Algebra 1 and 2 terms

Variable

A letter representing an unknown number (x in x plus 5 equals 10)

Constant

A number that does not change (5 and 10 in x plus 5 equals 10)

Coefficient

The number in front of a variable (3 in 3x)

Term

A part of an expression separated by plus or minus signs (2x 4y and negative 7 in 2x plus 4y minus 7)

Expression

A math phrase without an equal sign (2x plus 3)

Equation

A statement showing two expressions are equal (2x plus 3 equals 9)

Inequality

Compares two expressions using inequality symbols (x greater than 5)

Like Terms

Terms with the same variable and exponent (3x and 5x)

Combine Like Terms

Add or subtract the coefficients of like terms (3x plus 5x equals 8x)

Simplify

To make an expression shorter without changing its value (2x plus 3x becomes 5x)

Addition Subtraction Multiplication Division

Basic math operations

Exponent

Shows how many times to multiply a number by itself (3 squared equals 9)

Base

The number being multiplied by itself in an exponent (3 in 3 squared)

Power

An expression with a base and exponent (3 squared)

Square

A number multiplied by itself (4 squared equals 16)

Square Root

The number that when multiplied by itself equals another (square root of 16 equals 4)

Absolute Value

The distance of a number from zero (absolute value of negative 5 equals 5)

Inverse Operation

An operation that undoes another (addition and subtraction are inverses)

Distributive Property

Multiply a number by everything in parentheses (2 times x plus 3 equals 2x plus 6)

Associative Property

Changing grouping does not change the result ((2 plus 3) plus 4 equals 2 plus (3 plus 4))

Commutative Property

Changing order does not change the result (2 plus 3 equals 3 plus 2)

Identity Property Additive

Adding zero keeps the number the same (x plus 0 equals x)

Identity Property Multiplicative

Multiplying by one keeps the number the same (x times 1 equals x)

Inverse Property Additive

A number plus its opposite equals zero (x plus negative x equals 0)

Inverse Property Multiplicative

A number times its reciprocal equals one (x times 1 over x equals 1)

Solution

The value that makes an equation true (x equals 4 in x plus 3 equals 7)

Solve

To find the value of a variable in an equation (2x equals 10 gives x equals 5)

Isolate the Variable

Get the variable alone (2x equals 10 becomes x equals 5)

Balance the Equation

Do the same operation to both sides to keep equality

Check Your Solution

Substitute the solution to see if it works (4 plus 3 equals 7)

Function

A rule giving one output for each input (f of x equals x plus 2)

Domain

All possible input values (x values)

Range

All possible output values (y values)

Ordered Pair

A point written as x y (2 5)

Coordinate Plane

A grid made of the x and y axes

Slope

The steepness of a line (rise over run)

Y intercept

Where a line crosses the y axis (y equals 2x plus 3 has y intercept 3)

X intercept

Where a line crosses the x axis

Slope Intercept Form

Equation of a line written as y equals m x plus b

Point Slope Form

Equation written as y minus y one equals m times x minus x one

Standard Form

Equation written as A x plus B y equals C

Parallel Lines

Lines that never meet (same slope)

Perpendicular Lines

Lines that intersect at right angles (slopes are negative reciprocals)

Polynomial

A sum of terms with variables and exponents (2x cubed plus 5x squared minus 7x plus 4)

Degree

The highest exponent in a polynomial (degree 3 in 2x cubed plus 5x squared)

Monomial

A polynomial with one term (5x squared)

Binomial

A polynomial with two terms (x plus 3)

Trinomial

A polynomial with three terms (x squared plus x plus 1)

Factor

To break an expression into parts that multiply (x squared plus 3x equals x times x plus 3)

Greatest Common Factor

The largest shared factor (GCF of 6x and 9x squared is 3x)

Factoring Out

Removing the GCF from each term (6x plus 9x squared equals 3x times 2 plus 3x)

Difference of Squares

A squared minus B squared equals (A minus B) times (A plus B) (x squared minus 9 equals (x minus 3)(x plus 3))

Quadratic Trinomial

A trinomial in the form a x squared plus b x plus c (x squared plus 5x plus 6)

Factoring Trinomials

Breaking a trinomial into two binomials ((x plus 2)(x plus 3))

Quadratic Equation

An equation in the form a x squared plus b x plus c equals 0

Parabola

The U shaped graph of a quadratic equation

Vertex

The highest or lowest point on a parabola

Axis of Symmetry

The line dividing a parabola into two equal halves

Roots Zeros Solutions

The x values where the parabola crosses the x axis (x equals negative 2 and x equals negative 3)

Quadratic Formula

Formula for solving any quadratic (x equals negative b plus or minus square root of b squared minus 4 a c over 2 a)

Discriminant

Part of the quadratic formula (b squared minus 4 a c)

Completing the Square

Turning a quadratic into a perfect square trinomial

Vertex Form

Equation written as y equals a times x minus h squared plus k (h k is the vertex)

System of Equations

Two or more equations with the same variables

Solution of a System

The point where equations intersect (x equals 2 y equals 3)

Substitution Method

Solve one equation for a variable and substitute into the other

Elimination Method

Add or subtract equations to remove a variable

Graphing Method

Graph equations and find where they meet

Consistent

Has at least one solution

Inconsistent

Has no solution

Dependent

Has infinitely many solutions

Negative Exponent

Means reciprocal of the base (2 to the negative 2 equals 1 over 4)

Zero Exponent

Any nonzero number to the zero power equals one (5 to the zero equals 1)

Product Rule

Add exponents when multiplying like bases (x squared times x cubed equals x to the fifth)

Quotient Rule

Subtract exponents when dividing like bases (x fifth over x squared equals x cubed)

Power Rule

Multiply exponents ((x squared) cubed equals x to the sixth)

Radical

The root symbol (square root sign)

Radicand

The number inside the radical (25 in square root 25)

Index

The small number showing which root (3 in cube root of 8)

Simplifying Radicals

Reduce a radical to simplest form (square root of 50 equals 5 square root 2)

Rational Expression

A fraction with polynomials in numerator and denominator

Excluded Values

Values that make the denominator zero

Exponential Function

A function where the variable is in the exponent (y equals 2 to the x)

Logarithm

The inverse of an exponential (log base b of a equals x means b to the x equals a)

Sequence

An ordered list of numbers (2 4 6 8)

Arithmetic Sequence

A sequence adding a constant (add 2 each time)

Geometric Sequence

A sequence multiplying by a constant (multiply by 2 each time)

Series

The sum of a sequence

Probability

Chance of an event (1 out of 6 for rolling a 6)

Independent Events

Events that do not affect each other (rolling a die and flipping a coin)

Dependent Events

Events where one affects the other (drawing cards without replacement)

Mean

The average of numbers

Median

The middle number in a set

Mode

The most common number in a set

Range Statistics

The difference between highest and lowest values

Imaginary Unit

The square root of negative one

Complex Number

A number with real and imaginary parts (3 plus 2i)

Conjugate

Complex numbers with opposite imaginary signs (3 plus 2i and 3 minus 2i)

Interval Notation

Shows ranges of values ((a b) means between a and b)

Piecewise Function

A function with different rules for different intervals