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Algebra II > Flashcards > Flashcards

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

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 shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

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5
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 (when the rest of the variables are held constant).

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6
Q

common difference

A

the difference between two consecutive terms of an arithmetic progression.

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7
Q

common logarithm

A

That is, the power of 10 necessary to equal a given number. The common logarithm of x is written log x. For example, log 100 is 2 since 102 = 100.

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8
Q

common ratio

A

he amount we multiply by each time in a geometric sequence. Example: 1, 2, 4, 8, 16, 32, 64, 128, 256, … Each number is 2 times the number before it, so the Common Ratio is 2.

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9
Q

completing the square

A

a method, usually of solving quadratic equations, by which a quadratic expression, as x2 − 4x + 3, is written as the sum or difference of a perfect square and a constant, x2 − 4x + 4 + 3 − 4 = (x − 2)2 − 1, by addition and subtraction of appropriate constant terms.

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10
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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11
Q

complex fraction

A

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

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12
Q

complex number

A

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol called the imaginary unit, and satisfying the equation i² = −1

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13
Q

composition of functions

A

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

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14
Q

compound inequality

A

an inequality that combines two simple inequalities

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15
Q

conic section

A

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

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16
Q

consistent

A

a linear or nonlinear system of equations where at least one set of values for the unknowns satisfies each equation in the system

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17
Q

constant of variation

A

the constant (unchanged) ratio of two variable quantities.

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18
Q

continuous relation

A

a set of data is said to be discrete if the values belonging to the set are distinct and separate (unconnected values)

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19
Q

correlation coefficient

A

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

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20
Q

dependent

A

the variable that depends on the value of some other number

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21
Q

dimensions of a matrix

A

the number of rows by the number of columns

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22
Q

direct variation

A

a simple relationship between two variables

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23
Q

discriminant

A

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

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24
Q

ellipse

A

a plane curve surrounding two focal points

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25
Q

end behavior

A

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

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26
Q

exponential equation

A

a function of the form f(x)=ab^{x}, where b is a positive real number, and the argument x occurs as an exponent

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27
Q

extraneous solution

A

a solution that emerges from the process of solving the problem but is not a valid solution to the problem

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28
Q

extrema

A

collectively known as the maxima and minima of a function

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29
Q

factor theorem

A

a theorem linking factors and zeros of a polynomial

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

32
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

33
Q

greatest integer function

A

a function that returns a constant value for each specific interval

34
Q

growth factor

A

the factor by which a quantity multiplies itself over time

35
Q

hyperbola

A

a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set

-

36
Q

identity function

A

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

37
Q

imaginary unit

A

a solution to the quadratic equation x² + 1 = 0

38
Q

inconsistent

A

the study of commonplace mathematical objects, like sets, numbers, and functions, where some contradictions are allowed

39
Q

independent

A

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

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 integers

41
Q

interval notation

A

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

42
Q

inverse function

A

a function that “reverses” another function

43
Q

inverse relation

A

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

44
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

45
Q

joint variation

A

a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz

46
Q

latus rectum

A

the chord through a focus parallel to the conic section directrix

47
Q

linear programming

A

a method to achieve the best outcome 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

best for population, show large growth

50
Q

matrix

A

a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns

51
Q

n* root

A

a number r which, when raised to the power n, yields x (n as exponent)

52
Q

natural logarithm

A

logarithm to the base of the mathematical constant e

53
Q

negative exponent

A

how many times to divide by the number

54
Q

parabola

A

a plane curve which is mirror-symmetrical and is approximately U-shaped

55
Q

parent function

A

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

56
Q

piece-wise defined function

A

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

57
Q

point-slope form

A

derived from the concept of finding the slope of a line when two points are given

58
Q

quadratic function

A

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

59
Q

radicand

A

the thing we are finding the root of

60
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

61
Q

rational exponent

A

an exponent that is a fraction

62
Q

rational function

A

any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials

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

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

66
Q

relative maximum

A

a point where the function changes direction from increasing to decreasing

67
Q

relative minimum

A

all the points x, in the domain of the function, such that it is the smallest value for some neighborhood

68
Q

root

A

a value that, when multiplied by itself, gives the number

69
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

70
Q

sequence

A

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

71
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 {x : x > 0}

72
Q

step function

A

a function on the real numbers that can be written as a finite linear combination of indicator functions of intervals (not a continuous line)

73
Q

synthetic division

A

a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division

74
Q

vertex form

A

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

75
Q

vertical line test

A

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

76
Q

zeros

A

a member x of the domain of f such that f(x) vanishes at x

Algebra II (1 decks)

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