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Algebra II > Math Final > Flashcards

Math Final Flashcards

1
Q

Arithmetic Sequence

A

A list of numbers with a definite pattern.

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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

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

Combined variation 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 constant difference between consecutive terms of an arithmetic sequence is called the common difference.

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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 is called the common ratio.

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9
Q

Completing the square

A

Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial

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

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12
Q

Complex number

A

a Complex Number is just two numbers added together (a Real and an Imaginary Number).

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13
Q

Complex of functions

A

Complex Function. A function whose range is in the complex numbers is said to be a complex function, or a complex-valued function.

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14
Q

Compound inequality

A

A compound inequality is 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

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 constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. The formula for direct variation is. y=kx (or y=kx ) where k is the constant of variation .

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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

The correlation coefficient is 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 dependent variable is 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. Another way to put it is the dependent variable is the output value and the independent variable is the input value.

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21
Q

Dimensions of a matrix

A

The dimensions of a matrix are the number of rows by the number of columns. If a matrix has a rows and b columns, it is an a×b matrix.

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22
Q

Direct variation

A

Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y=kx. for some constant k , called the constant of variation or constant of proportionality .

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23
Q

Discriminant

A

an agent or characteristic that enables things, people, or classes to be distinguished from one another.

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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 end behavior of a function f describes the behavior of the graph of the function at the “ends” of the x-axis. In other words, the end behavior of a function describes 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

an equation involving exponential functions of a variable.

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27
Q

Extraneous solution

A

An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original

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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

the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem

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30
Q

Finite sequence

A

A finite sequence is a list of terms in a specific order. The sequence has a first term and a last term. The order of the terms of a finite sequence follows some type of mathematical pattern or logical arrangement.

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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

infinite sequence

A

An infinite sequence is 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, …}. … When the sum of an infinite series is finite and definable, then that series and its corresponding sequence converge.

34
Q

Greatest integer function

A

The greatest integer function is a function that returns a constant value for each specific interval. These functions are normally represented by an open and closed bracket, [ ]. These values are the rounded-down integer values of the expression found inside the brackets.

35
Q

Growth factor

A

The value of b on an exponential growth function of the form y=ab^x, where a > 1

36
Q

Hyperbola

A

a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

37
Q

Identity function

A

a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

38
Q

Imaginary unit

A

The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0.

39
Q

inconsistent

A

not staying the same throughout.

40
Q

Independent

A

An independent variable is a variable that represents a quantity that is being manipulated in an experiment. A dependent variable represents a quantity whose value depends on those manipulations.

41
Q

infinite sequence

A

An infinite sequence is 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, …}.

42
Q

interval notation

A

Interval notation is a way to describe continuous sets of real numbers by the numbers that bound them. Intervals, when written, look somewhat like ordered pairs.

43
Q

inverse function

A

Functions that undo each other

44
Q

inverse relation

A

An inverse relation is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).

45
Q

inverse variation

A

Two variables x and y show inverse variatin wen y=a/x, where a does not equal 0

46
Q

Joint variation

A

Joint variation 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.

47
Q

latus rectum

A

“Latus rectum” is a compound of the Latin latus, meaning “side,” and rectum, meaning “straight.

48
Q

linear programming

A

Linear programming (LP, also called linear optimization) is 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.

49
Q

logarithm

A

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

50
Q

logistic growth model

A

In logistic growth, 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).

51
Q

Matrix

A

a rectangular arrangement of numbers

52
Q

nth root

A

for inteder n greater than 1, if b^n=a, then b is an nth root of a.

53
Q

natural logarithm

A

a logarithm with base e, denoted by log e, or In.

54
Q

Negative Exponent

A

A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side.

55
Q

Parabola

A

The graph of a quadratic function

56
Q

Parent function

A

The most basic function in a family of functions

57
Q

Piece wise defined function

A

A function defined by two or more equations

58
Q

point slope form

A

the equation of a straight line in the form y − y1 = m(x − x1)

59
Q

quadratic function

A

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

60
Q

Radicand

A

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

In √x, “x” is the radicand

61
Q

Rate of Change

A

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then.

62
Q

Rational Exponent

A

A rational exponent is an exponent that is a fraction. For example, can be written as . Can’t imagine raising a number to a rational exponent? They may be hard to get used to, but rational exponents can actually help simplify some problems.

63
Q

Rational function

A

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

64
Q

Rationalizing the denominater

A

To rationalize the denominator means to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals.

65
Q

Recursive formula

A

A recursive formula is a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence.

66
Q

Regression line

A

In statistics, a regression line is a line that best describes the behavior of a set of data.

67
Q

Relative maximum

A

A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).

68
Q

root

A

Where a function equals zero. In this example, minus2 and 2 are the roots of the function

69
Q

scatter plot

A

A scatter plot (or scatter diagram) is a two-dimensional graphical representation of a set of data.

70
Q

sequence

A

A Sequence is a list of things (usually numbers) that are in order. Sequence 3,5,7,9,… Infinite or Finite.

71
Q

set builder notation

A

Set-Builder Notation. How to describe a set by saying what properties its members have. … A Set is a collection of things (usually numbers).

72
Q

step function

A

In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals.

73
Q

synthetic division

A

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor – and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

74
Q

vertex form

A

The vertex form of a quadratic is given by y = a(x – h)2 + k, where (h, k) is the vertex. The “a” in the vertex form is the same “a” as in y = ax2 + bx + c (that is, both a’s have exactly the same value). The sign on “a” tells you whether the quadratic opens up or opens down.

75
Q

vertex line test

A

The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection. … That is, every x-value of a function must be paired to a single y-value.

76
Q

zeros

A

no quantity or number; naught; the figure 0.

Algebra II (1 decks)

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