66628563 dictionary-of-math-terms

Dictionary of MATH TERMS

1

A

AA similarity

According to the AA similarity if two angles of a triangle are congruent to two angles of another

triangle, then the triangles are said to be similar to each other.

AAS Congruence

AAS congruence is called as angle-angle-side congruence. If there are two pairs of

corresponding angles and a pair of corresponding opposite sides that are equal in measure, then

the triangle is said to be congruent.

Abscissa

The X-coordinate of a point on the coordinate system is called abscissa. For example, in the

ordered pair P(2, 3, 5), 2 will be called the abscissa of the point P. In math terminology it will be

called as the length of the point(P) relative to the X-axis.

Absolute Value

A general concept of absolute value is that it makes a negative number positive. Absolute value

is also called a mod value. The absolute value of a number (say X) is denoted as |X|. Remember,

the absolute value uses bars so don't use parenthesis or any other symbol else the meaning

changes. To put it simply, |-7| = 7 and |7| = 7. Positive numbers and zero are left unchanged in

the absolute value.

Acceleration

The rate of change of velocity with time is called acceleration. Mathematically, the second

derivative of the distance traveled by an object is called acceleration.

Accuracy

The measure of the closeness of a value to the actual value of a result is called accuracy.

Acute Angle

An angle whose measure is less than 900 is called as an acute angle.

Acute Angled Triangle

A triangle in which all the interior angles are acute is known as an acute angled triangle.

Addition Rule Of Probability

Addition rule of probability is meant to find out the probability of occurrence of either or both

the events.

For Example, If P(A) and P(B) are mutually exclusive events, then the probability P(A or B) =

P(A) + P(B) else P(A or B) = P(A) + P(B) – P(A and B).


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Additive Inverse of a Matrix

If the sign of every matrix element is changed, then the matrix is said to be an inverse of the

original matrix. If A is the matrix, then -A will be the inverse of the matrix. If add a matrix and

its inverse, then the sum would be zero since the each element in the original matrix is negative

of the other.

Additive Property of Equality

Simply stated, additive property states that same number can be added on both side of the

equation. For example, x – 3 = 5 is same as x – 3 + 3 = 5 + 3.

Adjacent Angles

If the two angles share a common vertex and common plane and even have a same side but if

they don't overlap or one of the angles is not contained in the other then the angles are called

adjacent angles.

Adjoint Matrix

When we take the transpose of the co-factor of the original matrix, then it is known as adjoint

matrix.

Algebra

A branch of pure mathematics that uses alphabets and letters as variables. The variables are the

unknown quantities whose values can be determined with the help of other equations. For

example, 3X – 7 = 78, is an algebraic equation in one unknown variable (here it is X).

Algebraic Numbers

All rational numbers are the algebraic numbers. Numbers that are roots of the polynomials with

integer coefficients and are under the surd are also included as algebraic numbers. Any number

that is not a root of polynomial with integer coefficients is not an algebraic number. These

numbers are called transcendental numbers. e and Π are called the transcendental numbers.

Alternate Angles

If two or more parallel lines are cut by a transversal, then the angles formed in the alternate

direction to each other are called as alternate angles.

Alternate Exterior Angles

When two or more parallel lines are cut by a transversal and the alternate angles that are exterior

to one another is called alternate exterior angle.

Alternate Interior Angles

When two or more lines are cut by a transversal then the alternate angles that lie interior to each

other are called alternate interior angles.


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Altitude

Altitude is the shortest distance between the base to the apex of a figure like cones, triangle etc.

Altitude of a Cone

The distance between the apex of the cone and its base is called the height or the altitude of the

cone.

Altitude of a Cylinder

The distance between the circular bases of the cylinder or the length of the line segment between

two of its bases is known as altitude of a cylinder.

Altitude of a Parallelogram

The distance between the opposite sides of a parallelogram is called as altitude of a

parallelogram.

Altitude of a Prism

The distance between the two bases of a prism is called as the altitude of a prism.

Altitude of a Pyramid

The distance between the apex of the pyramid to the base is called as altitude of the pyramid.

Altitude of a Trapezoid

The distance between the two bases of the trapezoid is called as altitude of a trapezoid.

Altitude of a Triangle

The shortest distance between the vertex of the triangle and the opposite side is called as altitude

of the triangle.

Amplitude

A mathematical definition of amplitude is that it is means the measure of half the distance

between the maximum and minimum range. For example, if you consider a sine wave, then ½ of

the distance between the positive and negative curves in called amplitude. It is to be remembered

that only periodic functions with bounded range have amplitude.

Analytic Geometry

Analytical geometry is the branch of mathematics that deals with the study of geometric figures

with the help of co-ordinate axes. The points are plotted and with the help of the points we can

easily find out the required information.


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Analytic Methods

If you are asked to analytically solve a problem then it means that you are not suppose to use a

calculator. Analytical methods are used to solve the problems by the help of algebraic and

numeric methods.

Angle

Angle is defined as the figure formed by touching the end of two rays. Angle in other word is

two rays sharing a common point.

Angle Bisector

The line that bisects an angle into two equal halves is called as an angle bisector.

Angle of Inclination of a Line

The angle subtended by a line with the x-axis is called as angle of inclination of the line. The

angle of inclination is always measured in counter clockwise direction, that means positive

direction of the x-axis. The angle of inclination is always between the range 00 to 180

0.

Annulus

The area between two concentric circles of a ring (say) is called annulus.

Antiderivative of a Function

If F(x) = 2x2 + 3, then, its derivative F'(x) = 4x. Here 4x is called as the antiderivative of F(x).

Antipodal Points

In three dimensions the points diametrically opposite on a sphere is called antipodal points.

Apothem

Apothem is the same as the in radius of an inscribed circle in a regular polygon. If we define in

other words then it would mean the distance from any of midpoint of the sides of the polygon to

the center of the polygon.

Approximation by Differentials

By the rule of approximation of differentials the value of a function is approximated and the

principles of derivation are used in this method. The formula used in the approximation by

differentials is, f(x + ∆x) = f(x) + ∆y = f(x) + f'(x)∆x, where f'(x) is the differential of the

function.

Area of a Circle

The area of a circle is given by the formula Πr2.


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Arccos

The inverse function of a cosine function is called the arccos function. For example, cos-1

(1/2)

(read as cos inverse half) or"the angle whose cosine is equal to ½. As we all know it nothing but

600.

Arccosec

The inverse of a cosec function is called arccosec function. For example, cosec-1

(2) means the

angle whose cosecant is equal to 2. The answer is 300. It is to be noted that there can be many

more angles with the cosecant equal to 300. What we want is the most basic angle that gives the

cosecant equal to 300. For other angles, we need to consider the range of the function.

Arccot

Arc cot is the inverse of the cotangent function. For example, cot-1

(1) means the angle whose

cotangent is equal to 1. Cot-1

1 = 450.

Arcsec

The inverse of a secant function is called the arcsec function. For example, sec-1

2 means the

angle whose secant is equal to 2. Sec-1

2 = 600.

Arcsin

The inverse of a sine function is called arcsin function. For example, sin-1

(1/2) = 300.

Arctan

The inverse of a tangent function is called arctan function. For example, tan-1

(1) = 450

Area of an Ellipse

The area of an ellipse is given by the formula ∏ab, where a and b are the lengths of the major

and minor axis of the ellipse. If the ellipse has its center at (h, k) then,

Area = [(x-h)2/a

2 + (y-k)

2/b

2]

Area of an Equilateral Triangle

The area of an equilateral triangle is given by:

a2√3/4, where a = side of the equilateral triangle.

Area of a Kite

The area of a kite is given by:

½ (product of the diagonals) = ½ x d1d2.

Area of a Parabolic Segment

The area of a parabolic segment is given by 2/3 of the product of width and height.


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Area of a Parallelogram

Are of parallelogram = height x base of the parallelogram.

Area of a Rectangle

Area of rectangle = length x breadth

Area of a Regular Polygon

Area of regular polygon = ½ x apothem x perimeter.

Area of a Rhombus

Diagonals of a rhombus are perpendicular to each other. Area = ½ x product of diagonals or

Area= h x s, where h and s are the height and side of the rhombus.

Area of a Segment of a Circle

We all know the area of a circle, but what if the area of a segment is to be found out, well the

formula for area of a segment of a circle is:

Area = 1/2r2(θ – sinθ) (radians)

Area of a Trapezoid

Area of a trapezium = ½ x (sum of the non- parallel sides) x h = ½ x (b1 + b2) x h

Area of a Triangle

There are various formulas to calculate the area of a triangle that are as follows.

Area = A = ½ x base x height

A = ½ x ab SinC = ½ x bc SinA = I/2 x ca SinB, where A, B and C are the angles of the

triangle respectively.

Given s= a+b+c/2 (semi perimeter), by Heron's Formula, A= [s(s-a)(s-b)(s-c)]1/2

.

If 'r' and 'R' are the inradius and circumradius of the incircle and outercirlce of a triangle,

then the Area (A) = rs and A= abc/4R, a, b and c are the sides of the triangle.

Area Using Polar Coordinates

When the polar co-ordinates are involved in computation of the area then the area is given by:

The area between the graph r = r(θ) and the origin and also between the lines θ = α and θ = β is

given by the formula:

Area = ½ αʃβr2dθ


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Argand Plane

The complex plane is called as the argand plane. Basically, argand plane is use to denote the

complex numbers graphically. The x-axis is called as the real axis and the y-axis is called as the

imaginary axis.

Argument of a Function

The term or expression on which the function operates is called as argument of the function. The

argument of the function y= √x is x.

Argument of a Vector

The measure of an angle describing a vector or a line in the complex number analysis is called

the argument of the vector.

Arithmetic Mean

The most simple average technique that we use in day to day life.

For example, if there are 4 quantities then there arithmetic mean is given by,

Arithmetic mean = (a + b + c + c + d)/4

Arithmetic Progression

A mathematical series that has same common difference among its terms.

For example, 1, 3, 5, 7, 9.....up to infinity. The nth term of an arithmetic progression is given by,

Tn = a + (n-1)d, where a = 1st term, n = number of terms and d= common difference. It is also

called as arithmetic sequence. The sum of an arithmetic progression is given by: S = n/2[2a + (n-

1)d] or S = n(a1 + an)/2, here n= number of terms.

Arm of an Angle

One of the rays/line forming an angle with the other is called the arm of an angle.

Arm of a Right Triangle

Any of the sides of the right angled triangle is called the arm of a right angled triangle.

Associative

The operation a + (b+c) = (a + b) + c is called as associative operation. Addition and

multiplication are associative while division and subtraction are not. For example, (4+5)+ 7 = 4 +

(5+7)

Asymptote

An asymptote is a curve or line that approaches the curve very closely. There are horizontal and

oblique asymptotes but not vertical asymptotes.

Augmented Matrix

The matrix representation of a set of linear equations is called the augmented matrix.


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For example, 3x – 2y = 1 and 4x + 6y = 4, then in a matrix form 3, -2 and 1 (from 1st equation)

and 4, 6 and 4 (from 2nd equation) form the elements of 3x3 matrix respectively.

Average

Average is same as the arithmetic mean.

Average Rate of Change

Mathematically, the change in the slope of a line is called as the average rate of change of the

line. Also, the change in value of a quantity divided by time is average rate of change.

Average Value of a Function

For a function y =f(x), in the domain [a,b] the average value is given by the formula (1/b-

a)aʃbf(x)dx

Axes

The x and y, z axes are known as the axes of a co-ordinate system.

Axiom

A statement that has been assumed to be true without any proof.

Axis of a Cylinder

The line that passes exactly through the center of the cylinder and also passes through the bases

of the cylinder. Simply stated, the line that divides the cylinder into two equal halves vertically.

Axis of Reflection

A line across which the reflection takes place.

Axis of Rotation

An axis along which the rotation of the axis takes place.

Axis of Symmetry

A line along which the geometrical figure or the shape is symmetrical.

Axis of Symmetry of a Parabola

The axis of symmetry of a parabola is the line that passes through the focus and vertex of

parabola.


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B

Base (Geometry)

The bottom part of a geometrical figure like a solid object or a triangle is called the base of the

object.

Base of an Exponential Expression

Consider the expression ax. Then 'a' can be called as the base of the expression a

x.

Base of an Isosceles Triangle

The base of an isosceles triangle is the non-congruent side of the triangle. In other words, it is the

side other than the legs of the triangle.

Base of a Trapezoid

The trapezoid has four sides with two sides parallel. Either of the two parallel sides can be

considered as the base of the trapezoid.

Base of a Triangle

Base of a triangle is the side at which an altitude can be drawn. It is the side which is

perpendicular to the altitude.

Biconditional

It is the method of expressing a mathematical statement containing more than one conditions,

that means a condition and its converse. These statements are called as biconditionals.

Biconditionals are represented by the symbol ⇔. For example the following statements can be

called biconditionals: "A given triangle is equilateral" is same as "All the angles of a triangle

measure 60º."

Binomial

A binomial can be simply defined as a polynomial which has two terms, but they are not like

terms. For example, 3x – 5z3, 4x – 6y

2.

Binomial Coefficients

The coefficients of the various terms in the binomial expansion of the binomial theorem are

called as binomial coefficients. Mathematically, a binomial coefficients equals the number of r

items that can be selected from a set of n items. They are simply called as the binomial

coefficients because they are coefficients of the binomial expanded terms. Generally, they are

represented by nCr.

Binomial Coefficients in Pascal's Triangle

Pascal's triangle is an arithmetic triangle that is used to calculate the binomial coefficients of the

various numbers. The binomial coefficients (nCr) in the pascal's triangle are called as the


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binomial coefficients in pascal's triangle. Pascal's triangle finds major use in algebra and

probability/binomial theorem.

Binomial Probability Formula

The probability of getting m successes in n trials is called binomial probability formula. The

formula is given by:

Formula: P(m successes in n trials) = mCnp

kq

n-k, where,

n = number of trials

m = number of successes

n – m = number of failures

p = probability of success in one trial

q = probability of failure in one trial.

Binomial Theorem

A theorem used to expand the powers of polynomial terms and equations. It is given by:

(a + b)n =

nC0a

n +

nC1a

n-1b +..........+

nCn-1ab

n–1 +

nCn.

Boolean Algebra

Boolean algebra deals with the logical calculus. Boolean algebra takes only two values in the

logical analysis, either 1 or zero. Read more on Boolean Origination.

Boundary Value Problem

Any differential equation that has constrained on the values of the function (not that on the

derivatives) is called as the boundary value problem.

Bounded Function

A function that has a bounded range. For example, in the set [2, 9], 9 the upper bounded number

and 2 is the lower bounded number.

Bounded Sequence

A sequence that is bounded with upper and lower bounds. Like the harmonic series, 1, ½, 1/3,

¼,...up to infinity is a bounded function since the function lies between 0 and 1.

Bounded Set of Geometric Points

The bounded set of geometric points is called as the figure or set of points that can be enclosed in

a fixed space or co-ordinates.

Bounded Set of Numbers

A set of numbers with lower and upper bound. For example, [3, 7] is called as the bounded set of

numbers.


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Box

A rectangular parallelepiped is often referred to as a box. The volume of such a rectangular box

is given by the product of length, breadth and height.

Boxplot

A data that displays the five number summary in a diagrammatic form represented as:

Smallest 1st Quartile Median 3rd Quartile Largest

Braces

The symbolic representation {or} that is used to indicate sets etc.

Brackets

The symbol [ ] which signifies grouping. They work in a similar way parentheses do.

C

Calculus

The branch of mathematics that deals with integration, differentiation and various other forms of

derivatives.

Cardinal Numbers

Cardinal numbers are used to indicate the number of elements in an infinite or finite sets.

Cardinality

It is same as cardinal numbers. It is to be noted that cardinality of every infinite set is same.

Cartesian Coordinates

The Cartesian coordinates are the axes that are used to represent the coordinates of a point. (x,y)

and (x,y,z) are the Cartesian coordinates.

Cartesian Plane

The planes formed by horizontal and vertical axes like the x and y axis is called the Cartesian

plane.

Catenary

The curve formed by a hanging a wire or a ring is called as catenary. Generally, a catenary is

confused with a parabola. However, though the looks are similar, it is not same as the parabola.

The graph of a hyperbolic cosine function is called the catenary.


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Cavalieri’s Principle

A method to find the volume of solids by using the formula V = bh, where b = area of cross

section of the base (cylinder/prism) and h = height of the solid.

Central Angle

An angle in a circle with vertex at the circle's center.

Centroid

The intersection point of the three medians of a triangle.

Centroid Formula

The centroid of the points (x1, y1, x2, y2,....xn, yn) is given by:

(x1 + x2 + x3+......xn)/n , (y1 + y2 + y3+ …..yn)/n

Ceva’s Theorem

Ceva's theorem is a way that relates the ratio in which three concurrent cevian divides a triangle.

If AB, BC and CA are the three sides of a triangle and and AE, BF and CD are the three cevian

of the triangle, then according to Ceva's theorem,

(AD/DB)(BE/EC)(CF/FA) = 1.

Cevian

A line that extends from the vertex of a triangle to the opposite side like altitudes and medians.

Chain Rule

A method used in differential calculus to find the derivative of a composite function.

(d/dx)f(g(x)) = f'((g(x))g

'(x) or (dy/dx) = (dy/du)(du/dx)

Check a Solution

Checking a solution means putting the value of corresponding variables in the equation and

verify if the equations satisfy the given equation or systems of equation.

Chord

A chord is a line segment that joins the two points on a curve. In a circle, the largest chord is the

diameter that joins the two ends of the circle.

Circle

The locus of all points that is always at a fixed distance from a fixed point.

Circular Cone

A cone with a circular base.


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The volume of circular cone is given by V = 1/3πr2

Circular Cylinder

A cylinder with circle as bases.

Circumcenter

The center of a circumcircle is called as circumcenter.

Circumcircle

A circle that passes through all the vertices of a regular polygon and triangles is called as

circumcircle.

Circumference

The perimeter of a circular figure.

Circumscribable

A plan figure that has a circumcircle.

Circumscribed

A figure circumscribed by a circle.

Circumscribed Circle

The circle that touches the vertices of a triangle or a regular polygon.

Clockwise

The direction of the moving hands of a clock.

Closed Interval

A closed interval is the one in which, both the first and last terms are included while considering

the entire set. For example, [3,4].

Coefficient

The constant number that is multiplied with the variables and powers in an algebraic expression.

For example, in 234x2yz, 243 is the coefficient.

Coefficient Matrix

The matrix formed by the coefficients of a linear system of equations is called the coefficient

matrix


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Cofactor

When a determinant is obtained by deleting the rows and columns of a matrix in order to solve

the equation, it is called as the cofactors.

Cofactor Matrix

A matrix with the elements of the cofactors, term by term, in a square matrix is called as the

cofactor matrix.

Cofunction Identities

Cofunction identities are the identities that show the relation between the trigonometrical

functions like the sine, cosine, cotangent,

Coincident

If two figures are superimposed on each other, then they are said to be coincident. In other

words, a figure is coincident when all points are coincident.

Collinear

Two points are said to be collinear if they lie on the same line.

Common Logarithm

The logarithm to the base 10 is called as common logarithm.

Commutative

An operation is said to be commutative if x ø y = y ø x, for all values of x and y. Addition and

multiplication are commutative operations. For example, 4 + 5 = 5 + 4 or 6 X 5 = 5 X 6. Division

and subtraction are not commutative.

Compatible Matrices

Two matrices are said to be compatible for multiplication if the number of columns of 1st matrix

equals to the number of rows of the other.

Complement of an Angle

The complement of angle say 75º is 90º – 75º = 15º.

Complement of an Event

The set of all outcomes of an event that are not included in the event. The complement of set A is

written as Ac. The formula is given as: P(A

c) = 1 – P(A) or P (not A) = 1- P(A).

Complement of a Set

The elements of a given set that are not contained in the given set.


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Complementary Angles

If the sum of two angles is 90º, then they are said to be complementary angles. For example, 30º

and 60º are complementary to each other as their sum equals 90º.

Composite Number

A positive integer whose factors are the numbers other than 1 and the number itself. For

example, 4, 6, 9, 12 etc. 1 is not a composite number.

Compound Fraction

A compound fraction is a fraction that has at least one fraction term in the numerator and

denominator.

Compound Inequality

When two or more than two inequalities are solved together it is known as compound inequality.

Compound Interest

While calculating compound interest, the amount that is earned as an interest for a certain

principal is added to the principal and from that moment the interest is calculated on the new

principal. Thus, the interest is not only calculated on the original balance but the balance or

principal obtained after adding the interest.

Concurrent

If two or more than two lines or curves intersect at the same point then they are said to be

concurrent at that point.

Conditional Equation

A equation that is true for some values of the variables and is false for other values of the

variables. The equation has certain conditions imposed on it that are only satisfied by certain

values of the variables.

Cos-1

x

The inverse of cos function is read as 'cos inverse x'. For example, cos-1

½ = 60º.

Cot-1

x

By cot-1

x we mean the angle whose cotangent is equal to x. For example, when we are asked to

find the smallest angle whose cotangent is equal to 1? The answer is 45º. Thus, cot-1

1 = 45º.

Cube

Cube is a three dimensional figure bounded by six equal sides. The volume of cube is given by

l3, where l is the side of a cube.


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Cube Root

A cube root is a number denoted as x⅓

such that b3 = x For example, (64)

⅓ = 4.

Cubic Polynomial

A polynomial of degree 3 is known as the cubic polynomial. For example, x3 + 2x

2 + x.

Cuboid

Cuboid is a three dimensional box that has length, width and height. Rectangular Parallelepiped

is the other name for a cuboid.

D

De Moivre’s Theorem

De Moiver's Theorem is a formula that is widely used in complex number system in order to

calculate the powers and roots of complex numbers. Mathematically, it is given by:

[r(cosθ + isinθ)]n = r

n(cosnθ + isinnθ).

Decagon

A 10 sided polygon is called as decagon.

Deciles

In statistics, deciles are any of the nine values that divide the data into 10 equal parts. The first

decile cuts off at the lowest 10% of the data that is called as the 10th percentile. The 5th decile

cuts off the at the lowest 50% of the data that is called as 50th percentile or 2nd quartile or

median. The 9th decile cuts off lowest 90% of the data that is the 90th percentile.

Decreasing Function

A function whose value decreases continuously as we move from left to right of its graph is

called decreasing function. A line with negative slope is a perfect example of a decreasing

function where the value of the function decreases as we proceed on the x-axis. If the decreasing

function is differentiable then its derivative at all points (where the function is decreasing) will

be negative.

Definite Integral

An integral that is evaluated over an interval. It is given by aʃbf(x)dx. Here the interval is [a, b].

Degenerate Conic Sections

If a double cone is cut with a plane passing through the apex of the plane, it is called as the

degenerate conic sections. It has the general equations of the form:

Ax2 + Bxy + Cy

2 + Dx + Ey + F = 0


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Degree

Degree is the measure of the slope or the angle that a line or a plane subtends. Degree is

represented by the symbol °.

Degree of a Polynomial

The power of a highest term in an algebraic expression is called as the degree of the polynomial.

In the expression 2x5 + 3y

4 + 5x

3, the degree of the polynomial is 5.

Degree of a Term

In 5y7, degree of term is 7, in 5x

24y

3, the degree of the term is the sum of the exponents of 5x

and 4y, that means 5.

Denominator

The lower part of a fraction is called denominator. In fraction (4/5), 5 is the denominator.

Dependent Variable

Consider an expression y = 2x + 3, here, x is the independent variable and y is the dependent

variable. It is a general notion to plot the graph by taking independent variable on x axis and

dependent variable on Y-axis.

Derivative

The slope of a line tangent to a function is called as the derivative of the function. This is the

graphical interpretation of the derivative. As a differentiation operation, consider f(x) = x2 then

it's derivative is f'(x) = 2x.

Descartes' Rule of Signs

A method for determining the maximum number of positive zeros of a polynomial. According to

this rule, the number of changes in the sign of the algebraic expression gives the number of roots

of the expression.

Determinant

Determinants are the mathematical objects that are very useful in determining the solution of a

set of system of linear equations.

Diagonal Matrix

A square matrix that has zeroes everywhere except the main diagonal.

Diagonal of a Polygon

A line segment joining non-adjacent vertices of a diagonal. If a polygon is of n-sides then the

number of diagonals is given by the formula:

n(n-3)/2 diagonals.


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Diameter

The longest chord of a circle is called diameter. It can be also defined as the line segment that

passes through the center of the circle and touches both the ends of the circumference of the

circle.

Diametrically Opposed

Two points directly opposite to each other on a circle.

Difference

The result of subtracting two numbers is called as difference.

Differentiable

A curve that is continuous at all points of its domain is called as a differentiable function. In

other words if a derivative exists for a curve at all points of the domains variable, it is said to be

differentiable.

Differential Equation

A mathematical equation involving the functions and derivatives. For example, (dy/dx)2 = y

Differentiation

Performing the process of finding a derivative.

Digit

Any of the numbers among the nine digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Dihedral Angle

The angle formed by the intersection of two planes.

Dilation

Dilation refers to the enlargement of a geometrical figure by transformation method.

Dilation of a Geometric Figure

A transformation in which all distances are increased by some common factor. The points are

stretched from a common fixed point P.

Dilation of a Graph

In graphical dilation, the x-coordinates and y-coordinates are enlarged by some common factor.

The factor by which the transformation of the graph is done must be greater than 1. If the factor

is less than 1, it is called compression.


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Dimensions

The sides of a geometrical figure are often referred to as dimensions.

Dimensions of a Matrix

The number of rows and columns of matrix is called as the dimensions of the matrix. For

example if a matrix has 2 rows and 3 columns, its dimensions will be 2X3 (read as two cross

three).

Direct Proportion

When one of the variables is a constant multiple of the other, it is called as direct variation. For

example, y = kx (here y and x are the variables and k is a constant factor).

Directrices of an Ellipse

Two parallel lines on the exterior of an ellipse that are perpendicular to the major axis.

E

e

e is a transcendental number that has a value approximately equal to 2.718. It is frequently used

while working with logarithms and exponential functions.

Eccentricity

A number that indicates the shape of a curve. It is represented by the small letter 'e' (This e is in

no ways related to the exponential e = 2.718). In conic section, the eccentricity of the curves is a

ratio between the distance from the center to focus and either the horizontal or vertical distance

from the center to the vertex.

Echelon Form of a Matrix

An echelon matrix is used to solve a system of linear equations.

Edge of a Polyhedron

One of the line segments that together make up the faces of the polyhedron.

Element of a Matrix

The numbers inside the matrix in the form of rows and columns is called as the element of

matrix.

Element of a Set

Any point, line, letter, number etc. contained in a set is called as the element of the set.


20

Empty Set

A set that doesn't contains any element. The empty set is represented by {} or Ø.

Equality Properties of Equation

The equality properties of algebra that are used to solve the algebraic equations. The

mathematical definitions of these equality properties are as follows

x = y means, x is equal to y and y ≠ x means y is not equal to x. The operations of addition,

subtraction, multiplication and division all hold true for equality properties of equation.

Reflexive Property- x = x;

Symmetric Property- If x = y then y = x;

Transitive Property- If x = y and y = z then x = z

Equilateral Triangle

An equilateral triangle has all its three sides equal and the measure of each angle is 60º.

Equivalence Relation

Any equation that is reflexive, symmetric and transitive.

Equivalent Systems of Equation

Two sets of simultaneous equations that have same solution.

Even Function

A function whose graph is symmetric about y-axis. Also, f(-x) = f(x).

Even Number

The set of all integers that are divisible by 2. E= {0, 2, 4, 6, 8......}

Explicit Differentiation

The derivative of an explicit function is called as the explicit differentiation. For example, y = x3

+ 2x2 - 3x. Differentiating it gives,

y'= 3x2 + 4x – 3.

Explicit Function

In an explicit function, the dependent variable can be totally expressed in terms of independent

variable. For example, y= 5x2 - 6x.

Extreme Value Theorem

According to this theorem, there is always at least one absolute maximum and one absolute

minimum for any continuous function over a closed interval.


21

Extreme Value of a Polynomial

The graph of a polynomial of degree n has at most n-1 extreme values (either maxima or

minima)

F

Face of Polyhedron

Polygonal outer boundary of a solid object having no curved surfaces.

Factor of an integer

If the given integer is divided evenly by another integer then the resultant is called factor of an

integer. For example: 2, 4, 8, 16 etc, are the factors of 32.

Factor of polynomial

Polynomial P(x) is completely divided into Polynomial R(x) by Q(x) then Q(x) is called Factor

of polynomial. For example: P(x)= x2+6x+8, Q(x)=x+4 then P(x)/Q(x)= x+2. Q(x)=x+4 is the

factor.

Factor theorem

When x-a is factor of P(x), the value x in P(x) is replaced with a, then if the resultant value is 0,

such a theorem is called Factor theorem. For example: P(x)= x2+6x+24. Q(x)= x-(-4). If x is

replaced with a, that is -4, then P(x)= 0.

Factorial

The product of the an integer with all the consecutive smaller integers is called a factorial. It is

represented as "n!". For example: 5! = 5*4*3*2*1= 120.

Factoring Rules

These are the formulas that govern the factorization of a polynomial. For example

x2-(a+b)x +ab= (x-a)(x-b).

x2+2(a)x+a

2=(x+a)

2

x2-2(a)x +a

2=(x-a)

2

Finite

The term is used to describe a set in which all the elements can be counted using natural

numbers.

First Derivative

A function F(a), which governs the slope of the curve at any given point or the slope of the line

drawn tangent to the curve from that point in the plane is called the first derivative. It is


22

represented as F'. For F(x)= 5x2. F'(x)=10x will be the slope of the curve.

First Derivative test

A Technique which is used to determine the capacity of inflection point.(minimum, maximum or

neither)

First Order of the differential equation A differential equation P(a) who's order is 1. For

example: P(a)=3a, here the order of a is 1.

Flip

It is also known as axis of reflection. It is a line which divides the plane or a geometric figure

into two halves that are mirror images of each other.

Floor Function (Greatest Integer Function)

It is a function F(x) which is responsible for finding the greatest integer less that the actual value

of P(x). For example: P(x)= 5.5, here the greatest integer less than 5.5 is 5. The function which

gives F(x)=5 becomes floor function.

Foci of the Ellipse

They are the fixed two points inside the ellipse such that the vertical curve is governed according

to the equation L1+L2= 2a and horizontal curve according to equation L1+L2=2b where L is the

distance between the focal point and the curve, a is the horizontal radius and b is the vertical

radius.

Foci of hyperbola

They are fixed two points inside of the curve of hyperbola such that the determinant of the L1-L2

is always constant. L1 and L2 are the distances between point P (which is the curve) and

respective focus of the curve.

Focus

The curves of the conic sections are governed according to distances from a special point called

focus.

FOIL method

FOIL is an acronym for First Outer Inner Last. It is method by which binomials are multiplied.

The Multiplication order is

First terms of Binomials

Outer terms of Binomial

Inner terms of binomials


23

Outer terms of Binomials.

For example: (a+b)(a-b)= a.a+a.(-b)+b.a +b.(-b)

Formula

The relationship between various Variables (sometimes expressed in the form of an equation)

depicted using symbols. For example: a+b=7

Fractal

When every part of the figure is similar to every other part of other figure, then the figure is

called fractal.

Fraction

It is a ratio between two numbers. For example: 9/11.

Fraction Rules

The rules of algebra used for uniting various the fractions.

Fractional Equation

The expression in the form of A/B on both the sides of equal sign is called fractional equation.

For example: x/6= 4/3.

Function Operation

Various Operations such as additions, subtractions, multiplications, divisions and compositions

which have a combining effect on various functions. For example: F(a/b)= F(a)/F(b).

Fundamental theorem of Algebra

Every polynomial characterized by single variable having complex coefficients, will have a

minimum of at least one root which is also complex in nature.

Fundamental Theorem of Arithmetic

The statement that the factors of a prime number are always distinct and unequal is the

fundamental theorem of arithmetic.

Fundamental Theorem of Calculus

Differentiation and integration are two most basic operations of the calculus. The theorem that

establishes a relationship between them is called Fundamental theorem of Calculus.

G

Gauss-Jordan Elimination

A method of solving a system of linear equations. In this process the augmented form of the


24

matrix system is reduced into row echelon form by means of row operations.

Gaussian Elimination

A method of solving a system of linear equations. In Gauss elimination method, the augmented

form of matrix is reduced to row echelon form and then the system is solved by back

substitution.

Gaussian Integer

Gaussian integers are the integers in the complex numbers that are represented by a + bi. For

example, 3 + 2i, 5i and 6i + 5 are called Gaussian integers.

GCF

The largest integer that divides a certain set of numbers. Also called as Greatest Common Factor.

For example, the GCF of 20, 30 and 60 is 10.

General Form for the Equation of a Line

The general form of equation of a line is represented by the equation-

Ax + By + C = 0, where, A, B and C are integers.

Geometric Figure

A geometric figure is a set of points on the plane or space that leads to the formation of figure.

Geometric Mean

Geometric mean is a method of finding the average of certain set of numbers. For example, if

there are numbers a1, a2, a3,........anthen multiply the numbers and take the nth root of the product.

Geometric Mean = (a1, a2, a3,........an)½

Geometric Progression

A geometric progression is a mathematical sequence whose terms are in a constant ratio with the

previous terms. For example, 2, 4, 8, 16, 32.....128 are the terms of a geometric progression. Here

the common ratio is 2. (as 4/2 = 8/4 = 16/8....)

Geometric Series

Geometric series is a mathematical series whose successive terms are in a constant ratio. An

example of geometric series is 2, 4, 8, 16, 32........

Geometry

The study of geometric figures in two and three dimensions is called as geometry.


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Greatest lower bound

The greatest of all lower bounds of a set of numbers is called as the GLB or greatest lower

bound. For example, in the set [2,7], the GLB is 2.

Glide Reflection

A transformation in which a figure has to go through a combination of steps of translation and

reflection.

Global Maximum

The highest point on the graph of a function or a relation (in the domain of the function). The

first and second derivative tests are used to find the maximum values of a function. It is also

called as global maximum, absolute maximum and relative maximum.

Global Minimum

The lowest point on the graph of a function or a relation. The first and second derivative tests are

used to find the minimum values of a function. It is also called as the global minimum, absolute

minimum or global minimum.

Golden Mean

The ratio (1 + √5)/2 ≈ 1.61803 is called as the golden mean. The unique property of golden mean

is that the reciprocal of golden mean is about 0.61803. Hence, the golden mean is one plus its

reciprocal.

Golden Rectangle

If the ratio of length and breadth of a rectangle is equal to the golden mean then the rectangle is

called as the golden rectangle. It is believed that this rectangle is most pleasing to the eyes.

Golden Spiral

A spiral that can be drawn inside the golden rectangle.

Googol

The number 10100

is called as googol.

Googolplex

Googolplex can be written as 10100100

.

Graph of an Equation or Inequality

The graph obtained by plotting all the points on the coordinate system.


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Graphic Methods

The use of graphical methods to solve the mathematical problems.

Greatest Integer Function

The greatest integer function of any number (say x) is an integer 'less than or equal to x'. The

greatest integer function is represented as [x]. For example, [3.4] = 3 and [-2.5] = 3

H

Half Angle identities

The identities of trigonometry that are used to calculate the value of sine, cosine, tangent etc. of

half of a given angle.

The trigonometric identities are as follows:

sin2x = (1 – cos2x)/2

cos2x = (1 + cos2x)/2

Half Closed Interval/Half Open Interval

It is a set of all numbers containing only one end point.

Harmonic Mean

The inversion of the summation of the reciprocals of a set of numbers. For example: (1, 2, 3) are

in a set then their harmonic mean is 1/(1+ ½+ ⅓ )

Harmonic Progression

It is a sequence in which every term is the reciprocal of the natural number. For example 1, ½, ⅓,

¼.

Harmonic Series

The summation of all the terms in harmonic progression. For example: 1+ ½+ ⅓+ ¼

Height

The least measurable distance between the base and the top of a geometric figure is called as the

height. The top can be the opposite vertex, or an apex or even another base of the figure.

Height of the Cone

The distance between the center of the circular base and the vertex of the cone can be called as

the height of the cone.

Height of Cylinder

The distance between the centers of the circular bases of the cylinder is the height of the

cylinder.


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Height of a Parallelogram

The perpendicular distance between the parallel sides of a parallelogram (i.e. the base to the

opposite side).

Height of a Prism

The length of the shortest line segment between the bases of the prism.

Height of a Pyramid

The shortest distance between the vertex and extended base of the pyramid.

Height of a Triangle

The length of the shortest line segment between a vertex and the opposite side of the triangle.

Helix

It is a spiral shape curve in three dimensional space.

Heptagon

A heptagon can be called as a polygon which has seven sides. It's other name is septagon, but

heptagon is widely used.

Hero's Formula

Suppose all the three sides of the triangle are known. The formula used to calculate the area of

the triangle in this scenario is called Hero's formula. For example: √[s(s-a)(s-b)(s-c)]

Hexagon

It is a special geometric figure which has six sides and angles.

Hexahedron

A solid which has no curved surfaces and the number of surfaces are equal to six.

Hyperbola

A hyperbola is a geometric figure, which is a locus of two points called as foci, where the

difference between the distances to each point is constant.

Hyperbolic Geometry

Given two entities, a point and a line, there can be infinitely many lines passing through the point

and are parallel to first point. This is called Hyperbolic geometry.

Hyperbolic Trigonometry

The trigonometric functions sine cosine tangent etc. who's values are calculated using 'e'.

Mathematical definitions of hyperbolic trigonometry are as follows:


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sinhx = (ex - e

-x)/2,

coshx = (ex + e

-x)/2

tanhx = (sinhx/coshx) = (ex - e

-x)/(e

x + e

-x)/2

Hypotenuse

The hypotenuse is longest side of right angled triangle.

Hypotenuse-leg Congruence

Two different right angle triangles are said to be congruent when their hypotenuse and one of the

corresponding legs are equal in length.

Hypotenuse-leg Similarity

In two right angled triangles when the ratio of the corresponding sides have equal ratios, then

such triangles are having HL Similarity.

I

i

In complex number analysis, the letter i denotes iota. Mathematically, iota is given by negative

square root of 1, that means √-1. = i

Icosahedron

Icosahedron is a polyhedron with 20 faces. In the case of a regular icosahedron, the faces are all

equilateral triangles.

Identity (Equation)

An equation that is true for any values of the variable. For example, the identity, sin2θ + cos

2θ =

1 is true for all values of θ.

Identity Function

The function f(x) = x is called as the identity function.

Identity Matrix

A square matrix that has 1 as its element in the principal diagonal and rest all elements are zero.

Image of a Transformation

The image obtained after performing the operations of dilation or rotation or translation.

Imaginary Numbers

A complex number like 7i, that is free of the real part is called as the complex number.

Imaginary Part


29

Consider a complex number -7 + 8i, the coefficient of i called as the imaginary part of the

complex number.

Implicit Function or Relation

A function in which the dependent variable can't be exactly expressed as a function of the

independent variable.

Implicit Differentiation

Differentiating an implicit function. For example, consider 4x2 + 5y

5 - 6x = 1. Here, y can't be

written explicitly as a function of x.

Impossible Event

An event that is impossible to happen or an event whose probability is zero.

Improper Fraction

A fraction that has denominator greater than its numerator.

Improper Integral

A integration in which the bounds of integration has discontinuities in the graph. They can also

have limits between ∞ and -∞. The discontinuities between the bounds of integration makes the

use of limits necessary in evaluating improper integrals.

Improper Rational Expression

If the degree of a numerator polynomial is more than or equal to the degree of a denominator

polynomial than the rational expression is called as the improper rational expression.

Incenter

The center of a circle inscribed in a triangle or a polygon. Geometrically, incenter is the point of

intersection of the angle bisectors of a triangle.

Incircle

The largest possible circle that can be drawn inside a plane figure. All triangles and regular

polygons have incircle.

Inconsistent System of Equations

A system of equations that has no solutions.

Increasing Function

A function whose value increases continuously as we move from left to right of its graph is

called increasing function. A line with positive slope is a perfect example of increasing function

where the value of the function increases as we proceed on the x-axis. If the increasing function


30

is differentiable then its derivative at all points (where the function is increasing) will be

negative.

Indefinite Integral

I = a∫bf(x) dx, is known as the improper integral

Indefinite Integral Rules

Independent Events

If the occurrence or non-occurrence of two events is independent of each other it is called as the

independent event.

Independent Variable

The quantity in an equation whose values can be freely chosen in an equation without taking into

consideration the values of the other variables.

Indeterminate Expressions

An undefined expression that cannot be assigned any value. There are various forms of

indeterminate expressions:

0/0

±∞/±∞

00

1∞

∞0

∞ - ∞

Induction

A method of proving a mathematical problem by the help of a series of steps. Mathematical

induction is used to prove complex mathematical problems.

Independent Events

Two or more events are said to be independent events if the occurrence or non-occurrence of any

of these events doesn't affect the occurrence or non-occurrence of others. By the principle of

probability, if A and B are two independent events, then P(A|B) = P(A).

Independent Variable

Independent variables are those whose value can be chosen without any restriction. For example,

in the equation Y = 2x2 + 3x, y is the dependent variable and x is the independent variable.


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Indirect Proof

Proving a statement or a fact by the method of contradiction is known as indirect proof. This

means that the conjecture is taken to be false and then it is proved that the statement contradicts

the assumption made at the beginning of solving the problem.

J

Joint variation

When a quantity varies directly with the other quantity then it is called as the joint variation. For

example when we say x is directly proportional to the square of y, it means that x = ky2, where k

= proportionality constant.

K

Kite

A kite is nothing but a quadrilateral, with each pair of its adjacent sides congruent to each other

and diagonals perpendicular to each other.

L

L'Hospital's Rule

This is a technique that is used to find out the limit of the functions that evaluate to indeterminate

forms, like 0/0 or infinity/infinity. The solution is found out by individually calculating the limits

of the numerator and the denominator.

Lateral Surface Area

Lateral Surface Area is nothing but the surface area of the lateral surfaces of a solid. It does not

include the area of the base(s) of the solid.

Latus Rectum

It is the line segment that passes through the focus of a conic section and is perpendicular to the

major axis, with both its end points on the curve.

Law of Cosines

An equation that relates the cosine of an interior angle of a triangle to the length of its sides is

called the law of cosines.

If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between

a and c and C the angle between a and b, then the law of cosines states that c2 = a

2 + b

2 -

2abcosC, b2 = a

2 + b

2 - 2accosB and a

2 = b

2 + c

2 - 2bccosA

Law of Sine


32

An equation that relates the sine of an interior angle of a triangle to the length of its sides is

called the law of sines.

If a, b and c are the three sides of a triangle, A is the angle between b and c, B the angle between

a and c and C the angle between a and b, then the law of cosines states that

sin A/a = sin B/b = sin C/c

Least Common Multiple (LCM)

The smallest common multiple to which two or more numbers can be divided evenly. For

example, the LCM of 2, 3 and 6 is 12.

Leading Coefficient

The coefficient of a polynomials leading term or the term with the variable having the highest

degree.

For example, the leading coefficient of 7x4 + 5x

3 + 9

2 + 2x +21 is 7.

Leading Term

The term of a polynomial which contains the highest value of the variable is called the leading

term.

For example, the leading coefficient of 7x4 + 5x

3 + 9

2 + 2x +21 is 7x

4.

Least Common Denominator

The least common denominator is the smallest whole number that can be used as a denominator

for two or more fractions. The Least Common Denominator is nothing but the Least Common

Multiple of the denominators of the fractions.

For example, the least common denominator of 3/4 and 4/3 is 12. Since 3/4=6/8=9/12 and

4/3=8/6=12/9=16/12. Hence we see that the least common denominator is 12.

Least Integer Function

The least integer function of x is a step function of x, which is the least integer greater than or

equal to x. This function is sometimes written with reversed boldface brackets ]x[ or reversed

plain brackets ]x[.

Least Squares Regression Line

The Linear Squares Regression Line is the linear fit that matches the pattern of a set of paired

data, as closely as possible. Out of all possible linear fits, the least-squares regression line is the

one that has the smallest possible value for the sum of the squares of the residuals.

It is also known as Least Squares Fit and Least Squares Line.


33

Least-Squares Regression Equation

An equation of any form (linear, quadratic, exponential, etc) that helps in fitting a set of paired

data as closely as possible is called the least squares regression equation.

Least Upper Bound of a Set

The smallest of all upper bounds of a set of number is called the Least Upper Bound.

Leg of an Isosceles Triangle

Any of the two equal sides of an isosceles triangle can be referred to as the leg of the isosceles

triangle.

Leg of a Right Angle Triangle

Either of the sides of a right angle triangle, between which the right angle is formed can be

referred to as the leg of the right angle triangle.

Leg of a Trapezoid

Either of the two non parallel sides of a trapezoid that join its bases can be referred to as the leg

of the trapezoid.

Lemma

More accurately referred to as a helping theorem, a lemma helps in proving a theorem. But it is

not important enought to be a theorem.

Lemniscate

A curve that takes form on the numerical number 8, in any orientation can be referred to as the

lemniscate. Its equations are generally given in the polar coordinates. r2 = a

2cos2θ.

Like Terms

Terms that have the same variables and with the same power are called like terms. The

coefficients of the like terms can be directly added and subtracted. For example 5x3y

2 and

135x3y

2 are like terms and hence can be added directly to give the number 140x

3y

2.

Limacon

A limacon is a family of related curves usually expressed in polar coordinates.

Limit

The limit of a function is the value of the function as its variable tends to reach a particular value.

For example for f(x)=limx-><5>1/x2= 1/25. As x->5, the function f(x) tends to reach to 1/25.

Limit Comparison Test

The limit comparison test is performed to determine if a series is as good as a good series or as


34

bad as a bad series. The test is used specially in cases when the terms of a series are rational

functions.

Limit from Above

The limit from the above is usually taken in cases when the values of the variable is taken greater

than that to which the limit approaches. For example limx->0+1/x=infinity, is taken such that the

value of x>0. Limit from above is often referred to as limit from the right. This is a one sided

limit.

Limit from Below

The limit from the below is usually taken in cases when the values of the variable is taken less

than that to which the limit approaches. For example limx->0-1/x=-infinity, is taken such that the

value of x>0. Limit from below is often referred to as limit from the left. This is a one sided

limit.

Limit Involving Infinity

A limit involving infinity or an infinite limit is one whose result approaches infinity or the value

of the variable approaches infinity.

Limit Test for Divergence

A limit test for divergence is a convergence test which is based upon the fact that the terms of a

convergent series must have a limit of zero.

Line

A line is a geometric figure that connects two points and extends beyond both of them in both

directions.

Line Segment

A line segment is nothing but the set of points between any two points including those two

points.

Linear

The world linear means like a line. It is nothing but a graph or data that can be molded by a

linear polynomial.

Linear Combination

A linear combination is the sum of multiples of the variables in a set. For example, for the set {x,

y, z}, one possible linear combination is 7x + 3y - 4z.

Linear Equation


35

An equation that can be written in the form "linear polynomial" = "linear polynomial" or "linear

polynomial"=constant is known as a linear equation.

For example 3x + 26y = 34 is a linear polynomial.

Linear Factorization

If a polynomial can be factorized such that the factors formed after the factorization are linear

polynomials, then this factorization is known as a linear factorization. For example x2-9 can be

factorized as (x+3) and (x-3).

Linear Fit Regression Line

Any line that can be used as a fit in the process to model the pattern in a set of paired data.

Linear Inequality

An inequality that can be written such that the value of a polynomial is greater than, less than,

greater than equal to or less than equal to a particular number is called linear inequality. For

example 3x + 7y >9.

Linear Pair of Angles

When two lines intersect each other, then the adjacent angles formed due to intersection of the

two lines are called linear pair angles. The linear pair angles formed are supplementary.

Linear Polynomial

A linear polynomial is a polynomial with degree 1. The highest power of the variables involved

in the polynomial should be one. For example 9x + 7 is a linear polynomial.

Linear Programming

The linear programming is an algorithm that is used for solving problems. The method of using

linear programming is by asking the largest or smallest possible value of a linear polynomial. If

there are any restrictions, then the system of inequalities is used to present any restriction to the

equations.

Linear Regression

The process of finding a linear fit is referred to as the linear regression.

Linear System of Equations

If there are more than one equations such that each equation is a linear equation, then the system

of equations will be known as linear system of equations.

For example, 2x + 3y - 5z

9x + 7y + 12x = 19

15x - 6y + 11z = 9 is a linear system of equations, that can be used to determine the values of x,


36

y and z.

Local Behavior

The behavior of a function in the immediate neighborhood of any point is called the local

behavior. The local behavior of geometric figures can also be studied with respect to a particular

point.

For example, for the graph of the equation y=2x + 3, if studied closely can be said to have the

local behavior of a straight line parallel to the x-axis and at a distance of 3 units from the origin.

Local Maximum

The local maximum is the highest point in a particular section of the graph. It is also often

referred as the local max or relative maximum or relative max.

Local Maximum

The local minimum is the lowest point in a particular section of the graph. It is also often

referred as the local min or relative minimum or relative min.

Locus

A locus is nothing but the set of points that form a particular geometric figure. For example, a

circle with radius 2 cm is the locus of all points which are at a distance of 2 cms from a particular

point.

Logarithm

The logarithm of x with respect to the base c is the power to which the base c must be raised in

order to be equal to x. For example, logcx=z then cz=x.

Logarthmic Rules

The logarithmic rules are the algebra rules that need to be used when working with logarithms.

Some of them can be listed as under:

If log x = y then 10y=x. It means that if the base of the logarithm is not mentioned then consider

the base as 10.

If ln x = y then ey=x. It means that when log is replaced by ln then take the logartihm as natural

logartihm and has the base e.

log 1 = 0, since whatever be the base, if raised to the power 0 then the result is always 1.

log ab = log a + log b

lob (a/b) = log a - log b

log b3 = 3log b

logax = logbx/logba

Logarithmic Differentiation

It is the type of differentiation that is used in special circumstances. For example the equation y =


37

xtan x

can be differentiated, more easily if the logarithm of both the sides are taken.

On taking the logarithm of both the sides the equation can be reduced to log y = tan x. log x

(using logarithmic formula). Hence the process of differentiation becomes simple.

Logistic Growth

A logistic growth is shown by using an equation. It is used to determine the demand of products

in situations where the demand increases initially, then the demand goes down and finally

reaches a particular upper limit.

Long Division of Polynomials

The process of dividing polynomials is known as polynomial long division. The polynomial long

division is used to divide improper rational numbers into proper rational numbers or sum of

polynomials. The process of polynomial long division is same as that of long division of

numbers.

Lower Bound

The lower bound of a set is any number that is less than or equal to all the numbers in a set. For

example 1, 2 and 3 are all lower bounds of the interval [4, 5].

Low Quartile

The low quartile is the number for which 25% of the number is less than the number.

Least Upper Bound of a Set

The smallest of all the upper bounds of a set of numbers is called the least upper bound of the

set. For example the least upper bound of the interval [9, 10] is 10.

M

Maclaurin Series

The power series in x for a function f(x) is known as Maclaurin series.

Magnitude

The magnitude is the absolute value of a quantity. Magnitude is a value and it can never be a

negative number.

Magnitude of a vector

The magnitude of a vector is the length of the vector.

Main Diagonal of a Matrix: It is the numbers of a matrix taken diagonally starting from the

number at the upper left corner and ending at the lower right corner.


38

Major Arc

The longer of the two arcs between the two arcs of a circle is called the major arc of the circle.

Major Axis of an Ellipse

The line passing through the two foci, the two vertex and the center of the eclipse is called the

major axis of the ellipse.

Major Axis of a Hyperbola

The line passing through the two foci, the two vertex and the center of the hyperbola is called the

major axis of the hyperbola.

Major Diameter of an Ellipse

The line segment joining the two vertex of ellipse and passing through its center and two foci is

known as the major diameter of the ellipse.

Mathematical Model

Mathematical Model or model is nothing but a system of equations that is used for representing a

graphs, some data or even some real world phenomenon.

Matrix

A matrix is a rectangular or square array of numbers. All the rows of the matrix is equal lengths

and all the columns are also of equal lengths.

Matrix Addition

Two matrices with the same dimensions can be added using the process of matrix addition. The

process of matrix addition is such that the element in the position Row 1, Column 1 must be

added to the element at the location Row 1, Column 1 of the other matrix.

Matrix Element

Any number in a matrix is known as the matrix element. The position of the number in the

matrix is defined by the row number and column number.

Matrix Inverse

The matrix inverse of a matrix is the one, which on being multiplied with the matrix gives the

identity matrix. If the matrix is denoted by A, then its inverse is denoted by A-1

.

Matrix Multiplication

Two matrices can be multiplied only if the number of columns in the first matrix is equal to the

number of rows in the second matrix.

Maximum of a Function


39

The highest point in the graph of the function is often referred to as the maximum of the

function.

Mean

It is nothing but another word for average. When the word mean is used, it is generally referred

to the arithmetic mean of a function.

For example, the arithmetic mean of the numbers 1, 4, 6, 7, 8 is (1+4+6+7+8)/5.

Mean of a Random Variable

This is often referred to in the case of probability where a number of trials are performed to see

the most expected result. The average of all the outcomes of all these trials is considered the

mean of a random variable.

Mean Value Theorem

This is a theorem used in Calculus. It states that for every secant for the graph of a 'nice'

function, there is a tangent parallel to the secant.

Mean Value Theorem for Integrals

The mean value theorem for integrals states that for every function there is at least one point

where the value of the function equals the average value of the function.

Measure of an Angle

The value of an angle in radians or degrees is referred to as the measure of an angle.

Measurement

The process of assigning a value for any physical quantity (eg. Length, breadth, height, area,

volume, etc.) is called measurement.

Median of a Set of Numbers

The median of a set of numbers is the number which is greater than half the numbers in the set

and smaller than the remaining half. In case of two medians, simply find out the arithmetic mean

of the two numbers.

Median of a Trapezoid

The line joining the two non parallel lines of the trapezoid and parallel to the base of the

trapezoids is called the median of the trapezoid.

Median of a Triangle

The line segment joining the vertex of a triangle to the mid point of the opposite side is called the

median of the triangle. It is very clear from the definition that every triangle has three medians.


40

Members of an Equation For any equation, the polynomials on the two sides of the equation

are referred to as the members of the equation. For example; for the equation, 3x2+5=26x, the

members of the equation are 3x2+5 and 26x.

Menelaus' Theorem

The Menelaus' theorem is an equation that shows how the two cevians of a triangle divide the

two sides of the triangle and each other.

For example, if A, B and C are the three vertex of the triangles and BF is the line segment from

B to the side AC intersecting AC at F, CD is the line segment from C intersecting at B and BF

and CD intersect at the point P then, (AD/DB)(BP/PF)(FC/CA)=1.

Mensuration

The process of finding out the measurement of the physical quantities in geometry is refered as

mensuration.

Mesh of a Partition

In any partition, the width of the largest sub interval is called the mesh of the partition.

Midpoint

The point at exactly half of the distance from the two points on the line segment joining the two

points.

Midpoint Formula

The midpoint formula states the for any two points (x1, y1) and (x2, y2) the mid point is given by

((x1+x2)/2 ,(y1+y2)/2).

Max/Min Theorem

The max/min theorem states that for any continuous function f(x) in the interval [a,b] there exist

two numbers in the interval (say c and d) such that, for f(c) and f(d) the function has its absolute

maximum and minimum.

Minimum

The process of finding out the smallest possible value of the variable in a function is referred to

as the minimum of the function.

Minimum of a function

The minimum value of the function within a limited region or entire region of the function is

referred to as the minimum of the function.


41

Minor arc

If the circumference of the circle is divided into two arcs, then the smaller arc is referred to as the

minor arc of the circle.

Minor Axis of an Ellipse

The minor axis of an ellipse is the line passing through the center of the ellipse and perpendicular

to the major axis.

Minor Axis of a Hyperbola

The minor axis of a hyperbola is the line passing through the center of the hyperbola and

perpendicular to the major axis.

Minor Diameter of an Ellipse

The minor diameter of an ellipse is the line passing through the center of the ellipse and

perpendicular to the major diameter

Minute

A minute is a measurement equal to 1/60th of a degree. It is represented by the symbol '. Thus

12°36' is called 12 degree and 36 minutes.

Mixed Number

Mixed number is also called mixed fraction. This is a way of representing improper fraction as

the sum of a number and a proper fraction. For example 31/4 can be written as the mixed number

7 ¾, since 7+3/4 is 31/4.

Mobius strip

A mobius strip is a figure that can be represented as a strip of paper fixed at both the ends and

with a half turn in the middle.

Mode The number that occurs the maximum times in a list is referred as the mode of the

number. For example, in the series 1, 3, 3, 3, 5, 6. 6 the mode is 3 since, it occurs the maximum

number of times.

Modular Arithmetic

When normal arithmetic operations are performed and the result is given in modular form then

the process is known as modular arithmetic.

For example 15 – 3 = 12, but in mod(7) form the result is 15 – 3 = 5(mod 7).

Modular equivalence Two or more integers are considered to be in modular equivalence if they

leave the same integer on being divided by the same number. For example 10 and 16 are both


42

mod 3 equivalent numbers, because they leave the remainder 1 on being divided by 3.

Modular Equivalence Rules

The modular equivalence rules can be listed as under:

Suppose a and b are two mod n equivalent numbers.

a+c and b+c are modular equivalent.

Similarly a-c and b-c are modular equivalent.

a.c and b.c are modular equivalent. If ac and bc are modular equivalent numbers then a

and b are modular equivalent.

Modulo n

Modulo n or mod n of a number is the remainder of the number when divided by n. For example

the number 7 when written in mod 3 form can be written as 7 ≡ 1 (mod 3).

Modulus of a Complex Number

The modulus of a complex number is the distance of the number from the origin on the complex

plane. For example, for the number a+bi, the modulus of the number is given by (a2 + b

2)½. If the

number is given in polar coordinates and the number is rcos θ + irsin θ, then the modulus is

given by r.

Modus Ponens

Modus Ponens is a form of logical argument. For example if the pen is working the pencil is

working. Now, if the argument is that the pen is working then we can conclude that the pencil is

working.

Modus Tolens

Modus Tolens is a form of logical argument that employs the proof of contradiction. For

example, if the pen is working then the pencil is working. The pen is not working, hence the

pencil is not working.

Monomial

A polynomial with one term is called monomial.

Multiplication Rule

The multiplication rule is used in probability to find out if two events have occured. For

example, if there are two events A and B then, P(A and B) = P(A)P(B) or P(A and

B)=P(A).P(B|A).


43

Multiplicative Inverse of a Number

The multiplicative inverse of a number is nothing but the reciprocal of the number. In other

words, it is 1 divided by the number. For example, the multiplicative inverse of the number 3/5 is

1/(3/5)=5/3.

Multiplicative Property of Equality

The multiplicative property of equality states that if a and b are two numbers such that a = b, then

a.c = b.c.

Multiples

Multiples are the numbers that can be evenly divided by the number whose multiple we are

considering. For example, 16 is a multiple of 4 because 16 can be evenly divided by 4.

Multiplicity

The multiplicity of a polynomial is the number of times the number is zero for the given

polynomial. For example in the function f(x) = (x + 3)2(x-2)

4(x – 7)

3, the number -3 has

multiplicity 2, 2 has multiplicity 4 and 7 has multiplicity 3.

Multivariable

Any problem that involves more than one variable is called a multivariable problem.

Multivariable calculus

If the problems in calculus involve two or more independent or dependent variables then the

calculus is called multivariable calculus.

Mutually Exclusive

If the outcome of two events in probability have no common outcomes then the events are called

mutually exclusive.

N

Natural Numbers

All integers greater than 0 are called natural numbers.

Negative Direction

The negatively associated data is often described in the form of a scatterplot. This way of

describing natural numbers is known as negative direction.

Negative Exponent

A negative exponent is used to describe the reciprocal of the number. For example, 5-2

=1/52


44

Negative Number

Any real number less than 0 is called a negative number.

Negative Reciprocal

The process of taking the reciprocal of a number and then its negative is called the negative

reciprocal. For example the negative reciprocal of ¼ is -4.

Negatively Associated Data

If in a set of paired data, the value of one side increases with the decrease in the other, then the

data is referred to as the negatively associated data.

Neighborhood

The neighborhood of any number a is the open interval containing the number. For example, the

neighborhood of a can be written as (a + d, a - d).

n – gon

A polygon with n number of sides is called n – gon. For example, a hexagon can also be called 6-

gon.

Not Adjacent

Two angles or lines are said to be not adjacent to each other, if they are not near to each other.

Nonagon

A polygon having nine sides is called a nonagon.

Non collinear

The points that do not lie in a single line are said to be noncollinear points.

Non-Euclidean Geometry

To understand Non-Euclidean geometry we need to understant the parallel postulate. The

paraller postulate states that for an given point say P and a line l, not passing through P, there is

exactly one line that passes through P, which is parallel to l. The Non-Euclidean Geometry, thus

refers to that branch of geometry that does not obey the parallel postulate principle. The

hyperobolic geometry and elliptic geometry fall in the class of Non-Euclidean Geometry.

Nonnegative

Any quantity that is not less than zero is refered as nonnegative.


45

Nonnegative Numbers

The set of integers starting from 0 to infinity in the positive direction of the X-axis is referred to

as whole numbers.

Non-overlapping sets

Two sets of numbers which do not have a single element in common are called non-overlapping

sets.

Non real number

Any complex number of the form a + bi, where b is not equal to 0 is called a non real number. In

other words, any number with an imaginary part is called non real number.

Nonsingular Matrix

Nonsingular matrix is also called Invertible Matrix. Any square matrix whose determinant is not

0 is called a nonsingular matrix.

Nontrivial

The solution of an equation is said to be nontrivial, if the solution does not include zeroes.

Nonzero

Any positive or negative number is a nonzero number.

Normalizing a vector

The process of finding out a unit vector parallel to the given vector and of unit magnitude is

called normalization of the vector. The process is carried out by dividing the vector with its

magnitude.

n th derivative

The process of taking the derivative of a function n times is called nth derivative. If the

derivative of f(x) is taken n times, then its nth derivative will be represented as fn(x).

n th Partial Sum

The sum of the first n terms in an infinite series is called the nth partial sum.

n th Root

The n th root of a number is the number which when multiplied with itself n times gives the

number in question. The n th root of 5 can be represented as 51/n

.

Null Set Any set with no elements in it is called a null set.


46

Number Line

A line representing all real numbers is called the number line.

Numerator

The top part of any fraction is called the numerator. In case of integers, the number itself is the

numerator, as it is divided by 1.

O

Oblique

A line or a plane that is neither horizontal nor vertical but is tilted at some specific angle is called

oblique.

Oblique Cone

An oblique cone is a cone in which the center of the base of the oblique cone is not aligned (not

in line) with the center of the apex of the cone.

Oblique Cylinder

If the bases of the cylinder are not aligned just one above the other, it is called the oblique

cylinder.

Oblique Prism

A prism whose bases are not aligned directly one above the other is called as oblique prism.

Obtuse Angle

An angle whose measure is more than 90º but less than 180º.

Obtuse Triangle

If one of the angles of a triangle is an obtuse angle then it is called as the obtuse triangle.

Octagon

A polygon with 8 sides is called octagon. It may have equal or unequal sides.

Octahedron

Octahedron is a polyhedron with 8 faces. An octahedron appears like two square based pyramids

placed on one another. All the faces of an octahedron are equilateral triangles.

Octants

The eight parts into which the three dimensional space is divided by the co-ordinate axis.


47

Odd/Even Identities

Trigonometric identities show whether each trigonometric function is an odd or even function.

For example:

sin(-x) = sinx

cos(-x) = cosx

tan(-x) = tanx

csc(-x) = -cscx

sec(-x) = secx

tan(-x) = tanx

cot(-x) = -cotx

Odd Function

If the graph of a function is symmetric about x axis then the function is said to be an odd

function. Alternately, an odd function satisfies the condition, f(-x) = -f(x).

Odd Number

The set of integers that are not a multiple of 2. For example, {1, 3, 5, 7, 9, ...)

One Dimension

A dimension of the space where motion can take place in only two directions, either backward or

forward.

One-to-One Function

A one-one function is type of function in which every element of the range corresponds to at

least one element of the domain. A one-to-one function passes both the tests, the horizontal and

vertical test.

Open Interval

A set interval excluding the initial and final numbers of the domain. For example in the interval

of (2, 5) , 2 and 5 are the excluded from the set of numbers while performing any mathematical

operation.

Operations on Functions

The operations on functions are as follows:

Addition: (f +g)(x) = f(x) + g(x)

Subtraction: (f - g) = f(x) – g(x)

Multiplication: (fg)(x) = f(x). g(x)

Division: (f/g)(x) = f(x)/g(x)


48

Order of a Differential Equation

The power on the highest derivative of a differential equation is called as the order of differential

equation.

Ordered Pair

Two numbers written in the form (x,y) are called as the ordered pairs.

Ordinal Numbers

The numerical words that indicate order. The ordinal numbers are first, second, third etc,

Ordinary Differential Equation

A differential equation free of partial derivative terms.

Ordinate

The y coordinate of a point is usually called as the ordinate. For example, if P is a point (5,8)

then the ordinate is the 8.

Origin

The reference point of any graph indicated by (0,0) in 2-D and (0,0,0) in 3-D.

Orthocenter

The point of intersection of three altitudes of a triangle is called orthocenter.

Orthogonal

Orthogonal means making an angle of 90º

Outcome

The result of an experiment, like throwing a dice or taking out a pack of cards from a set of

cards.

Overdetermined System of Equations

An equation in which there are more equations than the number of variables involved.

P

Pi

Pie is defined as the ratio of circumference of a circle to its diameter. It is represented by the

Greek letter Π. Many great mathematicians have done pioneering work in researching on the

number pi like, Archimedes, Euler, William Jones etc, to name a few.


49

Point-Slope Equation of a Line

y – y1 = m (x – x1) is known as the point slope equation of a line, where m is the slope of the line

and (x1, y1) represents a point on the line.

For example, equation of a line passing through (3,4) and making an angle of 45 degrees with the

positive direction of x-axis is, y – 4 = 1(x – 3), here, (x1, y1) = (3,4) and slope = m = tan 45° = 1.

Polar Axis

The x axis is known as the polar axis.

Polar Conversion Formulas

The rules that are required to change the rectangular coordinates into polar coordinates are

known as the polar conversion formulas.

Conversion Formulas

Polar to rectangular- x = rcosθ , y = rsinθ

Rectangular to polar- r2= x

2 + y

2

Tanθ = y/x

Polar Curves

Spirals, lemniscates and lima cones are the curves that have equations in polar form. Such types

of curves with equations in the polar form are known as the polar curves.

Polar Integral Formula

Polar integral formula gives the area between the graph of curve r = r(θ ) and origin and also

between the rays θ= α and θ= β (where α ≤ β).

Polygon

A closed figure bounded by line segments. The name of the polygon describes the number of

sides of a polygon. Triangle, pentagon,hexagon etc are the examples of polygon.

Polygon Interior

All the points enclosed by a polygon is called as the polygon interior.

Polynomial Facts

An expression of the form, p(x) = anxn + an-1x

n-1 +.............+ a2 + a1x + a0 is called as the standard

polynomial equation. Examples of polynomial equations are 3x + 2y2 = 5 and 5x

2+ 3y = 3.

Polynomial Long Division

Polynomial long division is useful method to express a n improper rational expression as the sum

of a polynomial and a proper rational expression.


50

Positive Number

A real number greater than zero is known as a positive number.

Positive Series

A series that consists of only positive terms.

Postulate

A postulate is just like an assumption that is accepted to be true without proof.

Power

The number or variable (called as base) that is raised to the exponent is called as power.

Power Rule

Power rule is a formula that is used to find the derivative of power of a variable.

Power Series

A series that represents a function as a polynomial and whose power goes on increasing with

every term. In other it has no highest power of x.

Power series in x is given by:

n=0∑n=∞

anxn + a1x+ a2x

2 + a3x

3 +......

Prime Numbers

A number that has one and the number itself as the factors. For example, 1, 2, 3, 5, 7, 11....

Probability

The likelihood of occurrence of an event is called as probability. It is one of the most researched

areas of mathematics. There are some basic rules of probability:

For any event A, 0≤ P(A) ≤ 1

P = 1 for a sure event.

P = 0 for an impossible event

P (not A) = 1- P(A) or P(Ac) = 1 – P(A)

Proper Fraction

If the numerator of a fraction is less than the denominator then the fraction is said to be proper.

Proper Rational Expression

A rational expression having degree of the numerator less than the degree of denominator.


51

Pythagorean Theorem

According to Pythagoras theorem, the sum of squares of the two arms or legs of a right angled

triangle is equal to the sum of the square of the hypotenuse. If AB, BC and AC are the threes side

of a right angled triangle taken in same order then AC2 = AB

2 + BC

2 .

Q

Q1

Q1 or the first quartile is the median of the data which are less than the overall median. For

example, consider a set of data, 3, 5, 7, 8, 9, 10. The median of this set of data is 7. 3, 5 are the

only numbers less than the median. The median of the numbers 3 and 5 is 4, so the 1st quartile is

4.

Q3

Q3 or the third quartile is the median of the data which is more than the overall median. For

example, if we consider a set of data, 2, 3, 5, 6, 8 the median is 5. Now, 6 and 8 are the numbers

in this set that are greater than the overall median. These are called as Q3 or third quartile.

QED

QED stands for quod erat demonstrandum, which means "That which has to be proven".

Quadrangle

A polygon with four sides.

Quadrants

The four sections into which the x-y plane is divided by the x and y axis.

Quadratic

A two degree polynomial equation represented by the equation,

ax2 + bx + c = 0, where, a ≠ o.

Quadratic Polynomial

Any polynomial of degree 2.

Quadrilateral

A closed figure bounded by four lines.

Quadruple

Four times any number or a value is called as quadruple.

Quartic Polynomial


52

A polynomial of degree four.

Example: ax4 + bx

3 + cx

2 + dx + e = 0

Quintic Polynomial

A polynomial of degree 5

a5 + b

3 + c

Quintiles

From a set of data, the 20th and 80th percentiles are called the quintiles.

Quintuple

Multiplying any number by a factor of 5.

R

Radian

It is the unit of measuring angles. For example, 180 º = Π radians, 45 º = Π/4 radians etc,

Radical

The designated symbol for the square root of any mathematical entity is called radical.

Radicand

The mathematical quantity whose nth root is taken. It is the number under the radical symbol.

Radius of a circle

The distance or the measure of the line segment between center of circle and any point on the

circle is called the radius of the circle.

Range

The limit within which set of values reside. For example, the range of the function y = x2 is [0,

∞] or {y|y ≥ o}

Ratio

The resultant quantity derived by dividing one number with the other.

Rational Exponents

The exponents which are composed of rational numbers are called rational exponents.

Rational Function

Given two polynomials, one divided by another, the resultant is expressed as a function, then it is

called rational equation.


53

Rational numbers

The set of all ratios, made up of real numbers, which do not have zero as denominator.

Rational root theorem

All possible roots of a polynomial are provided by the rational root theorem.

Rationalizing Substitution

It is a method of integration capable of transforming a fractional integrand into more than one

kind of root.

Rationalizing the Denominator

The process of adjusting a fraction is such a way that denominator becomes a rational number.

Ray

A line having only one end point and extending infinitely in the other direction is called a ray.

Real numbers

It is a set of all numbers consisting of positive, negative, rational, square root, cube root etc. Real

numbers form the set of all the numbers on the number line.

Reciprocal Numbers

One divided by the given number is the reciprocal of the number.

Rectangle

A rectangle is a quadrilateral having all equal angles. They are equal to 900.

Rectangle Parallelepiped

Rectangle Parallelepiped is a polyhedron where every face is a rectangle.

Recursive Formula

In a series of numbers, the next term in the series is calculated by a formula which uses previous

terms in that same series. This term is called recursive term and the process is called recursive

formula.

Reducing a fraction

When numerator and denominator, both have common factors, we cancel out all of them until no

common factor remains.

Regular Octahedron

A polyhedron which has eight faces is called regular octahedron.


54

Regular Polygon

A regular polygon is one in which all angles and sides are are congruent to each other.

Regular Prism

Regular Prism is a prism in which all the face comprise of regular polygons.

Regular Pyramid

The pyramid who's base is made up of regular polygon is called regular pyramid.

Regular Right Prism

A regular right prism is one whose bases are made up of right polygons

Right Pyramid

Right Pyramid is a pyramid where base is a regular regular polygon and the apex is directly on

top of the center of the base of polygon.

Regular Tetrahedron

Regular Tetrahedron is a pyramid where all the faces of the polygon are triangles.

Related Rates

The set of all the problems, where the changes in various rates are calculated by means of

differentiation.

Relation

The ordered pair of entities which have some distinct abstraction between them is called a

relation.

Relative Maximum

Relative maximum is a point in the graph which is at the highest point for that particular section.

Relative Minimum

Relative minimum is a point in the graph which is at the lowest point for that particular section.

Relative Prime

Those numbers which have the greatest common factors as prime numbers are called relative

prime numbers.

Remainder

The number which is left over after the division as an undivided whole number is called


55

remainder.

Residual

The measure of a line which is parallel to Y axis and one end of which is touching the data point

is called residual.

Rhombus

The parallelogram having all equal sides is called rhombus.

Reimann Geometry

Reimann geometry is a type of geometry where all the lines are considered non parallel,

intersecting and happening on the surface of the sphere.

Right Circular Cone

A right circular cone is a cone whose base is a circle and any radius is making right angle to the

line segment from apex of the cone to center of the circle.

Right Circular Cylinder

Right circular cylinder cylinder whose bases is are circular.

Regular Hexagon

A hexagon with all sides equal to each other is called regular hexagon.

Rose Curve

The leaves of the curve which have complete symmetry over the center of the curve is called a

rose curve.

Rotation

When figure is transformed according to a fixed point is called rotation (generally in same

plane).

Rounding a Number

Without compromising the degree of accuracy to a large extent, the approximation of number to

the nearest value is called rounding of the number.

S

Scalene Triangle

Scalene Triangle is a triangle, wherein, all the sides of the triangle are unequal or of different

lengths.

Scalar


56

A scalar is the one with magnitude, but with no definite direction. Examples of scalars are

length, temperature and mass. Mathematically, a scalar is said to be any real number or any

quantity that can be measured by using a single real number.

Solid Geometry

Solid geometry is a term used for the surfaces and solids in space. It includes the study of

spheres, cones, pyramids, cylinders, prism, polyhedra, etc. It also involves the study of related

lines, shapes, points and regions.

Segment

A segment constitutes all points between two given points, including those two points.

Segment of a Circle

Segment of a circle is any internal region of a circle, that is bounded by an arc or a chord.

SAS Similarity

SAS similarity is side-angle-side similarity. When two triangles have corresponding angles as

congruent and corresponding sides with equal ratios, the triangles are similar to each other.

SSS Congruence

When two triangles have corresponding sides congruent, the triangles are said to be in SSS

congruency.

Semicircle

Semicircle is a half circle, with a 180 degree arc.

Spherical Trigonometry

Spherical trigonometry is a term used for the study of triangles on the surface of any sphere. The

sides of these triangles are arcs of great circles. This study is useful for navigation purposes.

Solving Analytically

A technique of solving a mathematics problem, by using numeric or algebraic methods. This

technique does not involve the use of a graphic calculator.

Solve Graphically

A technique of solving a mathematics problem, by using graphs and picture. Graphic calculators

are used to solve a problem graphically.

Spheroid

Spheroid actually refers to an oblate spheroid. But, in some cases, it refers to an ellipsoid that

looks more or less like a sphere.


57

T

Tan

The trigonometric function known as the tangent function, gives the ratio of opposite and

adjacent side of a triangle.

Tan-1

The angle that has tangent equal to 1, therefore, tan-1

= 45º. In radians tan-1

= Π/4

Tangent Line

A tangent line touches the curve instead of just crossing it. A tangent line can also be defined as

a line that intersects the differential curve at a point.

Tautochrone

Tautochrone is a Greek word that means at the same time. Tautochrone has a shape of cycloid

hanging downwards. The peculiar feature of a tautochrone is that a bead sliding down the

frictionless wire will always take the same time irrespective of the fact that how high or low is

the release point.

Taylor Polynomial

The Taylor polynomial is a partial sum of Taylor series. Using the Taylor's polynomial a

function can be approximated to a very close value provided the function possess sufficient

number of derivatives.

Taylor Series

Taylor series is given by: f(a) + f'(a)(x - a) + f''(a)/2(x - a)2 + f'''(a)/3(x – a)

3+.........+ f

n(a)/n(x –

a)n.

Term

The parts of a mathematical sequence or operations separated by addition or subtraction.

Tetrahedron

Tetrahedron is a polyhedron with four triangular faces. It can be viewed as a pyramid with

triangular base.

Three Dimensional Coordinates

The right handed system of coordinates that is used to locate a point in the three dimensional

space.


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Torus

If we revolve a circle (In 3-D) about a line that does not intersect the circle, then the surface of

revolution creates a doughnut shaped figure called as torus.

Transpose of a Matrix

The matrix which is formed by turning all the rows of the matrix into columns or vice-versa.

Transversal

A line that cuts two or more parallel lines.

Trapezium

A quadrilateral with one pair of parallel sides is referred to as trapezium.

riple (Scalar) Product

Multiplication of vectors using dot product.

If a, b and c are three vectors then triple scalar product is a. (b x c)

Trivial

Trivial solutions are the simple and obvious solutions of a equation. For example, consider the

equation x + 2y = 0, here x= 0, y =0 are the trivial solutions and x = 2, y = -1 are the non-trivial

solutions.

Truncated Cone or Pyramid

A cone or pyramid whose apex is cut off by intersecting plane. If the cutting plane is parallel to

the base it is called as the frustum.

Truncated Cylinder or Prism

A cylinder or prism that is cut by a parallel or oblique plane to the bases. The other base remains

unaffected by the cutting of the base.

Truncating a Number

A method of approximation wherein the decimals are dropped after a certain point instead of

rounding. For example, 3.45658 would be approximated to 3.4565.

Twin Primes

Prime numbers that have a difference of two between each other. For example, 3 and 5.

U

Unbounded Set of Numbers

Unbounded set of numbers can be defined as the set of numbers which is not bounded, either by

a lower bound or by an upper bound.


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Under determined System of Equations

Under determined System of Equations is defined to be a linear system of equations, wherein the

equations are comparatively less than the variables. The system might be consistent or

inconsistent. This depends upon the equations in it.

Uniform

Uniform means same, constant, or in the same pattern.

Undecagon

A polygon having 11 sides is called undecagon.

Unit Circle

Unit circle is defined to be a circle with radius one and is centered at the origin on the x-y plane.

Uncountable

Uncountable is a set that has comparatively more elements than the set of integers. It is an

infinite set, in which one cannot put its elements into a one-to-one correspondence with its set of

integers.

Upper Bound of a Set

Upper bound of a set is defined to be a number which is greater than or equal to all the elements

present in a set. For instance, 4 is a upper bound of the interval [0,1], similarly 3,2 and 1 also are

the upper bounds of this interval.

u-Substitution

u-Substitution is a method of integration, that necessarily involves the use of the chain rule in its

reverse form.

Union of Sets

Union of sets is defined as the combination of the elements of two sets or more than that. The

union is denoted by the U symbol.

Unit Circle Trigonometry Definitions

Unit circle trig definitions is the set of all the six trigonometry functions such as the sine, cosine,

tangent, cosecant, secant, and cotangent.

V

Variable

The independent quantity in an algebraic expression is called as variable.


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Varignon Parallelogram of a Quadrilateral

The parallelogram formed by joining the midpoints of the adjacent sides of any quadrilateral.

Vector

A quantity drawn as an arrow that has both magnitude and direction.

Vector Calculus

The problems involving calculus principles (derivatives, integrals etc) of the three dimensional

figures.

Venn Diagrams

Venn diagrams are the pictorial representation of the set operations.

Verify a Solution

We verify a solution by putting the obtained values of the variables and checking if those values

satisfy the expression.

Vertex

For a triangle, the meeting end of two sides is called a vertex.

Vertex of an Ellipse

The points on the ellipse where the ellipse takes a sharp turn. Mathematically, vertices of an

ellipse are the points that lie on the line through the foci (or the major axis)

Vertex of a Hyperbola

The points at which the hyperbola takes its sharpest turns. Vertices of a hyperbola are the points

that lie on the line through the foci.

Vertex of a Parabola

The point at which the hyperbola takes a sharp turn. The vertex of a parabola lies midway

between the focus and directrix.

Vertical Angles

Vertical angles are the opposite angles that are formed due to the intersection of two lines.

Vertical Compression

Vertical shrinking of a geometrical figure is called as vertical compression.

Vertical Dilation

Enlargement of a geometrical figure vertically is called as vertical dilation.


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Vertical Line Equation

The equation x = a is called the vertical equation of line.

Vertical Line Test

It is used to test if a relation is a function. It is a fact that if a vertical line cuts the graph of a

relation at more than one point then the given relation is not a function.

Vertical Reflection

A reflection in which a plane figure is vertically flipped. For a vertical reflection the axis of

reflection is always horizontal.

Vertical Shift

Shifting a geometrical figure vertically is called as vertical shift.

Vertical Shrink

Vertical shrink is the shrink in which the plane figure is distorted vertically.

Vertical Stretch

Stretching the dimensions of a figure by a constant factor K in the vertical direction is called

vertical stretch.

Vinculum

The horizontal line that is used in a fraction or radical.

W

Washer

The region between two concentric circles is called as washer. The radii of the two concentric

circles different.

Washer Method

Washer method is used to determine the volume of solid of revolution.

Weighted Average

A type of arithmetic mean calculation in which one of the sets among the various sets of

observation carries more importance than others (weight).

Whole Numbers

The numbers 0, 1, 2, 3, 4, 5....etc.


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X

x-intercept

The point at which a graph intersects the x-axis.

x-y Plane

The plane formed by the x and y axis of the coordinate system.

x-z Plane

The plane formed by the x and z axis of the coordinate system.

Y

y-intercept

y-intercept is defined as a point where the graph intersects the y-axis.

y-z Plane

y-z plane is simply defined as the plane formed by the y-axis and z-axis.

Z

z-intercept

The point at which a graph intersects the z-axis.

Zero

Zero is a digit and plays a crucial role in mathematics. Zero is considered as a neutral number as

it is neither positive nor negative. It is also an additive identity.

Zero Matrix

A matrix all whose elements are zero.

Zero of a Function

If f(x) = 0, then the value of x which gives f(x) = 0, is called zero of a function.

Zero Slope

Any horizontal line has a slope equal to zero. A horizontal line has same y-coordinate so from

the formula (y2 - y1)/(x2 - x1), we get the slope equal to zero.

Zero Vector

A vector with no magnitude and direction is called as a zero vector.


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66628563 dictionary-of-math-terms

Education

altitude of thecone

altitude of aparallelogram

calledadjacent angles

angles of anothertriangle

ofthe distance

cylinderthe distance

parallelogramthe distance

prismthe distance