| A | B |
|---|
| absolute value | The distance from the origin to the coordinate x. |
| absolute value of a complex number | The absolute value of a complex number a + bi is the square root of a square plus b square. |
| additive inverses | Pairs of real number that have the sum 0. |
| additive inverse of a matrix | For each matrix A, there is a matrix -A(the additive inverse of A), such that A + (-A) = Z. |
| algebraic expressions | Expressions that are made up of variables, numbers, grouping sym- bols, operation signs, and exponents. |
| amplitude | Half the difference between the maximum and minimum values of a periodic function. |
| angle or depression | An angle that measures between 0' and 90' formed by a horizontal ray and a ray from the observer to the object observed below. |
| angle of elevation | An angle that measures between 0 and 90 formed by a horizontal ray and a ray from the observer to the object observed above. |
| arithmetic mean | The sum of the num- bers in a set divided by the number of numbers in the given set. |
| arithmetic means | Terms of an arithmetic se- quence that are between two given terms. |
| arithmetic sequence | For each positive inte- ger n, the sequence with the first term a, and nth term a, is an arithmetic sequence if and only if an = a1 + (n - 1)d. |
| arithmetic series | The indicated sum of the terms of an arithmetic sequence. |
| asymptotes (of a hyperbola) | The lines within which the branches of the hyperbola lie, and which are approached by the branches as |x| increases. |
| augmented matrix | The coefficient matrix for a system of linear equations with a final column included for the constants of the equations. |
| axis of symmetry | A line in the plane of a graph such that the part of the graph on one side of the line is a reflection of the part on the other side. |
| biased -sample | A sample that is not random. |
| binomial | A polynomial with two terms. |
| boundary condition | An extreme value in an inequality problem. Solutions will be less than or greater than that value. |
| center of a circle | The point in a circle from which the distance to any point on the circle is a constant. |
| center of an ellipse | The intersection of the axes of symmetry. |
| central tendency of a set of numbers | A number considered to be the most typical or representative of that set. |
| circle | The set of all points in a plane such that the distance (radius) from a given point (center of the circle) is constant. |
| circular functions | Periodic functions related to the unit circle. |
| closure | A set of numbers is closed under an operation if combining any two elements in the set by that operation yields a number in the set. |
| coefficient | The constant factor of a monomial. |
| common ratio | The common ratio is a constant. |
| complement of an event | Event A is a com- plement of event B with respect to sample spaceS if and only if A and 8 include all outcomes of S, and A and B have no outcomes in common. |
| completing the square | A method used to solve a quadratic equation in which a number is added to both sides of the equation so that one side is a perfect square. |
| complex conjugate | For all real numbers a and b, a + bi and a - bi are complex conjugates. |
| complex fraction | A fraction that has frac- tions in either the numerator or the denominator or both. |
| complex number | A number of the form a + bi, where a and b are real numbers and i is the imaginary unit. |
| components or an ordered pair | The individual numbers in an ordered pair. |
| compound inequality | A sentence linking two conditions with "and" or "or". At least one of the conditions is an inequality. |
| conic section | A curve that has a sec- ond-degree equation and is defined in terms of the distance of its points from fixed points and/or lines. This includes circles, parabolas. ellipses and hyperbolas. |
| conjugate | Two binomials of the form (a + Nt/b) and (a - N/b). where a and b are rational numbers. |
| consistent system of equations | A system that has at least one solution. |
| constant | A number or a polynomial of degree 0. |
| constant difference | The difference be- tween successive terms in a sequence |
| constant of inverse variation | The number k in the inverse variation Y = K/X. |
| constant linear function | A function whose equation can be written in the form y = b and whose graph is a horizontal line. |
| constant term of a polynomial | The term a which can be considered the coefficient of x. |
| constant term of a quadratic equation | The term c in the form V = ax- + bx + r. |
| constant of variation | The number k in the direct variation y = kx or in the inverse variation Y = K/X. |
| continuous | A polynomial function whose graph is smooth without "jumps". |
| converge | If there is a real number that is the value of the infinite series, the series converges. |
| convex polygonal region | A region that has a polygon with no "indentations" as a boundary. |
| coordinate | The number associated with a particular point on a number line. |
| coordinate axes | Two perpendicular lines selected in a plane. |
| coordinates of a point | The numbers of an ordered pair. |
| correlation coefficient | A number between - I and + I which is a measure of the dispersion of data points about a regression line. |
| corresponding elements of matrices | For two matrices with the same dimensions. the elements in the same row and the same column. |
| cubic polynomial | A polynomial of degree 3. |
| cycle | The graph of a periodic function through one fundamental period. |
| decreasing function | function such that for any numbers a and b in the domain. if a > b. then f(a) < f(b). |
| degree of a monomial | The sum of the exponents of the variables. |
| degree of a polynomial | The degree of the term (or terms) of highest degree. |
| dependent events | Two events A and B are dependent if and only if (A and then B) * P(A) - P(B). |
| dependent system | A system whose gr-aphs coincide and that has infinitely many solutions. |
| dependent variable | If the value of a de- pends on the value of b, or if a is usually defined in terms of b, a is called the dependent variable. and it is graphed on the vertical axis. |
| depressed equation | The equation Q(x) = 0. where Q(x) is the quotient when a polynomial has been divided by a factor (x - r). |
| descending order | A polynomial is written in descending order when the term with highest de- gree is written first, followed by the term with next highest degree second, and so on. |
| determinant | A real number represented by a square array of numbers. |
| determinant of a matrix | The determinant of a matrix is the determinant with the same corre- sponding elements. |
| dimensions of a matrix | The number of rows and the number of columns. |
| direct variation | Two variables are said to vary directly if and only if there is a constant of variation or (constant of proportionality) k. k ¹ 0. such that y = kx. |
| directed network | A network that indicates the direction of flow on each arc. |
| directrix | A line used in the definition of a conic section. |
| discriminant | The expression b2 - 4ac of the quadratic formula that determines several characteristics of the roots of a quadratic equation. |
| dispersion | A measure of how closely a set of data are clustered about the mean. |
| distance formula | For points P1(X1, Y1) and P2(Y1, Y2), P1P2 = Ö (X2-X1)^2 + (Y2-Y1)^2. |
| diverge | If there is no real number that is the value of an infinite series, the series diverges. |
| domain of a relation | The set of first components of the ordered pairs in the relation. |
| double root | Two roots that are alike |
| eccentricity | A ratio used in some definitions of conic sections. |
| ellipse | The set of all points in a plane such that the sum of the distances (focal radii) from two given points (foci) is constant. |
| ellipsis | A symbol indicating that the pattern-continues in a sequence. |
| equivalent transformation | A transformation that results in an equation equivalent to the original. |
| event | A subset of a sample space. |
| explicit definition | A definition used to state the relationship between a term t. of a sequence and the number n of that term. |
| exponential equation | An equation with the variable in an exponent. |
| exponential function | For all real numbers x and for all positive numbers b, b ¹ 1, the equation y = b^x defines an exponential function with base b. |
| factorial notalion | For each positive integer n, n! = n(n - 1)(n - 2) ... 3 x 2 x 1. Also,0! = 1. |
| field | A set of numbers with two operations that has the closure, commutative, associative, identity, and inverse properties for addition and multiplication and distributive for multiplication over addition. |
| finite sequence | A sequence that has a last term. |
| fitted line | The line that best approximates the graph of the relationship between two vari- ables, if that relationship is nearly linear. |
| focus | The fixed point or points (foci) used to define a conic section. |
| fractional equation | An equation with a vari- able in the denominator of a fraction. |
| function | A relation in which each element of the domain is paired with exactly one element of the range. |
| function notation | Representing any number in the range of the function f as f(x). in which x is the corresponding number in the domain. |
| geometric mean | The square root of the product of two numbers. It is also called the mean proportional. |
| geometric means | The terms of a geometric sequence between two given terms. |
| geometric sequence | For each positive integer n, and for each real number r, r ¹ 0, the sequence with the first term a, and nth term a. is a geometric sequence if and only if a. = a1r^n-1. |
| geometric series | The indicated sum of the terms of a geometric sequence. |
| greatest common factor | The common factor that is a multiple of each common factor. |
| greatest integer function | A step function that pairs a real number with the greatest integer that is less than or equal to the real number. |
| half life | The length of time it takes half of an amount of radioactive material to decay. |
| harmonic mean | In a set of n numbers. n divided by the sum of the reciprocals of the number. |
| hyperbola | The set of all points in it plane such that the absolute value of the difference of the distances (focal radii) from two given points (foci) is constant. |
| hypotenuse | The longest side of a right triangle. It is opposite the right angle. |
| identity | An equation that is true for all elements of its domain. |
| identity element | A number which added to or multiplied times any number in a set yields that same number in the set. |
| identity properties | There are real numbers 0 and I such that for each real number a, a + 0, 0 + a = a and a x 1 = 1 x a = a. |
| imaginary number | A complex number that is not real. |
| inconsistent system of equations | A system with no soiution. |
| increasing function | A function such that for any numbers a and b in the domain. if a > b, then f(a) > f(b). |
| independent events | Two events not affected by each other. Two events A and B are independent if and only if P(A and then B) P(A) x P(B). |
| independent variable | If the value of a depends upon the value of b, or if a is usually defined in terms of b, b is called the independent variable, and it is graphed on the horizontal axis. |
| index | The number represented by n in nÖb. |
| index of summation | The variable used in sigma notation. |
| infinite geometric series | A geometric series with an infinitely large number of terms. |
| infinite sequence | A sequence that does not have a last term. |
| interquartile range | The difference between the upper and lower quartiles of a set of numbers. |
| inverse functions | Functions and g are inverse functions if and only if f(g(x)) = g(f(x)) =x for all numbers x in the domains of both f and 9. |
| inverse of a relation | Relation B is the inverse of relation A if it consists of the inverses of the individual ordered pairs in relation A. |
| inverse variation | Two quantities x and y vary inversely if and only if there is a constant k. k ¹ 0, such thatY = K/X. |
| irrational number | A real number that is not a rational number, i.e. cannot be expressed as the quotient of two integers. |
| latus chord | A segment whose endpoints are on a parabola. which passes through the focus, and is parallel to the directrix. |
| leading coefficient | The coefficient of the term of a polynomial with the highest degree. |
| like terms | Terms that contain identical vari- ables with identical exponents. |
| linear combination | An equation that is formed by adding multiples of two equations together. |
| linear equation in two variables | An equation of the form y = mx + b. |
| linear function | A function is a linear function if and only if its domain is the set of all real numbers and its equation can be written in the form y = mx + b. |
| linear polynomial | A polynomial of degree 1. |
| linear programming | A branch of mathematics based on the maximum-minimum property. |
| linear term of a quadratic equation | The term bx in an equation of the form y = ax^2+ bx + c. |
| literal equation | An equation in which con- stants are represented by letters. |
| logarithmic equation | An equation involving logarithms of expressions containing variables. |
| logarithmic function | For all positive real numbers x and b, b ¹ 1, there is a real number v such that v = logbx if and only if x = b^x |
| lowest terms (simplest form) | A fraction is expressed in lowest terms when its numerator and denominator have no common factors other than 1 or - 1. |
| main diagonal of a square matrix | The diagonal from the upper left to the lower right. |
| major axis | The longer axis of an ellipse. |
| mapping | An association from the elements of the domain to the elements of the range. |
| matrix matrices | A rectangular array of numbers arranged in Tows and columns. |
| maximum value | The Y-coordinate of the vertex of the graph of a quadratic function that opens downward. |
| mean | The sum of a set of numbers divided by the number of numbers in the set. |
| mean absolute deviation | The average absolute deviation from the mean for a set of numbers. |
| mean proportional | The geometric mean between two numbers. |
| median | The middle number in a set of numbers arranged in order. |
| midpoint | The point on a segment that is equidistant from the endpoints. |
| midpoint formula | If the coordinates of point A are (x1,y1) and the coordinates of point B are (x2,y2), then the coordinates of the midpoint of segment AB are {(x1+x2)/2, (y1+y2)/2} |
| minimum value | The y-coordinate of the vertex of the graph of a quadratic function that opens upward. |
| minor of an element | The determinant that remains after the row and column containing the element have been deleted. |
| minor axis | The shorter axis of an ellipse. |
| mode | The number that occurs most often in a set of numbers. |
| monomial | A constant (a number), a variable, or a product of constants and/or variables. |
| multiplicative inverse (or reciprocals) | Pairs of real numbers that have the product 1. |
| multiplicative identity matrix | A square matrix with I's on the main diagonal (upper lcft to lower right) and other entries 0. |
| mutually exclusive events | Two events A and B are mutually exclusive if and only if they have no outcomes in common. |
| natural logarithms | Base-e logarithms |
| negative exponents | For each nonzero number a and for each positive integer n, a^-n = 1/a^n. |
| negative reciprocals | Two numbers having a product of - 1. |
| negative square root | The negative of the principal square root. |
| negative square root function | The function with the equation y= -Öx |
| network | A set of points (vertices) connected by arcs. |
| nonequivalent transrormation | A transformation that results in an equation not equivalent to the original. |
| nonlinear system | A system of two or more equations at least one of which is nonlinear. |
| normal distribution | A specific bell-shaped algebraic function approximated by many frequency distributions. |
| opposites | Two numbers whose sum is zero. Also called additive inverses. |
| ordered pair | A pair of numbers that identifies the location of a particular point on a graph. |
| ordered triples (X, Y, Z) | The set that is the solution of an equation in three variables. |
| origin (on a graph) | The point of intersection of the coordinate axes. It is designated (0. 0). |
| origin (on a number line) | The point on the number line associated with zero. |
| outcome | The result of an experiment |
| parabola | The set of all points in a plane that are the same distance from a point (focus) as they are from a given line (directrix). it is the graph of a quadratic function having a U shape. |
| parallel lines | Lines that have equal slopes. |
| partial sum of a series | The sum of a finite number of terms of the series. |
| pascal's triangle | A triangular arrangement of numbers in which each number is the sum of the two numbers above it in the preceding row. |
| perfect square trinomial | The square of a binomial. with the form a2 ± 2ab + b2. |
| periodic function | A function y=f(x) is periodic if and only if there is a real number p such that for each x in the domain of f. f(x + p)=f(x). |
| permutation | An arrangement of a number of objects in a definite order |
| perpendicular lines | Lines with slopes that are negative reciprocals. |
| point matrix | A 2 x 1 matrix whose ele- ments are the coordinates of a point. |
| point-slope form | If (x1, y1) is a point on the line y = mx + b. then y - y1 = m(x - xl) is the point-slope form of the equation |
| polynomial | A monomial or the sum of monomials. |
| polynomial function | A function P whose values are defined by a polynomial. |
| power function | Functions with equations of the form y = x^n, with it a positive integer. |
| prime factorization | A representation of a number as the product of its prime factors. |
| principal cube root | The one real-number cube root of a real number. |
| principal square root | The positive square root, denoted by |
| principle square root function | The function with the equation Ö |
| probability of an event | The ratio of the number of outcomes in the event to the number of outcomes in the sample space. |
| pure imaginary number | Any number of the form ai. where a is real. |
| pure quadratic equation | A quadratic equation with no x-term. |
| quadrilateral | A quadrilateral is a polygon with four sides. |
| rational number | A number that can be expressed as the quotient of two integers. |
| rationalizing the denominator | The process of changing an irrational denominator to a rational one. |
| real numbers | The set of all rational and irrational numbers. |
| reciprocals | Pairs of real numbers that have the product 1. Also known as mulliplicarive inverses. |
| regression line | A fitted line determined by a specific algebraic technique. |
| relation | A set of ordered pairs. |
| repeating decimal | A decimal in which a digit or a group of digits repeats forever, e.g. 0.66666 ... or 0.846846846 ... . |
| repetend | The portion of a repeating decimal that repeats. |
| restrictions | The set of possible values for the variables for which an expression is real, or for which it is defined. |
| resultant | The sum of two vector. |
| row matrix | A matrix with one row. |
| sample space | The set of all possible outcomes of an experiment. |
| scalar | The real number that is a factor in scalar multiplication. |
| scalar multiplication | For any scalar c, number, and any m x n matrix A with elements aij, the product of c and A is the in m x n matrix whose elements are caij. |
| scientific notation | The product of a power of 10 and a number greater than or equal to 1 and less than 10. |
| second-order determinant | A determinant with two rows and two columns. |
| sequence | A function dcfined on the positive integers or a subset of consecutive positive integers starting with 1. |
| series | The indicated sum of the terms of a sequence. |
| set-builder notation | A mathematical sentence that "builds" the set by selecting the elements that belong to the set. |
| sigma notation | Expresses the sum of a series. |
| slope-intercept form | The form Y = mx + b of a linear equation in two variables. The slope is m and the y-intercept is b. |
| solving a triangle | Finding all the unknown measures of a triangle. |
| square matrix of order n | A matrix with n rows and n columns. |
| square root | If x^2 = y. then x is a square root of y. |
| step function | A function whose graph resembles a staircase. |
| subset | A set all of whose elements are elements in a larger set. |
| standard scores (or --scores) | An expression for each value in a frequency distribution in terms of the number of standard deviations it is above or below the mean. |
| substitution | A method of solving systems of equations by replacing one variable with another variable or variable expression that is equal to it. |
| system | A set of equations having the same variables. |
| terms of a sequence | The numbers in a sequence. |
| theorem | A statement that has been proven to be true. |
| third-order determinant | A determinant with three rows and three columns. |
| transformation matrix | A matrix used for multiplying a point matrix to give a new point matrix. |
| translation | A transformation made by substitutions that shift each point of a given graph to a different location without changing the shape of the graph. |
| trinomial | A polynomial with three terms. |
| unit circle | A circle with center at the origin and with a radius of one unit. |
| value of a series | The simplified sum of a series. |
| variable | A symbol, usually a letter, that represents, and may be replaced by, any number from a particular set of numbers. |
| vectors | Matrices with either one row or one column. |
| vertex of a parabola | The point on a parabola midway between the focus and the directrix. |
| vertical-line test | If no vertical line intersects a graph of a relation more than once, then the re- lation is a function. |
| vertices of an ellipse | The endpoints of the major and minor axes. |
| vertices of a hyperbola | The two points in which a hyperbola is intersected by the line through the two focus points. |
| vinculum | The bar over the radicand. |
| wrapping function | The function that maps the real numbers onto the points of the unit circle. |
| x-axis | The horizontal axis. |
| y-axis: | The vertical axis. |
| y-intercept of a graph | The y-coordinate of the point at which a line crosses the Y-axis. |
| zero matrix | An m x n matrix whose elements are all zero. It is denoted Z m x n or just Z. |
