# AFQT Mathematics Knowledge Test

#### (x + 4) (x-8) =

To calculate multiply out the brackets (FOIL): (x + 4)(x - 8) = x2 + (-8)x + 4x + (-32) = x2 – 4x – 32

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

One trick for dealing with consecutive numbers is to realize that the middle number in a group of consecutive numbers is equal to the average of the numbers. So of the seven consecutive even numbers, the middle or fourth number is 10, the third number is 8, the second number is 6, and the first or smallest number is 4.

#### Choose the correct answer

Answer is (D). You only have to approximate to identify this number. You know that the square of 100 = 10,000. Therefore, calculate the squares of the hundredth number and multiply by 10,000 to get the rough numbers. I.e. the square of 200 = 2 X 2 X 10,000 = 40,000. From this you can tell that 5 X 5 X 10,000 = 250,000 and 6 X 6 X 10,000 = 360,000. Therefore the answer is D.

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

Area equal length times width, so if the perimeter is 72 and one side is 24, the sum of AB and CD is: Perimeter – AD – BC = 72 - 24 -24 = 24. AB = CD because a rectangle length is the same on each side and width is the same on each side, therefore = CD or AB = 12 The area is length x width = 24 X 12 = 288.

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

Combine the terms: (y-3)(4y+7)=4y2+7y-12y-21=4y2-5y-21. The correct answer is choice (B).

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

The surface area of a rectangle is: 2 x (l x w) + 2 x (h x w) + 2 x (l x h) where l = length, w = width and h = height 2 x (3 x 5) + 2 x (7 x 5) + 2 x (3 x 7) = 2 x 15 + 2 x 35 + 2 x 21 = 142 inches

#### 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?

The field is 910 x 300 = 273,000 sq yards A rectangle lot is 120 x 65 = 7800 sq yards Therefore – 273,000 ÷ 7,800 = 35

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

5,876,984 + 1,035 5,878,019

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

Distribute the minus operation over the second set of parenthesis: (3b – 8) – (6 – b) = 3b – 8 – 6 – (-b) = 3b – 8 – 6 + b. Combining gives: 4b – 14.

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

As we know that x + y = 180 because they each make up a part of the straight line and the angle of a straight line is 180 degrees. We can sub in 4z for x and 5z for y and we have: x + y = 4z + 5z = 9z = 180, therefore: z = 20.

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

If you substitute for , the equation is . The two variables cancel out, and the correct answer is choice (A).

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

For any box, l x w x h, but this is a cube where all sides are 4 inches, so volume = 43 = 4 x 4 x 4 = 64in³.

#### Which of these statements is true for two obtuse angles?

An obtuse angle is one that is greater than 90° and less than 180°. (B) and (C) cannot be true as two minimal obtuse angles would be greater than 180°. (D) cannot be an answer as all three angles in a triangle are equal to 180°. If there are two obtuse angles, the sum of these two would exceed this. Therefore (A) is the only option available.

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