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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.