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Algebra II Terms Flashcards

(76 cards)

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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
End Behavior
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 −∞ ).
26
Exponential Equation
a function of the form f(x)=ab^x
27
Extraneous Solution
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.
28
Extrema
Any point at which the value of a function is largest (a maximum) or smallest (a minimum).
29
Factor Theorem
Used when factoring polynomials "completely"
30
Finite Sequence
A list of terms in a specific order.
31
Function
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
Geometric Sequence
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
Greatest Integer Funcition
A function that returns a constant value for each specific interval.
34
Growth Factor
The factor by which a quantity multiplies itself over time.
35
Hyperbola
An open curve with two branches, the intersection of a plane with both halves of a double cone.
36
Identify Function
A function that always returns the same value that was used as its argument.
37
Imaginary Unit
A solution to the quadratic equation x^2 + 1 = 0.
38
Inconsistent
When you graph some equations, both equations represent the same line. If a system has no solution it is this.
39
Independent
A variable in an equation that may have its value freely chosen without considering values of any other variable.
40
Infinite Sequence
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
Interval Notation
A way to describe continuous sets of real numbers by the numbers that bound them.
42
Inverse Function
A function that "reverses" another function.
43
Inverse Relation
The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
44
Inverse Variation
y=kx
45
Joint Variation
y=kxz
46
Latus Rectum
A chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix.
47
Linear Programming
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
Logarithm
A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
49
Logistic Growth Model
a common S-shaped curve with equation f(x) = L / 1+e^-k(x-x(0))
50
Matrix
A rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
51
n^th Root
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
Natural Logarithm
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
Negative Exponent
A number with a negative exponent should be put to the denominator, and vice versa.
54
Parabola
A plane curve which is mirror-symmetrical and is approximately U-shaped.
55
Parent Function
The simplest function of a family of functions that preserves the definition of the entire family.
56
Piece-wise Defined Function
A function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
57
Point-Slope Form
y − y1 = m(x − x1)
58
Quadratic Function
A polynomial function with one or more variables in which the highest-degree term is of the second degree.
59
Radicand
The quantity under a radical sign.
60
Rate of Change
The speed at which a variable changes over a specific period of time.
61
Rational Exponent
An exponent that is a fraction.
62
Rational Function
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
Rationalizing the Denominator
To eliminate any radical expressions in the denominator such as square roots and cube roots.
64
Recursive Formula
A formula that defines each term of a sequence using preceding term(s).
65
Regression Line
A straight line that describes how a response variable y changes as an explanatory variable x changes.
66
Relative Maximum
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
Relative Minimum
A function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood.
68
Root
A number y such that y² = x
69
Scatter Plot
A two-dimensional graphical representation of a set of data.
70
Sequence
A particular order in which related events, movements, or things follow each other.
71
Set-builder Notation
A mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.
72
Step Function
A finite linear combination of indicator functions of intervals.
73
Synthetic Division
A method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
74
Vertex Form
A point where two or more curves, lines, or edges meet.
75
Vertical Line Test
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
Zeros
A member x of the domain of f such that f(x) vanishes at x.

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