math

coefficient

number infront of a variable

expression

A mathematical phrase that contains operations, numbers, and/or variables. \n Does NOT have an equal sign. An expression can only be evaluated or simplified.

equation

A mathematical sentence that contains an equals sign. \n \n Unlike expressions, equations can be solved for a desired variable.

inequality

A statement that compares two quantities using <, >, ≤,≥, or ≠

variable

A symbol used to represent a quantity that can change

Commutative Property of Multiplication

ab=ba \n Changing the order of the factors does not change the product.

Commutative Property of Addition

Commutative Property of Addition

slope

the constant rate of change of a line. \n The variable, m, in y=mx+b represents the slope.

y-intercept

the y-coordinate of a point where a graph crosses the y-axis

x-intercept

the x-coordinate of a point where a graph crosses the x-axis

PEMDAS

Please Excuse My Dear Aunt Sally (Parenthesis, Exponents, Multiply, Divide, Add, Subtract); order in which an equation is worked out - multiplication and division as well as adding and subtracting can be interchanged, depending on which comes first (from left to right) in the equation

distributive property

a(b + c) = ab + ac

equivalence property

If a = b, then a + c = b + c and ac = bc.

associative property of addition

(a+b)+c=a+(b+c)

associative property of multiplication

(ab)c=a(bc)

standard equation of a line

Ax + By = C

slope-intercept form

y=mx+b

The goal when solving an equation…

To isolate the variable on one side of the equal sign!

When does an equation not have a solution

When you finishing solving the equation and get something that is not true! \n If you get something like 0=1, 2=4, etc. These statements are never true! So this means there are no solutions.

When does an equation have INFINITE solutions?

When you finish solving an equation and you get something that is ALWAYS true! \n For example: 2=2, 1=1. 2x=2x, or (famously) 0=0! \n When you have the same exact thing on both sides of the equal sign, this means you have infinite solutions!

arithmetic sequence

A sequence in which the difference between any two consecutive terms is the same.

domain

The set of x-values of a relation. (The inputs of functions)

range

The set of y-values of a relation. (The outputs of a function)

relation

A relationship between x-value and a y-value.

set

a collection of objects (usually called elements)

vertical line test

If any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.

common difference

The common difference is the difference between two numbers in an arithmetic sequence.

function

a relation in which each element of the domain is paired with exactly one element of the range.

NOTE: for a relation to be considered a function, you cannot have the same input related to different outputs. In other words, one y- value for each x.

subset

smaller sets inside of bigger sets

Natural #s

the set of counting numbers starting at 1. ex. 1,2,3,4… no ending

Integers

the set of all positive, neg, whole #s, including 0

integers

naturals are subsets of

Real #s

the set of all positive, neg, whole #s, fractions, irrational

Rational #s

numbers that can be expressed as a fraction

Irrational #s

numbers that can’t be expressed as fractions

negative slope graph

line going down

positive slope graph

line going up

m=0

no change (horizontal)

undefined slope

vertical