Multiplying Exponents

1
Multiplying Exponents
2
3
X (X )
2 3 5
5
X

x ( x )
1 1 2
2
X

2
Solving linear equations
Solve for x x 2 5 -2 -2
x 3
To get rid of 2 Subtract 2

x 3 7 3 3 x 11
To get rid of 3 Add 3
3
Solving linear equations
Solve for x
2 x 6
To get rid of multiplying x by 2 , divide by 2
2x 6
2
2
This is how u can check your work
2 ( 3) 6
2 x 6
X 3
4
How to graph points
y
.
.
Finding point (1,2)
2
1
x
1
2
(x, y)
5
Graphing linear equations
Y x
Y x2
Y x-2
y
x
2 , line goes up 2
The arrows means that the line keeps on going
- 2 , line goes down 2
6
Just multiply everything from ( x 2) (x 3) then
add them
2
( x 2) ( x3) X
1)
2)
( x 2) ( x3)
2x
3)
3x
( x 2) ( x3)
4)
2x 3x 5x
( x 2) ( x3)
6
5)
x
5x 6
2

7
Substitution X Y 1 Y 4x 1
2
Y 4x 1 X ( 4X 1 ) 1 X
4x X - 4X 0 X( X - 4 ) 0 X 0
X 4
2
2
2
8
Changing log form into exponent form
n
log x n B x
B
log 64 2
X
2
X 64
X 8
9
log X log Y log (XY)
B
B
B
log 4 2 log 3
B
B
2
log 4 log 3
B
B
log 4( 9)
log 36
B
B
10
B
log X - log Y log ( X )
B
B
Y
11
Compound interest A P( 1 i )
N
Brandon has 800 and is increasing 6 annual
increase, compound annually, How much will
Brandon have in 4 years?
4
A 800( 1 .06) 1009.98
12
Long Division X 3 X 10 X 21
x
2
7
X X
2
x
- (x 3 X )
2
X ( x 3) x 3X
7x 21
2
- ( 7x 21)
7( x 3 )
13
Y X
2
Y X
2
FOCUS
FOCUS
Directrix
Directrix
Y 4PX FOCUS (P ,0 ) DIRECTRIX X - P
2
X 4PY FOCUS ( 0, P) DIRECTRIX Y - P
2
2
Y 12 X SO.. 12
4P P 3 FOCUS ( 3 , 0 )
DIRECTRIX Y - 3
14
X Y A B
X Y B A
2
2
2
2
1
1


2
2
2
2
B
A
c
C FOCI C A - B
2
2
2
VERTICES
15
Sin 0 0
H
Cos 0 A
H
H
O
Tan 0 O
A
A
16
Y sin x
1
2 Pi
Pi
-1
17
Sec x 1 Cot x cos x
Cos x
Sin X
Csc X 1 / sin x
Prove Sec x ( cot x ) Csc x
1/ cos x ( cos x / sin x )
1/ sin x Cscx