Vocabulary Flashcards
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Arithmetic Sequence
A sequence in which the difference of consecutive terms is constant
Asymptote
A line that a graph approaches more and more closely but never touches.
Change of base formula
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
Circle
A polygon that has no sides or vertices, but also has one side while having an infinite number of vertices, all of which sum to 360*.
Combined Variation
Combined variation describes 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).
Combined Difference
The constant difference between consecutive terms of an arithmetic sequence is called the common difference. Example: Given the arithmetic sequence 9,7,5,3,… . To find the common difference, subtract any term from the term that follows it.
Common Logarithm
In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm.
Common Ratio
The constant factor between consecutive terms of a geometric sequence is called the common ratio. Example: … To find the common ratio , find the ratio between a term and the term preceding it. r=42=2. 2 is the common ratio.
Completing the square
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
Complex Conjugates
Pairs of complex numbers of the forms a=bi and a-bi, where a and b are real numbers
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 and b are real numbers
Composition of functions
An operation that can be performed with two functions
Compound inequality
A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.” “And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.
Conic Section
In mathematics, a conic section (or simply conic) 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.
Consistent
acting or done in the same way over time, especially so as to be fair or accurate
Constant of variation
The constant a in the inverse variation equation y=a/x, where a==0
continuous relation
A function is continuous as a relation if it is continuous in the usual sense and a composition of continuous relations is continuous. … A relation between compact Hausdorff spaces is continuous iff it is closed as a subset of X×Y, and thus continuity is symmetric in X and Y
Correlation Coeffecient
A number r from -1 to 1 that measures how well a line fits a set of data pairs (x,y)
Dependent
A variable that gets its identity from another variable in an equation
Dimensions of a matrix
The dimensions of a matrix with m rows and n columns are mxn (read “m by n”)
Direct Variation
An equation that is the product of k and x, k is a constant that changes between equations.
Discriminant
The expression b^2-4ac in the quadratic formula
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 a function as x approaches positive infinity or negative infinity
Exponential equation
Equations in which variable expressions occur as exponents
Extraneous Solution
Solutions that are not solutions of the original equation
Extreme
When solving proportions in math, the outer terms in the calculation are the extremes, and the middle terms are called the means. When setting the proportion equation a/b = c/d, the a and the d figures are the extremes.
Factor Theorem
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if (i.e. is a root)
Finite Sequence
A finite sequence is 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 relationship or expression involving one or more variables
Geometric Sequence
A sequence in which the ratio of any term to the previous term is a constant
Greatest integer function
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, [ ]. These values are the rounded-down integer values of the expression found inside the brackets
Growth factor
The value of b in an exponential growth function of the form y=ab^2, where a>0 and b>1
Hyperbola
a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone
Identity function
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.
Imaginary Unit
The square root of -1, denotd i = sqrt(-1)
Inconsistent
not staying the same throughout.
Independent
free from outside control; not depending on another’s authority
Infinite sequence
A sequence that goes on forever
Interval notation
Interval notation is a way of writing subsets of the real number line . A closed interval is one that includes its endpoints: for example, the set {x | −3≤x≤1} . An open interval is one that does not include its endpoints, for example, {x | −3
Inverse function
An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y). In other words, applying f and then g is the same thing as doing nothing
Inverse Relation
An inverse relation is 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)
Inverse Variation
Two variables x and y show inverse variation when y=a/x, where a==0
Joint Variation
Two variables x and y show joint variation when y=axz,where a==0
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
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships
Logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Logistic growth model
Logistic Growth Model - Background: Logistic Modeling … P(t) = P0 ert,. where P0 is the population at time t = 0.
Matrix
A matrix is a rectangular array of numbers (or other mathematical objects) for which operations such as addition and multiplication are performed
n^th root of a
for an integer n greater than 1, if b^n=a, then b is an nth root of a
Natural Logarithm
A logarithm with base e, denoted by loge or ln
Negative exponent
A negative exponent means how many times to divide by the number
Parabola
The graph of a quadratic function
Parent fucntion
The most basic function in a family of functions
Piece-wise defined function
A function defined by two or more equations
Point-slope form
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 point on the line
Quadratic function
A function that can be written in the form f(x)=a(x-h)^2+k
Radicand
The value inside the radical symbol
Rate of change
The rate of change (ROC) is the speed at which a variable changes over a specific period of time.
Rational exponent
A rational exponent is an exponent that is a fraction
Rational function
A functin that has the form f(x)=(p(x))/(q(x)), where p(x) and q(x) are polnomials and q(x) ==0.
Rationalizing A Denominator
‘To rationalize the denominator means 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
Recursive formula
A recursive formula is a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence.
Regression line
a regression line is a line that best describes the behavior of a set of data
Relative Maximum
A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph)
Relative minimum
a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph)
Root
A solution of the equation
Scatter plot
a graph in which the values of two variables are plotted along two axes, the pattern of the resulting points revealing any correlation present
Sequence
An ordered list of numbers
Set builder notation
A set-builder notation describes or defines the elements of a set instead of listing the elements
Step function
A piecewise function defined by a constant value over each part of its domain
Synthetic division
Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor – and it only works in this case
Vertex form
The vertex form of an equation is an alternate way of writing out the equation of a parabola. Normally, you’ll see a quadratic equation written as a x 2 + b x + c , which, when graphed, will be a parabola
Vertical Line test
Moving a straight item facing horizontally, then if it touches two points of the graphed lines at the same times, the graphed line is not a function
Zeros
Where the graphed line crosses the x - axis
