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Honors Algebra II > Algebra II Flashcards > Flashcards

Algebra II Flashcards

1
Q

Arithmetic Sequence

A

A sequence of numbers such that the difference between the consecutive terms is constant.

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2
Q

Asymptote

A

A line that continually approaches a given curve but does not meet it at any finite distance.

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3
Q

Change of base formula

A

The formula that will give you the answer of a log with a different base by using only log calculations with a base of 10.

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4
Q

Circle

A

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

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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

A logarithm to the base of 10

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8
Q

Common Ratio

A

The ratio of each term of a geometric progression to the term preceding it

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9
Q

Completing the square

A

Writing a quadratic in the form of a squared bracket and adding a constant if necessary.,

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10
Q

Complex conjugates

A

Two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign

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11
Q

Complex fraction

A

A rational expression that has a fraction in its numerator, denominator or both

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12
Q

Complex number

A

An element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit, and satisfying the equation i^2= -1.

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13
Q

Composition of functions

A

An operation where two functions say f and g generate a new function say h in such a way that h(x)=g(f(x)).
A function is applied to the function

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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 figure formed by the intersection of a plane and a right circular cone. Depending on the angle of the plane with respect to the cone, a conic section may be a circle, an ellipse, a parabola, or a hyperbola.

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16
Q

Consistent

A

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent.

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17
Q

Constant of Variation

A

The ratio between two variables in a direct variation or the product of two variables in an inverse variation.

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18
Q

Continuous relation

A

A relation is continuous if it is upper hemicontinuous and lower hemicontinuous.

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19
Q

Correlation coefficient

A

a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.

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20
Q

Dependent

A

A variable whose value depends upon independent variable s.

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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

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

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23
Q

Discriminant

A

A parameter of an object or system calculated as an aid to its classification or solution

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24
Q

Ellipse

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 the function at the “ends” of the x-axis

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26
Q

Exponential equation

A

equations in which variables occur as exponents

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27
Q

Extraneous Solution

A

Values that we get when solving equations that aren’t really solutions to the 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

a theorem that links factors and zeros of the polynomial

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30
Q

Finite Sequence

A

Sequences that end

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31
Q

Function

A

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

32
Q

Geometric Sequence

A

A sequence of numbers in which the ratio between consecutive terms is constant.

33
Q

Greatest integer function

A

A function that results in the integer nearer to the given real number

34
Q

Growth factor

A

The factor by which a quantity multiplies itself over time

35
Q

Hyperbola

A

Two-branched open curve, a conic section, produced by the intersection of a circular cone and a plane that cuts both nappes of the cone

36
Q

Identity function

A

the function which assigns every real number to the same real number

37
Q

Imaginary unit

A

The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x^2 + 1 = 0

38
Q

Inconsistent

A

A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel

39
Q

Independent

A

a variable that does not depend on any other variable for its value

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 of writing subsets of the real number line

42
Q

Inverse Function

A

A function that serves to “undo” another function

43
Q

Inverse relation

A

A relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation

44
Q

Inverse variation

A

A nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant

45
Q

Joint varation

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.

46
Q

Latus rectum

A

A chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix

47
Q

Linear Programming

A

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

48
Q

Logarithm

A

The exponent or power to which a base must be raised to yield a given number

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 set of numbers arranged in rows and columns so as to form a rectangular array

51
Q

nth root

A

A set of numbers arranged in rows and columns so as to form a rectangular array

52
Q

Natural logarithm

A

The logarithm to the base e , where e is the mathematical constant approximately equal to 2.718

53
Q

Negative exponent

A

The multiplicative inverse of the base, raised to the power which is opposite to the given power

54
Q

Parabola

A

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side

55
Q

Parent function

A

The simplest function that still satisfies the definition of a certain type of function

56
Q

Piece-wise defined function

A

One which is defined not by a single equation, but by two or more.

57
Q

Point-slope form

A

Used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

58
Q

Quadratic function

A

A polynomial function with one or more variables in which the highest exponent of the variable is two.

59
Q

Radicand

A

A number or expression inside the radical symbol

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

Exponents of numbers that are expressed as rational numbers

62
Q

Rational function

A

One that can be written as a polynomial divided by a polynomial

63
Q

Rationalizing the denominator

A

The process of moving a root, for instance, a cube root or a square root from the bottom of a fraction (denominator) to the top of the fraction (numerator)

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

66
Q

Relative maximum

A

A point (x,y) on the graph of the function whose y -coordinate is larger than all other y -coordinates on the graph at points “close to” (x,y). ( x , y ) .

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 solution to an equation, usually expressed as a number or an algebraic formula.

69
Q

Scatter Plot

A

A set of points plotted on a horizontal and vertical axes.

70
Q

Sequence

A

An ordered list of numbers

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.

72
Q

Step function

A

A piecewise constant function, that has only a finite number of pieces

73
Q

Synthetic division

A

A shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm

74
Q

Vertex form

A

A point where two or more curves, lines, or edges meet.

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

The values of x when f(x) is equal to 0.

Honors Algebra II (1 decks)

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