Algebra II extra credit Flashcards
arithmetic sequence
An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k.
asymptote
a line that continually approaches a given curve but does not meet it at any finite distance.
Change of Base Formula
Logb a = log a/ log b
Circle
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed 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 (when the rest of the variables are held constant).
common difference
the difference between two consecutive terms of an arithmetic progression.
Common logarithm
a logarithm to the base 10.
common ratio
the ratio of each term of a geometric progression to the term preceding it.
Completing the square
method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
complex conjugation
each of two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign.
complex fractions
When a “normal” fraction contains fractions in either the numerator or denominator or both, then we consider it to be a complex fraction. This type of fraction is also known as a compound fraction. There are two methods used to simplify such kind of fraction.
composition of functions
The composition of functions f(x) and g(x) where g(x) is acting first is represented by f(g(x)) or (f ∘ g)(x). It combines two or more functions to result in another function.
compound of equality
A compound inequality (or combined inequality ) is two or more inequalities joined together with or or and . To be a solution of an or inequality, a value has to make only one part of the inequality true. To be a solution of an and inequality, it must make both parts true.
conic functions
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.
“the parents are being consistent and firm in their reactions”
constant of variations
The ratio between two variables in a direct variation or the product of two variables in an inverse variation.
continuous relation
A relation XR→Y is continuous if it is upper hemicontinuous and lower hemicontinuous. Upper hemicontinuous at a∈X if for any open neighbourhood V of R(a) there exists an open neighbourhood U of a such that for all x∈U it holds R(x)⊂V.
correlation coefficient
a number between −1 and +1 calculated so as to represent the linear dependence of two variables or sets of data.
Dependent
contingent on or determined by.
dimension of a matrix
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. For example, the first matrix shown below is a 2×2 matrix; the second one is a 1×4 matrix; and the third one is a 3×3 matrix.
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
an agent or characteristic that enables things, people, or classes to be distinguished from one another.
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 end behavior of a function f describes the behavior of the graph of the function at the “ends” of the x-axis. In other words, the 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 −∞ ).
exponential equation
exponential equation
Extraneous solutions
Extraneous solutions are 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
It is a theorem that links factors and zeros of the polynomial.
finite sequence
A sequence is finite if it has a limited number of terms and infinite if it does not.
function
an activity or purpose natural to or intended for a person or thing.
geometric sequence
An ordered list of numbers in which each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio.
greatest integer function
a function that results in the integer nearer to the given real number.
growth factor
a substance, such as a vitamin or hormone, which is required for the stimulation of growth in living cells.
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 functions
The identity function is a function which returns the same value, which was used as its argument
imaginary unit
the positive square root of minus 1 denoted by i or + √-1.
inconsistent
not staying the same throughout.
independent
free from outside control; not depending on another’s authority.
infinite sequence
An infinite sequence is 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
Interval notation is a way of writing subsets of the real number line
inverse functions
an inverse is 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
the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value
joint relation
A relationship consisting of a nongendered division of labor in a household between partners.
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
a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost.
logarithm
a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
logistic growth model
In logistic growth, 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
matrix
nth root
the nth root of a number x is a number y which when raised to the power n, obtains x: yn=x.
natural logarithm
The natural logarithm of a number x is the logarithm to the base e , where e is the mathematical constant approximately equal to 2.718
negative exponent
A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number.
parabola
a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
Parent function
A parent function is the simplest function that still satisfies the definition of a certain type of function.
piece wise defined function
A piece wise-defined function is one which is defined not by a single equation, but by two or more.
point slope form
he 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.
quadratic function
A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.
radicand
Radicand - A number or expression inside the radical symbol. Radical equation - An equation containing radical expressions with variables in the radicands.
rate of change
a value that results from dividing the change in a function of a variable by the change in the variable velocity is the rate of change in distance with respect to time.
rational exponent
A rational exponent is an exponent that is a fraction.
rational function
a function that is the quotient of two polynomials also : polynomial.
rationalizing the denominator
rationalizing the denominator means moving the radical term (square root or cube root) to the numerator, such that a denominator is a whole number.
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 graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables; it summarizes how well the proposed model actually fits the sample data obtained.
relative maximum
relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a “peak” in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a “bottom” in the graph).
relative minimum
A relative minimum of a function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.
root
a solution to an equation, usually expressed as a number or an algebraic formula.
scatter plot
scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables.
sequence
a particular order in which related events, movements, or things follow each other.
set builder notation
Set-builder notation is a mathematical notation for describing a set by representing its elements or explaining the properties that its members must satisfy.
step function
a function that increases or decreases abruptly from one constant value to another.
a function that increases or decreases abruptly from one constant value to another.
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.
vertex form
a vertex form is a point where two or more curves, lines, or edges meet.
vertical line test
he vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.
Zeros
no quantity or number; naught; the figure 0.
