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Honors Algebra II > Vocab Final Flashcards > Flashcards

Vocab Final 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. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.

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4
Q

Circle

A

a polygon that has no corners and is a full 360

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

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6
Q

Common Difference

A

The constant difference d between consecutive terms of an arithmetic sequence

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7
Q

Common Logarithm

A

A logarithm with base 10. denoted as log10 or simply log

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8
Q

Common Ratio

A

The constant ratio r between consecutive terms of a geometric sequence

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9
Q

Completing the Square

A

To add a term c to an expression of the form x^2 + bx such that
x^2 + bx + c is a perfect square trinomial

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10
Q

Complex Conjugates

A

Pairs of complex numbers of the forms a +bi, where b =/= 0

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11
Q

Complex Fraction

A

A fraction that contains a fraction in its numerator or denominator

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12
Q

Complex Number

A

A number written in the form a + bi, where a and b are real numbers

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13
Q

Composition of Fractions

A

An operation that can be performed with two numbers

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14
Q

Compound Inequality

A

is an inequality that combines two simple inequalities.

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15
Q

Conic Section

A

In mathematics, a conic section is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.

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16
Q

Consistent

A

In mathematics and particularly in algebra, a linear or nonlinear system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system—that is, when substituted into each of the equations, they make each equation hold true as an identity.

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17
Q

Constant of Variation

A

The constant a in the inverse variation equation y= a/x, where a =/= 0

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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. Definition: 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 r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)

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20
Q

Dependent

A

a variable that relies on another variable usually the independent variable

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21
Q

Dimensions of a Matrix

A

The dimensions of a matrix with m rows and n columns are m X n
(read “m by n”)

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22
Q

Direct Variation

A

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

The expression b^2 - 4ac in the Quadratic Formula

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24
Q

Ellipse

A

In mathematics, an ellipse is 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. As such, it generalizes a circle, which is the special type of ellipse in which the two focal points are the same.

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25
Q

End Behavior

A

The behavior of the graph of a function as x approaches positive infinity or negative infinity

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26
Q

Exponential Equation

A

Equations in which variable expressions occur as exponents

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27
Q

Extraneous Solution

A

Solutions that are not solutions of the original equation

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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

The differences of consecutive y-values in a data set when the x-values are equally spaced

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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

Greatest integer Function

A

The function rounds -off the real number down to the integer less than the number. This function is also known as the Floor Function.

34
Q

Growth Factor

A

The value of b in an exponential growth function of the form y = ab^x, where a>0 and b>1

35
Q

Hyperbola

A

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

36
Q

Identity Function

A

In mathematics, an identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

37
Q

Imaginary Unit

A

The square root of -1, denoted i = sqrt(-1)

38
Q

Inconsistent

A

When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

39
Q

Independent

A

a variable that doesn’t depend on anything else

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, …}. … An infinite series is the sum of the values in an infinite sequence of numbers.

41
Q

Interval Notation

A

In mathematics, a interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval which contains 0, 1, and all numbers in between.

42
Q

Inverse Function

A

Functions that undo each other

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. 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).

44
Q

Inverse Variation

A

Two variables x and y show inverse variation when

y = a/x, where a =/= 0

45
Q

Joint Variation

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. We say z varies jointly as x and y if. z=kxy. for some constant k.

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. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.

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

f(x) = L/1+ e^{-k(x-x>0)} a common S-shaped curve with equation the x value of the sigmoid’s midpoint; L, the curve’s maximum value; k, the logistic growth rate or steepness of the curve.

50
Q

Martix

A

A rectangular arrangement of numbers

51
Q

Nth Root

A

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

52
Q

Natural Logarithm

A

A logarithm with the base e. denoted by log>e or ln

53
Q

Negative Exponent

A

6^-x = 1/6^x how many times to divide by the number. exponential grows

54
Q

Parabola

A

The graph of a quadratic function

55
Q

Parent Function

A

The most basic function in a family of functions

56
Q

Piece-Wise Defined Function

A

A function defined by two or more equations

57
Q

Point-Slope Form

A

The equation of a straight line in the form y − y>1 = m(x − x>1) where m is the slope of the line and (x>1, y>1) are the coordinates of a given point on the line

58
Q

Quadratic Function

A

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

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

an exponent that is a fraction.

62
Q

Rational Function

A

A function that has the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) =/= 0

63
Q

Rationalizing the Denominator

A

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.

64
Q

Recursive Formula

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. The equation is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.

66
Q

Relative Maximum

A

a point where the function changes direction from increasing to decreasing

67
Q

Relative Minimum

A

point where the function changes direction from decreasing to increasing

68
Q

Root

A

A solution of an equation or think square root

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. lots of dots can find line of best fit

70
Q

Sequence

A

An ordered list of numbers

71
Q

Set-Builder Notation

A

Uses symbols to define a set, in terms of the properties of the members of the set.

72
Q

Step Function

A

A piece wise function defined by a constant value over each part of its domain

73
Q

Synthetic Division

A

A shortcut method to divide a polynomial by a binomial of the form x - k

74
Q

Vertex Form

A

A quadratic function written in the form f(x) = a(x - h)^2 + k, where a =/= 0

75
Q

Vertical Line Test

A

drawing a vertical line on a graph to see if there are two points on a single part of the x axis to determine if it is a function or not

76
Q

Zeros

A

A x-value of a function f for which f(x) = 0

Honors Algebra II (1 decks)

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