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Algebra II > Final > Flashcards

Final Flashcards

1
Q

Arithmetic Sequence

A

a sequence in which the difference of consecutive terms in 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

change of base formula

A

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

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4
Q

circle

A

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

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5
Q

combined variation

A

a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are held constant).

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6
Q

common difference

A

The constant difference between consecutive terms of an arithmetic sequence

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7
Q

common logarithm

A

a logarithm to the base 10.

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8
Q

common ratio

A

The constant factor between consecutive terms of a geometric sequence

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9
Q

completing the square

A

to add a term c to an expression of the form x²+bx such that x²+bx+c is a perfect square trinomial

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10
Q

complex conjugates

A

pairs of complex numbers of the forms a+bi and a-bi, where b/=0

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11
Q

complex fractions

A

a fraction that contains a fraction in its numerator or denominator

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12
Q

complex number

A

a number written in the form a+bi, where a and b are real numbers

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13
Q

composition of functions

A

an operation that can be performed with two functions

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14
Q

compound inequality

A

a sentence with two inequality statements joined either by the word “or” or by the word “and.”

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15
Q

conic section

A

a figure formed by the intersection of a plane and a right circular cone.

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16
Q

consistent

A

a linear or nonlinear system of equations

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17
Q

constant of variation

A

the constant a in the inverse variation equation y-a/x, where a/=0

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18
Q

continuous relation

A

A set of data is said to be continuous if the values belonging to the set can take on ANY value within a finite or infinite interval.

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19
Q

correlation coefficient

A

a number r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)

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20
Q

dependent

A

the one that depends on the value of some other number. If, say, y = x+3, then the value y can have depends on what the value of x is.

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21
Q

dimensions of a matrix

A

The dimensions of a matrix with m rows and n columns are m x n

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22
Q

direct variation

A

a simple relationship between two variables

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23
Q

discriminant

A

The expression b²-4ac in the Quadratic Formula

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24
Q

elipse

A

a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base.

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25
Q

end behavior

A

The behavior of the graph of a function as x approaches positive infinity or negative infinity

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26
Q

exponential equation

A

equations in which variable expressions occur as exponents

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27
Q

extraneous solution

A

solutions that are not solutions of the original equation

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28
Q

extrema

A

the maximum or minimum value of a function.

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29
Q

factor theorem

A

Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus “x minus the number” is a factor.

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30
Q

finite sequence

A

a list of terms in a specific order.

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31
Q

function

A

a relationship or expression involving one or more variables.

32
Q

geometric sequence

A

a sequence in which the ratio of any term to the previous term is constant

33
Q

greatest integer function

A

a function that returns a constant value for each specific interval.

34
Q

growth factor

A

the value of b in an exponential growth function of the form y=ab*, where a>0 and b>1

35
Q

hyperbola

A

an open curve with two branches, the intersection of a plane with both halves of a double cone.

36
Q

identity function

A

a function that always returns the same value that was used as its argument.That is, for f being identity, the equality f(x) = x holds for all x.

37
Q

imaginary unit

A

the square root of -1, denoted i=(square root of)-1

38
Q

inconsistent

A

not staying the same throughout.

39
Q

independent

A

a variable (often denoted by x ) whose variation does not depend on that of another.

40
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 integer s {1, 2, 3, …}.

41
Q

interval notation

A

a way to describe continuous sets of real numbers by the numbers that bound them.

42
Q

inverse function

A

functions that undo each other

43
Q

inverse relation

A

the relation that occurs when the order of the elements is switched in the relation

44
Q

inverse variation

A

two variables x and y show inverse variation y=a/x, where a/=0

45
Q

joint variation

A

describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant. We say z varies jointly as x and y if. z=kxy. for some constant k.

46
Q

latus rectum

A

the line segment through the focus of a parabola

47
Q

linear programming

A

a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.

48
Q

logarithm

A

the inverse function to exponentiation.

49
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).

50
Q

matrix

A

a rectangular arrangement of numbers

51
Q

nth root

A

for an integer n greater than 1, if b*=a, then b is an nth root of a

52
Q

natural logarithm

A

s its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.

53
Q

negative exponent

A

that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

54
Q

parabola

A

the graph of a quadratic function

55
Q

parent function

A

the most basic function in a family of functions

56
Q

piece-wise defined function

A

a function defined by two or more equations

57
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 — compare slope-intercept form.

58
Q

quadratic function

A

a function that can be written in the form f(x)=a(x-h)²+k, where a/=0

59
Q

radicand

A

The value inside the radical symbol. The value you want to take the root of.

60
Q

rate of change

A

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

61
Q

rational exponent

A

an exponent that is a fraction.

62
Q

rational function

A

a function that has the form f(x)=p

9(x)/q(x), where p(x) and q(x) are polynomials and q(x)/=0

63
Q

rationalizing the denominator

A

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

64
Q

recursive formula

A

a formula that defines each term of a sequence using preceding term(s).

65
Q

regression line

A

a straight line that describes how a response variable y changes as an explanatory variable x changes.

66
Q

relative maximum

A

a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). high

67
Q

relative minimum

A

a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph). low

68
Q

root

A

a solution of an equation

69
Q

scatter plot

A

a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present.

70
Q

sequence

A

an ordered list of numbers

71
Q

set-builder notation

A

uses symbols to define a set, in terms of the properties of the members of the set

72
Q

step function

A

a piecewise function defined by a constant value over each part of its domain

73
Q

synthetic division

A

a shortcut method to divide a polynomial by a binomial of the form x-k

74
Q

vertex form

A

a quadratic function written in the form f(x)=a(x-h)²+k, where a/=0

75
Q

vertical line test

A

a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

76
Q

zeros

A

an x-value of a function f for which f(x)=0

Algebra II (1 decks)

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