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### 25 Cards in this Set

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Mathematics Knowledge - ASVAB (full) test
1: If a = 5/2 then 1/a = A. 2 B. 5 C. 2/5 D. 5/2 |
C. 2/5
C. Substitute 5/2 for a, giving you 1/a = 1/(5/2) = 1 x 2/5 = 2/5. |

Mathematics Knowledge - ASVAB (full) test
2: 12 is 15% of what number? A. 0.0125 B. 1.8 C. 18 D. 80 |
D. 80
D. Let n represent the number. If 12 is 15% of n, then 12 = 0.15n. Divide both sides by 0.15. Therefore, n = 80. |

Mathematics Knowledge - ASVAB (full) test
3: Evaluate 3x + 7 when x = -3. A. -2 B. 10 C. 16 D. 30 |
A. -2
A. Substitute -3 for x. Then 3(-3) + 7 = -9 + 7 = -2. |

Mathematics Knowledge - ASVAB (full) test
4: Find the diagonal of a square whose area is 36. A. 6 B. 6√2 C. 9 D. 9 √2 |
B. 6√2
B. The area of a square is s2 where s is a side of the square. If s2 = 36, then s = 6. The diagonal of a square forms two right triangles; d is the hypotenuse and the two legs are 6 units long. Using the Pythagorean theorem, d2 = 62 + 62 = 36 + 36 = 72. Therefore, d = √72 = 6√2. |

Mathematics Knowledge - ASVAB (full) test
5: If a + b = 6, what is the value of 3a + 3b? A. 9 B. 12 C. 18 D. 24 |
C. 18
C. 3a + 3b = 3(a + b). Since a + b = 6, 3a + 3b = 3(6) = 18. |

Mathematics Knowledge - ASVAB (full) test
6: Find the length of the radius in the following figure. A. 3 B. 4 C. 5 D. 10 |
C. 5
C. The hypotenuse of the triangle is the diameter of the circle. By the Pythagorean theorem, d2 = 62 + 82= 36 + 64 = 100. So d = √100 = 10 and the radius is 10/2=5. |

Mathematics Knowledge - ASVAB (full) test
7: (3 - 1)×7 - 12 ÷ 2 = A. 1 B. -2 C. 4 D. 8 |
D. 8
D. Following the correct order of operations produces: (3 - 1) × 7 - 12÷2 = 2 × 7 - (12÷2) = 14 - 6 = 8. |

Mathematics Knowledge - ASVAB (full) test
8: The greatest common factor of 24 and 36 is A. 6 B. 12 C. 36 D. 72 |
B. 12
B. Factors of 24 are 2 × 2 × 2 × 3. Factors of 36 are 2 × 2 × 3 × 3. The greatest common factor is 2 × 2 × 3 = 12. |

Mathematics Knowledge - ASVAB (full) test
9: Solve for m: 3m - 12 = -6 A. -6 B. 0 C. 2 D. 6 |
C. 2
C. 3m - 12 + 12 = -6 + 12; 3m = 6; Dividing both sides by 3 results in m = 2. |

Mathematics Knowledge - ASVAB (full) test
10: If 7p + 5q = -3, find q when p = 1. A. -1 B. -2 C. -1.142857143 D. -0.285714286 |
B. -2
B. Substitute 1 for p and solve for q. 7(1) + 5q = -3 and 7 + 5q = -3. 7 + 5q - 7 = -3 - 7 and 5q = -10. Dividing both sides by 5 results in q = -2. |

Mathematics Knowledge - ASVAB (full) test
11: The slope of the line shown is A. -2/5 B. -5/2 C. 2/5 D. 5/2 |
C. 2/5
C. Slope is found by identifying two points on the line and finding the (change in y)/(change in x). The points (0, 0) and (5, 2) form the slope (2 - 0)/(5 - 0) = 2/5. |

Mathematics Knowledge - ASVAB (full) test
12: Simplify (9x2y3z-12xy2z2)/3yz A. 3xy2z2 - 4xyz B. 3xy2z - 12xyz C. 3x2y2 - 4xyz D. 3y2 - 4xy2z2 |
C. 3x2y2 - 4xyz
C. (9x2y3z - 12xy2z2)/3yz = 9x2y3z/3yz - 12xy2z2/3yz = 3x2y2 - 4xyz |

Mathematics Knowledge - ASVAB (full) test
13: The value of x is A. 70° B. 110° C. 140° D. 210° |
B. 110°
B. The angle adjacent to the 140° angle is 40° since supplementary angles add to 180°. The angles of a triangle add to 180° so the angle adjacent to angle x is 180° - 70° - 40° = 70°. Angle x and 70° are supplementary, so x = 180° - 70° = 110°. |

Mathematics Knowledge - ASVAB (full) test
14: In a standard deck of playing cards, a king of hearts is drawn and not replaced. What is the probability of drawing another king from the deck? A. 1/4 B. 1/13 C. 1/17 D. 3/52 |
C. 1/17
C Probability is ?. Since one king was drawn and not replaced, three kings remain in the deck of 51 cards. So the probability of drawing another king is ?. |

Mathematics Knowledge - ASVAB (full) test
15: How many minutes are there in 1 week? A. 10,080 B. 1,440 C. 420 D. 168 |
A. 10,080
A. There are 60 minutes in 1 hour, 24 hours in 1 day, and 7 days in 1 week. So 1 week = ? = 7 × 24 × 60 = 10,080 minutes. |

Mathematics Knowledge - ASVAB (full) test
16: If 2b+3=1/8, b= A. -6 B. -3 C. 0 D. 2 |
A. -6
A. 1/8=1/23=2-3 so 2b+3=2-3 and b + 3 = -3. Therefore, b + 3 - 3 = -3 - 3 = -6. |

Mathematics Knowledge - ASVAB (full) test
17: The angles of a triangle are in the ratio 3:4:5. What is the measure of the smallest angle? A. 15° B. 30° C. 45° D. 75° |
C. 45°
C. Angles in a triangle add to 180°. So 3x + 4x + 5x = 180° and 12x = 180°. Dividing both sides by 12 results in x = 15°. The smallest angle is represented by 3x = 3(15°) = 45°. |

Mathematics Knowledge - ASVAB (full) test
18: Subtract (2x3-3x+1)-(x2-3x-2) A. 2x3-x2+3 B. 2x3-x2-6x-1 C. x3-6x-1 D. x2+3 |
A. 2x3-x2+3
A. Subtraction can be changed to addition by changing the signs in the entire term being subtracted. (2x3 -3x +1) - (x2-3x-2)=(2x3-3x+1) + (-x2+3x+2).. Combine like terms: 2x3-x2-3x+3x+1+2=2x3-x2+3. |

Mathematics Knowledge - ASVAB (full) test
19: If the area of a square is 400, what is the length of its side? A. 20 B. 40 C. 100 D. 200 |
A. 20
A. The area of a square is s2 where s is a side of the square. If s2 = 400, then s = √400 = 20. |

Mathematics Knowledge - ASVAB (full) test
20: Seven more than 3 times a number is equal to 70. Find the number. A. 10 B. 17 C. 21 D. 30 |
C. 21
C. Translate to a mathematical expression and solve. 3x + 7 = 70 so 3x + 7 - 7 = 70 - 7 and 3x = 63. Divide both sides by 3. Therefore, x = 21. |

Mathematics Knowledge - ASVAB (full) test
21: Which expression represents the volume of a cylinder whose height is equivalent to the length of the radius? A. pr2 B. pr3 C. (pr)2 D. (pr)3 |
B. pr3
B. The volume of a cylinder is given by the formula V = pr2h, where r is the radius of the circular base and h is the height. Since h = r, V = pr2r = pr3. |

Mathematics Knowledge - ASVAB (full) test
22: How many distinct prime factors are there in 120? A. 2 B. 3 C. 4 D. 5 |
B. 3
B. Prime factors of 120 are 2 × 2 × 2 × 3 × 5. Distinct factors are 2, 3, and 5. Therefore, there are three distinct prime factors. |

Mathematics Knowledge - ASVAB (full) test
23: What percent of 3/4 is 1/8? A. 9.38% B. 12% C. 16.67% D. 25% |
C. 16.67%
C. Let p represent the unknown percent. p×3/4=1/8. Solve for p by multiplying both sides by the reciprocal of 3/4. p×3/4×4/3=1/8×4/3=4/24=1/6. As a percent, 1/6 is 16 2/3%. |

Mathematics Knowledge - ASVAB (full) test
24: What is the area of the figure shown? A. 130 ft2 B. 145 ft2 C. 160 ft2 D. 175 ft2 |
B. 145 ft2
B. Divide the figure into a rectangle and triangle as shown. The area of the figure equals the area of the rectangle plus the area of the triangle. The rectangle = length × width or 10 × 13 = 130 ft2; the triangle = ? base × height or ? ?. Together, the area is 130 + 15 = 145 ft2. |

Mathematics Knowledge - ASVAB (full) test
25: If x is a positive integer, solve x2 + 6x = 16. A. 2 B. 4 C. 8 D. 10 |
A. 2
A. Set the equation equal to 0 and factor. x2 + 6x - 16 = 0 and (x + 8)(x - 2) = 0. Then, either x + 8 = 0 or x - 2 = 0, so x = -8 or x = 2. Since x is positive, x = 2 only. |