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Rules of Algebra
Quadratic Formula
Special Product Formulas
2 2 3 3 3 3 If a ≠ 0, the roots of
0
are
√ 4
2
Exponents and Radicals
⁄ √ √ √ √ √
! √
√
" √ 2 2 Binomial Theorem
⁄ √
⁄
Special Factoring Formulas
√
Absolute Value (p > 0)
|| * if and only if either * or
*,
which means
*
|| , * if and only if both , * and
- *,
which means
* , , *.
|| / * if and only if both / * and
0 *,
which means
* / / *.
|| - * if and only if either - * or
, *.
|| 0 * if and only if either 0 * or
/ *.
Inequalities
#
#
1
2
# ' '
% %
&
If a > b and b > c, then a > c.
If a > b, then a+c > b+c.
If a > b and c > 0, then ac > bc.
If a > b and c < 0, then ac < bc.
where
!
' '!
'!
Sequences and Series
Exponentials and Logarithms
Sum 1 of the first n terms of an arithmetic
sequence with first term and common
difference d
1 2 or 1 232 # 145
Sum 1 of the first n terms of a geometric
sequence with first term and common
ration r
1 7 8 8
or 19 7
8
Arithmetic mean A of n numbers
:
% #
Geometric mean G of n numbers
; " … ,
' - 0
log @A#B C log log log log log log log 8 D log EFGH I log I log 1 0
log 1
log logJ ln log L log M log M
log