integer

a whole number,

includes negative numbers and 0

even

any integers divisible by 2,

includes negative integers and 0

odd

any integers not divisible by 2,

includes negative numbers

prime

a number that is only divisible by itself and 1,

does not include negative numbers, 0, or 1

factor

a positive integer that divides evenly

into another positive integer (few)

multiple

the product of some integer and

any other positive integer (many)

absolute value

positive form of a number

IxI

A number is divisible by 3 when...

the digits add up to a multiple of 3.

A number is divisible by 4 when...

the last two digits are divisible by 4.

A number is divisible by 6 when...

the number is even and

the digits add up to a multiple of three.

A number is divisible by 8 when...

the last three digits are divisible by 8.

A number is divisible by 9 when...

the digits add up to a multiple of 9.

A number is divisible by 12 when...

when the digits add up to a multiple of 3 and

the last two digits are divisible by 4.

Order of Operations

                       1. parenthesis

                       2. exponents

                       3. multiplication and division (→)

                       4. addition and subtraction (→)

1/3

0.33…

1/5

0.2

 1/6

0.166…

1/8

0.125

1/9

0.11…

1/11

0.0909…

1/12

0.083…

The Golden Rule of Inequalities

When you multiply or divide both sides

of an inequality by a negative number,

the inequality sign flips.

When adding or subtracting inequalities...

the inequality signs must be going

in the same direction. 

(x + y)² =

x² + 2xy + y² 

(x – y)² =

x² – 2xy + y² 

(x + y)(x – y) = 

x² – y²

Area of a Triangle

(½ base)(height),

where the height is perpendicular to the base

Isosceles Triangle 

two equal sides with the

opposite angles also equal

Equilateral Triangle

three equal sides and

three equal angles measuring 60°

Right Triangle

 contains a 90° angle and

the side opposite the right angle is

called the hypotenuse
 

Pythagorean Theorem

a² + b² = c², where c is the hypotenuse

(relationships between the sides

of a right triangle)

45:45:90 Triangle

30:60:90 Triangle 

√2

1.4

√3

1.7

parallelogram

opposite sides are equal in length and parallel (rectangles and squares are types of parallelograms)

Area of a Parallelogram

(base)(height),

where the height is perpendicular to the base

rectangle

parallelogram with 4 right angles

Area of a Rectangle

(length)(width)

square

rectangle with 4 equal sides

Area of a Square

x²

Area of a Circle

∏r²

Perimeter of a Circle

2∏r