Math Glossary Honors Algebra Cty Online Course

Math Glossary Honors Algebra Cty Online Course absolute value

the measured distance on a number line from one location to the origin ( 0 ).

absolute value with greater than

all the solution values are outside the endpoints away from zero; |A| > B means A < -B or A > B

absolute value with less than

all the solution values are between the endpoints and zero: |A| < B means -B < A < B

adding complex numbers

combine like terms, the real numbers with themselves and the imaginary numbers with themselves

adding polynomials

combining all like terms in an algebraic expression

adding with signs

add like terms with the same signs; subtract like terms with opposite signs using the sign of the larger term for the answer

additive identity

the value that can be added without changing any number; i.e., 0

additive inverse

the value that can add with a number to produce 0; the number with the same absolute value but opposite sign as the given number; i.e., the inverse of a is -a

algebra of functions

process of adding, subtracting, multiplying or dividing functions with functions

and

connector used with inequalities to indicate that the solution set will include only values which satisfy both inequalities in the problem; sometimes referred to as an intersection.

approximation

a line or curve created to approximately represent the pattern produced by graphing single pieces of data on a plane.

arithmetic sequence

an ordered collection of numbers in which the difference between any two consecutive terms is a constant (d); these sequences follow the pattern an = a1 + (n - 1)d

arithmetic sequence general form

an = a1 + ( n - 1 )d

arithmetic series

associative property

the sum of the terms in an arithmetic sequence;  Sn =  

  n  ( a1 + aL )or Sn =  2  

 n  ( First term + Last term ) 2 

of addition, a + b + c = (a + b) + c = a + (b + c);

of multiplication, a · b · c = (a · b) · c = a · (b · c) asymptote

a line that the graph of a function approaches but never reaches. Asymptotes can be either horizontal or vertical

augmented matrix

an array for a system of equations which utilizes as elements both the coefficients of the variables and the constants in the equations

average

one number used to represent a group of values, calculated by adding all the values in the group then dividing by the number of values included in the group

axis of symmetry

the imaginary line that passes through the vertex of a parabola and is parallel to the axis along which the curve is opening

b

variable used to represent the y-intercept in the slope-intercept equation for a line.

base

the number or variable to which an exponent is attached

binomial

an algebraic expression composed of two monomial terms linked by addition or subtraction

binomial coefficient formula

binomial theorem

  

n m

 n!  = m!(n - m)! 

the principle that the coefficients in a binomial expansion follow directly the patterns developed in Pascal′s triangle.

cancellation

dividing both a numerator and a denominator by the same number so long as the numbers being divided are either both in the same fraction or are in fractions which are multiplying with each other.

Cartesian coordinates

the ordered pair, usually (x,y), that designates the location of a point on a Cartesian plane

Cartesian plane

the flat surface created by two number lines which intersect at right angles

Center of a circle

the fixed point that is a set distance from each point in the set of points that is the circle; usually designated as the ordered pair (h, k) where h is the x-value and k is the y-value of the point.

change-ofbase theorem

change of base theorem: logb x =

loga x loga b

allows revising a logarithm problem to be in a base that is easier to use in solving the problem

circle

the set of all the points at a fixed distance, the radius (r), from a specified point, the center (h,k); a completely symmetrical figure

clearing the denominator

practice of elminating a radical from the denominator of a fraction

coefficient

a constant multiplying with an algebraic variable

combined variation

a situation that mixes direct and indirect proportions

combining like terms

collecting terms that have the same variables each to the same degree or power

common denominator

a number that can be used as the denominator for every fraction in a problem; generally it is the lowest multiple common to all the existing denominators in the problem

common difference

( d )a constant value that separates each term in an artihmetic sequence from its neighboring term on each side; a constant value that multiplies with ( n - 1 ) to derive a product to add to a1 to create a specific term in an arithmetic sequence; the constant d in the general statement of an arithmetic sequence an = a1 + d(n - 1)

common ratio

( r )a constant value found when any term in a geometric sequence is divided by the preceding term; the constant value that multiplies with any term in a geometric sequence to produce the term following; r in the general formula for a geometric sequence an = a1 rn - 1

commutative property

of addition, a + b = b + a, where a and b are real numbers;

completing the square

the process of isolating on one side of the equation the terms containing the variable being solved for, then adding the value necessary for that side to be a perfect square to both sides of the equation, then factoring or taking the square root of both sides, and finally performing arithmetic as needed to solve for the variable.

complex fraction

a fraction which has one or more fractions in its numerator, denominator or both.

complex number

a value composed of both a real number and an imaginary number. Complex numbers are often written in the form a + bi, where a is the real number and bi is the imaginary number.

composite number

a value composed of prime numbers that are multiplying; a value with more than two factors

composition

multiple functions acting on each other in a specified order.

compound

two inequalities linked by and or or

of multiplication, ab = ba, where a and b are real numbers

inequality compound interest formula

A = P( 1 + r/m )mt

conditional statement

a linking of two individual statements in the form that if the first one is true, then the second one is also true; if p, then q

conic halves

the curves produced when conic equations are solved for or graphed only for the positive roots; also known as square root or half-conic functions

conic section

any curve which is derived by intersecting a cone with a plane, such figures include: the point (the plane touches the tip of the cone) line (the plane is tangent to the side of the cone) parabola (the plane intersects the cone parallel to its side) circle (the plane intersects the cone parallel to the base of the cone) ellipse (the plane intersects the cone at an angle), and hyperbola (the plane intersects the cone vertically).

consecutive even numbers

even numbers that follow one another when counting, i.e., 2, 4, 6, ... or x, x + 2, x + 4, ...

consecutive numbers

numbers that follow one another when counting; i.e., 3, 4, 5, ... or x, x + 1, x + 2, ...

consecutive odd numbers

odd numbers that follow one another when counting, i.e., 3, 5, 7, ..., or 2x + 1, 2x + 3, 2x + 5, ..., or x, x + 2, x + 4 ... given that x is an odd number

constant

a number which always has the same value, i.e., 7; the value in a function which does not change

constant velocity

a constant change in position with respect to time; traveling a distance over some amount of time at an even speed, can be determined using a formula that specifies that speed equals distance traveled divided by time used travelling

continuously compounded interest

A = Pert

where A is the interest accumulated, P is the principal

on which the interest is being accumulated, r is the interest rate, and t is the time in years.

contradiction

an equation with no solution; there is no value for the variable that produces a true mathematical sentence

contrapositive

a statement that links two clauses such that one originally stated as true and dependent on the other is now stated as false and controlling of the other

converse

a sentence that links two statements but changes their original order so that the one originally stated second and dependent on the first is not first and controling of the other; logically this combination cannot be held to be true without additional information

Cramer's rule

a process utilizing determinants to solve systems of linear equations

crossmultiplying

a practice used to eliminate denominators when one or more fractions are found in an equation; the procedure involves multiplying the common

denominator from one side of the equation with the numerators on the other side of the equation with the result that the multiplying denominator disappears into the receiving numerator cube root

cubic equation

the number r that multiplied with itself twice produces the given number; the number that with two more of itself and 1 are the only factors of the given number an equation in the third degree; y = ax3 + c

or x = ay3 + c.

curve fitting

superimposing a line or curve over the graph of single points of data to approximately represent the pattern produced in the graph

degree

the highest power used in any of the terms of an algebraic expression

degree of polynomial

highest power used in any of the terms of the algebraic expression

denominator

number or expression on the bottom, or doing the dividing, of a fraction

dependent system

a group of three equations in three unknowns that has an infinite number of solutions; the planes for the three equations intersect in a line

dependent variable

the quantity in an algebraic expession whose value changes as calculations are made subsequent to one or more substitutions for the independent variable, i.e., the variable whose value "depends" on what is substituted in for the other, or "independent," variable.

determinant

|D|, det(D), a number, or scalar, that represents the value of a matrix

difference of two cubes

x3 - y3 = ( x - y )( x2 + xy + y2 ).

difference of two squares

a2 - b2 = ( a - b )( a + b )

difference of two squares

x2 - y2 = ( x - y )( x + y ).

dimension of a matrix

the number of rows "x" the number of columns

direct proportion

two or more quantities increase or decrease in the same way to the same degree, each in accordance with its size

direct variation

two or more quantities increase or decrease in the same way to the same degree, each quantity in accordance with its size

directrix

the fixed line that helps determine the points in a parabola; a parabola of the form y = cx2 has its directrix as y = -

1 c. 4

discriminant

the algebraic expression under the radical in the quadratic formula; used to determine the number and type of roots for the equation. If the discriminant > 0, the equation has two real roots. If the discriminant = 0, the equation has one real root. If the discriminant < 0, the equation has two complex roots.

distance formula

an equation that determines the shortest distance between any two points on a Cartesian plane; _____________________

d=

√(x2 - x1 )2 + (y2 - y1 )2

distance on a number line

subtract the end values to determine the number of units apart the two endpoints are on the line

distributive property

(of multiplication over addition), a(b + c) = ab + ac, where a, b, and c are real numbers.

dividing by 0

result is undefined; never do it

domain

the set of all values that the independent variable for a function, usually x, can use in that function

domain of a rational

the set of all values available for the variable such that the denominator of the rational never equals zero