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Honors Algebra II > Final > Flashcards

Final Flashcards

1
Q

arithmetic sequence

A

a sequence in which the difference of consecutive terms is constant

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2
Q

asymptote

A

a line that a graph approaches more and more closely

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3
Q

common difference

A

the common difference d between consecutive terms of an arithmetic sequence

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4
Q

common logarithm

A

the logarithm with base 10

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5
Q

common ratio

A

constant factor between consecutive terms of a geometric sequence

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6
Q

completing the square

A

a technique for converting a quadratic polynomial of the form ax^{2}+bx+c to the form a^{2}+k} for some values of h and k

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7
Q

complex conjugates

A

the number with an equal real part and an imaginary part equal in magnitude but opposite in sign

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8
Q

complex fraction

A

a fraction in which numerator, denominator, or both are themselves fractions

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9
Q

complex number

A

a number that can be expressed in the form a + bi

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10
Q

composition of function

A

an operation that takes two functions f and g and produces a function h

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11
Q

compound inequality

A

an inequality that combines two simple inequalities

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12
Q

conic section

A

a curve obtained as the intersection of the surface of a cone with a plane

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13
Q

consistent

A

a linear or nonlinear system of equations

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14
Q

constant of variation

A

the constant ratio of two variable quantities

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15
Q

continuous relation

A

if the values belonging to the set can take on ANY value within a finite or infinite interval

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16
Q

correlation coefficiant

A

a number that is a measure of the strength and direction of the correlation between two variables

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17
Q

dependent

A

the one that depends on the value of some other number

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18
Q

dimensions of a matrix

A

the number of rows by the number of columns, if a matrix has a rows and b columns, it is an a×b matrix

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19
Q

direct variation

A

mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant

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20
Q

discriminant

A

a quantity that depends on the coefficients and determines various properties of the roots

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21
Q

elipse

A

a plane curve surrounding two focal points, such that for all points on the curve

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22
Q

end behavior

A

a function f describes the behavior of the graph of the function at the “ends” of the x-axis

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23
Q

exponential equation

A

a function of the form f(x)=ab^{x}

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24
Q

extraneous solution

A

a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original

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25
Q

extrema

A

any point at which the value of a function is largest

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26
Q

factor theorem

A

the factor theorem is a theorem linking factors and zeros of a polynomial

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27
Q

finite sequence

A

a list of terms in a specific order

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28
Q

function

A

a binary relation between two sets that associates to each element of the first set exactly one element of the second set

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29
Q

geometric sequence

A

a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio

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30
Q

greatest integer function

A

the function rounds -off the real number down to the integer less than the number

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31
Q

growth factor

A

the factor by which a quantity multiplies itself over time

32
Q

hyperbola

A

a hyperbola is a type of smooth curve lying in a plane

33
Q

identity function

A

a function that always returns the same value that was used as its argument

34
Q

imaginary unit

A

a solution to the quadratic equation x² + 1 = 0

35
Q

inconsistent

A

when you graph the equations, both equations represent the same line, if a system has no solution

36
Q

independent

A

a variable that represents a quantity that is being manipulated in an experiment

37
Q

infinite sequence

A

a list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers

38
Q

interval notation

A

a set of real numbers that contains all real numbers lying between any two numbers of the set

39
Q

inverse function

A

a function that “reverses” another function

40
Q

inverse relation

A

the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function

41
Q

change of base formula

A

a formula that allows you to rewrite a logarithm in terms of logs written with another base

42
Q

inverse variation

A

mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant

43
Q

joint variation

A

occurs when a variable varies directly or inversely with multiple variables

44
Q

latus rectum

A

the chord through a focus parallel to the conic section directrix

45
Q

linear programming

A

modeling technique in which a linear function is maximized or minimized when subjected to various constraints

46
Q

logarithm

A

the logarithm is the inverse function to exponentiation

47
Q

logistic growth model

A

a population’s per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the carrying capacity ( K)

48
Q

matrix

A

a rectangular array or table of numbers, symbols, or expressions,

49
Q

nth root

A

a number x is a number r which, when raised to the power n, yields r^{n}=x, where n is a positive integer,

50
Q

natural logarithm

A

its logarithm to the base of the mathematical constant e

51
Q

negative exponent

A

means how many times to divide by the number.

52
Q

parabola

A

a parabola is a plane curve which is mirror-symmetrical and is approximately u-shaped

53
Q

parent function

A

the simplest function of a family of functions that preserves the definition of the entire family

54
Q

piece - wise defined function

A

defined by multiple sub-functions, where each sub-function applies to a different interval in the domain

55
Q

point - slope form

A

the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line

56
Q

quadratic function

A

a polynomial function with one or more variables in which the highest-degree term is of the second degree

57
Q

radicand

A

the value inside the radical symbol, the value you want to take the root of. In √x, “x”

58
Q

rate of change

A

used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable

59
Q

rational exponent

A

an exponent that is a fraction

60
Q

rational function

A

any function which can be defined by a rational fraction

61
Q

rationalizing the denominator

A

means to eliminate any radical expressions in the denominator such as square roots and cube roots

62
Q

recursive formula

A

a formula that defines each term of a sequence using preceding terms

63
Q

regression line

A

an estimate of the line that describes the true, but unknown, linear relationship between the two variables

64
Q

relative maximum

A

a point where the function changes direction from increasing to decreasing

65
Q

relative minimum

A

all the points x, in the domain of the function

66
Q

root

A

a number x is another number, which when multiplied by itself a given number of times, equals x

67
Q

scatter plot

A

a type of plot or mathematical diagram using cartesian coordinates to display values for typically two variables for a set of data

68
Q

sequence

A

is an enumerated collection of objects in which repetitions are allowed and order matters

69
Q

set - builder notation

A

a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy

70
Q

step function

A

a function on the real numbers

71
Q

synthetic division

A

a method for manually performing euclidean division of polynomials

72
Q

vertex form

A

a point where two or more curves, lines, or edges meet

73
Q

vertical line test

A

a visual way to determine if a curve is a graph of a function or not

74
Q

zeros

A

of a real-, complex-, or generally vector-valued function

75
Q

circle

A

a shape consisting of all points in a plane that are at a given distance from a given point

76
Q

combined variation

A

describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others

Honors Algebra II (2 decks)

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