Chapter 8
Mathematics Practice Test
This mathematics practice test is pretty straightforward. It covers those math skills you need to successfully navigate this particular subject on the various flight aptitude tests. The mathematics test is a very important section because all military services place a high degree of importance on a potential aviator’s math skills.
Choose the most correct answer to each question.
Subtest 1: Whole Numbers and Integers
1. If x is an even integer, which of the following results in an odd integer?
(A) 2x + 2
(B) 2x – 1
(C) x + 2
(D) 
(E) None of the above
2. Which of the following is an integer?
(A) 0.1
(B) 0.4
(C) 0
(D) 2.1
(E) 2.2
3. An integer is
(A) Any positive number
(B) Any negative number
(C) A fraction
(D) A positive or negative whole number or zero
(E) None of the above
Subtest 2: Mathematical Operations
4. An athlete jogs 10 laps around a circular track. If the total distance jogged is 6.2 kilometers, what is the distance around the track?
(A) 0.25 meters
(B) 62 meters
(C) 6.2 meters
(D) 620 meters
(E) 0.62 meters
5. 3 + 4 + 2 – 16 =
(A) –7
(B) 7
(C) 4
(D) 6.8
(E) –6
6. 8 – 4 + 6 =
(A) 5
(B) –5
(C) –6
(D) 7
(E) 10
7. A gasoline generator has a 5-gallon tank and burns 4 gallons per hour. About how many times must the fuel tank be filled to run the generator from 6:30 p.m. to 7:00 a.m.?
(A) 10
(B) 11
(C) 5
(D) 6.2
(E) 12.0
8. 63 maintenance personnel require three meals per day for a training operation overseas expected to last 28 days. An MRE (meal, ready to eat) costs $4.20 per person, and a hot ration costs $6.40 per person. If one meal per day is an MRE, how much must be allocated to fund the food expense?
(A) $23,428
(B) $22,564
(C) $29,988
(D) $865
(E) None of the above
9. Suppose the unit in Question 8 deployed with an extra ten personnel with the same meal requirements. How long can they now conduct training with the same amount of meal funding?
(A) 16 days
(B) 24 days
(C) 18 days
(D) 22 days
(E) None of the above
10. 2 × 8 ÷ 12 =
(A) 1.7
(B) 2.1
(C) 3
(D) 1.3
(E) 4
Subtest 3: Maintaining Order
11. 4(a + b) – 4(a + 3b) =
(A) 6a – 10b
(B) 6a + 2b
(C) –8b
(D) 6a – 8b
(E) 6a + 10b
12. 5(4 – 1) + 2(3 + 2) ÷ 4 =
(A) 17.5
(B) 17
(C) 1.75
(D) 62.5
(E) 6.25
13. 
(A) 2ab + 4ab + 64b + 18b + 64
(B) 2a2 + 4ab2 + 64 + 18b2
(C) 4ab2 + 4ab + 64b + 18b + 64
(D) 4ab + 2ab + 64 + 16b2 + 64
(E) None of the above
14. (1 + 5) ÷ 4 + 2(2 + 3)3 ÷ 7 =
(A) 10
(B) 12
(C) 9.8
(D) 37.21
(E) 12.3
15. 
(A) 2a2 + 4ab + 2b + 2a2 + 6ab2 + 2b2 + 2a
(B) 2a2 + 4ab + 2b2 + 2a2 + 6a2b + 6ab + 2a + 2b
(C) 4a2 + 2ab + 2b3 + 2a2 + 6ab2 + 2b3 + 2a + 2b
(D) 2a + 4ab + 2b + 2a2 + 6a2b + 6ab + 2b
(E) None of the above
16. 32 + 3(2 – 3)2 – 12 ÷ 52 =
(A) 12.48
(B) 0.75
(C) 23/24
(D) 22/24
(E) 1.12
Subtest 4: Prime and Composite Numbers
17. Which of the following is the smallest prime number greater than 100?
(A) 101.5
(B) 102
(C) 101
(D) 104
(E) 105
18. Which of the following is a composite number?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
19. Which of the following is a prime number?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
20. Which of the following is a composite number?
(A) 5
(B) 7
(C) 11
(D) 13
(E) 15
21. Which of the following is a prime number?
(A) 9
(B) 10
(C) 12
(D) 13
(E) 15
Subtest 5: Exponents
22. If 4n = 9, what is the value of 4n + 1?
(A) 27
(B) 144
(C) 45
(D) 36
(E) None of the above
23. 100,000 may be represented as
(A) 104
(B) 105
(C) 106
(D) 107
(E) 108
24. 10x ÷ 10y =
(A) 
(B) 10xy
(C) 10x + y
(D) 10x – y
(E) None of the above
25. 10x × 10y =
(A) 
(B) 10xy
(C) 10x + y
(D) 10x – y
(E) None of the above
26. 4x6y3z2 ÷ 2x4y3z =
(A) 2x2z
(B) 4xyz
(C) 4x4y2z
(D) 2x2y2z
(E) None of the above
Subtest 6: Fractions
27. Sarah donates 4/15 of her paycheck to her favorite charity. If she donates $32.90, what is the amount of her paycheck?
(A) $125.80
(B) $123.38
(C) $187.10
(D) $131.50
(E) $198.40
28. A pound of margarine contains four equal sticks of margarine. The wrapper of each stick has markings that indicate how to divide the stick into eight 1-tablespoon sections. If a recipe calls for eight tablespoons of margarine, the amount to use is
(A) 1/16 pound
(B) 1/8 pound
(C) 1/4 pound
(D) 1/2 pound
(E) 3/4 pound
29. Fred earns $12.50 an hour plus an overtime rate equal to 11⁄2 times his regular pay for each hour worked above 40 hours per week. What are his total gross earnings for a 50-hour workweek?
(A) $636.00
(B) $710.25
(C) $499.50
(D) $687.50
(E) $599.90
30. When you add 200 gallons of oil to an oil tank that is 1/4 full, the tank becomes 1/3 full. The capacity of the oil tank is
(A) 2,400 gallons
(B) 2,390 gallons
(C) 2,430 gallons
(D) 2,470 gallons
(E) 1,510 gallons
31. The reciprocal of 9, rounded to the nearest thousandth, is
(A) 0.143
(B) 1.428
(C) 0.111
(D) 0.112
(E) 0.11
32. The reciprocal of 7, rounded to the nearest thousandth, is
(A) 14.28
(B) 1.428
(C) 14
(D) 0.143
(E) 49
33. The reciprocal of 4 is
(A) 1/4
(B) 1/8
(C) 1/6
(D) 1/2
(E) –4
Subtest 7: Dealing with Decimals
34. 0.0024 × 0.073 =
(A) 0.1752
(B) 0.0001752
(C) 0.001752
(D) 0.0021
(E) None of the above
35. 1.24 × 0.03 =
(A) 0.372
(B) 3.72
(C) 3.72 × 10–2
(D) 3.72 × 10–3
(E) None of the above
36. 0.04 ÷ 0.035 =
(A) 1.14
(B) 1.28
(C) 1.33
(D) 0.875
(E) None of the above
37. 0.12 ÷ 0.0003 =
(A) 187
(B) 40.0
(C) 0.0400
(D) 400
(E) None of the above
Subtest 8: Preparing Proportions
38. The ratio of 3x to 5y is 1:2; what is the ratio of x to y?
(A) 1:2
(B) 2:3
(C) 3:4
(D) 4:5
(E) 5:6
39. The ratio of 2x to 3y is 2:3; what is the ratio of x to y?
(A) 2:1
(B) 1:1
(C) 3:2
(D) 4:5
(E) 2:5
40. The ratio of 4x to 2y is 1:2; what is the ratio of x to y?
(A) 2:2
(B) 3:7
(C) 4:2
(D) 4:1
(E) 5:7
Subtest 9: Calculating Percentages
41. During a season, a basketball player attempted 67 shots and completed 57 of them. What is his completion percentage?
(A) 70.4 percent
(B) 85.1 percent
(C) 88.8 percent
(D) 87.7 percent
(E) 73.9 percent
42. Jan found a boat for $22,400. However, because the model had been discontinued, the dealer discounted the price to $21,150. What was the percentage of the reduction?
(A) 6.7 percent
(B) 6.0 percent
(C) 5.0 percent
(D) 6.9 percent
(E) 5.6 percent
43. After passports were required for travel to Canada, the traffic on the International Bridge declined from 14,680 cars per day to 9,480 cars per day. What was the percentage of the decline in traffic?
(A) 35.4 percent
(B) 22.5 percent
(C) 31.1 percent
(D) 28.9 percent
(E) 39.3 percent
44. Thomas earns an average of $24 an hour in tips as a parking lot attendant. If his hourly wage is $3.45 and he has to pay a 25-percent share of his tips to the doorman, how much does he take home at the end of a day when he has worked from 6:30 a.m. to 5:30 p.m.?
(A) $332.90
(B) $222.60
(C) $235.95
(D) $256.70
(E) $271.00
45. A jar contains red, green, and yellow marbles. 20 percent of those marbles are either red or green. What are the chances of blindly picking a yellow marble out of the jar?
(A) 1 out of 3
(B) 1 out of 5
(C) 2 out of 3
(D) 2 out of 5
(E) 4 out of 5
46. Deck cleaner contains approximately 10 percent bleach and 90 percent water in each gallon (128 ounces). Someone further dilutes the mixture by adding 32 additional ounces of water. What percent of the new solution is bleach?
(A) 4 percent
(B) 8 percent
(C) 9 percent
(D) 11 percent
(E) 12 percent
Subtest 10: Roots and Radicals
47. The expression 
reduces to
(A) 2.92
(B) 2.76
(C) 2.88
(D) 3.14
(E) 3.08
48. Find the square root of 105 to the nearest tenth.
(A) 10.1
(B) 10.2
(C) 10.3
(D) 10.4
(E) 10.5
49. The cube root of 4,096 is equal to the square of
(A) 16
(B) 8
(C) 5
(D) 4
(E) 3
50. 
(A) 1
(B) 2
(C) 0.83
(D) 0.67
(E) 80
Subtest 11: Converting Measurements
51. An Army infantry platoon did a 12-mile road march. How many kilometers did it march?
(A) 23 kilometers
(B) 18.2 kilometers
(C) 19.6 kilometers
(D) 24.7 kilometers
(E) 19.3 kilometers
52. A small, light-training aircraft flies at 122 miles per hour. How fast does it fly in knots?
(A) 106 knots
(B) 110 knots
(C) 140 knots
(D) 128 knots
(E) None of the above
53. A 122 millimeter insurgent rocket is used to attack your forward operating base. What is the diameter of the rocket in inches?
(A) 4.5 inches
(B) 4.8 inches
(C) 5.2 inches
(D) 4.2 inches
(E) None of the above
54. A patient is airlifted to the nearest medical center. His wife states that he weighs 180 pounds. The flight medic is giving a drug that calls for a dose of 0.1 milligrams per kilogram. How much of the drug should the medic give the patient?
(A) 82 milligrams
(B) 16.4 milligrams
(C) 8.2 milligrams
(D) 0.82 milligrams
(E) None of the above
55. A 450-gallon fuel tank contains how many cubic feet?
(A) 45 cubic feet
(B) 50 cubic feet
(C) 55 cubic feet
(D) 60 cubic feet
(E) 65 cubic feet
Subtest 12: Basic Algebra
56. One phone plan charges a $15 monthly fee and $0.07 per minute on every phone call made. Another phone plan charges an $11 monthly fee and $0.12 per minute for every call. At how many minutes will the charge be the same for each phone plan?
(A) 60 minutes
(B) 80 minutes
(C) 75 minutes
(D) 95 minutes
(E) 25 minutes
57. An older, “deuce and a half” vehicle can carry 2.5 tons of cargo, while an over-the-road hauler can carry 6 tons of cargo. If an equal number of both vehicles is used to ship 221 tons of cargo and each truck carries its maximum cargo load, how many tons of cargo are shipped on the 2.5-ton trucks?
(A) 65 tons
(B) 60 tons
(C) 75 tons
(D) 100 tons
(E) 120 tons
58. A large auditorium for a USO show contains x rows with y seats in each row. 50 seats are reserved for officers of the division staff. How many total seats are left for all the other service members who want to see the show?
(A) (x + y) – 50
(B) x – y
(C) (xy) – 50
(D) y – x
(E) 2x + y + 50
59. Solve for z: 4z – 4 + 3z = 22 – 6z
(A) z = 1
(B) z = 3
(C) z = –3
(D) z = 0
(E) z = 2
60. If 8x + 4y = 40 and x – y = 2, then y =
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
61. For the quadratic equation, 2x2 + 3x + 20 = x2 + 2x + 40, solve for x.
(A) 4; –5
(B) –4; –5
(C) 0; –4
(D) 3; –3
(E) None of the above
Subtest 13: Geometry
62. The sum of the angle measures of a triangle is
(A) 360 degrees
(B) 540 degrees
(C) 180 degrees
(D) 90 degrees
(E) 120 degrees
63. If one angle of a triangle measures 80 degrees, the sum of the other two angles is
(A) 110 degrees
(B) 100 degrees
(C) 280 degrees
(D) 65 degrees
(E) None of the above
64. An obtuse angle is
(A) Less than 90 degrees or more than 180 degrees
(B) Less than 90 degrees
(C) More than 180 degrees
(D) More than 90 degrees but less than 180 degrees
(E) None of the above
65. If one of the angles of a right triangle is 45 degrees, what are the degree measurements of the other two angles?
(A) 30 degrees; 120 degrees
(B) 60 degrees; 45 degrees
(C) 45 degrees; 90 degrees
(D) 40 degrees; 95 degrees
(E) 45 degrees; 120 degrees
66. A decagon is a polygon with how many sides?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
67. Using the Pythagorean theorem, figure out the length of the hypotenuse if the lengths of the other two sides are 10 meters and 16 meters.
(A) 21.06 meters
(B) 18.87 meters
(C) 19.00 meters
(D) 19.45 meters
(E) None of the above
Subtest 14: Calculating Perimeter and Area
68. The area of one circle is six times as large as a smaller circle with a radius of 3 inches. The radius of the larger circle is
(A) 7.34 inches
(B) 9.1 inches
(C) 8.65 inches
(D) 6.27 inches
(E) None of the above
69. How many meters does a point on the rim of a wheel travel if the wheel has a radius of 2 meters and makes 40 rotations?
(A) 340 meters
(B) 503 meters
(C) 410 meters
(D) 336 meters
(E) 240 meters
70. The forward operating base you’re assigned to is arranged in a perfect circle, with the headquarters exactly in the center. The headquarters is 1.2 kilometers to the perimeter road. How far must you travel to drive around the base one time on the perimeter road?
(A) 10.1 kilometers
(B) 6.89 kilometers
(C) 8.21 kilometers
(D) 7.54 kilometers
(E) 5.75 kilometers
71. The secure area of your airfield is 2 miles by 1 mile. The area of the secured area is
(A) 4 square miles
(B) 6 square miles
(C) 2 square miles
(D) 1 square mile
(E) None of the above
72. What’s the perimeter of the secured airfield in Question 71?
(A) 4 miles
(B) 6 miles
(C) 2 miles
(D) 1 mile
(E) None of the above
73. Two circles have the same center. If their radii are 5 centimeters and 15 centimeters, find the area that is part of the larger circle but not part of the smaller one.
(A) 300 square centimeters
(B) 200π square centimeters
(C) 51π square centimeters
(D) 71π square centimeters
(E) 91π square centimeters
74. The area of a right triangle that has a height of 10 centimeters and a base of 20 centimeters is
(A) 314 square centimeters
(B) 400 square centimeters
(C) 200 square centimeters
(D) 66 square centimeters
(E) 100 square centimeters
Subtest 15: Calculating Volume
75. If the weight of water is 52.4 pounds per cubic foot, the weight of the water that fills a cube with 2-foot sides is
(A) 395 pounds
(B) 257 pounds
(C) 419 pounds
(D) 344 pounds
(E) 624 pounds
76. What is the volume of a container that is 12 feet long, 14 feet wide, and 8 feet high?
(A) 1,344 cubic feet
(B) 1,450 cubic feet
(C) 1,795 square feet
(D) 1,795 cubic feet
(E) 1,280 cubic feet
77. The volume of a cylinder with a radius of 2 inches and a height of 6 inches is
(A) 75.4 cubic inches
(B) 67.2 cubic centimeters
(C) 67.2 cubic inches
(D) 75.4 cubic centimeters
(E) None of the above
78. A gallon contains 231 cubic inches. If a cylindrical container has a radius of 10 inches and a height of 20 inches, how many gallons of hydraulic fluid can it hold?
(A) 25.1 gallons
(B) 14.8 gallons
(C) 27.2 gallons
(D) 21.4 gallons
(E) 23.1 gallons
Subtest 16: Statistics
79. The following test scores were posted: 92, 91, 89, 87, 83, 83, 72. What is the mean score?
(A) 89
(B) 85.3
(C) 86.1
(D) 87
(E) 83
80. The following test scores were posted: 92, 91, 89, 87, 83, 83, 72. What is the median score?
(A) 89
(B) 85.3
(C) 86.1
(D) 87
(E) 83
Answer Key
1. B
2. C
3. D
4. D
5. A
6. E
7. A
8. C
9. B
10. D
11. C
12. A
13. E
14. D
15. E
16. A
17. C
18. D
19. B
20. E
21. D
22. C
23. B
24. D
25. C
26. A
27. B
28. C
29. D
30. A
31. C
32. D
33. A
34. B
35. C
36. A
37. D
38. E
39. B
40. D
41. B
42. E
43. A
44. C
45. E
46. B
47. A
48. B
49. D
50. C
51. E
52. A
53. B
54. C
55. D
56. B
57. A
58. C
59. E
60. B
61. A
62. C
63. B
64. D
65. C
66. E
67. B
68. A
69. B
70. D
71. C
72. B
73. B
74. E
75. C
76. A
77. A
78. C
79. B
80. D