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Honors Algebra II > Honors Algebra II Final > Flashcards

Honors Algebra II 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

For all positive numbers where a b and n where a and b are not equal to 1. log>b a = log>d a/log>d b

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4
Q

Circle

A

A shape consisting of all points in a plane that are at a given distance from a given 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

The process used to make a quadratic expression into a perfect square trinominal.

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10
Q

Complex Conjugates

A

Pairs of complex numbers of the forms a + bi and a - bi, where b doesn’t equal 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, b, c, and d are rational numbers.

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13
Q

Composition of Functions

A

An operation that can be performed with two functions.

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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 if 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 a in the inverse variation equation y = a/x, where a doesn’t equal 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.

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19
Q

Correlation Coefficient

A

A number that is a measure of the strength and direction of the correlation between two variables.

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20
Q

Dependent

A

A variable that depends on the value of some other number.

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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.

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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

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

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24
Q

Ellipse

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

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26
Q

Exponential Equation

A

Equation 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

The maxima and minima of a function, are the largest and smallest value of the function, either within a given range, or on the entire domain.

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29
Q

Factor Theorem

A

A theorem linking factors and zeros of a polynomial.

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30
Q

Finite Sequence

A

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 binary relation between two sets that associates to each element of the first set exactly one element of the second set.

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.

34
Q

Growth Factor

A

The value of b in an exponential; growth function of the form y + ab^x, where a is less than 0 and b is less than 1.

35
Q

Hyperbola

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.

36
Q

Identity Function

A

A function that always returns the same value that was used as its argument.

37
Q

Imaginary Unit

A

The square root of -1, denoted i + Square root of -1.

38
Q

Inconsistent

A

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 represents a quantity that is being manipulated in an equation.

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 integers

41
Q

Internal Notation

A

A set of real numbers that contains all real numbers lying between any two numbers of the set.

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.

44
Q

Inverse Variation

A

Two variables x and y show inverse variation when y + a/x, where a doesn’t equal 0.

45
Q

Joint Variation

A

Occurs when a variable varies directly or inversely with multiple variables.

46
Q

Latus Rectum

A

The Latus Rectum conic section is the chord through a focus parallel to the conic section directrix.

47
Q

Linear Programming

A

Modeling technique in which a linear function is maximized or minimized when subjected to various constraints.

48
Q

Logarithm

A

The inverse function to exponentiation.

49
Q

Logistic Growth Model

A

A common S-shaped curve with equation f(x)= \frac {L}{1+ e^{-k(x-x_0)}}

50
Q

Matrix

A

A rectangular arrangement of numbers.

51
Q

n* root

A

For any real numbers a and b, any positive integer n, a if a^n = b.

52
Q

Natural Logarithm

A

A logarithm with base e, denoted by log>e or 1n.

53
Q

Negative Exponent

A

Means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125.

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 multiple sub-functions, where each sub-function applies to a different interval in the domain.

57
Q

Point-Slope Form

A

y - y>1 = m(x-x>1)

58
Q

Quadratic Function

A

A function that can be written in the form f(x) = a(x - h)^2 + k, where a cannot equal 0.

59
Q

Radicand

A

What’s underneath the radical. In nth root ], the value inside in the symbol indicates the value that is being taken to the nth root.

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) can’t equal 0.

63
Q

Rationalizing the Denominator

A

Means 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). Must always state the initial term, or terms, of the sequence.

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 where the function changes direction from increasing to decreasing (making that point a “peak” in the graph).

67
Q

Relative Minimum

A

A point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).

68
Q

Root

A

Solutions of a quadratic equation.

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.

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

Synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.

74
Q

Vertex Form

A

A quadratic function written in the form f(x) = a(x - h)^2 +k, where a can’t equal 0.

75
Q

Vertical Line Test

A

The vertical line test is a visual way to determine if a curve is a graph of a function or not.

76
Q

Zeros

A

The x-intercepts of a graph of a function, the points of which f(x) = 0

Honors Algebra II (1 decks)

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