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Honors Algebra 2 > Spring finals review > Flashcards

Spring finals review Flashcards

1
Q

Arithmetic sequence

A

A sequence in which the difference of consecutive terms in 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.

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4
Q

Circle

A

A circle is a round shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.

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5
Q

Combined variation

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

common logarithm is the logarithm with base 10.

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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 + bx + c is a perfect square trinominal.

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10
Q

Complex conjugation

A

Paris of complex numbers of the forms a+bi and 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 functions

A

where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

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14
Q

Compound of inequality

A

two inequality statements joined either by the word “or” or by the word “and.”

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15
Q

Conic section

A

conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone.

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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 )

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18
Q

Continues 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 coefficiant

A

Correlation coefficients are expressed using the variable r, where r is between 1 and –1, inclusive.

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20
Q

Dependent

A

The dependent variable is the one 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 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

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23
Q

Discriminant

A

The discriminant is the part inside the square root.

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24
Q

ellipse

A

An ellipse is the set of all points (x,y) in a plane such that the sum of their distances from two fixed points is a constant.

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25
Q

End behavior

A

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

exponential equations are in the form ax=by .

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27
Q

Extraneous solution

A

Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.

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28
Q

extrema

A

is a point of a function at which it has the highest (maximum) or lowest (minimum) value.

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29
Q

Factor theorem

A

the factor theorem is a theorem linking factors and zeros of a polynomial.

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30
Q

Finite sequence

A

A sequence is finite if it has a limited number of terms and infinite if it does not.

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31
Q

Function

A

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

32
Q

Geometric sequence

A

A geometric sequence is an ordered list of numbers in which each term after the first is found by multiplying the previous one by a constant called r , the common ratio.

33
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, [ ].

34
Q

Growth factor

A

the factor by which a quantity multiplies itself over time.

35
Q

hyperbola

A

a conic section defined as the locus of all points in the plane the difference of whose distances and from two fixed points (the foci and ) separated by a distance is a given positive constant , (1)

36
Q

Identity function

A

the function which assigns every real number to the same real number. . It is identical to the identity map.

37
Q

Imaginary unit

A

a solution to the quadratic equation x2 + 1 = 0. … There are two complex square roots of −1, namely i and −i,

38
Q

Inconsistent

A

If a system has no solution, it is said to be inconsistent .

39
Q

Independent

A

An independent variable is a variable that does not depend on any other variable for its value.

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, …}.

41
Q

Interval notation

A

Interval notation is a way of writing subsets of the real number line

42
Q

Inverse function

A

An inverse function is a function that undoes the action of the 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

relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

45
Q

Joint variation

A

a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz.

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

48
Q

logarithm

A

is the power to which a number must be raised in order to get some other number

49
Q

logistic growth model

A

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).

50
Q

Matrix

A

a rectangular array of numbers (or other mathematical objects) for which operations such as addition and multiplication are defined.

51
Q

nth root

A

used n times in a multiplication to get the original value

52
Q

Natural logarithm

A

its 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

how many times to divide by the number

54
Q

parabola

A

is a symmetrical plane curve that forms when a cone intersects with a plane parallel to its side.

55
Q

parent function

A

is the simplest function of a family of functions. For the family of quadratic functions, y = ax2 + bx + c, the simplest function.

56
Q

piece-wise defined function

A

a piecewise-defined function (also called a piecewise function or a hybrid function) is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function’s domain (a sub-domain).

57
Q

point-slope form

A

the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form.

58
Q

Quadratic function

A

one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

59
Q

radicand

A

The value inside the radical symbol. The value you want to take the root of. In √x, “x” is the radicand.

60
Q

Rate of change

A

The rate of change (ROC) is 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 whose value can be expressed as the quotient of two polynomials (where the polynomial in the denominator is not zero).

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).

65
Q

regression line

A

a straight line that de- scribes how a response variable y changes as an explanatory variable x changes

66
Q

relative maximum

A

is 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

The root of a number x is another number, which when multiplied by itself a given number of times, equals x.

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 (or other elements like geometric objects), that often follow a specific pattern or function.

71
Q

set-builder notation

A

used to define the elements and properties of sets using symbols.

72
Q

Step function

A

a piecewise constant function, that has only a finite number of pieces.

73
Q

Synthetic division

A

a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.

74
Q

vertex form

A

a point where two or more curves, lines, or edges meet

75
Q

Vertical line test

A

used to determine if a graph of a relationship is a function or not. if you can draw any vertical line that intersects more than one point on the relationship, then it is not a function.

76
Q

Zeros

A

Where a function equals the value zero (0).

Honors Algebra 2 (1 decks)

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