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math > Algebra II Terms > Flashcards

Algebra II Terms Flashcards

1
Q

Arithmetic Sequence

A

A sequence where each term increases by adding/subtracting some constant k.

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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

Log(b) a = log(d) a / log(d) b

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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.

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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

Logarithm with 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

A technique for converting a quadratic polynomial of the form
ax^2 + bx + c
to the form
a(x-h)^2 + k

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10
Q

Complex Conjugates

A

Each of 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 fraction in which the denominator and numerator or both contain fractions.

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12
Q

Complex Number

A

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 i^2 = −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 such that h(x) = g(f(x)).

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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 as long as there is at least one set of values for the unknowns that 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 that is continuous when 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 statistical measure of the strength of the relationship between the relative movements of 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

The part of the quadratic formula underneath the square root symbol: b²-4ac.

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24
Q

Elipse

A

A plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

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25
Q

End Behavior

A

The trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

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26
Q

Exponential Equation

A

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

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27
Q

Extraneous Solution

A

A solution, such as that to an equation, 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

Any point at which the value of a function is largest (a maximum) or smallest (a minimum).

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29
Q

Factor Theorem

A

Used when factoring polynomials “completely”

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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 process or a relation that associates each element x of a set X, the domain of the function, to a single element y of another set Y (possibly the same set), the range of the function.

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 Funcition

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

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

36
Q

Identify 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 x^2 + 1 = 0.

38
Q

Inconsistent

A

When you graph some equations, both equations represent the same line. If a system has no solution it is this.

39
Q

Independent

A

A variable in an equation that may have its value freely chosen without considering values of any other variable.

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.

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

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

y=kx

45
Q

Joint Variation

A

y=kxz

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

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

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

49
Q

Logistic Growth Model

A

a common S-shaped curve with equation f(x) = L / 1+e^-k(x-x(0))

50
Q

Matrix

A

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

51
Q

n^th Root

A

A number r which, when raised to the power n, yields x: where n is a positive integer, sometimes called the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root.

52
Q

Natural Logarithm

A

A number’s logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459

53
Q

Negative Exponent

A

A number with a negative exponent should be put to the denominator, and vice versa.

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

y − y1 = m(x − x1)

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 quantity under a radical sign.

60
Q

Rate of Change

A

The speed at which a variable changes over a specific period of time.

61
Q

Rational Exponent

A

An exponent that is a fraction.

62
Q

Rational Function

A

Any function which can be written as the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero.

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 that is higher than the points directly beside it on both sides, and a relative minimum is a point that is lower than the points directly beside it on both sides.

67
Q

Relative Minimum

A

A function is 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 number y such that y² = x

69
Q

Scatter Plot

A

A two-dimensional graphical representation of a set of data.

70
Q

Sequence

A

A particular order in which related events, movements, or things follow each other.

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 finite linear combination of indicator functions of intervals.

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. A function can only have one output, y, for each unique input, x.

76
Q

Zeros

A

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

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