66628563 dictionary-of-math-terms

Dictionary of MATH TERMS

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.

2


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 1800.

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.

4


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-11 = 450.

Arcsec
The inverse of a secant function is called the arcsec function. For example, sec-12 means the
angle whose secant is equal to 2. Sec-12 = 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/a2 + (y-k)2/b2]

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

6


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 ax.

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 – 6y2.

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) = mCnpkqn-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 = nC0an + nC1an-1b +..........+nCn-1abn–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(Ac) = 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-1x
The inverse of cos function is read as 'cos inverse x'. For example, cos-1½ = 60º.

Cot-1x
By cot-1x 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-11 = 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 + 2x2 + 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 = rn(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 + Cy2 + 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 + 3y4 + 5x3, the degree of the polynomial is 5.

Degree of a Term
In 5y7, degree of term is 7, in 5x24y3, 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.

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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 = x 3
+ 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.

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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+a2=(x+a)2

 x2-2(a)x +a2=(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

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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

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 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
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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:

27


sinhx = (ex - e-x)/2,
coshx = (ex + e-x)/2
tanhx = (sinhx/coshx) = (ex - e-x)/(ex + 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 + cos2θ =
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

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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 + 5y5 - 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

29


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 = a2 + b2 -
2abcosC, b2 = a2 + b2 - 2accosB and a2 = b2 + c2 - 2bccosA

Law of Sine

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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 + 5x3 + 92 + 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 + 5x3 + 92 + 2x +21 is 7x4.

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.

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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 = a2cos2θ.

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 5x3y2 and
135x3y2 are like terms and hence can be added directly to give the number 140x3y2.

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

33


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

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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 x 2-9 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,

35


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 =

36


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.

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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

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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.

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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.

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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

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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 + b2)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).

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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

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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.

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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.

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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.

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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)

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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.

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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= x2 + y2
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-1xn-1 +.............+ a2 + a1x + a0 is called as the standard
polynomial equation. Examples of polynomial equations are 3x + 2y2 = 5 and 5x2+ 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.

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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=∞
n=0∑ anxn + a1x+ a2x2 + a3x3 +......

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.

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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 = AB2 + BC2 .

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

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A polynomial of degree four.
Example: ax4 + bx3 + cx2 + dx + e = 0

Quintic Polynomial
A polynomial of degree 5
a5 + b3 + 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.

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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.

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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

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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
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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.

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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+.........+ fn(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.

57


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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