Math Dictionary 25685m

A Absolute Value - always a positive number refers to the distance of a number from 0, the distances are positive. Acute Angle - an angle that has measure less than 90°. Adjacent Angles - two angles in a plane which shares a common vertex and a common side but do not overlap. Angles 1 and 2 below are adjacent angles. Algebra - a problem in which one or more number is unknown. Algebraic Equation - an equation of the form f (x) = 0 where f is a polynomial. Altitude - altitude is a distance measurement,

usually in the vertical or "up" direction. Angle - an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Arc - A connected section of the circumference of a circle. Axis - a fixed reference line for the measurement of coordinates. Axes - Plural of axis.

B Base - in plane geometry or solid geometry, the bottom of a figure. If the top is parallel to the bottom (as in a trapezoid or prism), both the top and bottom are called bases.

Beta (β) - the second letter of the Greek alphabet. Binomial - a polynomial with two which are not like . The following are all binomials: 2x – 3, 3x5 +8x4, and 2ab – 6a2b5. Bisector - a line segment, line, or plane that divides a geometric figure into two congruent halves. Bracket - The symbols [ and ].

C Cartesian plane - the plane formed by a horizontal axis and a vertical axis, often labeled the x-axis and y-axis, respectively. Center - the point inside a circle from which all points on the circle are equally distant.

Chord - a line segment on the interior of a circle. A chord has both endpoints on the circle. Circle - a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center). Circumference - a complete circular arc. Circumference also means the distance around the the outside of a circle. Clockwise - the direction that the hands of a clock move. Coefficient - the number multiplied times a product of variables or powers of variables in a term. Coordinates - on the coordinate plane, the pair of numbers giving the location of a point (ordered pair).

Congruent - Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent. Cosecant - the trigonometric function cosecant, written csc θ. Cosine - the trigonometric function cosine, which is written cos θ. Cotangent - the trigonometric function cotangent, written cot θ. Coterminal Angles angles which, drawn in standard position, share a terminal side. For example, 60°, -300°, and 780° are all coterminal.

Counter-Clockwise moving in the opposite direction of the arms on a clock.

D Decagon - a polygon with ten sides. Degree - a unit of angle measure equal to of a complete revolution. There are 360 degrees in a circle. Degrees are indicated by the ° symbol, so 35° means 35 degrees. Delta - the fourth letter of the Greek alphabet ( Δ, δ ), transliterated as ‘d.’ Diameter - a line segment between two points on the circle or sphere which es through the center. The word diameter is also refers to the length of this line segment.

Difference - the result of subtracting two numbers or expressions. For example, the difference between 7 and 12 is 12 – 7, which equals 5. Divisor - in the expression “a divided by b”, a is the dividend and b is the divisor. Domain - the set of values of the independent variable(s) for which a function or relation is defined. Typically, this is the set of x-values that give rise to real y-values.

E Endpoints - the points at which a line segment ends. Equation - a mathematical sentence built from expressions using one or more equal signs (=).

Equidistant - equally distant. For example, any two points on a circle are equidistant from the center. Evaluate - to figure out or compute. For example, "evaluate " means to figure out that the expression simplifies to 17. Even Number - an integer that is a multiple of 2. The even numbers are { . . . , –4, –2, 0, 2, 4, 6, . . . }. Exponent - x in the expression ax. For example, 3 is the exponent in 23. Expression - any mathematical calculation or formula combining numbers and/or variables using sums, differences, products, quotients (including fractions), exponents, roots,

logarithms, trig functions, parentheses, brackets, functions, or other mathematical operations. Expressions may not contain the equal sign (=) or any type of inequality.

F Factor - an exact divisor of a number. This 4 is a factor of 12; any of the numbers or symbols in mathematics that when multiplied together form a product. Fixed - constant. Not changing or moving. Formula - an expression used to calculate a desired result, such as a formula to find volume or a formula to count combinations. Formulas can also be equations involving numbers and/or variables, such as Euler's formula.

Fraction - a ratio of numbers or variables. Fractions may not have denominator 0. Function - a relation for which each element of the domain corresponds to exactly one element of the range. For example, is a function because each number x in the domain has only one possible square root. On the other hand, is not a function because there are two possible values for any positive value of x.

G Geometric Figure - any point, line, segment, ray, angle, polygon, curve, region, plane, surface, solid, etc. Formally, a geometric figure is any set of points on a plane or in space.

Geometric Mean - a kind of average. To find the geometric mean of a set of n numbers, multiply the numbers and then take the nth root of the product. Geometry - the study of geometric figures in two dimensions (plane geometry) and three dimensions (solid geometry). It includes the study of points, lines, triangles, quadrilaterals, other polygons, circles, spheres, prisms, pyramids, cones, cylinders, and polyhedra. Geometry typically includes the study of axioms, theorems, and two-column proofs. Graph - a visual representation of data that displays the relationship among variables, usually cast along x and y axes.

Greater Than - having a larger value than. Greatest Common Divisor - the greatest common divisor of a sequence of integers, is the largest integer that divides each of them exactly.

H Heptagon - a polygon with seven sides. Some authors also use the name septagon instead of heptagon. Hexagon - a polygon with six sides. Horizontal - perfectly flat and level. For example, the horizon is horizontal. So is the floor. Horizontal Line Test - a function is one-to-one if and only if every horizontal line intersects its graph at most once.

Hypotenuse - the side of a right triangle opposite the right angle. Note: The hypotenuse is the longest side of a right triangle.

I Imaginary Number - a complex number of the form xi where x is real and I = sqrt (-1). Improper Fraction - a fraction which has a larger numerator than denominator. For example, is an improper fraction. Integers - all positive and negative whole numbers (including zero). That is, the set {... , –3, –2, –1, 0, 1, 2, 3, ...}. Intersect - two figures are said to intersect if they meet or cross each other. Intersection - the point where two lines cross.

Interior Angle - an angle on the interior of a plane figure. Interval - the set of all real numbers between two given numbers. The two numbers on the ends are the endpoints. The endpoints might or might not be included in the interval depending whether the interval is open, closed, or half-open (same as half-closed). Irrational Number - a number which cannot be expressed as a quotient of two integers.

K Kite - a quadrilateral with two pairs of adjacent sides that are congruent. Note that the diagonals of a kite are perpendicular.

L Leading Coefficient - the coefficient of a polynomial's leading term. For example, 5 is the leading coefficient of 5x4 – 6x3 + 4x – 12. Leading Term - the term in a polynomial which contains the highest power of the variable. For example, 5x4 is the leading term of 5x4 – 6x3 + 4x – 12. Least Common Denominator - the smallest whole number that can be used as a denominator for two or more fractions. The least common denominator is the least common multiple of the original denominators. Leg of a Triangle - either of the two shorter sides of a right triangle. These two

sides together form the right angle in the right triangle. Like - which have the same variables and corresponding powers and/or roots. Like can be combined using addition and subtraction. that are not like cannot be combined using addition or subtraction. Length - the straight line distance between two points. Less Than - having the smaller value than. Line - the geometric figure formed by two points. A line is the straight path connecting two points and extending beyond the points in both directions. Linear - an equation or graph is linear if the graph of an equation is a straight line.

Linear Equation - An equation that can be written in the form "linear polynomial = linear polynomial" or "linear polynomial = constant". The following are examples of linear equations: 2x – 3 = 5, 4a + 9 = 8 – 9a, and 2x + 5y = 1. Logarithm - the exponent of the power to which a base number must be raised to equal a given number.

M Mean - another word for average. Mean almost always refers to arithmetic mean. In certain contexts, however, it could refer to the geometric mean, harmonic mean, or root mean square. Measurement - he process of asg a

number to a physical property. Examples of measurement include length, size of an angle, area, volume, mass, time, etc. Median - the midpoint of a set of data. Midpoint - the point halfway between two given points. Mixed Number - a number written as the sum of an integer and a proper fraction. Monomial - a polynomial with one term. The following are all monomials: 5x3, 8, and 4xy. Multiple - a number that is the product of a given number and some other number. Multiplication - the basic arithmetical operation of repeated addition.

N Negative Number - a real number less than zero. Zero itself is neither negative nor positive. Nonagon - a polygon with nine sides. Number - represents the value or quantity of something. Numerator - the number above the fraction bar that indicates the number of parts of the whole that are in a rational number, the number in the top half of the fraction.

O Obtuse Angle - an angle that has measure more than 90° and less than 180°. Obtuse Triangle - a triangle which has an

obtuse angle as one of its interior angles. Octagon - a polygon with eight sides. Odd Number - an integer that is not a multiple of 2. The odd numbers are { . . . , –3, –1, 1, 3, 5, . . . }. Opposite Reciprocal the result of taking the reciprocal of a number and then changing the sign. Ordered Pair - on the coordinate plane, the pair of numbers giving the location of a point (ordered pair). Ordinate - the ycoordinate of a point in the plane. Origin - the point at which the horizontal and vertical axes intersect, at zero (0, 0).

P Parallel Lines - two distinct coplanar lines that do not intersect. Parallelogram - a quadrilateral with two pairs of parallel sides. Parentheses - the symbols ( and ). Singular: parenthesis. Pentagon - a polygon with five sides. Perfect Square - any number that is the square of a rational number. For example, 0, 1, 4, 9, 16, 25, etc. are all perfect squares. Perimeter - the distance around the outside of a plane figure. For a polygon, the perimeter is the sum of the lengths of the sides.

Pi π - the ratio of the circumference of a circle to its diameter. Pi is written π and is a transcendental number. Plane - a flat surface extending in all directions. Any three non collinear points lie on one and only one plane. So do any two distinct intersecting lines. A plane is a twodimensional figure. Point - the geometric figure formed at the intersection of two distinct lines. Polygon - a closed plane figure for which all sides are line segments. The name of a polygon describes the number of sides. A polygon which has all sides mutually congruent and all angles mutually congruent is called a regular polygon.

Polynomial - an algebraic expression where the exponents of the variables are all nonnegative integers. Positive Number - a real number greater than zero. Zero itself is not positive. Power - either the number itself, or the product arising from using the number a certain number of times as a factor. Product - the result of multiplying a set of numbers or expressions. Proper Fraction - a fraction with a smaller numerator than denominator. Pythagorean Theorem the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

Q Quadrantal Angle - an angle with terminal side on the x-axis or y-axis. That is, the angles 0°, 90°, 180°, 270°, 360°, 450°, ... as well as –90°, –180°, – 270°, –360°, ... Quadrants - the four sections into which the x-y plane is divided by the xand y-axes. Quadratic Equation - an equation includes only second degree polynomials. Some examples are y = 3x2 – 5x2 + 1, x2 + 5xy + y2 = 1, and 1.6a2 +5.9a – 3.14 = 0. Quadratic Function - a function of the form f(x) = ax2 + bx + c where a is not equal to zero (in which

case the function turns into a linear function).

circular arc described by that angle.

Quadrilateral - a polygon with four sides.

Radical - The symbol, which is used to indicate square roots or nth roots.

Quadratic - an equation, graph, or data that can be modeled by a degree 2 polynomial. Quartic Polynomial - a polynomial of degree 4. Quintic Polynomial - a polynomial of degree 5. Quotient - the result of dividing two numbers or expressions. For example, the 40 divided by 5 has a quotient of 8.

R Radian - A unit for measuring angles. 180° = π radians, and 360° = 2π radians. The number of radians in an angle equals the number of radii it takes to measure a

Range - The set of yvalues of a function or relation. More generally, the range is the set of values assumed by a function or relation over all permitted values of the independent variable(s). Ray - A part of a line starting at a particular point and extending infinitely in one direction. Real Numbers - All numbers on the number line. This includes (but is not limited to) positives and negatives, integers and rational numbers, square roots, cube roots , π (pi), etc. Reciprocal - The reciprocal of x is 1/x. In other words, a reciprocal

is a fraction flipped upside down. Multiplicative inverse means the same thing as reciprocal. Rectangle - A box shape on a plane. Formally, a rectangle is a quadrilateral with four congruent angles (all 90°). Reference Angle - For any given angle, its reference angle is an acute version of that angle. In standard position, the reference angle is the smallest angle between the terminal side and the x-axis. The values of the trig functions of angle θ are the same as the trig values of the reference angle for θ, give or take a minus sign. Remainder - The part left over after long division. Right Angle - A 90° angle.

Right Triangle - A triangle which has a right (90°) interior angle.

S Secant - The trig function secant, written sec θ. Segment - all points between two given points (including the given points themselves). Semicircle - half a circle. That is, a 180° arc. Set - a group of numbers, variables, geometric figures, or just about anything. Sets are written using set braces {}. For example, {1,2,3} is the set containing the elements 1, 2, and 3. Similar - identical in shape, although not necessarily the same size. Sine - the trig function sine, written sin θ. For acute angles, sin θ can be

found by the SOHCAHTOA definition as shown below on the left. The circle definition, a generalization of SOHCAHTOA, is shown below on the right. Finally, f(x) = sin x is a periodic function with period 2π. Solution Set - any and all value(s) of the variable(s) that satisfies an equation, inequality, system of equations, or system of inequalities. Solve - find all solutions to an equation, inequality, or a system of equations and/or inequalities. Square - a rectangle with all four sides of equal length. Formally, a square is a quadrilateral with four congruent sides and four congruent angles (all 90°). Square Root - a nonnegative number that must be multiplied times

itself to equal a given number. Subtraction - is a mathematical operation that represents the operation of removing objects from a collection. Sum - the result of adding a set of numbers or algebraic expressions. Symmetric - describes a geometric figure or a graph consisting of two parts that are congruent to each other. Synthetic Division - a shortcut for polynomial long division that can be used when dividing by an expression of the form x – c or x + c. Note: This allows an improper rational expression to be written as a sum of a polynomial and a proper rational expression.

T

Tangent - the trig function tangent, written tan θ. Term - parts of an expression or series separated by + or – signs, or the parts of a sequence separated by commas. Theorem - an assertion that can be proved true using the rules of logic. A theorem is proven from axioms, postulates, or other theorems already known to be true. Theta θ - the eighth letter of the Greek alphabet ( Θ, θ ), transliterated as ‘th.’ Triangle - a polygon with three sides. Trigonometry - the study of triangles, with emphasis on calculations involving the lengths of sides and the measures of angles. Trigonometry is also known as trig. Trigonometry is based on

the six functions sine, cosine, tangent, cosecant, secant, and cotangent. Trig also includes studies of the properties of these functions and their graphs. Trigonometric Functions - the six functions sine, cosine, tangent, cosecant, secant, and cotangent. These functions can be defined several different ways. These include SOHCAHTOA definitions, circle definitions (below), and unit circle definitions. Trinomial - a polynomial with three which are not like . The following are all trinomials: x2 + 2x - 3, 3x5 - 8x4 + x3, and a2b + 13x + c. Triple Root - a root of a polynomial equation with multiplicity 3. Also refers to a zero of a polynomial

function with multiplicity 3.

representing such a quantity.

Undefined Slope - the "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate.

Vertex - a corner point of a geometric figure. For a polygon, vertices are where adjacent sides meet. For an angle, the vertex is where the two rays making up the angle meet.

Uniform - all the same or all in the same manner; constant.

Vertical - straight up and down. For example, a wall is vertical.

Unit - a single thing used as a standard or measure.

Vertical Line Test - a test use to determine if a relation is a function. A relation is a function if there are no vertical lines that intersect the graph at more than one point.

U

Unit Circle - the circle with radius 1 which is centered at the origin on the x-y plane.

V Variable - a quantity that can change or that may take on different values. Variable also refers to a letter or symbol

W Whole Numbers - the numbers 0, 1, 2, 3, 4, 5, etc.

X

x-intercept - a point at which a graph intersects the x-axis. The xintercepts of a function must be real numbers, unlike roots and zeros.

Y y-intercept - point at which a graph intersects the y-axis.

Z Zero - the number which indicates no quantity, size, or magnitude. Zero is neither negative nor positive.