SOME MATHEMATICAL TERMS: (S-Z)

S

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

Scalar
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.

T

Takeout Angle
The angle cut out from a piece of paper, so that the paper can be rolled into a right circular cone is called as the takeout angle.

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.

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.

Triple (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.

Under determined System of Equations
Under determined System of Equations is defined to be a linear system of equations, wherein the equations are comparatively less than the variables. The system might be consistent or inconsistent. This depends upon the equations in it.

Uniform
Uniform means same, constant, or in the same pattern.

Undecagon
A polygon having 11 sides is called undecagon.

Unit Circle
Unit circle is defined to be a circle with radius one and is centered at the origin on the x-y plane.

Uncountable
Uncountable is a set that has comparatively more elements than the set of integers. It is an infinite set, in which one cannot put its elements into a one-to-one correspondence with its set of integers.

Upper Bound of a Set
Upper bound of a set is defined to be a number which is greater than or equal to all the elements present in a set. For instance, 4 is a upper bound of the interval [0,1], similarly 3,2 and 1 also are the upper bounds of this interval.

u-Substitution
u-Substitution is a method of integration, that necessarily involves the use of the chain rule in its reverse form.

Union of Sets
Union of sets is defined as the combination of the elements of two sets or more than that. The union is denoted by the U symbol.

Unit Circle Trigonometry Definitions
Unit circle trig definitions is the set of all the six trigonometry functions such as the sine, cosine, tangent, cosecant, secant, and cotangent.

V

Variable
The independent quantity in an algebraic expression is called as variable.

Varignon Parallelogram of a Quadrilateral
The parallelogram formed by joining the midpoints of the adjacent sides of any quadrilateral.

Vector
A quantity drawn as an arrow that has both magnitude and direction.

Vector Calculus
The problems involving calculus principles (derivatives, integrals etc) of the three dimensional figures.

Venn Diagrams
Venn diagrams are the pictorial representation of the set operations.

Verify a Solution
We verify a solution by putting the obtained values of the variables and checking if those values satisfy the expression.

Vertex
For a triangle, the meeting end of two sides is called a vertex.

Vertex of an Ellipse
The points on the ellipse where the ellipse takes a sharp turn. Mathematically, vertices of an ellipse are the points that lie on the line through the foci (or the major axis)

Vertex of a Hyperbola
The points at which the hyperbola takes its sharpest turns. Vertices of a hyperbola are the points that lie on the line through the foci.

Vertex of a Parabola
The point at which the hyperbola takes a sharp turn. The vertex of a parabola lies midway between the focus and directrix.

Vertical Angles
Vertical angles are the opposite angles that are formed due to the intersection of two lines.

Vertical Compression
Vertical shrinking of a geometrical figure is called as vertical compression.

Vertical Dilation
Enlargement of a geometrical figure vertically is called as vertical dilation.

Vertical Line Equation
The equation x = a is called the vertical equation of line.

Vertical Line Test
It is used to test if a relation is a function. It is a fact that if a vertical line cuts the graph of a relation at more than one point then the given relation is not a function.

Vertical Reflection
A reflection in which a plane figure is vertically flipped. For a vertical reflection the axis of reflection is always horizontal.

Vertical Shift
Shifting a geometrical figure vertically is called as vertical shift.

Vertical Shrink
Vertical shrink is the shrink in which the plane figure is distorted vertically.

Vertical Stretch
Stretching the dimensions of a figure by a constant factor K in the vertical direction is called vertical stretch.

Vinculum
The horizontal line that is used in a fraction or radical.

W

Washer
The region between two concentric circles is called as washer. The radii of the two concentric circles different.

Washer Method
Washer method is used to determine the volume of solid of revolution.

Weighted Average
A type of arithmetic mean calculation in which one of the sets among the various sets of observation carries more importance than others (weight).

Whole Numbers
The numbers 0, 1, 2, 3, 4, 5....etc.

X

x-intercept
The point at which a graph intersects the x-axis.

x-y Plane
The plane formed by the x and y axis of the coordinate system.

x-z Plane
The plane formed by the x and z axis of the coordinate system.

Y

y-intercept
y-intercept is defined as a point where the graph intersects the y-axis.

y-z Plane
y-z plane is simply defined as the plane formed by the y-axis and z-axis.

Z

z-intercept
The point at which a graph intersects the z-axis.

Zero
Zero is a digit and plays a crucial role in mathematics. Zero is considered as a neutral number as it is neither positive nor negative. It is also an additive identity.

Zero Dimensions
When we talk of zero dimensions it means that no motion is possible without leaving that point.

Zero Matrix
A matrix all whose elements are zero.

Zero of a Function
If f(x) = 0, then the value of x which gives f(x) = 0, is called zero of a function.

Zero Slope
Any horizontal line has a slope equal to zero. A horizontal line has same y-coordinate so from the formula (y₂ - y₁)/(x₂ - x₁), we get the slope equal to zero.

Zero Vector
A vector with no magnitude and direction is called as a zero vector.

SOME MATHEMATICAL TERMS: (N-R)

N

n-dimensions
n-dimensions is the property of space that indicates that n mutually perpendicular directions for movement of any particle in that space is possible.

Natural Domain
It is an alternative term for domain. It is the range within which the function exists or has definite values. The term natural domain is used to signify that the domain is not restricted.

Natural Logarithm
When the logarithm of a number is taken with respect to the base e, then the logarithm is said to be natural logarithm. The natural logarithm is represented as ln a, where a is the number.

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

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.

Noncollinear
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.

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 5^1/n.

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

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

Oblate Spheroid
If we revolve an ellipse about its minor axis then the 3 dimensional sphere obtained will be of the shape called oblate spheroid. Earth is an example of oblate spheroid.

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.

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-Sided Limit
Taking the limit of a term either from the left hand side or right hand side is called the one-sided limit.

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)

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.

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 limacones 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) = a_nxⁿ + a_n-1x^n-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.

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

Positive Series
A series that consists of only positive terms.

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

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

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

Power Series
A series that represents a function as a polynomial and whose power goes on increasing with every term. In other it has no highest power of x.
Power series in x is given by:
_n=0∑^n=∞a_nxⁿ + 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(A^c) = 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.

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
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.

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.

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 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

SOME MATHEMATICAL TERMS: (J-M)

J

Jacobian
The term Jacobian is used to denote the jacobian matrix in vector calculus. In vector calculus, the jacobian matrix is the matrix of the first order partial derivatives of a vector valued function. Conceptually, the jacobian of a function represents the orientation or inclination of a tangent plane to the function at a given point.

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
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.

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)=lim_x-><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 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 lim_x->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 lim_x->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 DivergenceA 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
An equation that can be written in the form "linear polynomial" = "linear polynomial" or "linear polynomial"=constant is known as a linear equation.

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

Linear Factorization
If a polynomial can be factorized such that the factors formed after the factorization are linear polynomials, then this factorization is known as a linear factorization. For example x²-9 can be factorized as (x+3) and (x-3).

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

Linear Inequality
An inequality that can be written such that the value of a polynomial is greater than, less than, greater than equal to or less than equal to a particular number is called linear inequality. For example 3x + 7y >9.

Linear Pair of Angles
When two lines intersect each other, then the adjacent angles formed due to intersection of the two lines are called linear pair angles. The linear pair angles formed are supplementary.

Linear Polynomial
A linear polynomial is a polynomial with degree 1. The highest power of the variables involved in the polynomial should be one. For example 9x + 7 is a linear polynomial.

Linear Programming
The linear programming is an algorithm that is used for solving problems. The method of using linear programming is by asking the largest or smallest possible value of a linear polynomial. If there are any restrictions, then the system of inequalities is used to present any restriction to the equations.

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

Linear System of Equations
If there are more than one equations such that each equation is a linear equation, then the system of equations will be known as linear system of equations.
For example, 2x + 3y - 5z
9x + 7y + 12x = 19
15x - 6y + 11z = 9 is a linear system of equations, that can be used to determine the values of x, 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, log_cx=z then c^z=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 10^y=x. It means that if the base of the logarithm is not mentioned then consider the base as 10.
If ln x = y then e^y=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
log_ax = log_bx/log_ba

Logarithmic Differentiation
It is the type of differentiation that is used in special circumstances. For example the equation y = x^{tan 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.

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
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.

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.

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 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.

These were the modular equivalent rules for normal modular arithmetic operations.

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).

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 varialbes then the calculus is called multivariable calculus.

Mutually ExclusiveIf the outcome of two events in probability have no common outcomes then the events are called mutually exclusive.