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30 Cards in this Set

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Closure Property
Addition: a + b is a real number.
Mult: ab is a real number.
Communtative
Add: a + b= b + a
Mult: ab= ba
Associative
Add: (a+b)+c = a+(b+c)
Mult: (ab)c=a(bc)
Identity
Add: a+0=a, 0+a=a
Mult: a*1=a, 1*a=a
Inverse
Add: a +(-a)=0
Mult: a*(1/a)=1, a never = 0
Distributive
a(b=c)=ab+ac
Order of Operations
1. Do operations that occur within grouping symbols.
2. Evaluate powers.
3. Do multiplications and divisions left to right.
4. Do additiond and subtractions fromleft to right.
Distance Formula
d=rt

distance equals rate times time.
Simple Interest
I=Prt

Interest equals principal rate times time
Temperature
F= 9/5C+ 32
Area of Triangle
A=1/2bh

Area equals 1/2 base times height
Area of Rectangle
A=lw

Area equals length times width
Perimeter of Rectangle
P= 2l+2w
Area of Trapezoid
A= 1/2(b1+b2)h
Area of Circle
A= pie R squared
Circumference of Circle
C=2 pie R
Slope
M=(y2-y1)/ (x2-x1)
rise over run

Classification of lines by slope:
parallel: same
perpendicular: reciprocal
Horizontal: 0
Vertical: Undefined
Slope Intercept Form
y= mx+b
Point Slope Form
y-y1= m(x-x2)
Two Points
m= (y2-y1)/ (x2-x1)
Then y-y2= m(x-x2)
Area of a Triangle Matrix
Area= +- x1 y1 1
x2 y2 1
x3 y3 1

x1-3 and y1-3 given.
Cramer's Rule 2X2 matrix
2X2:
ax+by= e
cx+dy= f

det not equal 0, x= e b
f d
___
det a
y= a e
c f
___
det a
Cramer's Rule 3X3
ax+by+cz= j
dx+ey+fz= k
gX+hy+iz= l

X= j b c
k e f
l h i
over det a

y= a j c
d k f
g l i
over det a

z= a b j
d e k
g h l
over det a
Quadratic Functions
y= ax^2+bx+c
X coordinate of vertex
-b/ 2a
Axis of symmetry
Vertical line
x= -b/2a
Vertex Form of Quadratic Functions
y=a(x-h)^2+k

vetex= (h,k)
Axis of symmetry x=h
Intercept Form of Quadratic
y= a(x-p)(x-q)

X intercepts= p and q
Axis of symm: halfway between
(p,0) and (q,0)
Complex Numbers
Square root of -r = i square root of r

i^2= -1
(i-/ r)^2= -r
Completing the square
ax^2+bx+c=0

1. Move constant to the right side of the equation
2. take 1/2 of b, square it, and add to both sides of the equation.
3. rewrite left side as binomial squared and simplify right side.
4. take square root of both sides.
5. solve for x and simplify.