Math Vocabulary


Word Definition Examples


Absolute Value Distance of a number from zero on a number line. Since distance is always positive, the absolute value of any number must be positive.
Caution: be careful when taking the absolute value of a variable, since you may have several possible correct solutions.

| 5 | = 5

|- 5| = 5

Acute angle An angle that measures between 0 and 90 degrees

0 < x < 90

Acute triangle All angles in the triangle are acute A 40 - 60 - 80 triangle is acute
Additive Identity 0 - zero
When you add zero to anything it does not change the value.
0 is the additive identity in algebra because
a + 0 = 0 + a = a
Additive Inverse A number and its opposite When you add them they equal zero. 5 and -5 are inverses
because 5 + (-5) = 0
Adjacent angles Two coplanar angles with a common side, a common vertex, and no common interior points
Adjacent arcs Two arcs in the same circle that have exactly one point in common.
Algebra The study of equations using variables. At Capitan High School, the study of algebra is broken into Algebra 1 and Algebra 2.
Algebraic expression A collection of letters (variables) and real numbers (constants) combined using the operations of addition, subtraction, multiplication, division, and exponentiation.
Alpha Α α Greek letter frequently used to represent angles
Alternate exterior angles When two lines are cut by a transversal, the alternate exterior angles are on opposite sides of the transversal and the outside of the two lines
Altitude The height of an object measured perpendicular (90 degrees) from the bottom to the top
Amplitude of a periodic function Half the difference between the maximum and minimum values of the function
Angle The shape formed by two rays (called sides of the angle) with the same endpoint (called the vertex of the angle).

In geometry an angle can be defined by the vertex or by the rays and vertex. The symbol for angle is ∠

M or ∠ LMN

Angle bisector A ray that divides an angle into two congruent (equal) angles
Angle in standard position An angle that has its vertex at the origin and its initial side along the positive x-axis
Angle of Depression An angle from the horizontal down to a line of sight The angle between the viewer and something below them
Angle of Elevation An angle from the horizontal up to a line of sight The angle between the ground and something above the ground
Apothem A line segment that is drawn from the center of a regular polygon perpendicular to one side of the polygon.
Arc Part of a circle Exactly half the circle is called a semicircle.
Less than half is a minor arc and more than half is a major arc.
Arithmetic Mean The arithmetic mean of numbers is the sum of the numbers divided by how many numbers you added - also called the average The mean of 3 and 8 is 5.5
Arithmetic Sequence A numerical pattern where the difference between consecutive terms is a constant The arithmetic sequence 1, 4, 7, 10, 13, ... has a common difference of 3
Associative Property Changing the grouping of addends or factors does not change the sum or product. Grouping doesn't matter when adding or multiplying (2 + 3) + 4 = 5 + 4 = 9
2 + (3 + 4) = 2 + 7 = 9

(2 x 6) x 5 = 12 x 5 = 60
2 x (6 x 5) = 2 x 30 = 60

Asymptote A line the graph of a function gets close to but does not cross
Axis of Symmetry The line about which you can reflect a graph onto itself
also the vertical line containing the vertex of a parabola
When you fold a graph on the axis of symmetry, both sides match For the parabola,
y = x2 + 4x - 5 the axis of symmetry is the line x = -b/2a = -2
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Back-to-Back Stem and Leaf Plot A stem-and leaf plot used to compare two related sets of data
Bar Graph A graph where data is shown in bars that are used to compare amounts. The length of each bar represents the frequency
Base In an expression of the form xn, x is the base and n is the exponent.  
Best Fit Line The straight line that most closely approximates the data in a scatter plot.  
Beta Β β Greek letter frequently used to represent angles
Binomial Polynomial expression with two terms - bi means two 2x + 3
Binomial Experiment An experiment that has only two possible outcomes Tossing one coin is binomial because you only get heads or tails
Binomial Theorem The expansion of (a + b)n where n is a positive integer is:
(a + b)n= C0an + C1an-1b1 + C2an-2b2 + ... + Cn-1a1bn-1 + Cnbn
(x + 3)2= x2 + 6x + 9 is a binomial expansion
Bounded intervals Intervals with defined end points on the real number line used to define the domain of an inequality. See unbounded intervals [a,b] means a < x < b, a closed interval
(a,b) means a < x < b, an open interval
[a,b) means a < x < b
(a,b] means a < x < b
Box and Whisker Plot A diagram that divides a set of data into four parts: lower quartile, below the mean (average), above the mean, and highest quartile.
Branch Each piece of a discontinuous graph. y = (x + 5)/(x-5) has two branches
and is discontinuous at x = 5
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Calculus The study of infinitely small changes in slope and area, used to solve complicated real-world problems that cannot be solved using Algebra, geometry, or Trigonometry.
Central angle An angle whose vertex is the center of a circle  
Centroid The point in a triangle where the medians of the triangle intersect. Click here for an animated example of the centroid.
Central tendency The tendency of data to be grouped near the center of the data. Measured using mean, median, and mode.
Certain Event An event whose probability is one (1) or 100% Something that always happens
Circle The set of all points in a plane that are a constant distance of r from a given point called the center. If the center is at (h,k) and the radius is r, the equation of the circle is (x-h)2 + (y-k)2 = r2 (x-2)2 + (y-3)2 = 52 is a circle with center at (2,3) and a radius of 5
Circular function The trig functions, because they can be defined as points along the radius of the unit circle.
Circle Graph A graph that represents the frequency of data as slices of a circle. The size of each slice represents the frequency, usually recorded as a percent.
Circumcenter The point in a triangle where the perpendicular bisectors of the sides of the triangle intersect. Click here for an animated example of the centroid.
Closed interval An interval that includes both of its end points.
Coefficient The numerical factor when a term has a variable - a number that is multiplied by a variable in an equation or expression. The number next to a letter  5y
5 is the coefficient and y is the variable
Cofunction In trigonometry, the function pairs: sine and cosine, tangent and cotangent, and secant and cosecant.
Collinear Points that lie on the same line Points that all line up
Combination An arrangement or listing where the order is not important. Picking three students out of a classroom
Common factors Numbers, variables, and any products formed from the prime factors that appear in all terms of an expression For 2x2 -6x
2 and x are the common factors
Common logarithm A base 10 logarithm  
Commutative Property Changing the order of addends or factors does not change the sum or product Order doesn't matter when adding or multiplying 2 + 3 = 3 + 2 = 5

5 x 4 = 4 x 5 = 20

Compass A tool used to draw circles and parts of circles
Complementary angles Two positive angles whose measures add to 90 degrees

A + B = 90

Completing the Square One method used to solve a quadratic equation. Other methods include factoring and the quadratic formula.
Complex fraction A fraction where the numerator, denominator, or both has a fraction
5   1/2
Complex Number A number of the form a + bi, where a and b are real numbers and i is the square root of -1. Also called an imaginary number
Concave polygon When a diagonal contains points outside the polygon.
Congruent Objects that are the same size and the same shape. The symbol for congruent is an equal sign with a squiggle over it.
Conjecture The conclusion reached in a math statement based on reasoning - a guess based on observations.
Constant a value or number that never changes   5
Constant Term A term that has no variable factor - a number in an equation that is not multiplied by a variable A number that stands alone 7x + 3
3 is the constant term
Construction Using only a compass and a straight edge to draw a geometric figure.
Continuous Data Measures that change between data points Things that could be measured at any time - they always exist temperature, height, time, blood pressure, average grade
Continuous Function Function whose graph is an unbroken curve - it does not have any holes, gaps, or jumps  
Convex polygon No diagonal contains points outside the polygon - all the vertices of the angles point away from the center of the polygon.
Coordinate of a point On a number line, it is the distance of the point from the origin. On a coordinate axit is is the pair (x, y) that defines the location.
Coordinate pair A pair of numbers of the form (x, y) that gives the location of a point in the coordinate plane.
Coordinate Plane Formed when two number lines intersect at right angles. The x-axis is the horizontal axis and the y-axis is the vertical axis. The two axes meet at the origin (0,0). Click here for another explaination.
Coplanar Points and lines that are in the same plane
The VLA west of Socorro, NM, is a group of 27 radio telescopes that are coplanar.
Correlation A trend between two sets of data. A trend may show positive correlation (both sets of data get bigger together) negative correlation (one set of data gets bigger while the other gets smaller), or no correlation.
Corresponding parts Matching sides and angles in a polygon. For a simple game on corresponging parts in a triangle, click here.
Corollary A statement that follows directly from a theorem. Once you prove a theorem, the corollary is easily proven.
Cosine The ratio of the length of the side adjacent to an angle and the hypotenuse in a right triangle side adjacent divided by hypotenuse see Trigonometry
Coterminal Angles Two angles that share two sides in standard position. The sum of the absolute values of the angles adds to 360. 150 and -210 are coterminal angles
Cubic Equation An equation in the form 
ax3 + bx2 + cx + d = y, where a, b, c, and d are real numbers and a ≠ 0
Largest exponent is 3 2x3 + 3x2 -5x + 7 = y
Cycloid A curve that represents a path traced by a fixed point on the circumference of a circle rolling along a line. Used in Trigonometry and Calculus. x = at - a sin t
y = a - a cos t
for t any real number
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Last Updated: 03/16/2012
K. A. Shearer 2005-2012
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