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MATH

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Outlier Data

A piece of data separate from the majority

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Curve of Best Fit (Linear)

a curve the best approximates the trend on a scatter plot.

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Curved of Best Fit (Quadratic)

a curve the best approximates the trend on a scatter plot.

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Curved of Best Fit (Exponential)

a curve the best approximates the trend on a scatter plot.

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No Correlation

Dots or pieces of data spread across a graph, unable to form a trend line.

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Negative Linear Relationship (Correlation)

a relationship where data of the y value decreases, while data of the x value increases

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Positive Linear Relationship (Correlation)

a relationship where data of the y value increases, while data of the x value increases

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Scatterplot

numerical data on a visual graph

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Mode

the value that appears most out of a data set

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Median

for pieces of data that has an odd number, the middle value is the median. however, for pieces of data with en even number, take the mean of the two middle value to get the median.

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Mean

the average of all values in a data set. (find the sum of all values in a data set, then divide the sum by the number of values)

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Summation

The sum of all values in a data set.

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Combination (and its formula)

the number of possible ways to arrange or select objects when there is no order.

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Geometric Sequence

sequence of numbers where the terms is being continuously multiplied by a rate

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Inverse of a Function

the process of when x & y value switch place; (2,9) → (9,2); y=7x-4 → y=(x/7)+(4/7)

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Discontinuity

a point at which a function is discontinuous or undefined.

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Linear Function (Vertical Dilation)

vertical dilation (stretch or compression) of the parent function, f(x) = x

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Transformations of Parent Function (Translation)

translations of a function strictly affects the ‘C’ and ‘D’

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Transformations of Parent Function (Dilation)

dilation of a function strictly affects the ‘A’ and ‘B’ values,

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Transformations of Parent Function (Reflection)

reflection of a function strictly affects the ‘A’ and ‘B’ values when turned negative.

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21

Parent function: Exponential vs. Logarithmic

EXPONENTIAL: f(x) = b^x where b > one.

LOGARITHMIC: f(x) = log-base-b (X), where ‘b’ >1

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Parent function: Rational

f(x) = 1/x, where x isn’t ‘0’

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23

Parent Function: Cubic vs. Cube Root

CUBIC: f(x)=x^3

CUBE ROOT: f(x)=∛x

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Parent Function: Absolute Value vs. Square Root

ABS VAL: f(x) = |x|

SQ RT: f(x) = √x

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25

Function Notation

one input per output using the term ‘f(x)’

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End Behavior

term used to dictate the domain and range of a function; i.e.:

x→∞, f(x) →∞

x→-∞, f(x)→-∞

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Extrema

the amount of vertices on a function.

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Increasing/Decreasing

a function can be described as increasing/decreasing/constant for either an interval or for the entire domain

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Range

all ‘y’ values in a function

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Domain

all ‘x’ values in a function

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Function

relationship between x & y values that forms data that could be represented through a line on a graph

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Relations

a set of ordered pairs

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Quadratic Formula

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Vertex of a Quadratic Function

The global/absolute maximum or minimum of the function.

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Graph of a Quadratic Equation

Parabola/f(x)=ax^2+bx+c

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Dependent/Independent Variable

X-value serves as an independent value (time, age, ect)

Y-value serves as a dependent variable (money, population, ect.)

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System of Linear Inequalities

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Graphing Linear Inequalities

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Systems of Equations (Linear)

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Systems of Equations (Quadratic)

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Systems of Equations (Linear) (Elimination)

the process of scaling and subtracting two equations from each other to find an ordered pair.

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Systems of Equations (Linear) (Substitution)

the process of scaling two functions and setting them equal to each other to find an ordered pair.

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Systems of Equations (Linear) (Graphing)

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Parallel Lines

Two linear functions of a graph that will never intersect

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Perpendicular Lines

Two linear functions that intersect at a 90 degree angle

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Slopes of Lines

change in y/change in x

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Slope Formula

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Slope

‘m’ in ‘y=mx+b’

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Equivalent Forms of A Linear Equation

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Linear Equation Point-Slope Form

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Linear Equation Slope-Intercept Form

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Linear Equation Standard Form

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Absolute Value Inequalities

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Division Property of Inequalities

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Multiplication Property of Inequality

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Addition/Subtraction Property of Inequality

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Transition Property of Inequality

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Graphing of an Inequality

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Inequality

an algebraic sentence or function comparing two quantities

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Quadratic Equation (number/types of roots)

two distinct real roots; one real w/ multiplicities; zero real, two complex roots

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Quadratic Equation

f(x)=ax^2+bx+c

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Horizontal Line

y=c; c can be any real #; constant function

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Vertical Line

x=a; a can be any real #; constant function

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Literal Equation

formula/equation that consists primarily of variables

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Coordinate Plane

two dimensional graph with ability to plot points and functions

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X-intercept

where a function intercepts when y=0

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Zeros

where a function intercepts when y=0

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Solutions or Roots

solve using ‘zero product property’

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Zero Product Property

if ab = 0, then a = 0 or b = 0.

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Add/Subtract Radical Expressions

add/subtract numerical factors of the like radicals.

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Square Root

Two factors of a value identical to each other that when multiplied, gives you that value.

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Prime Polynomial

Cannot be factored into a product of lesser degree polynomial factors.

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Cube Root

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nth root

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Product Property of Radical

the nth root of a product equals the product of the nth roots

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Simplify Radical Expressions

simplify radical and combine like terms when possible

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Quotient Property of Radicals

the nth root of a quotient equals the quotient of the nth roots of the numerator and denominator

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Divide Polynomials (Monomial Divisor)

divide each term of the dividend by the monomial divisor

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Divide Polynomials (Binomial Divisor)

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Factoring Sum and Difference of Cubes

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Difference of Squares

DOTS! a^2-b^2

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Permutation (Formula)

calculates the # of permutations

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Perfect Square Trinomial

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Arithmetic Sequence

a sequence of values that has a constant difference between every two consecutive terms

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Continuity

a function that is continuous at every point in its domain

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Multiple Representations of Functions

functions can be represented through a Table, Words, Equation, or Graph.

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Graph of an Inequality

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Factor by Grouping

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Parent Function: Linear vs. Quadratic

LINEAR: f(x)=x

QUADRATIC: f(x)=x^2

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Graphing Linear Inequalities

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System of Linear Equations (Number of Solutions)

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Mathematical Notation

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Greatest Common Factor

get the gcf of all terms of the polynomial and then apply distributive property.

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Factors of a Monomial

number(s) and/or variable(s) multiplied to form a monomial

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Multiply Binomials

use distributive property!!!!

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Multiply Binomials (Model)

use distributive property!!!!!

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Multiply Binomials (Graphic Organizer)

apply distributive property!!!!!!

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Multiply Binomials (Squaring a Binomial)

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Multiply Binomials (Sum and Difference)

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Real Numbers

the set of all rational and irrational numbers, including: natural, whole, and integers.

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