Algebra II Flashcards
Arithmetic Sequence
A sequence of numbers such that the difference between the consecutive terms is constant.
Asymptote
A line that continually approaches a given curve but does not meet it at any finite distance.
Change of base formula
The formula that will give you the answer of a log with a different base by using only log calculations with a base of 10.
Circle
A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (center).
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.
Common difference
The difference between two consecutive terms of an arithmetic progression.
Common logarithm
A logarithm to the base of 10
Common Ratio
The ratio of each term of a geometric progression to the term preceding it
Completing the square
Writing a quadratic in the form of a squared bracket and adding a constant if necessary.,
Complex conjugates
Two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign
Complex fraction
A rational expression that has a fraction in its numerator, denominator or both
Complex number
An element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit, and satisfying the equation i^2= -1.
Composition of functions
An operation where two functions say f and g generate a new function say h in such a way that h(x)=g(f(x)).
A function is applied to the function
Compound inequality
An inequality that combines two simple inequalities
Conic section
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.
Consistent
A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent.
Constant of Variation
The ratio between two variables in a direct variation or the product of two variables in an inverse variation.
Continuous relation
A relation is continuous if it is upper hemicontinuous and lower hemicontinuous.
Correlation coefficient
a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.
Dependent
A variable whose value depends upon independent variable s.
Dimensions of a matrix
The number of rows by the number of columns.
Direct variation
Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other
Discriminant
A parameter of an object or system calculated as an aid to its classification or solution
Ellipse
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.
End Behavior
The behavior of the graph of the function at the “ends” of the x-axis
Exponential equation
equations in which variables occur as exponents
Extraneous Solution
Values that we get when solving equations that aren’t really solutions to the equation.
Extrema
the maximum or minimum value of a function.
Factor Theorem
a theorem that links factors and zeros of the polynomial
Finite Sequence
Sequences that end
Function
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Geometric Sequence
A sequence of numbers in which the ratio between consecutive terms is constant.
Greatest integer function
A function that results in the integer nearer to the given real number
Growth factor
The factor by which a quantity multiplies itself over time
Hyperbola
Two-branched open curve, a conic section, produced by the intersection of a circular cone and a plane that cuts both nappes of the cone
Identity function
the function which assigns every real number to the same real number
Imaginary unit
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x^2 + 1 = 0
Inconsistent
A system of equations is called an inconsistent system of equations if there is no solution because the lines are parallel
Independent
a variable that does not depend on any other variable for its value
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 {1, 2, 3, …}.
Interval notation
A way of writing subsets of the real number line
Inverse Function
A function that serves to “undo” another function
Inverse relation
A relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation
Inverse variation
A nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant
Joint varation
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.
Latus rectum
A chord of a conic section (such as an ellipse) that passes through a focus and is parallel to the directrix
Linear Programming
Mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints
Logarithm
The exponent or power to which a base must be raised to yield a given number
Logistic growth model
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)
Matrix
A set of numbers arranged in rows and columns so as to form a rectangular array
nth root
A set of numbers arranged in rows and columns so as to form a rectangular array
Natural logarithm
The logarithm to the base e , where e is the mathematical constant approximately equal to 2.718
Negative exponent
The multiplicative inverse of the base, raised to the power which is opposite to the given power
Parabola
A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side
Parent function
The simplest function that still satisfies the definition of a certain type of function
Piece-wise defined function
One which is defined not by a single equation, but by two or more.
Point-slope form
Used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
Quadratic function
A polynomial function with one or more variables in which the highest exponent of the variable is two.
Radicand
A number or expression inside the radical symbol
Rate of change
Used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
Rational Exponent
Exponents of numbers that are expressed as rational numbers
Rational function
One that can be written as a polynomial divided by a polynomial
Rationalizing the denominator
The process of moving a root, for instance, a cube root or a square root from the bottom of a fraction (denominator) to the top of the fraction (numerator)
Recursive formula
A formula that defines each term of a sequence using preceding term(s).
Regression Line
An estimate of the line that describes the true, but unknown, linear relationship between the two variables
Relative maximum
A point (x,y) on the graph of the function whose y -coordinate is larger than all other y -coordinates on the graph at points “close to” (x,y). ( x , y ) .
Relative minimum
All the points x, in the domain of the function, such that it is the smallest value for some neighborhood
Root
A solution to an equation, usually expressed as a number or an algebraic formula.
Scatter Plot
A set of points plotted on a horizontal and vertical axes.
Sequence
An ordered list of numbers
Set-builder notation
A mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.
Step function
A piecewise constant function, that has only a finite number of pieces
Synthetic division
A shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm
Vertex form
A point where two or more curves, lines, or edges meet.
Vertical line test
A graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
Zeros
The values of x when f(x) is equal to 0.
