Honors Math BC: FLASHCARDS

MATH

Outlier Data

A piece of data separate from the majority

Curve of Best Fit (Linear)

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

Curved of Best Fit (Quadratic)

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

Curved of Best Fit (Exponential)

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

No Correlation

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

Negative Linear Relationship (Correlation)

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

Positive Linear Relationship (Correlation)

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

Scatterplot

numerical data on a visual graph

Mode

the value that appears most out of a data set

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.

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)

Summation

The sum of all values in a data set.

Combination (and its formula)

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

Geometric Sequence

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

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)

Discontinuity

a point at which a function is discontinuous or undefined.

Linear Function (Vertical Dilation)

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

Transformations of Parent Function (Translation)

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

Transformations of Parent Function (Dilation)

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

Transformations of Parent Function (Reflection)

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

Parent function: Exponential vs. Logarithmic

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

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

Parent function: Rational

f(x) = 1/x, where x isn’t ‘0’

Parent Function: Cubic vs. Cube Root

CUBIC: f(x)=x^3

CUBE ROOT: f(x)=∛x

Parent Function: Absolute Value vs. Square Root

ABS VAL: f(x) = |x|

SQ RT: f(x) = √x

Function Notation

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

End Behavior

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

x→∞, f(x) →∞

x→-∞, f(x)→-∞

Extrema

the amount of vertices on a function.

Increasing/Decreasing

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

Range

all ‘y’ values in a function

Domain

all ‘x’ values in a function

Function

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

Relations

a set of ordered pairs

Quadratic Formula

Vertex of a Quadratic Function

The global/absolute maximum or minimum of the function.

Graph of a Quadratic Equation

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

Dependent/Independent Variable

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

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

System of Linear Inequalities

Graphing Linear Inequalities

Systems of Equations (Linear)

Systems of Equations (Quadratic)

Systems of Equations (Linear) (Elimination)

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

Systems of Equations (Linear) (Substitution)

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

Systems of Equations (Linear) (Graphing)

Parallel Lines

Two linear functions of a graph that will never intersect

Perpendicular Lines

Two linear functions that intersect at a 90 degree angle

Slopes of Lines

change in y/change in x

Slope Formula

Slope

‘m’ in ‘y=mx+b’

Equivalent Forms of A Linear Equation

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Linear Equation Point-Slope Form

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Linear Equation Slope-Intercept Form

Linear Equation Standard Form

Absolute Value Inequalities

Division Property of Inequalities

Multiplication Property of Inequality

Addition/Subtraction Property of Inequality

Transition Property of Inequality

Graphing of an Inequality

Inequality

an algebraic sentence or function comparing two quantities

Quadratic Equation (number/types of roots)

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

Quadratic Equation

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

Horizontal Line

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

Vertical Line

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

Literal Equation

formula/equation that consists primarily of variables

Coordinate Plane

two dimensional graph with ability to plot points and functions

X-intercept

where a function intercepts when y=0

Zeros

where a function intercepts when y=0

Solutions or Roots

solve using ‘zero product property’

Zero Product Property

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

Add/Subtract Radical Expressions

add/subtract numerical factors of the like radicals.

Square Root

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

Prime Polynomial

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

Cube Root

nth root

Product Property of Radical

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

Simplify Radical Expressions

simplify radical and combine like terms when possible

Quotient Property of Radicals

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

Divide Polynomials (Monomial Divisor)

divide each term of the dividend by the monomial divisor

Divide Polynomials (Binomial Divisor)

Factoring Sum and Difference of Cubes

Difference of Squares

DOTS! a^2-b^2

Permutation (Formula)

calculates the # of permutations

Perfect Square Trinomial

Arithmetic Sequence

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

Continuity

a function that is continuous at every point in its domain

Multiple Representations of Functions

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

Graph of an Inequality

Factor by Grouping

Parent Function: Linear vs. Quadratic

LINEAR: f(x)=x

QUADRATIC: f(x)=x^2

Graphing Linear Inequalities

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System of Linear Equations (Number of Solutions)

Mathematical Notation

Greatest Common Factor

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

Factors of a Monomial

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

Multiply Binomials

use distributive property!!!!

Multiply Binomials (Model)

use distributive property!!!!!

Multiply Binomials (Graphic Organizer)

apply distributive property!!!!!!

Multiply Binomials (Squaring a Binomial)

Multiply Binomials (Sum and Difference)

Real Numbers

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