Variable

A symbol or letter used to represent a quantity that can change.

Constant

A value that does not change. Ex. 5, 7, -10

Coefficient

A number multiplied by a variable.

Term

A part of an expression to be added or subtracted.

Algebraic Expression

A mathematical phrase that can contain ordinary numbers, variables (like x or y³) and operators (like add,subtract,multiply, divide).

Product Property of Exponents

When multiplying like bases you add the exponents.

x⁴ x⁵ = x⁹

x⁴ x⁵ = x⁹

Quotient Property of Exponents

When dividing like bases you subtract the exponents

x⁶/x⁴ = x²

x⁶/x⁴ = x²

Power Property of Exponents

When raising a base to a power then another power you multiply the exponents. (x³)² = x⁶

Base of a power

The number or variable used a factor Ex. x⁵ the x indicates it is used as a factor

Exponent

An expression that indicates how many times the base is used as a factor. Ex. x⁵ the 5 indicates the base is used 5 times.

Power

Another name for the exponent.

PEMDAS

The order of operations - Parenthesis, Exponents, Multiply & Divide L->R, Add & Subtract L->R

Absolute Value

The distance of a number on the number line from zero. Represented by to vertical bars |x|.

Distance

Always represented by a positive number it represents the space between two locations.

Rule for Adding Real Numbers - Same Sign

Add the numbers and keep the sign

Rule for Adding Real Numbers - Different Signs

Subtract the numbers' absolute values and keep the sign of the greater number

Rules for Subtracting Real Numbers

KFC - Keep the sign of the first number

- Flip the subtract sign to an add sign

- Change the sign of the second number

- Flip the subtract sign to an add sign

- Change the sign of the second number

Rules for Multiplying/Dividing Non-Zero Real Numbers

Same Signs = Positive Opposite Signs = Negative

Ex. (-4)(2) = -8 | (-4)(-2) = 8

(4)/(-2) = -2 | (-4)/(-2) = 2

Ex. (-4)(2) = -8 | (-4)(-2) = 8

(4)/(-2) = -2 | (-4)/(-2) = 2

Distributive Property

For all real numbers a( b + c ) = ab + ac

a( b - c ) = ab - ac

a( b - c ) = ab - ac

Like Terms

Two or more terms that have the same variable(s) with the same power(s)

Dimensional Analysis

a process for converting measures into different units by using unit multipliers

Area of a square

A = s²

Area of a rectangle

A = lw

Area of a parallelogram

A = bh

Area of a circle

A = πr²

Area of a triangle

A = ½bh

Square Root √x

The number multiplied by itself to give x

Perfect Square

A number that is a square of an integer.

Probability

A measure of how likely a given event, or outcome, will occur. Represented by a fraction, decimal, or percent. (# ways to get what you want)/(Total # of possibilities)

Solve an equation

To find the value or values of a variable which will make the statement true. There is always a possibility of no solution or all numbers are a solution.

Inverse Operations

Operations that undo each other.

Addition ↔ Subtraction Multiplication ↔ Division

Addition ↔ Subtraction Multiplication ↔ Division

Independent variable

The variable whose value can be chosen. INPUT

Dependent variable

The variable whose value is determined by the input value of another variable. OUTPUT

Stem-and-leaf plot

A display where the data is organized by PLACE VALUE, very useful if you need to find the mean, median, or mode of the data set.

Bar Graph

A display where the data is represented by vertical or horizontal bars.

Mean

The average of a set of numbers. The sum of values in a data set divided by the number of data values.

Median

The middle number in a set of numbers when they are arranged in order. If there is an even number of data values in the set, find the mean of the two middle numbers.

Mode

The value or values that occur most frequently in a data set. If all values occur the same number of times, then it does not exist.

Domain

The set of possible values for the independent variable. The x values.

Range

The set of possible values for the dependent variable.

The y values.

The y values.

Ordered Pair

A point on the coordinate plane (x,y)

Relation

A set of ordered pairs where each number in the domain is matched to one or more numbers in the range.

Function

A special relation where every x value in the domain pairs with exactly one value in the range (y).

Function Notation

f(x) This is read as "f of x" This does NOT mean f times x. This is a special way to show an expression is a function. It can use other letters but must have the same format where (?) is the independent variable. A(l) G(e) B(r)