Maths+Dictionary

Maths Dictionary abscissa: x-coordinate. The abscissa of the point (a, b) is a. absolute value: the distance of a number from zero. The positive value. acceleration: the rate of change of velocity. If position is represented by s(t), then velocity

is s'(t) and acceleration is s"(t). acute angle: a positive angle that measures less than 90 degrees. acute triangle: a triangle each of whose angles measures less than 90 degrees. additive identity: The number zero is called the additive identity because when you add it to a number, N, the result you get is the same number, N. additive inverse: the additive inverse of a number, N, is the number that when you add it to N, the result that you get is zero. The additive inverse of 7 is -7. The additive inverse of -3 is 3. adjacent angles: two angles that share both a side and a vertex. altitude: the perpendicular distance from the base of a figure to the highest point of the figure. amplitude: half the difference between the largest and smallest function value of a periodic function. angle: the union of two rays with a common endpoint. antecedent: the hypothesis of conditional statement. The "if" part of an "if-then" statement. antiderivative: the antiderivative of a function, f(x), is a function, F(x), whose derivative is f(x). Also called the indefinite integral. apothem: the perpendicular distance from the center to a side of a regular polygon. arc: the set of points on a circle that lie in the interior of a central angle. arc length: s = integral (sqrt (1 + (dy/dx)2)) dx. arccos: If x = cos y, then y = arccos x. The inverse of the cosine function. arccsc: If x = csc y, then y = arccsc x. The inverse of the cosecant function. arccot: If x = cot y, then y = arccot x. The inverse of the cotangent function. arcsec: If x = sec y, then y = arcsec x. The inverse of the secant function. arcsin: If x = sin y, then y = arcsin x. The inverse of the sine function. arctan: If x = tan y, then y = arctan x. The inverse of the tangent function. argument: The independent variable in a function. arithmetic mean: The sum of a set of numbers divided by the number of numbers. Also called the average. arithmetic sequence: a sequence of numbers of the form

arithmetic series: the sum of an arithmetic sequence. associative property of addition: (a + b) + c = a + (b + c) associative property of multiplication: (a * b) * c = a * (b * c) asymptote: a straight line that is a close approximation to a curve as the curve goes off to infinity. average: same as arithmetic mean. axiom: a statement that is assumed to be true without proof. Postulate. axis of symmetry: a line that passes through a figure in such a way that the part of the

B between: point B is between points A and C if AB + BC = AC. biconditional statement: a compound statement that says one sentence is true if and only if the other sentence is true. binary number system: the number system that uses only 0's and 1's. The places in the binary numbers are .......2n.......25, 24, 23, 22, 21, 20. binomial: an algebraic expression that is the sum of two terms. binomial theorem: the theorem that tells how to expand the expression (a + b)n. bisect: to cut something in half.

C cartesian coordinates: a system whereby points on a plane are identified by an ordered pair of numbers, representing the distances to two or three perpendicular axes. center: the point that is the same distance from all the points on a circle. The point that is the same distance from all the points on a sphere. The point inside an ellipse where the major and the minor axes intersect. The center of a circle that can be inscribed in a regular polygon. center of mass: centroid. central angle: an angle that has its vertex at the center of a circle. centroid: the center of mass of an object. The point where the object would balance if supported by a single support. The point in a triangle where the three medians intersect. chain rule: dy/dx = dy/du * du/dx. chord: a line segment that connects two points on a curve. circle: the set of points in a plane that are a fixed distance from a given point. circular functions: same as trigonometric functions. circumcenter: the point in a triangle that is the center of the circle that can be circumscribed about the triangle. The intersection of the perpendicular bisectors of the triangle. circumference: the distance around a closed curve. The circumference of a circle is 2*pi*r where r is the radius of the circle. circumscribed circle: a circle that passes through all of the vertices of a regular polygon. closed interval: an interval that contains its endpoints. coefficient: a constant that multiplies a variable. In Ax + By = C, A and B are coefficients of x and y. cofunction: the cofunction of a trigonometric function, f(x), is equal to f(pi/2 - x). The cofunction of the sine is the cosine. The cofunction of the secant is the cosecant. The cofunction of the tangent is the cotangent. collinear: points are collinear if they lie on the same line. commutative property: a + b = b + a. a*b = b*a. complementary angles: two angles are complementary if their sum is 90 degrees. completing the square: the method of adding an expression to both sides of an equation so that one side becomes a perfect square trinomial. complex fraction: a fraction that contains a fraction in its numerator and/or denominator. complex number: the sum of an imaginary number and a real number written in the form a + bi or r(cos x + isin x). component: the components in the vector (a, b, c) are a, b, and c. composite function: a function that consists of two functions arranged in such a way that the output of one function becomes the input of the other function. composite number: a natural number that is not prime. concave: a figure is concave if a line segment can be drawn so that it goes in, out, then back into the figure. conclusion: the part of an if - then statement that follows the word "then". Consequent. conditional statement: an if - then statement. cone: the union of all line segments that connect a point and a closed curve in a different plane from the point. congruent: shapes or angles are congruent if you could put one on top of the other, and they would look like just one shape. Equal. conic section: parabola, hyperbola, ellipse, circle. Formed by the intersection of a plane with a right circular cone. conjecture: a statement that seems to be true, but has not yet been proven. conjugate: the conjugate of a complex number is formed by reversing the sign on the imaginary part of the number. The conjugate of a + bi is a - bi. conjunction: a statement that is really two statements joined by the word AND. Both parts must be true for the statement to be considered true. consequent: the part of an "if - then" statement that follows the "then". Conclusion. constant: a value that does not change. continuous: a function is continuous if you can draw it without lifting your pencil off the paper. y = f(x) is continuous at a if 1. f(a) exists. 2. lim as x-->a f(x) exists. And 3. lim as x-->a of f(x) = f(a). contrapositive: the contrapositive of A-->B is Not B>Not A. convergent series: an infinite series that has a finite sum is called convergent. converse: the statement made by interchanging the hypothesis and the conclusion of a statement. convex: a set of points such that for any two points in the set, the line segment that connects them is also in the set. coordinates: a set of numbers that identifies the location of a point. coplanar: points that lie within the same plane are called coplanar. corollary: a statement that can be easily proven once a theorem is proved. cosecant: csc x = 1/sin x cosine: In a triangle, the cosine of an angle = (length of the adjacent side)/(hypotenuse) cotangent: cot x = 1/tan x coterminal angles: angles whose measures are 2kpi apart. counting numbers: natural numbers. The numbers you use to count. critical point: the point on a curve where the first derivative equals zero. Extremum. cube: a solid figure with six square faces. cubic: a polynomial of degree 3. cylinder: the union of all line segments that connect corresponding points on congruent circles in parallel planes.

D decagon: a polygon with ten sides. decimal numbers: the numbers in the base 10 number system. decreasing function: a function is considered to be decreasing if f(b) < f(a) when b > a. deduction: a conclusion arrived at by reasoning. definite integral: the definite integral of f(x) between a and b represents the area under the curve y = f(x), above the x - axis, to the right of the line x = a, and to the left of the line x = b. The definite integral of f(x) = F(b) - F(a) where F is an antiderivative function for f(x). degree: 1/360 of a full rotation. There are 360 degrees in a circle. Unit of measure of an

angle. denominator: the bottom part of a fraction. dependent variable: the output of a function. derivative: the rate of change of a function. The derivative at x of f(x) is the slope of the

tangent line at (x, f(x)). y' = f ' (x) = [f(x + delta x) - f(x)] / delta x. determinant: the determinant | a b | = ad - bc. diagonal: the line segment connecting two nonadjacent vertices in a polygon. diameter: the line segment joining two points on a circle and passing through the center. difference: the result of subtracting two numbers. differentiable: a function is differentiable over an interval if it is continuous over the
 * c d |

interval and if the derivative exists everywhere on the interval. differential: an infinitesimally small change in a variable, represented by d, as in dx, or dy. differentiation: the process of finding a derivative. digit: the ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits. Example: the number 365

has three digits: 3, 6, and 5. dimension: The dimension of a space is the number of coordinates needed to identify a location in that space. directly proportional: y is directly proportional to x if y = kx. discriminant: the discriminant of a quadratic equation, ax2 + bx + c = 0 is b2 - 4ac. The discriminant tells how many roots there are for the equation and the nature of the roots. disjoint: having no elements in common. disjunction: an OR statement. distributive property: a(b + c) = ab + ac divergent series: a series whose sum is infinite. dividend: In a / b = c, a is the dividend. division: the opposite operation of multiplication. divisor: In a / b = c, b is the divisor.

E

eccentricity: A number that indicates the shape of a conic section. The eccentricity of an ellipse is given by e = sqrt(a2 - b2) a element: a member of a set. ellipse: the set of all points in a plane such that the sum of the distances to two fixed points is a constant. The equation of an ellipse with center at the origin is x2 + y2 = 1 a2 b2 ellipsoid: a solid of revolution formed by rotating an ellipse about one of its axes. empty set: a set that contains no elements. equation: a mathematical statement that says that two expressions have the same value. equilateral triangle: a triangle that has three equal sides. equivalent equations: two equations whose solutions are the same. For example: x + 3y = 10, and 2x + 6y = 20. even function: a function that satisfies the property that f(x) = f(-x). even number: a natural number that is divisible by 2. event: in probability, a set of outcomes. exponent: a number that indicates the operation of repeated multiplication. exponential function: a function of the form f(x) = ax, where a is a constant known as the

base. extremum: a point where a function reaches a maximum or a minimum. F factor: one of two or more expressions that are multiplied together. factor theorem: If P(x) is a polynomial, then if P(r) = 0, then (x - r) is a factor of P(x). factorial: the product of all the integers from 1 up to the integer in question. The (!) exclaimation point is used to mean factorial. Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.... The sequence in which every number is the sum of the two preceding numbers

G geometric mean: the geometric mean of two numbers is the square root of the product of

the numbers. The geometric mean of n numbers is the nth root of the product of the numbers. geometric sequence: a sequence of numbers of the form a, ar, ar2, ar3,....., arn-1. geometric series: the sum of a geometric sequence. graph: the graph of an equation is the set of points that make the equation true. great circle: the circle formed by the intersection of a plane passing through the center of a sphere. greatest common factor: the greatest common factor of two numbers, a and b, is the

largest number that divides both a and b evenly.

H half plane: the set of all points in a plane that lie on one side of a line in the plane. harmonic sequence: a sequence is a harmonic sequence if the reciprocals of the numbers

in the sequence form an arithmetic sequence. heptagon: a polygon with seven sides. Heron's formula: a formula for the area of a triangle: _ A = (s(s - a)(s - b)(s - c)) where a, b, and c are the lengths of the sides of the triangle, and s is half the perimeter. hexadecimal number: a number written in base sixteen. hexagon: a polygon with six sides. hexahedron: a polyhedron with six faces. A regular hexahedron is a cube. hyperbola: the set of all points in a plane such that the difference of the distances to two fixed points is a constant. The general equation for a hyperbola is x2 - y2 = 1 a2 b2 hyperbolic functions: the hyperbolic functions are defined as follows: hyperbolic cosine: cosh x = (1/2)(ex + e-x) hyperbolic sine: sinh x = (1/2)(ex - e-x) hyperbolic tangent: tanh x = sinh x

cosh x hypotenuse: the longest side of a right triangle. The side opposite the right angle in a

right triangle. hypothesis: a proposition that is being investigated, it has yet to be proven.

I

icosohedron: a polyhedron with 20 faces. identity: an equation that is true for all values of the variable. identity element: If * is an operator, then the identity element, I, for * is the number such that I * a = a. The identity for addition is zero, and the identity for multiplication is 1. identity matrix: a square matrix with ones along the diagonal and zeros everywhere else. If I is an identity matrix, then IA = A. imaginary number: a number of the form ni, where n is a real number, and i2 = -1. implication: a conditional statement. improper fraction: a fraction with a numerator that is greater than the denominator. incenter: the center of a circle that is inscribed in a triangle. The intersection of the angle bisectors of the triangle. incircle: the circle that can be inscribed in a triangle. increasing function: a function is increasing if f(a) > f(b) when a > b. increment: a small change, usually indicated by the greek letter delta. indefinite integral: the sum of the antiderivative of a function and an arbitrary constant. independent variable: the input number to a function. infinity: a limitless quantity. inflection point: a point on a curve such that the curve is concave up on one side of the

point, and concave down on the other side of the point. inscribed polygon: a polygon placed inside a circle so that each vertex of the polygon

touches the circle. integers: the set of numbers containing zero, the natural numbers, and all the negatives of the natural numbers. lintergral: If dF(x)/dx = f(x), then F(x) is an integral of f(x). The area under the curve of a function above the x - axis. integrand: a function that is to be integrated. integration: the process of finding an integral. intercept: the x-intercept of a curve is the point where the curve crosses the x - axis, and

the y - intercept of a curve is the point where the curve crosses the y - axis. inversely proportional: y is inversely proportional to x if y = k/x. irrational number: a number that cannot be expressed as the ratio of two integers. isometry: a transformation of a figure that does not change the distances of any two

points in the figure. isosceles triangle: a triangle with at least two equal sides.

J joint variation: y varies jointly as x and z if y = kxz.

L law of cosines: c2 = a2 + b2 - 2abCosC law of sines: a/sin A = b/sin B = c/sin C least common denominator: the least common denominator of two fractions, a/b and c/d, is the smallest number that contains both b and d as factors. least common multiple: the least common multiple of two numbers, a and b, is the smallest number that contains both a and b as factors. lemma: a theorem that is proved mainly as an aid in proving another theorem. like terms: two terms each of whose parts, with the exception of their coefficients, is the same. line: a straight set of points that extends off into infinity in both directions. line segment: two points on a line, and all the points between those two points. logarithm: if y = bx, then logb y = x. logic: the study of sound reasoning.

M major arc: an arc of measure greater than 180 degrees. major axis: the line segment connecting the two vertices that are farthest apart in an ellipse. matrix: a table of numbers arranged in rows and columns. maxima: the points on a curve where the value is greater than that of the surrounding points. mean: average, arithmetic mean. median: the number in a group of numbers such that there are an equal number of numbers in the set greater than the number as are less than the number. midpoint: a point, M, on a line segment, AB, such that AM = MC. minima: the points on a curve where the value is less than that of the surrounding points. minor arc: an arc on a circle that is less than 180 degrees. minor axis: the shortest distance across an ellipse through the center. minute: the unit of measure of an angle that is 1/60 of a degree. mode: the number that occurs most frequently in a set of data. modulus: the absolute value of a complex number. monomial: an algebraic expression that does not involve any additions or subtractions. multiplicand: in the equation ab = c, a and b are multiplicands. multiplication: the operation of repeated addition. multiplicative identity: the number 1 is the multiplicative identity because 1 * a = a for all a. multiplicative inverse: the number, b, that when multiplied by a number, a, gives a result

N

natural logarithm: the logarithm with the base of e. Written: ln x. natural numbers: the counting numbers. negative number: a real number less than zero. normal: perpendicular. null set: same as empty set. A set with no elements. number line: a line on which every point represents a real number. numeral: a symbol that stands for a number. numerator: the top of a fraction.

O obtuse triangle: a triangle with an obtuse angle. octagon: a polygon with 8 sides. octahedron: a polyhedron with 8 faces. octal number: a number in base 8. odd function: a function that satisfies the property that f(-x) = -f(x). odd number: a whole number that is not divisible by 2. open interval: an interval that does not contain both its endpoints. ordered pair: a set of two numbers in which the order has an agreed upon meaning.

Such as the cartesian coordinates (x, y), where it is agreed that the first coordinate represents the horizontal position, and the second coordinate represents the vertical position. ordinate: the second coordinate of a cartesian ordered pair. origin: the point (0, 0) on a Cartesian Coordinate System. orthocenter: the point in a triangle where the three altitudes intersect. orthogonal: perpendicular.

P parabola: the set of all points in a plane that are equally distant from a fixed point (called the focus) and a fixed line, (called the directrix). paraboloid: a surface that is formed by rotating a parabola about its axis. parallel: two lines are parallel if they are in the same plane and never intersect. parallelepiped: a solid figure with six faces such that the planes containing two opposite faces are parallel. Each face is a parallelogram. parallelogram: a quadrilateral with opposite sides parallel. pentagon: a five sided polygon. percent: a fraction in which the denominator is assumed to be 100. perfect number: a number that is the sum of all its factors except itself. For example, 6. perimeter: the sum of the lengths of the sides of a polygon. period: the measure of how often a function repeats its same values. periodic function: a function that keeps repeating the same values. permutation: the permutation of n things taken j at a time is: n!

(n - j)! perpendicular: two lines are perpendicular if the angle between them is 90 degees. pi: the ratio of the circumference of a circle to its diameter. plane: a flat surfaces that stretches off into infinity. polar coordinates: a coordinate system of ordered pairs in which the first number of the pair represents distance from the origin, and the second number of the pair represents the angle of inclination from the horizontal axis. polygon: the union of several line segments that are joined together so as to completely enclose an area. polyhedron: a solid that is bounded by plane polygons. polynomial: an algebraic expression of the form: axn + bx(n-1) + .......+ cx3 + dx2 + ex + k positive number: a real number greater than zero. postulate: a fundamental statement that is assumed to be true without proof. power: a number that indicates the operation of repeated multiplication. prime number: a number whose only factors are itself and 1. product: the result of two numbers being multiplied. proper fraction: a fraction whose numerator is less than its denominator. proportion: an equation of fractions in the form: a/b = c/d proportional: If y = kx, then y is said to be proportional to x. protractor: a device for measuring angles. pyramid: the union of all line segments that connect a given point and the points that lie on a given polygon. Pythagorean Theorem: the theorem that relates the three sides of a right triangle: a2 + b2 = c2 pythagorean triple: three natural numbers that satisfy the pythagorean theorem.

Q quadratic equation: an equation involving the second power, but no higher power of an unknown. The general form of a quadratic equation in two unknowns is: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0. quadratic formula: the formula that says that the solution to the equation ax2 + bx + c = 0 is: _ x = -b + - (b2 - 4ac) 2a quadrilateral: a polygon with 4 sides. quartic: a polynomial of degree 4. quintic: a polynomial of degree 5. quotient: the answer to a division problem.

R

R: abbreviation for the real numbers. radian: the ratio of an arc of a circle to the radius of the circle. On a unit circle, a full rotation around the circle is 2pi radians. On any circle, a full rotation is 2pi r radians. radius: the distance from the center to a point on a circle. The line segment from the center to a point on a circle. range: the set of all possible values for the output of a function. ratio: the ratio of two real numbers, a and b, is a/b. rational number: a number that can be expressed as the ratio of two integers. real numbers: the union of the set of rational numbers and irrational numbers. reciprocal: the reciprocal of a number, a, is 1/a, (a cannot be zero). rectangle: a quadrilateral with four 90 degree angles. rectangular coordinates: same as Cartesian Coordinates. reflection: mirror image. reflexive property: x = x for all x. Every number equals itself. regular polygon: a polygon in which all the angles are equal and all of the sides are equal. regular polyhedron: a polyhedron whose faces are congruent, regular polygons. relation: a set of ordered pairs. remainder: if m = nq + r, then m/q has quotient q and remainder r. repeating decimal: a decimal in which the digits endlessly repeat a pattern. rhombus: a quadrilateral with four equal sides. right angle: an angle whose measure is 90 degrees. right circular cone: a cone whose base is a circle located so that the line connecting the vertex to the center of the circle is perpendicular to the plane containing the circle. right circular cylinder: a cylinder whose bases are circles and whose axis is perpendicular to its bases. right triangle: a triangle that contains a right angle. root: the root of an equation is the same as the solution to the equation

S scalar: a quantity that has size but no direction. scalene triangle: a triangle with three unequal sides. secant: a line that intersects a circle or a curve in two places. secant: the reciprocal of the cosine. second: the unit of measure of an angle that is 1/60 of a minute. sector: a region bounded by two radii of a circle and the arc whose endpoints lie on those radii. segment: the union of a point, A, and a point, B, and all the points between them. series: the sum of a sequence. set: a well defined group of objects. similar: two polygons are similar if their corresponding sides are proportional. simoultaneous equations: a group of equations that are all true at the same time. sine: in a right triangle, the length of a side opposite an angle divided by the length of the hypotenuse of the triangle. skew: two lines that are not in the same plane. slope: the slope of a line is the change in the vertical coordinates/the change in the horizontal coordinates of any two points on the line. solid: a three dimensional object that completely encloses a volume of space. sphere: the set of all points in space that are a fixed distance from a given point. square: a quadrilateral with four equal sides and four 90 degree angles. square root: of a number, x, is the number that, when multiplied by itself gives the number, x. subset: A set, B, is a subset of another set, A, if every element in B is also an element of A. sum: the result of adding. supplementary: two angles are supplementary if their sum is 180 degrees. symmetric: two points are symmetric with respect to a third point if the segments joining them to the third point are equal. Two points are symmetric with respect to a line if the line is the perpendicular bisector of the segment joining the points.

T tangent: a line that intersects a circle in one point. tangent: in a triangle, (the side opposite an angle) (the side adjacent the same angle). term: a part of a sum in an algebraic expression. terminating decimal: a fraction whose decimal representation contains a finite number of digits. tetrahedron: a polyhedron with four faces. theorem: a statement that has been proven. trajectory: the path that a body makes as it moves through space. transitive property: the property that states that if a = b, and b = c, then a = c. translation: a shift of the axes of the Cartesian Coordinate System. transversal: a line that intersects two other lines. trapezoid: a quadrilateral that has exactly two sides parallel. triangle: a three sided polygon. trinomial: a polynomial with exactly three terms.

U union: the union of two sets, A and B, is the set of all elements that are either in A, or in B, or in both A and B. unit vector: a vector of length 1. It is customary to designate i as the unit vector in the x direction, j as the unit vector in the y direction, and k is the unit vector in the z direction.

V variable: a symbol used to represent a value. vector: a quantity that has both magnitude and direction. velocity: the rate of change of position. The first derivative of the position function. vertex: the point on an angle where the two sides intersect. volume: measurement of space.

W whole numbers: the set of numbers that includes zero and all of the natural numbers.

X x-axis: the horizontal axis in a Cartesian Coordinate System. x-intercept: the value of x at the point where a curve crosses the x-axis.

Y

y-axis: the vertical axis in a Cartesian Coordinate System. y-intercept: the value of y at the point where a curve crosses the y-axis.

Z zero: the additive identity. The number that when you add it to a number, n, you will get n as a result.