Topic 
Helpful
Information 
Example 
Absolute Value 
Absolute value = the distance a number is
from 0 on a number line 
The absolute value of 5 and 5 equals 5
because they are both 5 units from 0 
AxiomAdditive
axiom 
If a > b, then a + c > b + c. 

AxiomPositive
multiplication axiom: 
If c > 0, then a > b if, and only if, ac > bc. 

AxiomTransitive
axiom 
If a
> b and b > c, then a > c 

BinomialsMultiplying two binomials 
Formula = (a+b) (c+d) =ac + ad + bc + bd Use the FOIL method
First Outside Inside Last 
(b+2)
( b +3) F b*b = b^{2} O b*3 = 3b I 2*b =2b
L 3*2 =6 Combine:
b^{2} + 5b +6 
Combining like terms 
In order to combine they must have
like variables and exponents. 1. Place like terms together. 2.Combine each set 3. Put the answers to each combine
set together 
2a + 4b + 5a – 2b  2c + 4c
Step
1.2a + 5a +4b – 2b 2c + 4c 4b 2b =2b 4c 2c =2c 
EquationsLinear equations 
Slopeintercept form y
= mx +b 
Y = 3x + 9 where m=3 and b=9 4x + y = 20, a=4 and b=1 and c = 20 
EquationsSolving Equations 
Step 1 All
variables can be moved to the left of the equal sign and the numbers can be
on the right. Move integers by adding the
opposite sign of the integer.

Step 1. 2b + 3 =7 
EquationsSolving literal equations 
Step 1 The
desired variable should be on the left 
Solve for a 
EquationsWriting Equations 
Look for key words, for
example “the product of” means you should place the constant before a variable
“less than” and
“ more than” means
you should flip the order
Substitute equal when you see “is” If there are not any key
words create an equation in the order that the words are written. 
The product of 5 and x is 14 5x = 14 3 + y =15 x  10 = 5 11 + y =13 
Exponents And Rules for Exponents 
Exponents tell you how many times
to use the number in multiplication The
Rules x^{m} * x^{n} = x^{(m+n)} (x^{n})^{m}
= x^{(nm)} (xy)^{m}
= x^{m}y^{m} 
3^2 =
3*3 =9
3^3 =
3*3*3= 27 3^4 =
3*3*3*3 = 81 2^{2} * 2^{3} = 2^{(2+3) }= 2^{5} (2^{3})^{2} = 2^{(2*3)
}= 2^{6} (2*3)^{3} = 2^{3}*3^{3}
= 8*27 = 216 
ExponentsNegative exponents 
Move the term to the denominator,
make the exponent positive then apply the power. 
3^{2} = 1/3*3 = 1/9 3^{3} = 1/3*3*3= 1/27 