PRACTICE ACT MATHEMATICS TEST: 60 Minutes – 60 Questions
DIRECTIONS: Solve each problem and choose the correct answer. Do not linger over problems that take too
much time. Solve as many as you can; then return to the others in the time you have left for this test. You are
permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some
of the problems may best be done without using a calculator.
NOTE: Unless otherwise stated, all of the following should be assumed.




Illustrative figures are NOT necessarily drawn to scale.
Geometric figures lie in a plane.
The word line indicates a straight line.
The word average indicates arithmetic mean.
1. What is the y intercept of a line that intersects points
(4, 2) and ( 7, 5) ?
4. Which of the quadratic equations below has solutions
x  4a and x  2b ?
A.
2
F. x  4 x  8ab  0
2
G. x  8ab  0
H. x 2  2 x(2ab)  8ab  0
2
B. 1
C. 0
D. - 2
E.
6
2. You have a curve that is expressed by
y  .05 x 2  10 x  100 . What is the y coordinate when
x  10 ?
F. 500
G. 420
H. 360
J. 75
J.
K. x 2  x(2a  b)  8ab  0
K. 5
1
5.
3. Which of the functions is described?
x 2  2 x(b  2a)  8ab  0
A.
f ( x)  x 2  2 x  6 and g ( x)  x 2 . What is
1
7
B.
1
3
C. 3
D. 7
g (9)
f (3)
E.
?
21
6. The skid marks left by John’s motorcycle when it comes
to a complete stop are shown with the following function.
Where x is the speed in meters per second. If John doesn’t
want more than 200 meters of skid marks, what is his
maximum speed in meters/second?
200 
A.
B.
f ( x)  x 2  4 for x  2, x  5 for x  4
f ( x)  x  4
C.
f ( x)  x 2  4 for x  2, x  5 for x  4
D.
f ( x)  x 2  4
E.
f ( x)  x 2  4 for x  2, x  5 for x  4
F. 25
G. 32
2( x 2  5 x)
20
H. 35
J. 42
K. 52
7. If f ( x)  x 2  6 x  25 and g ( x)  x 2 , what is f ( g ( x))
when x  2 ?
A. 8
B. 16
C. 41
D. 62
E. 65
8. Jan buys running shorts for $15 and pays $2/week to go
to the gym. If she works out for w weeks, which
expression represents her total cost?
13. Jason eats 1 14 cups of cereal for breakfast each
morning. How much cereal will he consume in a week?
F. 15  2w
G. 17w
A.
7 14 cups
B.
7 12 cups
J . 15
2 w
K. 67
D.
8 12 cups
E.
8 34 cups
H. 15w  2
9. Lines a and b are parallel. d is perpendicular to a and b
and e intersects all 3 lines. What is the measure of angle
y?
1
C. 8 4 cups
14. 5 x 2 y  6 xy 2  3x 2 y is equal to?
F.
J.
8x 2 y
5 x 2 y  3 xy 2
H. 2 x 2 y  6 xy 2
G.
8xy 2
K.
5 x 2 y  6 xy 2  3x 2 y
15. The table below shows a linear relationship between the
variables x and y. Which equation represents this
relationship?
A. 10
B. 20
C. 70
D. 90
10. What is the quotient of any number x and its opposite
reciprocal?
F. -1
G. 1
J. x 2
K.
2
H.  x
Which equation is NOT equal to y  2 x 2  12 x  19 ?
A.
y  1  2 x 2  12 x  18
y  2( x  3)2  1
E.
x
3
B.
y  1  2( x  3) 2
2
 1 0 1  1 1 0 

 

12. Add:  1 1 0    0 1 1
 0 1 1   1 0 1 
F.
H.
K. Impossible to solve
6
18
13
A. 2 x  2 y  18
C.
5 x  2 y  3
E.
x y 3
-2
-2
-10
-22
B. 5 x  y  6
D. 5 x  2 y  6
16. A fence is going to diagonally divide a 30 foot by 24
foot rectangular garden in half. Approximately how long
will the fence be?
2
D. ( x  3)  2( y  1)
y 1
 2 1 1
 1 0 1


 1 1 2 
 0 1 1
 1 2 1 


 1 1 0 
4
Cannot be determined
11.
C.
x
y
E. 110
G.
J.
 0 1 1
 1 2 1 


 1 1 0 
1 0 0 
 0 1 0 


 0 0 1 
F. 19.0 feet
G. 27.0 feet
J. 46.5 feet
K. 54.0 feet
H. 38.4 feet
17. Simplify 3i  4i  0i
A.
7i
B. 12i
C. 15i
D. 36i
E.
0
18. In this series, the difference between each consecutive
number is constant. Fill in the missing numbers.
10 12 ,
F. 6 14 ,  2
J.
6 12 ,  2 12
,
, 2 14
G.
6 14 ,  2 14
K
6 34 ,  2 14
H. 6 14 ,  2 12
19. Simplify: a
( x y ) ( x y )
2x
A. a
a
B. a
D. ax 2  2 xy  y 2
2y
C. ax 2  2 xy  y 2
E. ax 2  y 2
3
20. If x is a negative integer and x 2  16 , then x  x
equals
F. -224
G. -68
H. -64
J. 68
K. -60
3
21. A cube has a volume of 15.625 cm . What is the
length of one edge?
A. 1.7 cm
D. 3.8 cm
B. 2.5 cm
E. 3.9 cm
C. 2.6 cm
22. A bag contains 5 dimes, 8 quarters and 7 pennies.
What is the probability of randomly drawing a coin that is
not divisible by 5?
F. 25%
G. 35 %
H. 40%
J. 60%
K. 65%
26. A recipe calls for 1 12 cups of sugar and makes 24
cookies. How much sugar is needed to make just 20
cookies?
F. 34 cup
G. 1 cup
J. 1 14 cup
K. 1 13 cup
H. 1 16 cup
27. A rectangle has diagonals of 65 cm each. If the height
of the rectangle is 33 cm, what is the area of the entire
rectangle?
2
A. 178 cm
2
D. 2145 cm
2
B. 1820 cm
2
E. 3640 cm
2
C. 1848 cm
28. If x, y, and z are all positive integers, and x  y  z ,
which of the following is the greatest?
y
G. xz
F. xy
H. z
J.
z
x
K. None of these
23. The following chart shows the Grade Point
Equivalence for each letter grade. Sue this chart to answer
the following question.
29. Write this equation is slope-intercept form:
6 x  2 y  12  0
A. x 
(2 y  12)
B. 6 x  2 y  12
6
C. y  3x  6
E. x  13 y  2
D. y  3x  6
30. Triangle DEF is a right triangle. What is sin D ?
Michael earned two B-, two C+, one A- and one B+.
What is his grade point average rounded to the nearest
tenth?
A. 2.8
B 3.2
C. 3.3
D. 3.4
E. 4.3
24. Point A has the coordinates (-4,3). If it is reflected
over the x-axis, then over the y-axis, what are its new
coordinates?
F. (3, 4)
J. (4,-3)
G. (-3, 4)
K. (-4, -3)
F.
f
d
25. At an ice cream social, students can chose between 4
different flavors of ice cream and four different toppings
(sprinkles, whipped cream, chocolate sauce, and caramel).
How many distinct sundaes can be made using one flavor
of ice cream and two different toppings?
B. 24
C. 36
e
d
H.
d
f
J.
d
e
K.
H. (4, 3)
31.
A. 12
G.
D. 48
E. 64
F  95 C  32
If the temperature outside is 14 Fahrenheit, what is the
temperature in Celsius? Round to the nearest tenth.
A. -32.4
D. -6.8
B. -25.6
E. 57.2
C. -10.0
f
e
32. Which of the following are equivalent to
F.
H.
K.
x2  y 2
x 2  2 xy  y 2
G.
x2  y 2
x 2  2 xy  y 2
x2  y 2
J.
x y
?
x y
x 2  2 xy  y 2
A. 38 miles
D. 48 miles
x2  y 2
x y
B. 42 miles
E. 50 miles
C. 46 miles
x2  y 2
x 2  2 xy  y 2
2
37. Two boats set sail from a mid-ocean docking station.
The first boat travels due North at 30 miles/hour. The
second boat travels due West at 40 miles/hour. How far
apart are the boats after 45 minutes? Round your answer to
the nearest mile.
2
33. Triangle DEF is a right triangle. If the hypotenuse is
equal to 12 inches and the sin D  54 , what is the length of
leg f ?
38. The Toyota Prius averages 48 miles/gallon. The Honda
Civic Hybrid averages 42 miles/gallon. If gas currently costs
$3.29/gallon, how many more miles can the Prius travel on
$26 than the Civic? Round your answers to the nearest
tenth.
F. 19.7
J. 156.0
G. 47.4
K. 331.8
H. 81.6
39. If x   54 , y  16 , and z  12 , what is the value of
0
A. 7.0 inches
D. 9.0 inches
B. 7.2 inches
E. 9.6 inches
C. 8.1 inches
 x yz
 x yz ?


A. -1
34. Point I is the midpoint of Segment GH. Point J is the
midpoint of Segment IH. Point K is the midpoint of
Segment JH, and Point L is the midpoint of Segment GK.
If the length of Segment GL is equal to x, what is the
length of Segment GH?
F. 2x
G. 83x
x
H. 25
16
x
J. 32
25
K. 167x
35. The graph below shows the number of loaves of bread
baked at the Grateful Bread on Monday through Friday.
What is the median number of loaves baked daily?
B.  77
99
C. 0
D. 77
99
E. 1
40. What is the greatest common factor of 24xy , 16xyz ,
and 32 y ?
F. 8
G. 8y
H. 8xy
J. 8xyz
K. 16y
41. Jack has twice as much money as Nancy and he has half
the amount of Elina. Elina has 36 more dollars than Nancy.
How much money do they have in total?
A. $36
B. $48
C. $60
D. $72
E. $84
42. The length of a rectangular prism is equal to twice the
width. The height of the prism is equal to twice the length.
If x is the width, what is the surface area of the prism?
2
F. 12x
A. 350
B. 375
C. 400
D. 425
E. 450
2
G. 14x
2
H. 16x
2
J. 24x
2
K. 28x
43. Quadrilateral ABCD is a parallelogram. What is the
value of x?
36. A couple is planning to start a family. If they plan to
have three children, what is the probability that they will
have at least 2 girls?
F. 18
G. 14
H. 12
J. 34
K. 78
A. 59
B. 62
C. 118
D. 124
E. None of these
44. Points C, D, and E make up three vertices of a
parallelogram. Which of the points is a possible location
for the fourth vertex?
49. Find x.
A.
D.
F. (-2, -1)
J. (-2, 1) or (0, 3)
G. (0, 3)
H. (4, -1)
K. (-2, -1), (0, 3), or (4, -1)
B. 108
E. None of these
106
112
C. 110
50. Triangle ABC is similar to Triangle DEF. What is the
perimeter of Triangle ABC?
45. The radius of a wheel is 16 inches. How far will a
point on the edge of the wheel travel when it makes six
complete rotations?
A. 96 inches
D. 192 inches
B. 144 inches
C. 160 inches
256

inches
E.
46. What is the measure (in degrees) of the small angle
that forms when the hands of a clock are exactly at 8:45
F. 7.5
G. 15
H. 18
J. 25
K. 30
47. A blueprint shows a room that is 2 12 inches by 3 23
inches. In real life the longer side of the room is to be 33
feet. How long will the shorter side be?
A.
20 13 feet
B. 21 feet
D.
22 feet
E.
C. 21 12 feet
G. 11 15
K. None of these
8
H. 27 15
51. The formula for the surface area of a cone is
2
SA   r   rs where r is the radius of the circular base and s
is the length of the slant. If the surface area of the cone is
84 , what is the length of the radius?
A.
B.
C.
D.
E.
6
8
10
12
14
22 12 feet
48. On Mondays and Wednesdays, the cross country team
runs 7.5 miles. On Tuesdays and Thursdays they run 5
miles. On Fridays they run 6.8 miles. What is the average
distance per weekday?
F. 3.86 miles
J. 6.43 miles
F. 9 13
J. 30 54
G. 4.85 miles
K. 10.6 miles
H. 6.36 miles
2
52. Which of the following is a factor of 2 x  5 x  3 ?
G. 2 x  1
K. x  3
F. x
J. x  1
H. 2 x  3
53. What is the slope of a line parallel to 2 x  6 y  1 ?
A. 13
B.  13
C. 3
D. -3
E. -2
54. Solve for x. 4 x  6  2( x  3)
F. -6
G. -1
H. 0
J. 1
K 6
55. Triangle ABC is an isosceles triangle. Which of the
following could be the measure (in degrees) of two of its
angles?
A. 30 and 100
D. 50 and 80
B. 35 and 70
E. 60 and 65
C. 40 and 75
56. The angles in a quadrilateral have a ratio of 1:2:3:4.
What is the measure of the largest angle?
F. 36
G 106
H. 108
J. 136
K. 144
57. A box is 22 x 14 x 10 inches. How many small cubic
boxes (3 inches per side) can fit inside?
A. 28
B. 34
C. 84
D. 114
E. 342
58. What are the coordinates of the midpoint of a segment
with endpoints (-3, -1) and (2, -4)?
F. (-2.5, 1.5)
J. (0.5, 2.5)
G. (-1, -5)
K. (2.5, 1.5)
H. (-0.5, -2.5)
59. What is the length of a segment with endpoints
(-3, -1) and (2, -4)?
A. 2 2
B.
10
C. 2 3
D.
34
60.
f ( x)  log 6 216 . What is f ( x) ?
F. 3
E. 8
G. 6
H. 36
J. 216
K. 360