# Glossary

 acute angle An angle measuring less than 90º. acute triangle A triangle with three angles that each measure between 0º and 90º. addend A number added to one or more other numbers to form a sum. addition property of equality For all real numbers a, b, and c, if a = b, then a + c = b + c. If two expressions are equal to each other and you add the same value to both sides of the equation, the equation will remain equal. additive identity The number 0 is called the additive identity because when you add it to a number, the result you get is the same number. For example, 4 + 0 = 4. additive inverse Any two numbers whose sum is zero, such as 3 and -3, because 3 + (-3) = 0. adjacent side For a given acute angle in a right triangle, the adjacent side to that angle is the side that, along with the hypotenuse, forms that acute angle. amplitude The distance between the highest point and the rest position (zero position) in a wave. amplitude Half the difference between the maximum and the minimum values of a periodic function. angle A figure formed by the joining of two rays with a common endpoint. area The amount of space inside a two-dimensional shape, measured in square units. arithmetic operations The operations of addition, subtraction, multiplication and division. associative property of addition For three or more real numbers, the sum is the same regardless of how you group the numbers. For example, (6 + 2) + 1 = 6 + (2 + 1). associative property of multiplication For three or more real numbers, the product is the same regardless of how you group the numbers. For example, (3 • 5) • 7 = 3 • (5 • 7). asymptote A line that a graph of a function will come close to, but not cross or even touch. axis One of two perpendicular lines of a coordinate place that intersect at the origin. The plural form of axis is axes. bar graph A graph that uses horizontal or vertical bars to represent data. base The expression that is being raised to a power when using exponential notation. In 53, 5 is the base, which is the number that is repeatedly multiplied. 53 = 5 • 5 • 5. In ab, a is the base. base The expression that is being raised to a power when using exponential notation. In 53, 5 is the base, which is the number that is repeatedly multiplied. 53 = 5 • 5 • 5. In ab, a is the base. binomial A polynomial with exactly two terms, such as 5y2 – 4x and x5 + 6. boundary line A line that divides the coordinate plane into two regions. If points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included then a dotted line is used. box-and-whisker plot A graph that uses a number line to show the distribution of a set of data. categorical data Data that details non-numerical features of an object. Examples of categorical data include eye color, blood type, and types of computers. central angle An angle whose vertex is at the center of a circle. circle graph Also called a pie chart, a type of graph where categorical data is represented as sections of a whole circle. circumference The distance around a circle, calculated by the formula C = d. coefficient A number that multiplies a variable. cofunctions Two trigonometric functions, such as sine and cosine, for which the value of the first function at an acute angle equals the value of the second function at the complement of that angle. common logarithm A logarithm using 10 as the base (log10). commutative property of addition Two real numbers can be added in any order without changing the sum. For example, 6 + 4 = 4 + 6. commutative property of multiplication Two real numbers can be multiplied in any order without changing the product. For example, 8 • 9 = 9 • 8. complementary angles Two angles whose measurements add up to 90º. completing the square A method for solving quadratic equations by rewriting one side of the equation as a squared binomial. complex conjugate Two complex numbers for which the real parts are equal and the imaginary parts are additive inverses. a + bi and a – bi are complex conjugates. complex fraction A quotient of two fractions. complex number A number in the form a + bi, where a and b are real numbers and i is the square root of −1. complex rational expression A quotient of two rational expressions. compound event An event with more than one outcome. compound inequality A statement including two inequality statements joined either by the word “or” or “and.” For example, 2x − 3 < 5 and x + 14 > 11. cone A solid figure with a single circular base and a round, smooth face that diminishes to a single point. congruent Having the same size and shape. conjugate One binomial in a conjugate pair. Given the binomial a + b, the conjugate is a – b; given a – b, the conjugate is a + b. conjugate pair A pair of binomials that, when multiplied, follow the pattern: The product of a pair of binomials that are conjugates is the difference of two squares. consistent system of linear equations A system of linear equations that has at least one solution. constant A symbol that represents a quantity that cannot change. It can be a number, letter or a symbol. constant of variation Represented by the variable k in variation problems, the constant of variation is a number that relates the input and the output. coordinate plane A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis. corresponding angles Angles of separate figures that are in the same position within each figure. corresponding sides Sides of separate figures that are opposite corresponding angles. cosine If A is an acute angle of a right triangle, then the cosine of angle A is the ratio of the length of the side adjacent to angle A over the length of the hypotenuse. coterminal angles The description of two angles drawn in standard position that share their terminal side. counting numbers Also called natural numbers, the numbers 1, 2, 3, 4, … cube A six-sided polyhedron that has congruent squares as faces. cube root The number which, when multiplied together three times yields the original number. For example, the cube root of 64 is 4 because 4 • 4 • 4 = 64. cycle Any part of a graph of a periodic function that is one period long. cylinder A solid figure with a pair of circular, parallel bases and a round, smooth face between them. data Mathematical term for information such as values or measurements. degree The value of an exponent. degree of a monomial The degree of a monomial is the power to which the variable is raised. For example, the monomial 5y2 has a degree of 2. If the monomial contains several variables then the degree of the monomial is the sum of the degree of all the variables. For example, the monomial 7x2y3 has a degree of 5. degree of a polynomial The highest exponent or sum of exponents of a term in a polynomial. For example, 7x2y3 + 3x2y − 8 is a 5th degree polynomial because the highest sum of exponents in a term is 2 + 3 = 5. dependent linear equations Equations that graph as the same straight line. diameter The length across a circle, passing through the center of the circle. A diameter is equal to the length of two radii. direct variation A type of variation where the output varies directly with the input. Direct variation is represented by the formula y = kx. discriminant In the Quadratic Formula, the expression underneath the radical symbol: b2 – 4ac. The discriminant can be used to determine the number and type of solutions the formula will reveal. distribute To rewrite the product of the number and a sum or difference using the distributive property. distributive property of multiplication The product of a sum (or a difference) and a number is the same as the sum (or difference) of the product of each addend (or each number being subtracted) and the number. For example, 3(4 + 2) = 3(4) + 3(2), and 3(4 – 2) = 3(4) – 3(2). distributive property of multiplication The product of a sum (or a difference) and a number is the same as the sum (or difference) of the product of each addend (or each number being subtracted) and the number. For example, 3(4 + 2) = 3(4) + 3(2), and 3(4 – 2) = 3(4) – 3(2). distributive property of multiplication over addition The product of a sum and a number is the same as the sum of the product of each addend and the number. For example, 3(4 + 2) = 3(4) + 3(2). divisor The number that you are dividing by in a division problem. In the problem , 2 is the divisor. domain The set of all possible input values for the variable in a function. domain of a function The set of all input values or x-coordinates of the function. e An irrational number, approximately 2.718281828459; sometimes called Euler’s number. elimination method A method of solving a system of equations. Given a system, the elimination method allows you to add the two equations in order to eliminate a common variable. equally likely Having the same likelihood of occurring, such that in a large number of trials, two equally likely outcomes would happen roughly the same number of times. equation A mathematical statement that two expressions are equal. equilateral triangle A triangle with 3 equal sides. evaluate To find the value of an expression. event A collection of possible outcomes, often describable using a common characteristic, such as rolling an even number with a die or picking a card from a specific suit. event space The set of possible outcomes in an event: for example, the event “rolling an even number” on a die has the event space of 2, 4, and 6. excluded value A value for the variable that is not included in the domain because it would cause the function to be undefined. exponent When a number is expressed in the form ab, b is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing. exponent When a number is expressed in the form ab, b is the exponent. The exponent indicates how many times the base is used as a factor. Power and exponent mean the same thing. exponential decay An exponential function of the form f(x) = bx, where 0 < b < 1. The function decreases as x increases. exponential function A function of the form f(x) = bx, where b > 0 and b ≠ 1. exponential growth An exponential function of the form f(x) = bx, where b > 1, and b ≠ 1. The function increases as x increases. exponential notation A shorter way to write repeated multiplication. For example, 24 means 2 • 2 • 2 • 2. Two is used as a factor 4 times. expression A mathematical phrase that can contain a combination of numbers, variables, or operations. extraneous solution A solution of the simplified form of an equation that does not satisfy the original equation and must be discarded. face The flat surface of a solid figure. factor A number or mathematical symbol that is multiplied by another number or mathematical symbol to form a product. For example, in the equation 4 • 5 = 20, 4 and 5 are factors. factoring The process of breaking a number down into its multiplicative factors. formula An equation or an expression that states a rule for a relationship among quantities. For example, the formula for finding the area of a rectangle can be represented as A = l • w, or simply l • w. function A relation that assigns to each x-value exactly one y-value. function notation An equation that takes the form f(x) =, and is read “f of x is…” For example, f(x) = 3x + 7. Fundamental Counting Principle If one event has p possible outcomes, and another event has m possible outcomes, then there are a total of p • m possible outcomes for the two events. greatest common factor The largest number (or expression) that is a factor of a set of two or more numbers (or expressions). greatest common factor (GCF) The product of the prime factors that two or more terms have in common. The greatest common factor of xyz and 3xy is xy. grouping symbols Symbols such as parentheses, braces, brackets, and fraction bars that indicate the numbers to be grouped together. half-life The amount of time it takes a substance to decrease to half its original amount. histogram A graph using bars to show continuous quantitative data over a series of similar-sized intervals. The height of the bar shows the frequency of the data, and the width of the bar represents the interval for the data. hypotenuse The side opposite the right angle in any right triangle. The hypotenuse is the longest side of any right triangle. hypotenuse The side opposite the right angle in any right triangle. The hypotenuse is the longest side of any right triangle. identity An equation that is true for any possible value of the variable. identity property of 0 When you add 0 to any number, the sum is the same as the original number. For example, 55 + 0 = 55. identity property of 1 When you multiply any number by 1, the product is the same as the original number. For example, 9(1) = 9. imaginary number A number in the form bi, where b is a real number and i is the square root of −1. imaginary part The imaginary term, bi, in a complex number a + bi. inconsistent system of linear equations A system of linear equations that has no solutions. independent linear equations Equations that graph as different straight lines. index The small positive integer just outside and above the radical symbol that denotes the root. For example, denotes the cube root. inequality A mathematical statement that shows the relationship between two expressions where one expression can be greater than or less than the other expression. An inequality is written by using an inequality sign (>, <, ≤, ≥, ≠). initial side The stationary ray that forms an angle in standard position and lies on the positive x-axis. integers The numbers …, -3, -2, -1, 0, 1, 2, 3… inverse function If you take a function and reverse its inputs and outputs, then you get its inverse function. inverse operations A mathematical operation that can reverse or “undo” another operation. Addition and subtraction are inverse operations. Multiplication and division are inverse operations. inverse variation A type of variation where the output varies inversely with the input. Inverse variation is represented by the formula . irrational numbers Numbers that cannot be written as the ratio of two integers—the decimal representation of an irrational number is nonrepeating and nonterminating. isolate a variable A method for solving an equation that involves rewriting an equivalent equation in which the variable is on one side of the equation and everything else is on the other side of the equation. isosceles trapezoid A trapezoid with one pair of parallel sides and another pair of opposite sides that are congruent. isosceles triangle A triangle with 2 equal sides. joint variation A type of variation where the output varies jointly with multiple inputs. Joint variation is represented by the formula y = kxz. least common denominator The smallest number (or expression) that is a multiple of all the denominators in a group of fractions (or rational expressions). least common multiple The smallest number (or expression) that is a multiple of a set of two or more numbers (or expressions). leg In a right triangle, one of the two sides creating a right angle. like terms Terms that contain the same variables raised to the same powers. For example, 3x and −8x are like terms, as are 8xy2 and 0.5xy2. line A line is a one-dimensional figure, which extends without end in two directions. line graph Used to show continuous data, a graph where individual data points are connected with line segments. Line graphs are typically used for data sets that track a quantity over time. line of reflection The line that cuts a parabola into two halves (which are mirror images of each other). line segment A finite section of a line between any two points that lie on the line. linear equation An equation in two variables whose ordered pairs graph as a straight line. linear inequality A mathematical statement in two variables using the inequality symbols <, >, ≤, or ≥ to show the relationship between two expressions. When the inequality symbol is replaced by an equal sign, the resulting related equation will graph as a straight line. linear relationship A linear relationship exists between two variables if, when you plot their values on a coordinate system, you get a straight line. logarithm A calculation in which the exponent y in x = by is found when given x and b; the corresponding notation is logbx = y. logarithmic function A function using a logarithm, in the of the form . A calculation in which the exponent y in x = by is found when given x and b; the corresponding notation is logbx= y. mean The sum of all the data values in a data set divided by the number of items in the data set; also called the average. median The middle number or the mean of the two middle numbers of a set of ordered data. midrange The mean of the greatest and least values of a data set. mode The number that appears most often in a data set. monomial A polynomial with exactly one term. 4x, −5y2, and 6 are all examples of monomials. multi-step equation An equation that requires more than one step to solve. multiplication property of equality For all real numbers a, b, and c, c ≠ 0: If a = b, then ac = bc. If two expressions are equal to each other and you multiply both sides of the equation by the same non-zero number, the equation will remain equal. multiplicative inverse Two numbers are multiplicative inverses if their product is 1. For example, . natural logarithm A logarithm using e as the base (loge). natural numbers Also called counting numbers, the numbers 1, 2, 3, 4, … negative numbers Numbers less than 0. nonrepeating decimals Numbers whose decimal parts continue without repeating—these are irrational numbers. nonterminating decimals Numbers whose decimal parts continue forever (without ending in an infinite sequence of zeros)—these decimals can be rational (if they repeat) or irrational (if they are nonrepeating). obtuse angle An angle measuring more than 90º and less than 180º. obtuse triangle A triangle with one angle that measures between 90º and 180º. one-step equation An equation that requires only one step to solve. opposite An opposite of a number is the number with the opposite sign, but same absolute value. For example, the opposite of 72 is -72. A number plus its opposite is always 0. opposite side For a given acute angle in a right triangle, the opposite side to that angle is the side that is not one of the two sides that form that acute angle. order of operations The rules that determine the sequence of calculations in an expression with more than one type of computation. ordered pair A pair of numbers that indicates a point on a coordinate plane. origin The point where the x-axis and the y-axis intersect on the coordinate plane (0, 0). outcome A result of a trial. parabola A u-shaped graph which is produced by a quadratic function. parallel lines Two or more lines that lie in the same plane but which never intersect. parallel lines Two or more lines that lie in the same plane but which never intersect. parallelogram A quadrilateral with two pairs of parallel sides. perfect cube A number whose cube root is an integer. perfect square A square of a whole number. Since 12 = 1, 22 = 4, 32 = 9, etc., 1, 4, and 9 are perfect squares. perfect square trinomial A trinomial that is the product of a binomial times itself, such as a2 + 2ab + b2 (from (a + b)2), and a2 – 2ab + b2 (from (a – b)2). perfect square trinomial A trinomial that is the product of a binomial times itself, such as a2 + 2ab + b2 (from (a + b)2), and a2 – 2ab + b2 (from (a – b)2). perimeter The distance around a two-dimensional shape. period The length of the smallest interval that contains exactly one copy of the repeating pattern of a periodic function. periodic function A function whose graph has a pattern that repeats forever in both directions. perpendicular lines Two lines that lie in the same plane and intersect at a 90º angle. perpendicular lines Two lines that lie in the same plane and intersect at a 90º angle. pi The ratio of a circle’s circumference to its diameter. Pi is denoted by the Greek letter . It is often approximated as 3.14 or . pictograph A graph that uses small icons or pictures to represent data. plane In geometry, a two-dimensional surface that continues infinitely. Any three individual points that don’t lie on the same line will lie on exactly one plane. point A zero-dimensional object that defines a specific location on a plane. It is represented by a small dot. polygon A closed plane figure with three or more straight sides. polyhedron A solid whose faces are polygons. polynomial A monomial or the sum or difference of two or more monomials. positive number Numbers greater than 0. power In an exponent ab, the power is represented by b. The power indicates how many times the base is used as a factor. Power and exponent mean the same thing. power rule for exponents To raise a power to a power, multiply the exponents. (xa)b = xa•b prime factor A factor that only has itself and 1 as factors. prime factorization The process of breaking down a number (or expression) into its prime multiplicative factors. For example, the prime factorization of 12xy is 2 • 2 • 3 • x • y. prime factorization The process of breaking down a number (or expression) into its prime multiplicative factors. For example, the prime factorization of 12xy is 2 • 2 • 3 • x • y. prime number A prime number is a natural number with exactly two distinct factors, 1 and itself. The number 1 is not a prime number because it does not have two distinct factors. principal In finance, the amount of money on which interest is calculated. principal root The positive square root of a number, as in . By definition, the radical symbol always means to find the principal root. Note that zero has only one square root, itself (since 0 • 0 = 0). Principle of Zero Products If ab = 0, then either a = 0 or b = 0, or both a and b are 0. probability A measure of how likely it is that something will occur. product raised to a power rule The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)x = ax • bx product raised to a power rule The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)x = ax • bx product rule for exponents To multiply two exponential terms with the same base, add their exponents. (xa)(xb) = xa+b pyramid A polyhedron with a polygonal base and a collection of triangular faces that meet at a point. Pythagoras A Greek philosopher and mathematician who lived in the 6th Century B.C. Pythagorean Theorem The formula that relates the lengths of the sides of any right triangle: , where c is the hypotenuse, and a and b are the legs of the right triangle. quadrant The x– and y-axes divide the coordinate plane into four regions. These regions are called quadrants. quadratic equation An equation that can be written in the form ax2 + bx + c = 0, where x is a variable, and a, b and c are constants with a ≠ 0. quadrilateral A four-sided polygon. quantitative data Numerical data. Examples of quantitative data include height, weight, and test scores. quartile The name of quarter sections of an ordered set of data. quotient The result of a division problem. In the problem , 4 is the quotient. quotient raised to a power rule For any real numbers a and b (b ≠ 0) and any positive integer x: For any real numbers a and b (b ≠ 0) and any positive integer x: quotient rule for exponents For any non-zero number x and any integers a and b: radian measure A measure of a central angle given by the ratio of the arc length to the radius. radical equation An equation that contains a radical expression. radical expression An expression that contains a radical. radical symbol The symbol, , used to denote the process of taking a root of a quantity. radicand The number or value under the radical symbol. radius The distance from the center of a circle to any point on the circle. range The set of all possible outputs in a function. Also the difference between the greatest value of a data set and the least value. range The set of all possible outputs in a function. Also the difference between the greatest value of a data set and the least value. range of a function The set of all output values or y-coordinates of the function. rational equation An equation that contains one or more rational expressions. rational exponent An exponent that is a fraction. rational expression A fraction that contains a polynomial as the numerator, denominator, or both. rational formula A formula expressed as a rational equation. rational numbers Numbers that can be written as the ratio of two integers, where the denominator is not zero. rationalizing a denominator The process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator. ray A half-line that begins at one point and goes on forever in one direction. real numbers All rational or irrational numbers. real part The real term, a, in a complex number a + bi. reciprocal A number that when multiplied by a given number gives a product of 1. For example, and are reciprocals of each other. rectangle A quadrilateral with two pairs of parallel sides and four right angles. rectangular prism A polyhedron that has three pairs of congruent, rectangular, parallel faces. reference angle The angle formed by the terminal side of an angle in standard position and the x-axis, whose measure is between 0° and 90°. reflection A mirror-image of a graph. If the reflection is over the x-axis, then the part of the original graph that was below the x-axis will be above the x-axis, and vice versa. relation A correspondence between sets of values or information. repeating decimals Numbers whose decimal parts repeat a pattern of one or more digits—these are all rational numbers. rhombus A quadrilateral with four congruent sides. right angle An angle measuring exactly 90º. right triangle A triangle containing a right angle. rise The vertical change between two points on a line. run The horizontal change between two points on a line. sample space The set of all possible outcomes. scalene triangle A triangle in which all three sides are a different length. scientific notation A positive number is written in scientific notation if it is written as a x 10n where the coefficient a has a value such that 1 ≤ a < 10 and n is an integer. set A collection or group of things such as numbers. similar Having the same shape but not necessarily the same size. simple event An event with only one outcome. sine If A is an acute angle of a right triangle, then the sine of angle A is the ratio of the length of the side opposite angle A over the length of the hypotenuse. slope The ratio of the vertical change to the horizontal change of two points on a line. slope-intercept form A linear equation written in the form y = mx + b, where m represents the slope of the line, and b represents the y-value of the y-intercept, (0, b). sphere A solid, round figure where every point on the surface is the same distance from the center. square A quadrilateral whose sides are all congruent and which has four right angles. square root A number that when multiplied by itself gives the original nonnegative number. For example, 6 • 6 = 36 and −6 • −6 = 36 so 6 is the positive square of 36 and −6 is the negative square root of 36. square root property If x2 = a2, then x = a or x = −a. standard position The placement of an angle upon a set of coordinate axes with its vertex at the origin, its initial side placed along the positive x-axis, and a directional arrow pointing to the angle’s terminal side. stem-and-leaf plot A type of graph used to visualize quantitative data. In a stem-and-leaf plot the digits of each number are organized separately to display a set of data. straight angle An angle measuring exactly 180º. substitute The replacement of a variable with a number. substitution method A method of solving a system of equations. Given a system, the substitution method allows you to create a simpler, one-variable equation by substituting one quantity in for an equivalent quantity. supplementary angles Two angles whose measurements add up to 180º. symmetric about the y-axis The left and right halves of the graph are mirror images of each other over the y-axis. system of linear equations Two or more linear equations with the same variables. system of linear inequalities Two or more linear inequalities with the same variables. tangent If A is an acute angle of a right triangle, then the tangent of angle A is the ratio of the length of the side opposite angle A over the length of the side adjacent to A. term A number or product of a number and variables raised to powers. 4x, −5y2, 6, and x3y4 are all examples of terms. terminal side The ray that has been rotated around the origin to form an angle with the stationary ray that is the initial side of the angle. terminating decimals Numbers whose decimal parts do not continue indefinitely but end eventually—these are all rational numbers. trapezoid A quadrilateral with one pair of parallel sides. tree diagram A diagram that shows the choices or random outcomes from multiple trials, using branches for each new outcomes. trial A random action or series of actions. triangle A polygon with three sides. trigonometric functions A function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, cosecant. trinomial A polynomial with exactly three terms, such as 5y2 – 4y + 4 and x2 + 2xy +y2. unit circle A circle centered at the origin that has radius 1. variable A letter or symbol used to represent a quantity that can change. vertex A turning point in a graph. Also the endpoint of the two rays that form an angle. vertex A turning point in a graph. Also the endpoint of the two rays that form an angle. volume A measurement of how much it takes to fill up a three-dimensional figure. Volume is measured in cubic units. whole number The numbers 0, 1, 2, 3, …., or all natural numbers plus 0. x-axis The horizontal axis of a coordinate plane. Also the horizontal axis of a bar graph or histogram. x-axis The horizontal axis of a coordinate plane. Also the horizontal axis of a bar graph or histogram. x-coordinate The first number in an ordered pair, which tells the distance to the right or left from the origin when graphing in a coordinate plane. x-intercept The point where the graph of a linear equation intersects the x-axis (x, 0). y-axis The vertical axis of a coordinate plane. Also the vertical axis of a bar graph or histogram. y-axis The vertical axis of a coordinate plane. Also the vertical axis of a bar graph or histogram. y-coordinate The second number in an ordered pair, which tells the distance to move up or down from the origin when graphing in a coordinate plane. y-intercept The point where the graph of a linear equation intersects the y-axis (0, y).