ASVAB Math Answers and Explanations

1. B: The perimeter of a figure is the sum of all of its sides. Since a rectangle's width and length will be the same on opposite sides, the perimeter of a rectangle can be calculated by using the following formula: perimeter = 2(width) + 2(length) Using the numbers given in the question: perimeter = 2(7cm) + 2(9cm) perimeter = 14cm + 18cm perimeter = 32cm

2. D: First, gather the like terms on opposite sides of the equation to make it easier to solve: -3q - 4q > -30 - 12 -7q > -42 Then, divide both sides by -7 to solve for q: -7q/-7 > -42/-7 q > 6 Finally, when both sides are divided by a negative number, the direction of the sign must be reversed: q < 6

3. C: To solve for x, it is necessary to add 6 to both sides to isolate the variable: x - 6 + 6 = 0 + 6 x = 6

4. A: To calculate the value of this expression, substitute -3 for x each time it appears in the expression: 3(-3)3 + (3(-3)+ 4) - 2(-3)2 According to the order of operations, any operations inside of brackets must be done first: 3(-3)3 + (-9+ 4) - 2(-3)2 3(-3)3 + -5 - 2(-3)2 Then, the value of the expression can be calculated: 3(-27) + -5 - 2(9) -81 + -5 - 18 -104

5. C: First, combine like terms to make the equation easier to solve: 3x + 2x = 45 + 30 5x = 75 Then, divide both sides by 5 to solve for x: 5x/5 = 75/5 x = 15

6. A: First, add 25 to both sides to isolate x: 1/4x - 25 + 25 = 75 + 25 1/4x = 100 Then, multiply both sides by 4 to solve for x: 1/4x * 4 = 100 * 4, x = 400

7. A: First, add 5 to both sides to isolate x: x - 5 + 5 = 20 + 5 x = 25 Then, take the square root of both sides to solve for x, = , x = 5

8. B: First, we must calculate the length of one side of the square. Since we know the perimeter is 8cm, and that a square has 4 equal sides, the length of each side can be calculated by dividing the perimeter (8cm) by 4: 8cm / 4 = 2cm The formula for the area of a square is length2 Therefore, to calculate the area of this square: 2cm2 or 2cm * 2cm Area = 4cm2

9. D: To find the value of this expression, substitute the given values for x and y into the expression: 3(4)(2) - 12(2) + 5(4) Then, calculate the value of the expression: 3*8 - 12*2 + 5*4 24 - 24 + 20 20

10. D: First, subtract 10 from both sides to isolate x: 0.65x + 10 - 10 = 15 - 10 0.65x = 5 Then, divide both sides by 0.65 to solve for x: 0.65x/0.65 = 5/0.65 x = 7.69

11. B: Use the FOIL method (first, outside, inside, and last) to get rid of the brackets: 12x -18x + 20x -30 Then, combine like terms to simplify the expression: 12x -18x + 20x -30 12x + 2x -30

12. B: To simplify this expression, it is necessary to follow the law of exponents that states: x/x = x First, the 50 can be divided by 5: 50/5 = 10 Then, it is simply a matter of using the law of exponents described above to simplify the expression: 10xtwz 10xtwz.

13. D: To calculate the value of this permutation, it is necessary to multiply each number between one and 4: 1 * 2 * 3 * 4 = 24

14. D: Because it is a cube, it is known that the width and the height of the cube is also 5cm. Therefore, to find the volume of the cube, we must cube 5cm: 5cm3 This is the same as: 5 * 5 * 5 = 125 The volume of the cube is 125cm3.

15. A: First, factor this equation to make solving for x easier: (x - 6) (x - 7) = 0 Then, solve for both values of x: 1) x - 6 = 0 x = 6 2) x - 7 = 0 x = 7

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