Math-ASVAB
Speed =
Distance/time
If (3.2 + 3.3 + 3.5)w = w, then what is the value of w?
First add up the three numbers that are in parentheses: 10w = w 10w = w will only be true when w = 0.
11 x 12
132
15 x 9
135
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
In a classroom of 32 students, 14 are male. What percentage of the class is female?
First, solve how many females are in the class: Number of females = 32 - 14 = 18 To compute for the percentage of females in the class: Percentage = (18/32)(100%) = 56.25% = 56%
4 x 8
32
3 x 12
36
4 x 9
36
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.
13 x 3
39
3^5 x 3^3 = ?
3^8
4^5 % 4^2 = ?
4 ^ (5-2) 4 ^3
14 x 3
42
6 x 7
42
7 x 6
42
15 x 3
45
5 x 9
45
4 x 12
48
6 x 8
48
(4x + 2) (x + 1) =
4x^2 + 6x + 2
13 x 4
52
6 x 9
54
14 x 4
56
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
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.
If a square box has a volume of 125 in3in3 what's the perimeter of each side of the box?
A square box is a cube which means that length = width = height. Volume for a cubic box is the length of one side of the box cubed or V = s3s3 where s is the length of one side of the box. The cube root of 125 is 5 so the size of each side of the box is 5. The perimeter of a box is 2w + 2h which, in our case, is: (2 inches x 5) + (2 inches x 5) = 10 inches + 10 inches = 20 inches
To convert temperatures in degrees Celsius to Fahrenheit...
multiply by 1.8 (or 9/5) and add 32.
Fraction to Percent without using calculator
multiply the top by 100 first then divide by the bottom number
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*
18 x^3 - 57 x^2 - 85 x + 100
(x - 4) (3 x + 5) (6 x - 5)
4^-2 = ?
--> 1/4^2 1/16
12 x 5
60
√50 = ?
√ (25 x 2) 5√2
√(27/3) = ?
√27/√3 √27 --> √ (3 x 9) = √3 x √9 = 3√3 (3√3)/√3 3 √(3/3) 3 √ (1) 3
If y + 3y + 5y = −18, then what is the value of y?
-2
0^4 and 0^6
0
x^0 = ?
1
Area of a triangle =
1/2(base)(height)
Karen is 6 years older than her sister Michelle, and Michelle is 2 years younger than their brother David. If the sum of their ages is 62, how old is Michelle?
18
15 x 12
180
all the angles of a right triangle add up to?
180 degrees
sum of the interior angles of a triangle
180 degrees
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
3 X 7
21
3 X 8
24
3 x 9
27
8 x 9
27
4 x 7
28
diameter of a circle
2r
Firs 6 digits of Pi
3.141592
13 x 6
78
12 x 7
84
14 x 6
84
15 x 6
90
Degrees of a right angle
90 degrees
13 x 7
91
8 x 12
96
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
(1/2) % (5/6) = ?
(1/2) x (6/5) (1x6)/(5x2) 6/10 %2 to each # (3/5)
calculating simple interest
(interest = principal x interest rate)
x^2 + 3 x - 10
(x - 2) (x + 5)
x^2 - 9 x + 18
(x - 3) (x - 6)
2 x^2 - 5 x - 12
(x - 4) (2 x + 3)
x^2 + 2 x - 24
(x - 4) (x + 6)
(x^2-y^2)/ (x-y) = ?
(x+y) (x-y)/ (x-y) (x + y)
13 x 8
104
15 x 7
105
9 x 12
108
14 x 8
112
13 x 9
117
How much greater is 3x + 5 than the value of 3x − 7?
12
15 x 8
120
11 x 11
121
14 x 9
126
13 x 11
143
12 x 12
144
14 x 11
154
13 x 12
156
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)
15 x 11
165
14 x 12
168
13 x 13 = ?
169
3 X 6
18
15 x 4
60
5 x 12
60
9 x 7
63
13 x 5
65
14 x 5
70
6 x 12
72
15 x 5
75
A barista averages making 16 coffees per hour. At this rate, how many hours will it take until she's made 1,200 coffees?
75
How many 1/3 pound paperback books together weigh 25 pounds?
75 25/1 x 3/1 25 x 3
14 x 7
98
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.
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
Mean, Median, and Mode
Average, middle, most common
Circumference of Circle
C=2πr
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 8
Check the last three digits.if the last three digits of a number are divisible by 8, then so is the whole number.
Cory's average score after 8 tests is 91%. If he gets a 78% on his 9th test, what will his new average be?
For the 8 tests, the average is presented as 91, so you can assign the value of 91 to each of the 8 previous scores. This gives us 8 tests with a score of 91 each. 91⋅8=728 91⋅8=728 To get new average after the 9th test, use the same formula: 728+789=8069=89.5 728+789=8069=89.5 Since there are 2 answer choices that are very close to this, and you don't know which way the .5 will be rounded, extend the division another place by adding a 00 to the dividend, then divide. You find that the answer is now 89.5589.55, which rounds up to 89.689.6. Therefore, you now know that 89.589.5 would not be correct. Always extend the decimal places when 2 answer choices are as close as these and you don't know which one is correct. 89.6%
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
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.
The volume of the brick is
L x W x H
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.
P =
P = W ÷ time
order of operations
PEMDAS parentheses or brackets Exponents and roots Multiplication Division Addition Subtraction
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
To convert temperatures in degrees Fahrenheit to Celsius...
Subtract 32 and multiply by .5556 (or 5/9).
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
There are two pizza ovens in a restaurant. Oven 1 burns three times as many pizzas as oven 2. If the restaurant had a total of 12 burnt pizzas on Saturday, how many pizzas did oven 2 burn?
The correct answer is (A). Begin by setting up a system of equations to represent the situation, letting x represent oven 1 and y represent oven 2. x = 3y and x + y = 12 Substituting the first equation into the second: 3y + y = 12 so y = 3.
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.
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.
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
4!
The factorial function (symbol: !) means to multiply a series of descending natural numbers 4 × 3 × 2 × 1 = 24
Julie gives 7 pieces of candy to each of her friends. If Julie gives all of her candy away, which amount of candy could have been the amount she distributed?
The problem states that all of Julie's friends received 7 pieces each. There is no mention about the number of friends Julie gave the candies to. But no matter how many friends Julie gave the candies to, the total number of candies she has given away must be divisible by 7. There is no other way to solve the problem but try each given choice and pick one that is divisible by 7 and results in a whole number. 1617=23 1617=23 1287=18.28 1287=18.28 1457=20.71 1457=20.71 1627=23.14 1627=23.14 Therefore, the answer is 161 candies (distributed to 23 friends with 7 candies each).
Trapezoid question
The trapezoid consists of two smaller shapes: a triangle and a rectangle. Draw a line from point A across this figure to form the two shapes. Find the area of each shape and then add them together to find the area of the trapezoid. Area of rectangle = length x width. Therefore, the area of the rectangle is 18x20 = 360 Area of a triangle = 1/2(base)(height). The base of the triangle is 20. The height of the triangle is unknown. Use the Pythagorean Theorem to find the triangle's height. c2 = a2 + b2 where c is the triangle's hypotenuse. 292 = 202 + (height)2 841 = 400 + (height)2 441 = (height)2 The square root of 441 is 21 height = 21. Therefore, area of the triangle = (1/2)(20)(21) = 210. The total area of the trapezoid = 360+210 = 570.
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.
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
Second Law of Motion
acceleration imparted upon an object is directly related to the strength of the force and inversely related to the object's mass and always occurs in the direction of the force.
supplementary angles
added = 180 degrees
complementary angles
added = 90 degrees
Whole numbers
all positive integers and zero 0, 1, 2, 3
First Law of Motion
an object at rest tends to remain at rest unless acted upon by an outside force and that an object in motion tends to remain in motion at the same speed and at the same direction unless acted upon by an outside force
Rational numbers
any number that can be written as a fraction with integer numerator and denominator -2/5, -1/3, 0, 1, 4/3
Irrational numbers
any number that is not a rational number and that cannot be written as a fraction or as a non repeating decimal Pi (3.1415...), √3 (1.7320...)
compound interest
calculate simple interest for each year making sure to use the new principal + accumulated interest for each year's new interest calculation
torque =
force x distance Torque is a measure of moments of rotational force around a specific point
Reflex angle
greater than 180, less than 360
Obtuse
greater than 90 degrees, less than 180
Area of rectangle =
length x width.
Acute angle
less than 90 degrees
Salt helps to melt ice because it
lowers the temperature at which water freezes.
If 5^11 = 5^2 x 5^m, what is the value of m?
m = 9
radius of a circle
measures the length from the center of the circle to any point on its curve
The least common multiple
of two numbers is the smallest number that both numbers factor into evenly. The first five multiples of of 4 are {4, 8, 12, 16, 20} making the least common multiple of 3 and 4 equal to 12.
Real numbers
set of all rational and irrational numbers -√7, -1/3, 0, 1, 3/4
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
Third Law of Motion
states that for every action there is an equal and opposite reaction.
multiples
the set of numbers formed by multiplying a number by other numbers. For example, the first five multiples of 3 are {3, 6, 9, 12, 15}.
Integer
whole number (-3, 0, 3)
Volume for a cylinder
πr2h
Area of Circle
πr^2
