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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 (9x2y3z12xy2z2)/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=23 so 2b+3=23 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 (2x33x+1)(x23x2) A. 2x3x2+3 B. 2x3x26x1 C. x36x1 D. x2+3 
A. 2x3x2+3
A. Subtraction can be changed to addition by changing the signs in the entire term being subtracted. (2x3 3x +1)  (x23x2)=(2x33x+1) + (x2+3x+2).. Combine like terms: 2x3x23x+3x+1+2=2x3x2+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. 