Arithmetic, Math, Science For The Asvab

Front 1

Science:

Hydrogen; Helium;Carbon

Nitrogen; Oxygen; Sodium

Iron; Copper; Gold

Mercury; Lead

Uranium; Plutonium

Back 1

1; 2; 6

7; 8; 11

26; 29; 79

80; 82

92; 94

Front 2

Arithmetic:

A rectangle has a perimeter of 36 feet and is 4 feet wide. What is it's area?

Back 2

Area of rectangle = LW

P of a rectance = 2L + 2W

36 (P) - 2 (4) = (36-8)

28 : 2 = 14

A rectangle = 14 x 4 = 56 sq ft

Front 3

Math:

Solve for x in the equation (x-7)2 -4

Back 3

Multiply out what is in parentheses and simplify:

(x-7)2 - 4 = (x + 1)2

(x - 7)(x - 7) - 4 = (x + 1)(x + 1)

x2 - 7x - 7x + 49 - 4 = x2 + x + x + 1

x2 - 14x + 45 = x2 + 2x + 1

-14x + 45 = 2x + 1

-16x + 45 = 2x + 1

-16x = -44

x = 11/4 = 2 3/4

Front 4

Arithmetic: Profit:

A printing plant produces basketball cards with a monthly overhead of $ 6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards need to be sold for a profit?

Back 4

x = # of cards sold each month

$ 0.18 to print $ 0.30 sale price

The cost is equal to $ 6,000. Revenue = 0.30x

Revenue > Cost 0.30x > 6,000 + 0.18x

0.30x > 6,000 + 0.18x

- 0.18x (0.30x) > 6,000 + 0.18x - 0.18x

0.12x > 6,000

0.12x/0.12 > 6,000/0.12

x > 50,000 need to be sold.

Front 5

Artihmetic: Population Growth/ Percentage:

A population grew by 600,000 people between 1995 and 2005. This growth has 1/5 more than the town council predicted that it would grow. What was the town council's prediction?

Back 5

x = original prediction

(1/5 + 5/5 = 6/5 = 120 growth of x)

1.2x = 600,000

1.2x/1.2 = 600,000/1.2

x = 500,000 which is the original prediction

Front 6

Arithmetic: Inches/ feet:

A carpenter needs to cut four sections each 3 feet 8 inches long. If the board is only sold by the foot, what is the shortest length of board he can buy?

Back 6

3 feet 8 inches = 44 inches

44 in. x 4 = 176 in. (total needed)

176 inches : 12 in. = 14 2/3 feet which is about 15 feet for the shortest length to buy.

Front 7

Arithmetic: Quadratic Equation: Pytogorean Theorem:

A rectangle is 1 inch longer than it is wide. It's diagonal is 5 inches. What is the width of the rectangle?

Back 7

D2 = L2 + W2

Quadratic Equation Formula for L of a diagonal of a rectangle is also the pytogorean theorem).

L + W = sides of the triangle D = hypotenuse

D = 5 L = W + 1

Quadratic Equation Formula:

52 = (w + 1)2 + w2

52 = (w + 1) (w + 1) = w2

25 = 2w2 + 2w + 1

0= 2w2 + 2w - 24

1/2(0) = 1/2 (2w2 + 2w -24)

0 = w2 + w - 12

0 = (w - 3) (w + 4)

w - 3 = 0 w + 4 = 0

w = 3 w = -4 = (not a possible solution)

Front 8

Arithmetic: Rectangle / width in inches:

A rectangle is 1 1/2 times as long as it is wide. The perimeter of the rectangle is 100 inches. What is the length of the rectangle?

Back 8

P = 2L + 2W

P = 100 L = 1.5W

100 = 2 (1.5W) + 2W

100 = 3W + 2W

100 = 5W

w = 20 inches (width)

1.5 x 20 = 30 inches because L is 1 1/2 times the width.

Front 9

Arithmetic: Probability:

There is a 0.15 probability that a computer produced is defective. If 5 computers are produced, what is the probability that all of them will be defective?

Back 9

0.15 x 5 0r 0.15 x 0.15 x 0.15 x 0.15 = 0.0000759

which is about 0.000076 probability.

Front 10

Arithmetic: Calories:

Janet has half a cup of pudding at 150 calories. A half cup of broccoli has 60 cal. How much broccoli can Janet eat to equal the same number of calories in the 1/2 cup of pudding?

Back 10

2.5 x 0.5 = 1.25 = 1 1/4 cups broccoli = 150 cal.

Note: The 0.5 represents the 1/2 cup of pudding.

Front 11

Arithmetic: Minutes / Hours:

A dog barks at a raccoon every 15 minutes. The first bark is at 10 pm. How many times will the dog have barked by 2 am?

Back 11

Every 15 minutes = 4 times an hour

10 pm - 2 am = 4 hours

4 times x 4 hours = 16 times

(4 x 4) + 1 = 16 + 1 = 17 hours

Add 1 because he also barked 1 time at 10 pm.

Front 12

Math: Equation:

If 0.05x = 1, then x equals ?

Back 12

0.05x / 0.05 = 1/0.05

x = 1: 0.05 or x = 20

To check the answer substitute 20 in the original equation: 0.05(20) = 1 which is correct.

Front 13

Arithmetic: Inches of rain in min / hours:

If i inches of rain fall in one minute, how many inches fall in h hours?

Back 13

i (60) = hour hour = 60 i

In h hours the amount of rain is 60 ih.

Front 14

Math: Equation

If x = y, then 6 + 4 (x - y) = ?

Back 14

x = y, so plug in x for each y

6 + 4 (x - x) = 6 + 4 (0) = 6 + 0 = 6

Front 15

Math: Exponent:

(x3)2 = ?

Back 15

Add the exponents:

(x3)2 = (x3) (x3) = x3+3 = x6

Front 16

Math: The value of x?

(3 x 3) (5 - 3) (6 + 2) 2 What is the value of X?

Back 16

(3x3) (5-3) (6+2)

(9) (2) (8) = 1442

The square root of 144 = 12 x = 12

Front 17

Math: Factoring:

Factor 9X3 + 18X2 - x - 2

Back 17

9X3 + 18X2 - X - 2 = 9X2 (X+2) (X-2)

= (9X2 -1) (X + 2)

The fully factored answer is (3X + 1) (X + 2) but that is not what the question asks. Make sure to look for the answer to the question.

Front 18

Math: Area of a Circle:

A circle measures 12 feet in diameter. What is the area to the nearest foot?

Back 18

Area of circe = pie(r2) r circle = 1/2 d d= 12 in.

Acircle = pie(6)2 = 36 pie

pie = about 3.14

3.14 X 36 = about 113 ft2 (approx area of the circle).

Front 19

Math: Solve for X:

3(2x-5) - 2 (4x + 1) = 5 (x + 3) - 2

Back 19

3(2x - 5) - 2 (4x + 1) = 5 (x + 3) - 2

6x - 15 - 8 - 2 = - 5x - 15 - 2

- 2x - 17 = 5x - 17

3x - 17 = -17

Front 20

Arithmetic: Probability:

A two-sided dice is rolled. What is the probability of not rolling a five on either die?

Back 20

1 out of 6 = 1/6

1 - 1/6 = 5/6 (1 die)

5/6 x 5/6 = 25/36 = the probability of not rolling a five on either die is 25/36.