s| true?
F. Always
G. Only when r = s
H. Only when r = 0 or s = 0
J. Only when r > 0 and s < 0
K. Never

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PRACTICE TEST 3 MATHEMATICS TEST 205

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49. What is the value of log4 64? DO YOUR FIGURING HERE.
A. 3
B. 4
C. 8
D. 10
E. 16
50. How many different positive three-digit integers can be
formed if the three digits 3, 4, and 5 must be used in
each of the integers?
F. 6
G. 8
H. 12
J. 15
K. 24
51. Which of the following is the set of all real numbers x
such that x − 3 < x − 5?
A. The empty set
B. The set containing only zero
C. The set containing all nonnegative real numbers
D. The set containing all negative real numbers
E. The set containing all real numbers
52. What is the slope of a line that is perpendicular to the
line determined by the equation 7x + 4y = 11?
F. −4
7
G. −
4
11
H.
4
J. 4
4
K.
7
53. If each element in a data set is multiplied by 3, and
each resulting product is then reduced by 4, which of
the following expressions gives the mean of the resulting
data set in terms of x?
A. x
B. 3x − 4
4
C. x +
3
x
D. + 4
3
4
E. x +
3

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206 PRACTICE TEST 3 MATHEMATICS TEST

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3 π DO YOUR FIGURING HERE.
54. If cos θ = − and < θ < π, then tan θ = ?
5 2
5
F. −
4
4
G. −
3
3
H. −
5
3
J.
4
4
K.
3
55. The City Council has approved the construction of a
circular pool in front of City Hall. The area available
for the pool is a rectangular region 12 feet by 18 feet,
surrounded by a brick wall. If the pool is to be as large
as possible within the walled area, and edge of the pool
must be at least 2 feet from the wall all around, how
many feet long should the radius of the pool be?
A. 14
B. 10
C. 7
D. 5
E. 4
56. Kate rode her bicycle to visit her grandmother. The trip
to Kate’s grandmother’s house was mostly uphill, and
took m minutes. On the way home, Kate rode mostly
downhill and was able to travel at an average speed
twice that of her trip to her grandmother’s house. Which
of the following expresses the total number of minutes
that Kate bicycled on her entire trip?
F. 3m
G. 2m
1
H. m +
2
3m
J.
2
m
K.
2
57. Let n equal 3a + 2b − 7. What happens to the value of
n if the value of a increases by 2 and the value of b
decreases by 1?
A. It is unchanged.
B. It decreases by 1.
C. It increases by 4.
D. It decreases by 4.
E. It decreases by 2.

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PRACTICE TEST 3 MATHEMATICS TEST 207

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58. In the figure below, !ABC is a right triangle with legs DO YOUR FIGURING HERE.
that measure x and 3x inches, respectively. What is the
length, in inches, of the hypotenuse?

√
F. √10x
G. √3x
H. 2x
J. 2x
K. 4x
59. If the edges of a cube are tripled in length to produce a
new, larger cube, then the larger cube’s surface area is
how many times larger than the smaller cube’s surface
area?
A. 3
B. 9
C. 18
D. 27
E. 54
60. Considering all values of a and b for which a + b is
at most 9, a is at least 2, and b is at least −2, what is
the minimum value of b − a?
F. 0
G. −7
H. −11
J. −13
K. −15

END OF THE MATHEMATICS TEST.

STOP! IF YOU HAVE TIME LEFT OVER, CHECK YOUR WORK ON THIS SECTION ONLY.