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Factors
For integers...the set of numbers that can be divided into that integer

Prime #'s have only 2 of these
Composite #'s have at least 3
Multiples of an Integer
Values produced when the integer is multiplied by another integer.

3= 3,6,9,12 and so on
integers
{...3,2,1,0-1,-2,-3...} 0= even in order w no gaps = consecutive
place value
increase power 10 move left 543= 3 in 10s place 4 in 100s .543 = 5 in 10\"th\", 4 in 100\"th\"
prime/ composite
divided evenly by itself or one 3 yes always positive, whole and odd(except 2) / 4 no (can also be divided by 2)
5/2
2 r1
Decimals
1/4 = .25

adding/subtracting = same decimal places as term w most

multiplting = sum of places in two terms

dividing = move decimal on devisor to create an integer

Variables
Letters that represent an unknown number

do to one side , you must do to the other
Order of operations
Parentheses
exponent
X
/
+
-
"please excuse my dear aunt sally"
Exponent
2 (to the 5th power)

negative = same as 1 over number = x to -1 power = 1/x
multipying w exponents
same base, diff exponent = base same, add exponents

diff base, same exponent = multiple base, exponent stays the same

(3 to 2nd power)3rd power = 3 to 6th power

dividing - same base different exponent = subtract exponent

fraction as exponent = exponent given to both numerator & denominator
Decimal notation

Scientific notation
3000 = 3 x 10³

0.05 = 5 x 10-²(negative for #'s less than 1)
Square roots
# multiplied by itself 2x2=4 also -2x-2=4
positives have 2
 
negative numbers do not have square roots

sq rt of 0 = 0

Standard notation √= - √2

multiply = √2 x √2 = √4

divide = √8 / √4 = √2
z4 - 16 =
(z2 + 4)(z2 - 4)

factored down
Quadratic Equation
x= -b+/-√b² -4ac
            2a

ax² +2x
Inequalities
≠ is not equal to
< is less than
> is greater than
≤ is less than or equal to
≥ is greater than or equl to

when dividing negative numbers by each sice of inequality sign, flip the direction of the sign.
Pythagorean Theorem
a2 + b2 = c2
Quadrilaterals
Q = 4 sides = 360 degrees

square = 4 90degree angles

rhombus = equal sides diff angles

rectangle = 4 equal sides - 90 degree 2 opposite but equal

parallelogram = 2 opposite & equal pairs of sides, 2 equal pairs of non right angles

trapezoid = 4 unequl angles, 1 pair of parallel sides.
Polygons
closed figure

regular = all sides and all angles equal

5 = pentagon
6 = hexagon
7 = heptagon
8 = octagon
9 = nonagon
10 = decagon

(#of sides - 2)180degrees = sum of interior angles

sum of interior angles / # of sides = measure of each angle
circle

(x-A)2+(y-b)2=r2

A= coordinate of x-axis
B = coordinate of y axis
radius = center to border

chord = line from one edge to another

diameter = chord through center of circle

tangent = line intersects w circle in one point

concentric circles = 2 or more circles share center have diff diameters

arch = points connecting on edge I(degrees)

circumference = around circle

c=2(pie)(r)
Area of a triangle
1/2 (base x height)
Area of square, rectangle, parallelogram
L x W
Area of Rhombus
1/2(product of 2 diagonals)

(lies drawn between the vertices of opposing angles)
area of a circle
(pie)r2
Cylindar

(can shaped)
Area=(pie X r2) + 2(pie)rh

volume = (pie)r2h
rectangle solid
Area = 2(wl+lh+wh)

volume = lwh
x-axis

runs horizontally


quadrants numbered = counterclockwise starting upper right corner
y-axis

runs vertically


intersect at origin
slope
rise/run

slope = (y1-y2)/(x1-x2)
mean
same as average
median
middle value (set arranged from least to greatest)
1,3,5...,=meadiam = 3

adding together 2 middle values / 2
2,4,6,8...4+6=10/2 = meadian =5
mode
set of data that appears the most

Finding the range
take mean (ie 6) and standard deviation (ie 2) multiply standard diviation by 2= 4

add to mean on either side to show range. 2-10
d=rxt
distance=rate x time

time = distance/rate

rate = distance/time
units the same
interest problems
I=prt

I=interest
p=principal
r=rate of interest
t=time
Measurement

3ft = 1 yard
5280 ft = 1 mile
8oz = 1 cup
2 pints = 1 quart
4 quarts = 1 gallon

16oz = 1lb
2000 lbs = 1 ton
meter - length
liter-volume
gram-mass/weight

kilo - 1000
hector - 100
deka - 10
deci - 0.1
centi - 0.01
milli - 0.001


1liter = 1 quart
1kg = 2.2lbs
1inch = 2.54cm
28 grams = 1 oz
1yard=1meter
x of y cards