009 common equations and formulas for asvab math

COMMON
EQUATIONS AND
FORMULAS FOR
ASVAB MATH
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Common Equation and Formulas for ASVAB Math
Multiplication Table
* 1 2 3 4 5 6 7 8 9 10 11 12
1 1 (12) 2 3 4 5 6 7 8 9 10 11 12
2 2 4 (22) 6 8 10 12 14 16 18 20 22 24
3 3 6 9 (32) 12 15 18 21 24 27 30 33 36
4 4 8 12 16 (42) 20 24 28 32 36 40 44 48
5 5 10 15 20 25 (52) 30 35 40 45 50 55 60
6 6 12 18 24 30 36 (62) 42 48 54 60 66 72
7 7 14 21 28 35 42 49 (72) 56 63 70 77 84
8 8 16 24 32 40 48 56 64 (82) 72 80 88 96
9 9 18 27 36 45 54 63 72 81 (92) 90 99 108
10 10 20 30 40 50 60 70 80 90 100(102) 110 120
11 11 22 33 44 55 66 77 88 99 110 121(112) 132
12 12 24 36 48 60 72 84 96 108 120 132 144(122)

The table above is the standard multiplication table taught to
most students. The diagonal line of cells that bisects the table is
the line of perfect squares. This is the result of multiplying a
number by itself once.

Primes
Prime numbers are numbers that only have two
factors: 1 and the number itself. Here is a list of prime
numbers from 1 to 100.

1, 2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, and 97.

The most commonly referenced prime numbers will be
from 1 through 19.


First Outer Inner Last (F.O.I.L)
This method is handy technique for distributing. Use this when
you have an equation that is in factored form already, and you
need to distribute it back out.
First Outer Inner Last
(x+2)(2x-3)
Multiply the first terms. x*2x =2x2
Multiply the outer terms. x*(-3)= -3x
Multiply the inner terms. 2*2x=4x
Multiply the last terms. 2*(-3)= -6
Now put them together in descending order of powers and simplify.
2x2 – 3x + 4x – 6

And your completed answer is: 2x2 +x – 6
Now to factor that, you’ll need to look at the term with the largest
power of x, as well as the constant.

F.O.I.L
2x2 tells us that there are two factors (x2 = x times itself once. If it were x3 we
would know that there are three factors.) Since the coefficient of x2 is 2, and
the factors of 2 are 1 and 2, we know that the answer will have this in it.
(x )(2x )

Now look at -6. We know that because the end result is a ( – ) number, that
we will be multiplying a negative times a positive. We also know that the
factors of 6 are 1,2,3, and 6. We need to find out what factors will result in
the middle two terms adding up to +1.

After experimenting with these few factors, we can see that the correct
factors are 2 and 3, which gives us(x+2)(2x-3).


Squares and Rectangle
Perimeter
The perimeter of this shape is the sum of all of its sides. P=2L+2W
In the case of a perfect square, this can be simplified to P=4W, since all four
sides are equal.
Now, if L=3 and W = 2, we can find the perimeter.
P=2L+2W
P=2(3)+2(2)
P=6+4
P=10
Area
The area of a rectangle is the length multiplied to the width: A=L*W
In the case of a perfect square, this can be simplified to A=L2, or A=W2, as
they are equal.
If the length is 2in and the width is 3in, then the area is 6in2.
A=L*W
A=2in*3in
A=6in2

Triangles
Perimeter
The perimeter of a triangle can be found by adding all three sides. P=A+B+C

Area
The formula for the area of a triangle is A= ½*B*H where A=area, B=base
(side A in the illustration above) and H=height (not shown above, but shown
as the vertical straight line in the illustration below).

You can find the height by drawing a straight line from the top angle to the
base, so that the new triangle is a right triangle, with the angle between the
base and the height being the right angle. Remember, the new side, height,
cuts the base in half. Here’s that new triangle.

Pythagorean Theorem
If you are given a right triangle, and the two legs are given, you should be
able to find the hypotenuse using this equation c2=a2+b2

Triangles
If leg a is given as 2, and leg b is given as 3, we can find the hypotenuse, or c.
c2=a2+b2
c2=22+32
c2=13
c=√13

The square root of 13 is not an easy number to define without a calculator,
and often the hypotenuse will not be the result of a perfect square. Don’t
worry about this. On the test, since you’re not allowed to use a calculator, if
you see a question like this, you’ll likely see the answers listed in that same
simplified format as the above answer. You should be able to figure out that
the hypotenuse is the square root of 13, but no one is going to expect you to
calculate the exact square root of 13.


Circles
With circles, there are a couple of new terms introduced.
Circumference is the distance around all the way around the circle on
the outside. Here, Circumference=C.

Radius is the distance from the exact center of the circle to any point
on circle’s perimeter or circumference. Let Radius=r

Diameter is the distance of a straight line that touches the
circumference of the circle twice, and bisects the center point of the
circle. It is twice the radius. Diameter=D, or 2r.

Pi is a number that is used to in the calculation of circle area. It is
approximately 3.14, but that simply rounded to the nearest
hundredth.
Pi does not end, nor does it repeat. Pi=π

Circles
Circumference, Radius, Diameter
To find the Circumference of a circle, use this
equation: C=πD, or C=2πr.
If you are given the radius, you can find the diameter simply by
multiplying it by 2
D=2r
If you are given the diameter you can find the radius by dividing
it by 2, or multiplying by ½.
r= D/2, or r= ½ D
Area
You can find the area of a circle by multiplying pi and the radius
squared.
A=πr2

Rectangular Solid
Surface Area
The surface area is the areas of all of the planes added
together. Surface area = S
S=2(WH+LH+HL)

Volume
The volume of a rectangular solid (V) can be found by
multiplying length to width and then to height. It is
simply area with one more dimension added.
V=LWH


Cones
Surface area of a cone is S=π*r*√(r2+h2)+π*r2
Multiply pi and the radius of the base circle to the square
root of r2 + h2, and then add it to pi times r2
Volume of a cone is 1/3 *π*r2*h

Spheres
To find the surface area of a sphere,
multiply radius squared by pi and four.
S= 4*r2*π
To find the volume, multiply 4/3 by pi times
the radius cubed.
S= 4/3 * π *r3

Cylinders
To find the surface area of a sphere, multiply radius
squared by pi and four.
S= 4*r2*π

To find the volume, multiply 4/3 by pi times the radius
cubed.
S= 4/3 * π *r3


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009 common equations and formulas for asvab math

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009 common equations and formulas for asvab math