numerical expression

consists of numbers and operations

evaluate

to find the value of an expression

order of operations

the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction

variable

a letter used to represent one or more numbers

variable expression

consists of numbers, variables, and operations

power

is a number made of repeated factors

exponent

a mathematical notation indicating the number of times a quantity is multiplied by itself

base

is the number that is repeatedly multiplied in a power

equation

a mathematical sentence with an equal sign that shows that two expressions are equivalent

solving an equation

finding all the solutions of an equation

formula

An equation that shows a relationship among two or more quantities

perimeter

The sum of the lengths of the sides of a polygon

area

the number of square units needed to cover a flat surface

integers

Positive and Negative Whole Numbers and 0. Examples: …. -3, -2, -1, 0, 1, 2, 3…..(Does not include fractions or decimals)

absolute value

the distance a number is from 0 on the number line, value of n is written l n l

additive identity property

The sum of a number and zero is always that number.

additive inverse property

The sum of a number and its opposite is zero.

multiplication identity property

The product of any number and one is that number.

mean

the sum of the values in a data set divided by the number of values in the set

commutative property of addition

In a sum, you can add terms in any order, a + b = b + a

commutative property of multiplication

the order of the factors does not change the product a x b = b x a

associative property of addition

changing the grouping of terms will not change the sum, (a + b) + c = a + (b + c)

associative property of multiplication

changing the grouping of factors will not change the product, (ab)c = a(bc)

distributive property

a(b + c) = ab + ac

an + ac = a(b+ c)

an + ac = a(b+ c)

terms

in an expression are separated by addition and subtraction signs

like terms

terms that have identical variable parts raised to the same power

coefficient

number in front of a variable

constant

a term that has no variable and does not change

coordinate plane

A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.

aka “the Cartesian plane” after René Descartes

aka “the Cartesian plane” after René Descartes

ordered pair

A pair of numbers, (x, y), that indicate the position of a point on a coordinate plane.

quadrant

one of four sections into which the coordinate plane is divided

Inverse Operation

operations that undo each other, such as addition and subtraction

Isolate the variable

To get a variable alone on one side of an equation or inequality in order to solve the equation or inequality

Equivalent Equations

equations that have the same solution

base

the bottom of a triangle

height

the perpendicular (90 degrees) distance from the base of a triangle to the opposite vertex

Inequality

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

Equivalent Inequalities

inequalities that have the same solution

prime number

A whole number that has exactly two factors, 1 and itself.

composite

a number that has more than two factors

monomial

a single term made up of numbers and variables

prime factorization

a number written as the product of its prime factors

greatest common factor

The largest factor that two or more numbers have in common.

simplest form

when the GCF of the numerator and denominator is 1

equivalent fractions

fractions that have the same value and the same simplest form

multiple

skip-counting by any given number Ex: 4, 8, 12, 16…

least common multiple

the smallest multiple that two or more numbers have in common

least common denominator

The least common multiple of the denominators of two or more fractions.

scientific notation

a method of writing very large or very small numbers by using powers of 10

reciprocal

one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2

rational number

A number that can be written as a/b where a and b are integers, but b is not equal to 0.

repeating decimal

a decimal in which one or more digits repeat infinitely

median

is the middle value in a data set where the numbers are ordered least to greatest

mode

is the value in a data set that occurs most often. If all values occur the same amount of times there is no mode for that set.

range

is the difference of the greatest value and the least value in a set of data.

circle

is the set of all points that are an equal distance from a point called the center

center

the point in the exact middle of a circle

radius

a line segment from the center of a circle to any point on the circle (is also half the diameter)

diameter

the distance across a circle through its center (is also twice the radius)

circumference

The distance around a circle.

ratio

a comparison of two numbers by division

rate

a ratio that compares two quantities measured in different units

unit rate

a rate that has a denominator of 1

equivalent ratios

Ratios that have the same value.

proportion

an equation that states that two ratios are equal

Ex: 1/2 = x/10

Ex: 1/2 = x/10

scale model

a model of an object in which the dimensions are in proportion to the actual dimensions of the object.

percent

a ratio whose denominator is 100

interest

is the amount paid for borrowing or lending money

principal

the original amount of money loaned or borrowed

annual interest rate

apr, the percent of the principal you pay or earn a year

probability of an event

number of favorable outcomes divided by total number of possible outcomes

theoretical probability

what should occur in a probability experiment…an experiment is not actually done

experimental probability

probability based on what happens when an experiment is actually done

opposite

the number that is on the other side of 0 and is exactly the same distance away from 0

radical expression

an expression that contains a square root

perfect square

a number that has a whole number for a square root ex: 9, 16, 121

irrational number

a number that can not be written a/b

Pythagorean Theorem

a² + b² = c²

Pythagorean triple

a set of three positive integers that work in the pythagorean theorem

Pi

3.1415…. is an irrational number resulting from the ratio of a circle’s circumference to its diameter

cube

special polyhedron with faces that are all squares

surface area

The total area of the 2-dimensional surfaces that make up a 3-dimensional object.

volume

the amount of 3-dimensional space occupied by an object

input

the x-value in a function

output

the y-value in a function

function

a relation that assigns exactly one output value for each input value

domain

the set of all the input (x-values) for a function

range

the set of all the output (y-values) for a function

linear equation

an equation whose answers are ordered pairs (x,y) and whose answers graph a straight line

x-intercept

the point where a graph crosses the x-axis

y-intercept

the point where a graph crosses the y-axis

slope

the steepness of a line on a graph, rise over run

slope intercept form

y = mx + b

tree diagram (probability)

a diagram used to show the total number of possible outcomes in an experiment

odds

the ratio of the number of ways the event can occur to the number of ways the event cannot occur. Favorable over Unfavorable.

independent event (probability)

an event that is not affected by another event.

dependent event (probability)

an event who’s outcome does depend on the outcome of a previous event

fundamental counting principle

…

combinations

…

permutations

…