Algebra/PreAlgebra terms

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Complex numbers

Numbers that have a real number component and an imaginary number component (which is a real number multiplied by the square root of -1). 

Counting/Natural/Whole numbers

The counting numbers start at 1 and increase by 1 (1, 2, 3, 4,...). The whole numbers include 0 and the natural numbers sometimes do include 0 and sometimes don't.

Dependent variable

The dependent variable, often labeled y in an x, y scheme, is the variable that gets its value from an equation's operation(s) on the independent variable.

Domain

The domain is a list of all the values of a function that are allowable. For instance, in the function 1 / x, x cannot equal 0 (because dividing by 0 makes a fraction undefined. Think of taking a pizza and cutting it into 0 slices... but even having the pizza means that there is at least one slice. And so we'd have to get rid of the pizza... and having a fraction talking about a pizza that is completely non-existent makes the whole fraction become undefined.

FOIL

This is the method used to multiply two binomials together, such as

• First terms - in our case that's
• Outside terms - in our case that's 
• Inside terms - in our case that's 
• Last terms - in our case that's 

All this gives: 

Imaginary numbers

Whole numbers multiplied by the square root of -1, which is symbolized with the letter i.

Independent variable

The independent variable, often labeled x in an x, y scheme, is the variable that is acted upon by an equation and which results in a resulting value.

Integer numbers

The positive and negative whole numbers (...,-3, -2, -1, 0, 1, 2, 3,...)

Irrational numbers

Numbers along a number line that can't be expressed as the fraction of two integers (ex. pi). 

Line equation, Double intercept form

An equation in the form of 

Line equation, Point-slope form

An equation in the form of , where m is the slope and  is a point on the line

Line equation, Slope-intercept form

An equation in the form of , where m is the slope and b is the y-intercept

Line equation, Standard form

An equation in the form of  where A, B, and C are all integers and A is positive.

Counting/Natural/Whole numbers

The counting numbers start at 1 and increase by 1 (1, 2, 3, 4,...). The whole numbers include 0 and the natural numbers sometimes do include 0 and sometimes don't. 

Order of Operations (PEMDAS)

This is the order in which we work expressions/equations:

• P = Parentheses (also known as Brackets)
• E = Exponentials
• M = Multiplication (same weight as Division)
• D = Division (same weight as Multiplication)
• A = Addition (same weight as Subtraction)
• S = Subtraction (same weight as Addition)

Quadratic Formula

where the trinomial is in the form ax^2 + bx + c 

Range

The range is the list of all the values that arise from the equation working on the domain. For example, in the equation y = |x| (y equals the absolute value of x), y will never be negative (because the absolute value operation takes whatever is inside and makes it positive). Therefore, the range is y >= 0.

Rational numbers

Numbers that can be expressed as the fraction of two integers. 

Real numbers

All the numbers along a number line and is comprised of both Rational and Irrational numbers. 

Counting/Natural/Whole numbers

The counting numbers start at 1 and increase by 1 (1, 2, 3, 4,...). The whole numbers include 0 and the natural numbers sometimes do include 0 and sometimes don't.