Mathematics Knowledge ASVAB

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.

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.

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.

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.

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.

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.

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.

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°.

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.

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.

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.

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.

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.

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 ?.

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%.

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.

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.

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.

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.

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.

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

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°.

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.

(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.

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.