# AFOQT Math Practice Test

#### The volume of a cube is 64 cubic feet. What is the cube's surface area?

Explanation:

A cube is made up of equal length sides (s).

The volume of a cube is s x s x s.

Therefore, s=4 in this case (4x4x4=64).

A cube is made up of 6 squares, each with an area of s x s.

Therefore, the surface area of a cube is 6 x s x s = 6 x 4 x 4 = 96

#### What does A equal if F = M x A?

Explanation:

If you divide both sides of the formula by M, then A = F/M

#### 3,451 out of 7,562 college students have participated in an intramural sports program. What percentage of students have participated in intramural sports?

Explanation:

3451/7562=.4563

#### The result of dividing 40 by.08 is

Explanation:

40 divided by .08 = 500

#### With four shirts and five ties, how many different combinations of shirts and ties are possible?

Explanation:

With each of the 4 shirts you can wear one of the 5 ties,

so the total number of combinations is 4 x 5 = 20

#### How much does ¾ pound of rice cost if a pound of rice costs $4.20?

Explanation:

$4.20/4 = $1.05

$4.20 - $1.05 = $3.15

#### If 0.05z equals 1, then z equals

Explanation:

Divide both sides by 0.05.

Therefore, z= 1/0.05=20

#### What does 4(x-y) + 7 equal if x = y?

Explanation:

If x = y,

then you can subsitute x for y in the 2nd equation - so 4(x-x)+7 =

4(0)+7=7

#### The length of a shipping container is 327 feet, and the width is 15.3 feet. What is the volume of the container (rounded to the next whole number) if the height is 12.6 feet?

Explanation:

V=LxWxH

L (327) x W(15.3) x H(12.6) =

63,039 cubic feet

#### What is the value of 4 cubed?

Explanation:

4 cubed is 4 x 4 x 4 = 64

#### Which of the numbers below is NOT a prime number?

Explanation:

93 is not a prime number since it is equal to 31 x 3.

If you add up the digits of a number and they are divisible by 3,

then the number is also divisible by 3.

#### Canmore has a temperature of -1°C. What is the temperature in degrees Fahrenheit using the formula F° = C°x (9/5) + 32?

Explanation:

-1 × 1.8 + 32 = 30.2

#### What percentage of the office workforce is present if 1/3 of the staff is on vacation and 1/4 of those who are not on vacation are sick?

Explanation:

If 1/3 are on vacation, then 2/3 are not. Of those 2/3 not on vacation,

3/4 are NOT sick. Therefore 2/3 x 3/4 are in the office (not on vacation and not sick)

= (2x3)/(3x4)=6/12=1/2

#### If x + y + 15 equals 30, and x + y equals z, then 40 - z equals

Explanation:

If x + y + 15 = 30, then z+ 15 = 30 (substitute x + y = z)

which means that z = 15. If z = 15, then 40 - z = 40 - 15 = 25

#### Which of the options below completes the equation: (9 x 2) + (4 x 3) = (_____)

Explanation:

(10×3) = 30

12+18 = 30

#### A woman has a budget of Z dollars. How much money does she have left after she spends $500?

Explanation:

You need to subtract the money that she spent ($500) from the original money that she had (Z).

#### Three baseball cards, three football cards, and six hockey cards make up a stack of sports cards. What is the chance that one of the cards chosen at random is a hockey card?

Explanation:

There are 12 cards in total. Therefore,

the probability of picking a hockey card is 6/12 or 1/2.

#### What is the median of the data set including -3x, -6x, x, -9x, and 5x if x > 0?

Explanation:

-9x, -6x, -3x, x, 5x

Since we know x is positive, the terms can be placed in order from smallest to largest.

By definition the median is the middle term in this list

#### There are 4 Chocolate Rolls, 3 Lollipops, 5 Toblerone, and 6 Starbursts in a bag of candy. What's the chance you'll get a lollipop if you pick one piece of candy at random?

Explanation:

There are 18 total pieces of candy and 3 lollipops.

Therefore, the probability of picking one lollipop is 3/18 which simplifies to 1/6

#### The card set for a game consists of seven red cards and twenty-one green cards. What is the chance that one of these cards will be red if a player chooses one at random?

Explanation:

There are a total of 28 cards – 7 red; 21 green.
Therefore the probability of selecting an red card is: 7/28 = 1/4)

#### When 6a – 1 Equals 2(a + 1), what is the value of a?

Explanation:

After distributing the 2, the equation is equivalent to 6a -1 = 2a + 2.

Simplifying, 4a = 3, so a = 3/4

#### When 5x – 5 Equals 6x + 8, what is the value of x?

Explanation:

The goal here is to isolate the variable to one side with the constants on the other.

By subtracting 5x from both sides, you can rewrite the equation as: -5 = x + 8.

This simplifies to x = -13 when 8 is subtracted from both sides

#### What is the size of a rectangle with a diagonal of 25 meters and a width of 15 meters in square meters?

Explanation:

The diagonal forms a right triangle with the width and the length acting as legs.

Using the Pythagorean theorem, the length of the triangle will be √25^2 – 15^2 =

√400 = 20, and the area will be 20 x 15 = 300

#### Each member in a room is a sophomore or freshman. The number of freshmen in the room outnumbers the number of sophomores by a factor of seven. The number of individuals in the room could be one of the following. Make a list of all such numbers.

Explanation:

If the number of sophomores in the room is x, then the number of freshman is 7x.

The total number of people in the room is 7x + x = 8x. The number of people in the

room (8x) must be a multiple of 8.)

#### At vertex X, the exterior angle of the triangle XYZ is 130°, whereas at vertex Y, the exterior angle is 110°. At vertex Z, what is the internal angle?

Explanation:

The sum of the exterior angles of any polygon is 360°, so the exterior angle at vertex Z is 360°-130°-110° = 120°.

However, this is not the value of the question asked. Since the sum of the interior angle of a polygon and its

exterior angle is 180°, the interior angle at vertex Z is 180°-120° = 60°