Trig Mid Term

Front 1

Closure Property

Back 1

Addition: a + b is a real number.
Mult: ab is a real number.

Front 2

Communtative

Back 2

Add: a + b= b + a
Mult: ab= ba

Front 3

Associative

Back 3

Add: (a+b)+c = a+(b+c)
Mult: (ab)c=a(bc)

Front 4

Identity

Back 4

Add: a+0=a, 0+a=a
Mult: a*1=a, 1*a=a

Front 5

Inverse

Back 5

Add: a +(-a)=0
Mult: a*(1/a)=1, a never = 0

Front 6

Distributive

Back 6

a(b=c)=ab+ac

Front 7

Order of Operations

Back 7

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.

Front 8

Distance Formula

Back 8

d=rt

distance equals rate times time.

Front 9

Simple Interest

Back 9

I=Prt

Interest equals principal rate times time

Front 10

Temperature

Back 10

F= 9/5C+ 32

Front 11

Area of Triangle

Back 11

A=1/2bh

Area equals 1/2 base times height

Front 12

Area of Rectangle

Back 12

A=lw

Area equals length times width

Front 13

Perimeter of Rectangle

Back 13

P= 2l+2w

Front 14

Area of Trapezoid

Back 14

A= 1/2(b1+b2)h

Front 15

Area of Circle

Back 15

A= pie R squared

Front 16

Circumference of Circle

Back 16

C=2 pie R

Front 17

Slope

Back 17

M=(y2-y1)/ (x2-x1)
rise over run

Classification of lines by slope:
parallel: same
perpendicular: reciprocal
Horizontal: 0
Vertical: Undefined

Front 18

Slope Intercept Form

Back 18

y= mx+b

Front 19

Point Slope Form

Back 19

y-y1= m(x-x2)

Front 20

Two Points

Back 20

m= (y2-y1)/ (x2-x1)
Then y-y2= m(x-x2)

Front 21

Area of a Triangle Matrix

Back 21

Area= +- x1 y1 1
x2 y2 1
x3 y3 1

x1-3 and y1-3 given.

Front 22

Cramer's Rule 2X2 matrix

Back 22

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

Front 23

Cramer's Rule 3X3

Back 23

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

Front 24

Quadratic Functions

Back 24

y= ax^2+bx+c

Front 25

X coordinate of vertex

Back 25

-b/ 2a

Front 26

Axis of symmetry

Back 26

Vertical line
x= -b/2a

Front 27

Vertex Form of Quadratic Functions

Back 27

y=a(x-h)^2+k

vetex= (h,k)
Axis of symmetry x=h

Front 28

Intercept Form of Quadratic

Back 28

y= a(x-p)(x-q)

X intercepts= p and q
Axis of symm: halfway between
(p,0) and (q,0)

Front 29

Complex Numbers

Back 29

Square root of -r = i square root of r

i^2= -1
(i-/ r)^2= -r

Front 30

Completing the square

Back 30

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.