Glossary

a b c d e f g h i j k l m n o p q r s t u v w x y z
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Abscissa
The x-coordinate, or first coordinate of an ordered pair.
Absolute value
The distance of a number from 0 on the number line.
Acute angle
Any angle with measure less than ninety degrees.
Algebra
The use of symbols, usually letters, to represent numbers so that they can be manipulated without stating their values.
Algebraic expression
An expression consisting of constants, variables, grouping symbols, and symbols of operations arranged according to the rules of algebra.
Angle
The formation of two rays with a common endpoint.
Arc
The portion of a circle that lies between any two points on the circle.
Area
A measure of the surface of a figure, given as the number of square units needed to precisely cover the figure.
Associative property
An algebraic property of an operation. The associative property of addition is (a + b) + c = a + (b + c); the associative property of multiplication is (ab)c = a(bc)
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Base
A number or expression to be raised to a power. In the expression x2, x is the base.
Binomial
A polynomial with two terms.
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Chord
The line segment connecting two given points on a circle.
Circumference
The distance around a circle; the perimeter of a circle.
Coefficient
A constant multiplied by a term. In the expression 5x2,
5 is the coefficient of x2.
Common logarithm
A logarithm with base 10, usually written "log."
Commutative property
An algebraic property of an operation. The commutative property of addition is a + b = b + a; the commutative property of multiplication is ab = ba.
Complex fraction
A fraction where the numerator, the denominator, or both are fractions themselves.
Complimentary angles
Two angles whose measures add to 90 degrees.
Composite number
A natural number greater than 1 that is not a prime number, i.e. it has natural number factors besides itself and 1.
Conditional equation
An equation such that whether it is true or false depends on the value of a variable or variables.
Consistent System
A system of equations that has at least one solution.
Constant
A value that does not change, either represented by its value or a letter.
Contradiction
A contradiction is an equation that is always false; i.e. 1=0.
Counting numbers
The set {1, 2, 3, ...} of all positive whole numbers, also called the natural numbers.
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Decimal
The symbol "." used to separate the integer value from the non-integer value of a real number.
Degree
The degree of a nonzero monomial is the sum of the exponents of the variables. The degree of a polynomial is the highest degree of any one of its monomial terms.
Denominator
The number or expression in the bottom of a fraction or rational expression. The denominator of ¾ is 4.
Dependent System
A system of equations with an infinite set of solutions.
Dependent Variable
The variable, often denoted y, which represents values in the range of a function. The values of the dependent variable are the output values of the function.
Direct variation
A relationship between to values of the form a = kb.
Distributive property
An algebraic property of how two operations relate to one another. The statements a(b + c) = ab + ac and (b + c)a = ba + ca describe how multiplication distributes over addition.
Domain
The set of acceptable values for the independent variable of a function.
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Empty set
Also called the null set, the empty set is the set that contains no elements.
Endpoint
A point on the boundary of a line segment. The endpoints of the interval [0, 1] are 0 and 1.
Equation
An algebraic expression that uses an equal sign ("=") to state that two expressions have the same value.
Equilateral triangle
A triangle such that all three sides have the same length.
Equivalent equations
Equations that have exactly the same set of solutions.
Evaluate
To plug in known values of an expression in order to find its numerical value.
Exponent
The power of an expression. In the expression x2, 2 is the exponent.
Exponential notation
The notation used to show that an expression is being raised to a power.
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Factor
A value or expression that divides another expression. "2 is a factor of 4" means that 2 divides 4.
Factoring
Writing an expression as a product of factors.
First-degree equation
An equation that can be written in the form Ax + By = C; i.e. a polynomial equation of degree 1.
Function
A correspondence between two sets such that to each element of the first set (the domain) there is assigned to exactly one element of the second set (the range).
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Graph
The graph of a function is the set of all points whose coordinates are corresponded by the function; i.e. the graph of the function f(x) is the set of all points of the form (x, f(x), where x is an element of the domain of f.
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Hexagon
A six-sided polygon.
Horizontal line
A line of the form y = b; i.e. a line with slope 0.
Hypotenuse
The longest side of a right triangle, which is the side opposite the right angle.
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Identity
An equation that is always true.
Imaginary numbers
The set of numbers bi, where b is a real number and i denotes the square root of -1.
Improper fraction
A fraction whose numerator has a greater value than the denominator.
Inconsistent
An equation or system of equations with no solution.
Independent variable
The variable, often denoted x, which represents values in the domain of a function. The values of the independent variable are the input values for the function.
Inequality
An algebraic expression that uses one of the relations "greater than," "less than," "greater than or equal to," or "less than or equal to" to state a relationship between the values of two expressions. The solutions of inequalities are intervals.
Integers
The set {... -3, -2, -1, 0, 1, 2, 3, ...} of all whole numbers and their negatives.
Intercept method
A method for graphing a linear equation by first graphing its x-intercept and its y-intercept.
Intersection
The set of points that belong to two given sets or geometric figures.
Inverse variation
A relationship between to values of the form a = k/b.
Irrational numbers
The set of numbers on the number line that are not rational numbers; i.e. that cannot be expressed in the form p/q where p and q are integers.
Isosceles triangle
A triangle with at least two congruent angles.
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Joint variation
A relationship between three variables in which one variable depends on the value of two other variables.
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Least common multiple
The smallest number or simplest expression that is divisible by two or more given values or expressions.
Legs
The two sides of a right triangle that form the right angle.
Like Terms
Terms in an expression that have the same variable part. In the expression 5x2 + 3x2 + 2x, the first two terms are like terms, because their variable parts are identical.
Linear equation
An equation that can be written in the form Ax + By = C.
Linear function
A function that can be written in the form f(x) = mx + b; equivalently, a function whose graph is a line.
Literal equation
An equation that contain numbers, constants and at least two variables.
Lowest terms
An expression that is written in its simplest or most reduced form. A fraction is in lowest terms when the numerator and denominator have no common natural number factors except 1.
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Mathematical model
A collection of functions or expressions used to predict behaviors and approximate values of quantities in the world.
Mixed number
A number which expresses a value as the sum of an integer and a fraction; 3 ¾ is a mixed number.
Monomial
An algebraic expression that is a single term of a polynomial; monomials are constants or the product of a constant and one or more variables raised to whole-number powers.
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N
The letter used to represent the set of natural numbers or counting numbers.
Natural logarithm
A logarithm with base e, usually written "ln."
Natural numbers
The set {1, 2, 3, ...} of all positive whole numbers, also called the counting numbers.
Null set
Also called the empty set, the null set is the set that contains no elements.
Numerator
The number or expression in the top of a fraction or rational expression. The numerator of ¾ is 3.
Numerical coefficient
A constant, expressed as a number, multiplied by a term. In the expression 5x2,
5 is the numerical coefficient of x2.
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Obtuse angle
Any angle with measure greater than 90 degrees.
One-to-one function
A function f such that for each value y of the range, there is one unique value x of the domain that corresponds to y.
Ordered pair
A set of two numbers (x, y) that represents a point on the coordinate plane.
Ordinate
The y-coordinate, or second coordinate of an ordered pair.
Origin
The point (0, 0) that corresponds to the intersection of the coordinate axes.
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Parabola
The graph of a quadratic equation.
Parallel lines
Two lines with the same slope; i.e. lines such that if they intersect, they are the same line.
Parallelogram
A four-sided polygon in which all opposite sides are parallel.
Pentagon
A five-sided polygon.
Percent
Part of a hundred.
Perfect square
A number that is the square of a positive integer. The numbers 4, 9, and 16 are perfect squares.
Perpendicular lines
Two lines that intersect at a right angle.
Place value
The value associated with the location of a digit in a decimal number.
Point
The smallest unit on a graph; a single location on the coordinate plane which has no width or height.
Polynomial
A finite sum of monomials.
Power
The exponent of an expression, i.e. the number of times a base is to be multiplied by itself. In the expression x2, 2 is the power.
Prime Number
A natural number not equal to 1 whose only natural number factors are itself and 1.
Product
The result of the multiplication of two or more values or expressions.
Proportion
A ratio between two quantities or expressions that is to remain constant.
Pythagorean theorem
If the legs of a right triangle are a and b, then they are related to the length c of the hypotenuse by the equation a2 + b2 = c2.
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Quadrant
One of four regions separated by the x- and y-axes of the rectangular coordinate system.
Quadratic equation
Any equation of the form ax2 + bx + c = 0 where a is not zero.
Quadrilateral
A four-sided polygon.
Quotient
The result of the division of two quantities or expressions.
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R
The letter used to represent the set of real numbers.
Radical
The symbol used to denote the operation of taking a root.
Radical expression
An expression containing one or more radicals.
Radicand
The quantity or expression below a radical; the expression whose root is being taken.
Radius
The common distance from all points of a circle to the center.
Range
The set of possible values for the dependent variable of a function.
Ratio
The quotient of two values or expressions.
Rational numbers
The set of numbers that can be expressed in the form p/q where p and q are integers.
Rationalizing
To simplify a radical expression in order to remove the radical sign.
Ray
A portion of a line with one endpoint that goes off to infinity.
Real numbers
The collection of all rational and irrational numbers; all the numbers found on the number line.
Reciprocal
The result of exchanging the numerator and the denominator of a fraction. The reciprocal of any number a is 1/a.
Reduced
A fraction in lowest terms; i.e. such that the numerator and denominator share no common factors.
Relation
A set of ordered pairs (x, y), which often denotes a relationship between x and y. For instance, the relation "is equal to" denotes the set of all ordered pairs of the form (x, x).
Right angle
An angle of measure 90 degrees.
Right triangle
A triangle with one 90 degree angle.
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Scalene triangle
A triangle with no angles of the same measure.
Scientific notation
A number of the form ax10n, where n is any integer and a is between 1 and 10. Scientific notation is useful to express values that are either very large or very small.
Secant
The line through two give points on a circle.
Set
A well-defined collection of objects.
Signed number
A number that indicates both a quantity and a direction (either positive or negative).
Slope
The ratio of horizontal to vertical change that the graph of a line makes from one point to another.
Slope-intercept form
A linear equation of the form y = mx + b, where m is the slope of the graph and b is its y-intercept.
Solution
The value or set of values that satisfies a condition, usually expressed as an equation, inequality, or system of equations and inequalities.
Square root
The square root of a number a is a solution to the equation x2 = a; i.e. a number whose square is a.
Straight angle
An angle of measure 180 degrees.
Subset
Any set made up of the members of a parent set.
Substitution
A method of solving equations in which a variable of one equation is replaced by an equivalent expression in terms of other variables.
Sum
The result of an addition of expressions or values.
Supplementary angles
Any two angles whose measures have sum 180 degrees.
System of equations
A set of equations in the same variables, so that the solution of the system is the set of values such that all of the equations are simultaneously satisfied.
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Tangent
Intersecting a circle at exactly one point. For general curves, tangents intersect the curve at one point near that point.
Term
A value or expression being added to another.
Theorem
A mathematical statement or rule that is proven to be true.
Transversal
Any line that intersects another line or collection of lines.
Trapezoid
A quadrilateral such that at least one set of opposite sides are parallel.
Triangle
A three-sided polygon.
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Undefined
An expression that cannot be given a value without implying a false statement. For instance, 1/0 is undefined, for if 1/0 = a, then 0 x a = 1 which must be false.
Union
The collection of all elements of two or more sets.
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Variable
A letter that represents a numerical value.
Vertex
The endpoint of an edge of a polygon. Also the minimum or maximum point of a graph.
Vertical line
A line of the form x = a; i.e. a line whose slope is undefined.
Volume
A measure of the space occupied by a three-dimensional figure, given as the number of cubic units needed to precisely fill the figure.
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W
The letter used to represent the set of whole numbers.
Whole numbers
The set {0, 1, 2, 3, ...}.
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x-axis
The horizontal axis of the rectangular coordinate system.
x-intercepts
The x values of the points where a graph crosses the x-axis; i.e. for the graph of a function f, the solutions of the equation f(x) = 0.
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y-axis
The vertical axis of the rectangular coordinate system.
y-intercepts
The y values of the points where a graph crosses the y-axis; i.e. for the graph of a function f, the value f(0).
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Z
The letter used to represent the set of integers.
Zero exponent
A non-zero expression or value raised to the power 0. The resulting value is always 1.