AFQT Mathematics Knowledge Flashcards

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

Answer: 142

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.

(x + 4) (x-8) =

Answer: x2 – 4x – 32

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.

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

Answer: 20

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.

Choose the correct answer

Answer: 500 and 600

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.

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

Answer: 64 in³

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).

Which of these statements is true for two obtuse angles?

Answer: The sum of the two angles will always be greater than 180°

An obtuse angle is defined as an angle that measures greater than 90 degrees but less than 180 degrees. If you have two obtuse angles, each will be individually greater than 90 degrees. Therefore, their combined sum must always be greater than 90 degrees + 90 degrees, which is 180 degrees.

If the number 5, 876, 984 is increased by 1, 035, what will the result be?

Answer: 5,878,019

The problem requires a straightforward addition of the two given numbers. Aligning the numbers by place value and adding from right to left (ones, tens, hundreds, etc.) yields the sum. Specifically, 5,876,984 increased by 1,035 results in 5,878,019.

A field is 910 yards by 300 yards. What is the greatest number of rectangle lots of 120 yards by 65 yards that can be placed on the field?

Answer: 35

To find the greatest number of rectangle lots that can be placed on the field, calculate the total area of the field and divide it by the area of a single lot. The field's area is 910 yards * 300 yards = 273,000 square yards. Each lot has an area of 120 yards * 65 yards = 7,800 square yards. Dividing the total field area by the area of one lot (273,000 / 7,800) gives 35, indicating that 35 such lots can fit if the dimensions allow for perfect tiling.

In the figure, if the perimeter of ABCD is 72, what is the area of the shape?

Answer: 288

Assuming ABCD is a rectangle, its perimeter is given by 2 * (length + width). If the perimeter is 72, then length + width = 36. To find the area, we look for two numbers that sum to 36 and multiply to one of the answer choices. The numbers 12 and 24 satisfy this: 12 + 24 = 36, and their product, 12 * 24, equals 288. Therefore, the area of the rectangle is 288.

If a=2b, then 5+7 (a-2b) =

Answer: 5

The problem provides an algebraic expression and a relationship between variables. By substituting the given condition, a = 2b, into the expression 5 + 7(a - 2b), the term (a - 2b) simplifies to (2b - 2b), which is 0. Multiplying 7 by 0 results in 0, leaving the final simplified value as 5 + 0, which is 5.

( y-3) ( 4y+7) =

Answer: 4y2-5y-21

To expand the product of two binomials (y - 3)(4y + 7), use the FOIL method. This involves multiplying the First terms (y * 4y = 4y^2), Outer terms (y * 7 = 7y), Inner terms (-3 * 4y = -12y), and Last terms (-3 * 7 = -21). Combining the like terms (7y - 12y) results in -5y, leading to the simplified expression 4y^2 - 5y - 21.

Simplify ( 3b - 8 ) - ( 6 - b )

Answer: 4b – 14

To simplify the expression (3b - 8) - (6 - b), first distribute the negative sign to each term within the second parenthesis, changing (6 - b) to (-6 + b). Then, combine the like terms: 3b + b equals 4b, and -8 - 6 equals -14. The simplified expression is therefore 4b - 14.

If the average of 7 consecutive even numbers is 10, then the smallest number is:

Answer: 4

For a set of consecutive even numbers, the average is always the middle number when there's an odd count of numbers. Since there are 7 consecutive even numbers and their average is 10, the fourth number in the sequence is 10. Counting backwards by 2 (because they are even numbers), the numbers before 10 are 8, 6, and 4. Therefore, the smallest number in the series is 4.