ASVAB Math

One in every 9 people in a town vote for party A. All others vote for party B. How many people vote for party B in a town of 810?

(8x810)/(9x1) --- 6480 % 9 = 720

If the tire of a car rotates at a constant speed of 552 times in one minute, how many times will the tire rotate in half-an-hour?

16,560 (552 x 30 = 16,560)

A motorcycle cost $7,250. If it depreciates by 12% per year, how much will it be worth after one year?

3 X 6

18

3 X 7

21

3 X 8

24

3 x 9

27

3 x 12

36

4 x 7

28

4 x 8

32

4 x 9

36

4 x 12

48

5 x 12

60

5 x 9

45

6 x 7

42

6 x 8

48

6 x 9

54

6 x 12

72

8 x 9

27

8 x 12

96

9 x 7

63

9 x 12

108

11 x 11

121

11 x 12

132

12 x 5

60

12 x 7

84

12 x 12

144

7 x 6

42

13 x 3

39

13 x 4

52

13 x 5

65

13 x 6

78

13 x 7

91

13 x 8

104

13 x 9

117

13 x 11

143

13 x 12

156

14 x 3

42

14 x 4

56

14 x 5

70

14 x 6

84

14 x 7

98

14 x 8

112

14 x 9

126

14 x 11

154

14 x 12

168

15 x 3

45

15 x 4

60

15 x 5

75

15 x 6

90

15 x 7

105

15 x 8

120

15 x 9

135

15 x 11

165

15 x 12

180

√(27/3) = ?

√27/√3

√27 --> √ (3 x 9) = √3 x √9 = 3√3

(3√3)/√3

3 √(3/3)

3 √ (1)

3

The volume of the brick is

L x W x H

(x^2-y^2)/ (x-y) = ?

(x+y) (x-y)/ (x-y)

(x + y)

To convert temperatures in degrees Fahrenheit to Celsius...

Subtract 32 and multiply by .5556 (or 5/9).

x^2 + 3 x - 10

(x - 2) (x + 5)

x^2 + 2 x - 24

(x - 4) (x + 6)

x^2 - 9 x + 18

(x - 3) (x - 6)

2 x^2 - 5 x - 12

(x - 4) (2 x + 3)

18 x^3 - 57 x^2 - 85 x + 100

(x - 4) (3 x + 5) (6 x - 5)

To convert temperatures in degrees Celsius to Fahrenheit...

multiply by 1.8 (or 9/5) and add 32.

Salt helps to melt ice because it

lowers the temperature at which water freezes.

Integer

whole number (-3, 0, 3)

Prime Number

Only can divide by itself and 1 (i.e. 2, 3, 5, 7..etc) (ONE IS NOT A PRIME NUMBER) *the smallest prime number is 2*

Area of Circle

πr^2

Composite Number

A positive, whole number that can be divided evenly by numbers other than 1 or itself. Composite numbers have more than 2 factors.

Trick to see if the number is divisible by 3

Add up the digits: if the sum is divisible by three, then the number is as well

Trick to see if the number is divisible by 4

Look at the last two digits. If the number formed by its last two digits is divisible by 4, the original number is as well.

Trick to see if the number is divisible by 5

If the last digit is a five or a zero, then the number is divisible by 5.

Trick to see if the number is divisible by 6

Check 3 and 2. If the number is divisible by both 3 and 2, it is divisible by 6 as well.

Trick to see if the number is divisible by 7

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again.

Trick to see if the number is divisible by 8

Check the last three digits.if the last three digits of a number are divisible by 8, then so is the whole number.

Trick to see if the number is divisible by 9

Add the digits. If that sum is divisible by nine, then the original number is as well.

(1/2) % (5/6) = ?

(1/2) x (6/5)

(1x6)/(5x2)

6/10

%2 to each #

(3/5)

√50 = ?

√ (25 x 2)

5√2

4!

The factorial function (symbol: !) means to multiply a series of descending natural numbers

4 × 3 × 2 × 1 = 24

How much greater is 3x + 5 than the value of 3x − 7?

12

Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 12 more photos than Claire. How many photos has Claire taken?

6

The sum of 7 numbers is greater than 140 and less than 210. Which of the following could be the average (arithmetic mean) of the numbers?

20, 26, 30, 34 ?

26

The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days?

The correct answer is (C). There are 360 degrees in a complete circle, so 360/30 = 12 hours to make one full circle. In 6 days there are 24 hours x 6 = 144 hours total. The total number of rotations will be 144/12 = 12.

3^5 x 3^3 = ?

3^8

Which of the following expressions is equal to 38 when

p = 3^5?

The correct answer is 27p

38 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3

or

3^5 x 3^3 = p x 3^3

p x 3^3 = 27p

If y + 3y + 5y = −18, then what is the value of y?

-2

If b does not equal zero, and ab = b/4, what is the value of a?

solve for a, divide both sides of the equation by b

ab = b/4

(ab)/b = (b/4)/b

a = (b/4)*1/b

a = 1/4

If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?

The correct answer is (D). This word problem requires careful translation. Let's say t = total current inventory of chairs. The first sentence states that 50 + t = (3/2)t. First solve for the current inventory:

50 + t = (3/2)t

50 = (3/2)t − t

50 = (1/2)t

100 = t

The manager wants to increase this by 40%.

40% of 100 is 40, so the new inventory will be 140.

How many 1/3 pound paperback books together weigh 25 pounds?

75

25/1 x 3/1

25 x 3

The first four terms in a sequence are shown below. What is the sixth term in the sequence?

{3, 6, 11, 18, ...}

38

Begin by examining the sequence for a pattern. In order to go from 3 to 6, 3 must be added; moving from 6 to 11 requires 5 to be added; moving from 11 to 18 requires 7 to be added. The pattern emerges here — adding by consecutive odd integers.

The 5th term is equal to 18 + 9 = 27, and the 6th term is equal to 27 + 11 = 38.

Each year, a cyber café charges its customers a base rate of $25, with an additional $0.30 per visit for the first 50 visits, and $0.10 for every visit after that. How much does the cyber café charge a customer for a year in which 72 visits are made?

Translate the information into arithmetic. The café charges $25 + $0.30(first 50) + $0.10(additional after 50). For 72 visits there are 50 visits with an additional 22 visits.

$25 + $0.30(50) + $0.10(22)

=$25 +$15 + $2.20

=$42.20

If Jill needed to buy 9 bottles of soda for a party in which 12 people attended, how many bottles of soda will she need to buy for a party in which 8 people are attending?

We can set up a proportion to solve:

9 bottles / 12 people = x bottles / 8 people.

Cross-multiply to solve a proportion:

(9)(8) = (12)(x)

72 = 12x

6 = x

Steve bought a total of 6 packages of pens, and each package contained either 3 or 7 pens. If exactly 4 of the packages Steve bought contained 7 pens, how many pens did Steve buy?

If Steve bought 4 packages of 7 pens and 6 packages total, then he must have purchased 2 packages of 3 pens.

4(7) + 2(3) = 28 + 6 = 34

Blair's average (arithmetic mean) on two physics tests is 7. What should Blair's score be on the next test to have an overall average of 8 for all the tests?

The arithmetic mean is defined as the sum of the terms divided by the number of terms.

7 = sum / 2

14 = sum

Adding the next test's score will change the average to an 8, and the total terms to 3.

8 = (14 + new score) / 3

24 = 14 + new score

10 = new score

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

4x^2 + 6x + 2

2 − 8 ÷ (24 ÷ 2) =

Remember your order of operations:

Complete operations within parentheses first.

Calculate exponents.

Then multiply and divide in order from left to right.

Then add and subtract in order from left to right.

2 − 8 ÷ (24 ÷ 2) =

2 − 8 ÷ (16 ÷ 2) =

2 − 8 ÷ 8 =

2 − 1 =

1

Mean, Median, and Mode

Average, middle, most common

4^5 % 4^2 = ?

4 ^ (5-2)

4 ^3

x^0 = ?

1