AFQT Mathematics Knowledge Test

Question 1

A box has dimensions of 3 inches, 5 inches and 7 inches. What is the surface area?

Accepted Answer

142

Answer

The surface area of a rectangular box is calculated using the formula 2(lw + lh + wh), where l, w, and h are the length, width, and height. For dimensions 3, 5, and 7 inches, the calculation is 2 * ((7*5) + (7*3) + (5*3)) = 2 * (35 + 21 + 15) = 2 * 71 = 142 square inches. This formula accounts for the area of all six faces of the box.

Question 2

(x + 4) (x-8) =

Accepted Answer

x2 – 4x – 32

Answer

To multiply two binomials like (x + 4)(x - 8), we use the FOIL method (First, Outer, Inner, Last). First terms: x * x = x². Outer terms: x * -8 = -8x. Inner terms: 4 * x = 4x. Last terms: 4 * -8 = -32. Combining these gives x² - 8x + 4x - 32, which simplifies to x² - 4x - 32.

Question 3

In the figure, x = 4z and y = 5z. What is the value of z?

Accepted Answer

20

Answer

Assuming x and y are angles that form a straight line (supplementary angles), their sum is 180 degrees. Substituting the given expressions, we have 4z + 5z = 180. Combining like terms gives 9z = 180. Dividing both sides by 9 yields z = 20. This is a common geometric setup when a figure is implied but not shown.

Question 4

Choose the correct answer

Accepted Answer

500 and 600

Answer

Without the accompanying image, it's impossible to provide a specific calculation. However, in typical math questions of this type, a point or value would be shown on a number line or graph, and the task would be to identify the interval it falls within. The correct answer '500 and 600' implies that the value in the missing image is greater than 500 but less than 600.

Question 5

A cube has 4 inch sides. What is its volume?

Accepted Answer

64 in³

Answer

The volume of a cube is calculated by cubing the length of one of its sides (side * side * side, or s³). Given that the cube has 4-inch sides, the volume is 4 inches * 4 inches * 4 inches. This calculation results in 16 * 4, which equals 64 cubic inches (in³).

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AFQT Mathematics Knowledge Test