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Title: Mathematic formula of all Algebra
Description: Your skills is not more power at mathmatics in Algebra? Here you will get all kinds of Algebra formula or law.It,s need for doing any kineds of sum.So no tention with algebra .
Description: Your skills is not more power at mathmatics in Algebra? Here you will get all kinds of Algebra formula or law.It,s need for doing any kineds of sum.So no tention with algebra .
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Algebra Cheat Sheet
Basic Properties & Facts
Arithmetic Operations
Properties of Inequalities
If a < b then a + c < b + c and a − c < b − c
a b
If a < b and c > 0 then ac < bc and <
c c
a b
If a < b and c < 0 then ac > bc and >
c c
b ab
a =
c c
ab + ac = a ( b + c )
a
a
b =
c
bc
a
ac
=
b b
c
a c ad + bc
+ =
b d
bd
a c ad − bc
− =
b d
bd
a −b b−a
=
c−d d −c
Properties of Absolute Value
if a ≥ 0
a
a =
if a < 0
−a
a ≥0
−a = a
a+b a b
= +
c
c c
a
ad
b =
c bc
d
ab + ac
= b + c, a ≠ 0
a
a+b ≤ a + b
(a )
n m
an
1
= a n−m = m−n
m
a
a
( ab )
a 0 = 1, a ≠ 0
n
n
a −n =
a
b
= a nm
−n
1
an
n
bn
b
= = n
a
a
n
m
1
a = an
m n
a = nm a
( x2 − x1 ) + ( y2 − y1 )
2
2
n
Complex Numbers
i = −1
( ) = (a )
a = a
Properties of Radicals
n
d ( P , P2 ) =
1
a
a
= n
b
b
1
= an
−n
a
= a nb n
Triangle Inequality
Distance Formula
If P = ( x1 , y1 ) and P2 = ( x2 , y2 ) are two
1
points the distance between them is
Exponent Properties
a n a m = a n+m
a
a
=
b
b
ab = a b
1
m
n
n
1
m
i 2 = −1
−a = i a , a ≥ 0
( a + bi ) + ( c + di ) = a + c + ( b + d ) i
( a + bi ) − ( c + di ) = a − c + ( b − d ) i
( a + bi )( c + di ) = ac − bd + ( ad + bc ) i
( a + bi )( a − bi ) = a 2 + b 2
n
ab = n a n b
a + bi = a 2 + b 2
n
a na
=
b nb
( a + bi ) = a − bi Complex Conjugate
2
( a + bi )( a + bi ) = a + bi
n
a n = a, if n is odd
n
Complex Modulus
a n = a , if n is even
For a complete set of online Algebra notes visit http://tutorial
...
lamar
...
© 2005 Paul Dawkins
Logarithms and Log Properties
Definition
y = log b x is equivalent to x = b y
Logarithm Properties
log b b = 1
log b 1 = 0
log b b x = x
b logb x = x
log b ( x r ) = r log b x
Example
log 5 125 = 3 because 53 = 125
log b ( xy ) = log b x + log b y
Special Logarithms
ln x = log e x
natural log
x
log b = log b x − log b y
y
log x = log10 x common log
where e = 2
...
If b 2 − 4ac = 0 - Repeated real solution
...
x=
x 2 + ( a + b ) x + ab = ( x + a )( x + b )
x3 + 3ax 2 + 3a 2 x + a 3 = ( x + a )
x3 − 3ax 2 + 3a 2 x − a 3 = ( x − a )
3
3
Square Root Property
If x 2 = p then x = ± p
x3 + a3 = ( x + a ) ( x 2 − ax + a 2 )
x3 − a 3 = ( x − a ) ( x 2 + ax + a 2 )
x −a
2n
2n
= (x −a
n
n
)( x
n
+a
n
)
If n is odd then,
x n − a n = ( x − a ) ( x n −1 + ax n − 2 + L + a n −1 )
xn + a n
Absolute Value Equations/Inequalities
If b is a positive number
p =b
⇒
p = −b or p = b
p
⇒
−b < p < b
p >b
⇒
p < −b or
p>b
= ( x + a ) ( x n −1 − ax n − 2 + a 2 x n −3 − L + a n −1 )
Completing the Square
(4) Factor the left side
Solve 2 x − 6 x − 10 = 0
2
2
(1) Divide by the coefficient of the x 2
x 2 − 3x − 5 = 0
(2) Move the constant to the other side
...
math
...
edu
...
Line/Linear Function
y = mx + b or f ( x ) = mx + b
Graph is a line with point ( 0, b ) and
slope m
...
Parabola/Quadratic Function
y = ax 2 + bx + c f ( x ) = ax 2 + bx + c
The graph is a parabola that opens up if
a > 0 or down if a < 0 and has a vertex
b
b
at − , f −
...
2a 2 a
Circle
2
2
( x − h) + ( y − k ) = r 2
Graph is a circle with radius r and center
( h, k )
...
Hyperbola
( x − h)
2
( y −k)
−
2
( x − h)
2
=1
a2
b2
Graph is a hyperbola that opens left and
right, has a center at ( h, k ) , vertices a
units left/right of center and asymptotes
b
that pass through center with slope ±
...
a
For a complete set of online Algebra notes visit http://tutorial
...
lamar
...
−
© 2005 Paul Dawkins
Common Algebraic Errors
Error
Reason/Correct/Justification/Example
2
2
≠ 0 and ≠ 2
0
0
Division by zero is undefined!
−32 ≠ 9
−32 = −9 ,
(x )
(x )
2 3
2 3
≠ x5
a
a a
≠ +
b+c b c
1
≠ x −2 + x −3
2
3
x +x
− a ( x − 1) ≠ − ax − a
x2 + a2 ≠ x + a
x+a ≠ x + a
( x + a)
≠ x n + a n and
n
= 9 Watch parenthesis!
= x2 x2 x2 = x6
( x + a)
≠ x2 + a2
2
2
1
1
1 1
=
≠ + =2
2 1+1 1 1
A more complex version of the previous
error
...
More general versions of previous three
errors
...
You can not
factor out a constant if there is a power on
the parethesis!
2
1
− x2 + a2 ≠ − x2 + a2
a
ab
≠
b c
c
a
ac
b ≠
c
b
− x2 + a2 = ( − x2 + a 2 ) 2
Now see the previous error
...
math
...
edu
Title: Mathematic formula of all Algebra
Description: Your skills is not more power at mathmatics in Algebra? Here you will get all kinds of Algebra formula or law.It,s need for doing any kineds of sum.So no tention with algebra .
Description: Your skills is not more power at mathmatics in Algebra? Here you will get all kinds of Algebra formula or law.It,s need for doing any kineds of sum.So no tention with algebra .