Honors Algebra II Final Flashcards
Arithmetic Sequence
A sequence in which the difference of consecutive terms is constant.
Asymptote
A line that a graph approaches more and more closely.
Change of Base Formula
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
Circle
A shape consisting of all points in a plane that are at a given distance from a given point, the 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 constant difference between consecutive terms of an arithmetic sequence.
Common Logarithm
Logarithm with base 10
Common Ratio
The constant factor between consecutive terms of a geometric sequence.
Completing the Square
The process used to make a quadratic expression into a perfect square trinominal.
Complex Conjugates
Pairs of complex numbers of the forms a + bi and a - bi, where b doesn’t equal 0.
Complex Fraction
A fraction that contains a fraction in its numerator or denominator.
Complex Number
A number written in the form a + bi, where a, b, c, and d are rational numbers.
Composition of Functions
An operation that can be performed with two functions.
Compound Inequality
An inequality that combines two simple inequalities.
Conic Section
A curve obtained as the intersection of the surface of a cone with a plane.
Consistent
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.
Constant of Variation
The constant a in the inverse variation equation y = a/x, where a doesn’t equal 0.
Continuous Relation
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.
Correlation Coefficient
A number that is a measure of the strength and direction of the correlation between two variables.
Dependent
A variable that depends on the value of some other number.
Dimensions of a Matrix
The dimensions of a matrix with m rows and n columns are m x n.
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
The expression b^2 - 4ac in the Quadratic Formula.
Ellipse
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.
End Behavior
The behavior of the graph of a function as x approaches positive infinity or negative infinity.
Exponential Equation
Equation in which variable expressions occur as exponents.
Extraneous Solution
Solutions that are not solutions of the original equation.
Extrema
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.
Factor Theorem
A theorem linking factors and zeros of a polynomial.
Finite Sequence
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.
Function
A binary relation between two sets that associates to each element of the first set exactly one element of the second set.
Geometric Sequence
A sequence in which the ratio of any term to the previous term is constant.
Greatest Integer Function
The function rounds -off the real number down to the integer less than the number.
Growth Factor
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.
Hyperbola
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.
Identity Function
A function that always returns the same value that was used as its argument.
Imaginary Unit
The square root of -1, denoted i + Square root of -1.
Inconsistent
The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Independent
A variable that represents a quantity that is being manipulated in an equation.
Infinite Sequence
A list or string of discrete objects, usually numbers, that can be paired off one-to-one with the set of positive integers
Internal Notation
A set of real numbers that contains all real numbers lying between any two numbers of the set.
Inverse Function
Functions that undo each other.
Inverse Relation
The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
Inverse Variation
Two variables x and y show inverse variation when y + a/x, where a doesn’t equal 0.
Joint Variation
Occurs when a variable varies directly or inversely with multiple variables.
Latus Rectum
The Latus Rectum conic section is the chord through a focus parallel to the conic section directrix.
Linear Programming
Modeling technique in which a linear function is maximized or minimized when subjected to various constraints.
Logarithm
The inverse function to exponentiation.
Logistic Growth Model
A common S-shaped curve with equation f(x)= \frac {L}{1+ e^{-k(x-x_0)}}
Matrix
A rectangular arrangement of numbers.
n* root
For any real numbers a and b, any positive integer n, a if a^n = b.
Natural Logarithm
A logarithm with base e, denoted by log>e or 1n.
Negative Exponent
Means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125.
Parabola
The graph of a quadratic function.
Parent Function
The most basic function in a family of functions.
Piece-Wise Defined Function
A function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain.
Point-Slope Form
y - y>1 = m(x-x>1)
Quadratic Function
A function that can be written in the form f(x) = a(x - h)^2 + k, where a cannot equal 0.
Radicand
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.
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
An exponent that is a fraction
Rational Function
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.
Rationalizing the Denominator
Means to eliminate any radical expressions in the denominator such as square roots and cube roots.
Recursive Formula
A formula that defines each term of a sequence using preceding term(s). Must always state the initial term, or terms, of the sequence.
Regression Line
An estimate of the line that describes the true, but unknown, linear relationship between the two variables.
Relative Maximum
A point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph).
Relative Minimum
A point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).
Root
Solutions of a quadratic equation.
Scatter Plot
A type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.
Sequence
An ordered list of numbers.
Set-Builder Notation
Uses symbols to define a set, in terms of the properties of the members of the set.
Step Function
A piece wise function defined by a constant value over each part of its domain.
Synthetic Division
Synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
Vertex Form
A quadratic function written in the form f(x) = a(x - h)^2 +k, where a can’t equal 0.
Vertical Line Test
The vertical line test is a visual way to determine if a curve is a graph of a function or not.
Zeros
The x-intercepts of a graph of a function, the points of which f(x) = 0
