ASVAB Math Knowledge
Stanford University
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Asvab Arithmetic Reasoning Actual Practice Test questions and answers 2023
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Two automobiles start together at the same and travel along the same route. The first averages 40 miles per hour, the second averages 55 miles per hour. How many miles further along the route is the second automobile at the end of 5 hours? 
Answer; 55×5-40×5 
Distance =ratetime, A=60 Mph ×3 hours= 180. 
 
 
 
Find the total thickness of two pieces of wood that a carpenter glued together if one is 5/16 inches thick and the other is 7/8. 
Answer: 1 3/16 
(5/16)+(7/8) = (5/16)+(14/16) = 19/16= 1...
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ASVAB Math Knowledge Formulas
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Triangle 
AREA: 1/2 of base x height 
A= 1/2bh 
PERIMETER: a+b+c 
 
 
Square 
AREA: length x width 
A= lw 
PERIMETER: side+side+side+side 
P=4s 
 
 
Rectangle 
AREA: length x width 
A=lw 
PERIMETER: 2xlength + 2xwidth 
P= 2l+ 2w 
 
 
Parallelogram & Rhombus 
AREA: base x height 
A= bh 
PERIMETER: 2xlength + 2xwidth 
P=2l + 2w 
 
 
Trapezoid 
AREA: sum of 2 bases Divide by 2 x height 
A= (b1 + b2/ 2) h 
PERIMETER: a+b1+b2+c 
 
 
Circle 
C=piD= 2piR 
A=piR^2 
Pi= 3.14 or 22/7 
 
 
Cube 
VOLUME: si...
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ASVAB Math Practice questions fully solved & updated 2023
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Whole number: 
Positive numbers including zero. 
 
 
 
Integer: 
All positive and negative numbers including zero. 
 
 
 
Rational number: 
A number that can be written as a fraction. (numerator and denominator) 
 
 
 
Real number: 
All rational and irrational numbers. Example: -1/3 or 10/3 
 
 
 
Finding the sums= 
adding 
 
 
 
Finding the difference= 
subtracting 
 
 
 
Finding the product= 
multiplying 
 
 
 
Finding the quotient= 
dividing 
 
 
 
A Ratio means it has a: 
Numerator and Denom...
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ASVAB Math Knowledge test questions with 100% correct answers(verified for accuracy).
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Whole number: 
Positive numbers including zero. 
 
 
 
Integer: 
All positive and negative numbers including zero. 
 
 
 
Rational number: 
A number that can be written as a fraction. (numerator and denominator) 
 
 
 
Real number: 
All rational and irrational numbers. Example: -1/3 or 10/3 
 
 
 
Finding the sums= 
adding 
 
 
 
Finding the difference= 
subtracting 
 
 
 
Finding the product= 
multiplying 
 
 
 
Finding the quotient= 
dividing 
 
 
 
A Ratio means it has a: 
Numerator and Denom...
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ASVAB math vocabulary with verified definitions.
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Integer 
An integer is any positive or negative whole number or zero. The ASVAB often requires you to work with integers, such as -6, 0, or 27. 
 
 
 
Factor 
Factors are integers (whole numbers) that can be divided evenly into another integer. To factor a number, you simply determine the numbers that you can divide into it. For example, 8 can be divided by the numbers 2 and 4 (in addition to 1 and 8), so 2 and 4 are factors of 8. 
 
 
 
Composite number 
is a whole number that can be divided ev...
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Mathematics Knowledge ASVAB questions with verified correct answers
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Mathematics Knowledge - ASVAB (full) test 
1: If a = 5/2 then 1/a = 
 
A. 2 
B. 5 
C. 2/5 
D. 5/2 
C. 2/5 
C. Substitute 5/2 for a, giving you 1/a = 1/(5/2) = 1 x 2/5 = 2/5. 
 
 
 
Mathematics Knowledge - ASVAB (full) test 
2: 12 is 15% of what number? 
 
A. 0.0125 
B. 1.8 
C. 18 
D. 80 
D. 80 
D. Let n represent the number. If 12 is 15% of n, then 12 = 0.15n. Divide both sides by 0.15. Therefore, n = 80. 
 
 
 
Mathematics Knowledge - ASVAB (full) test 
3: Evaluate 3x + 7 when x = -3. 
 
A. -2 ...
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ASVAB Math exam questions with verified solutions(graded A+).
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System of equations 
A set of equations with the same variables. The solution is where they intersect on a graph; substitution or elimination 
 
 
 
Substitution 
-3x - 4y = -2 
y = 2x - 5 
substitute for y 
-3x - 4(2x - 5) = -2 
-3x - 8x + 20 = -2 
-11x = -22 
{x = 2} 
substitute for x 
y = 2(2) - 5 
y = 4 - 5 
{y = -1} 
solution = (2,1) 
 
 
 
Elimination/addition 
2x - 3y = 15 
5x + 3y = 27 
make sure either both x's OR both y's are the same 
2x - 3y = 15 
5x + 3y = 27 
add to get rid of y...
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ASVAB Mathematics Knowledge Practice Set 1 questions fully solved
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What is the height of a rectangle box with volume of 140, length of 10, and width of 7? 
2 
 
 
 
If x = square root 3, y = 2, and z = 1/2, then x^2 - 5yz + y^2 = ? 
2 
 
 
 
Solve for a: a/-2 +20 < -100 
a > 240 
 
 
 
( 3d - 7 ) - ( 5 - 2d ) = ? 
5d - 12 
 
 
 
Which of the following are possible values of x, if x^2 - x - 20 = 0? 
-4, 5 
 
 
 
The following two points lie on a line on the coordinate grid; ( -2, 0) and ( 4, 6). Which of the following is the equation of the line? 
y = x + ...
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2023 ASVAB Practice Test Part IV Mathematics Knowledge questions and answers
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1. Which of the following is the smallest prime number greater than 200? 
211 
 
 
 
2. If 40% is equal to the fraction of x/30, what is the value of x? 
12 
 
 
 
3. The expression "5 factorial" equals 
120 
 
 
 
4. What is the result of subtracting 3x² - 5x - 1 from 8x² + 2x + 9? 
5x² +7x - 8 
 
 
 
5. What is the meaning of the statement -30 < -5 
Negative 30 is less than negative 5 
 
 
 
6. Solve for x: 8x - 2 - 5x 
8=3 1/3 
 
 
 
7. A woman has $500 in a bank account. Every week, ...
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ASVAB math test questions and answers(verified for accuracy)
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To change a percent to fraction 
Multiply the percent by 1/100 and drop the percent sign 
 
5%=5x1/10=5/100 * 100 is always in the bottom 
 
 
 
To change a percent to a decimal 
Move decimal point over two places to the left and drop the percent sign 
 
5%=0.05 
 
 
 
Inverse operations 
Opposite operations the opposite of addition is sub 
Opposite of multiplication is division the inverse of 5 is 1/5 
 
 
 
Opposite of a number 
5 is a negative 5 
 
 
 
Ratio 
Represent any relationship betwee...
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