Maths

Integration by Substitution

The integration of a function f(x) is given by F(x) and it is represented by: ∫f(x)dx = F(x) ...

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Problems on Area and Circumference of a Circle

Perimeter is associated with any closed figure like triangle, quadrilateral, polygons or circles. It ...

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Dot Product of Vectors

The Dot Product of Vectors can be defined in two ways: Geometrically Algebraically Dot Product ...

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Truth Table

Truth Table is used to perform logical operations in Maths. These operations comprise boolean algebra ...

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Integration

Integration is the calculation of an integral. Integrals in maths are used to find many useful quantities ...

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Solving Puzzles Which Involve Numbers and Letters

Number system is one of the most innovative and interesting invention by human beings. Various tricks ...

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Eccentricity

The eccentricity in the conic section uniquely characterises the shape where it should possess a non-negative ...

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Two Lines of Symmetry

Let us take up an activity to understand line of symmetry. Say you are asked to carve a ‘heart’ out ...

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Integrals of Some Particular Function

S.No Integral function Integral value 1 \(\int \frac{dx}{x^{2}- a^{2}}\) \(\frac{1}{2a} ...

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Similar Triangles

Similar triangles are the triangles which have the same shape but their sizes may vary. All equilateral ...

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Elementary Operation of Matrix

A matrix is an array of numbers arranged in the form of rows and columns. The number of rows and columns ...

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Types of Angles

There are various types of angles in geometry. Angles form the core of the geometry in mathematics. They ...

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Integral Calculus

Integral Calculus is the branch of calculus where we study about integrals and their properties. Integration ...

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Synthetic division

What is Synthetic Division? The Synthetic division is a shortcut way of polynomial division, especially ...

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Ellipse

An ellipse is the locus of all those points in a plane such that the sum of their distances from two ...

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Types of Fractions

Fractions are one of the most common terms used in Maths, to determine the parts of a whole object. Apart ...

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Integers as Exponents

Exponents are used to show repeated multiplication of a number by itself. Writing large numbers sometimes ...

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Differentiation Rules

The differentiation rules help us to evaluate the derivatives of some particular functions, instead of ...

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Empirical and Theoretical Probability

We come across a number of situations every day where we need to predict the outcome of an event before ...

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Types of Polygon

Before we start learning about types of polygon, let us first learn the definition of a polygon. A polygon ...

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Inflection Point

In Mathematics, a function is a special relationship between two sets (input set and output set). Every ...

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T-test Table

In Statistics, a t-test, can be expressed as a statistical hypothesis test where the test statistic maintains ...

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Equation of a Line in Three Dimensions

Equation of a line is defined as y= mx+c, where c is the y-intercept and m is the slope. Vectors can ...

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Types of Sets

Set is defined as a well-defined collection of objects. These objects are referred to as elements of ...

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Index

Index (indices) in Maths is the power or exponent which is raised to a number or a variable. For example, ...

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Equation of Sphere

A sphere is defined as a completely round geometrical object in a three-dimensional space just like a ...

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Types of Vectors

There are 10 different types of vectors that are generally used in maths and science. To recall, vectors ...

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Indefinite Integrals

An integral which is not having any upper and lower limit. F(x) is the way function f(x) is integrated ...

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Equation of a Plane: 3 Non-Collinear Points

The physical quantities which have magnitude, as well as directly attached to them, are known as vectors. Position ...

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Mathematical Induction

Mathematical Induction is introduced to prove certain things and can be explained with this simple example. ...

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Implicit Function

An implicit function is a function, written in terms of both dependent and independent variables, like ...

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Equation of a Plane in the Normal Form

The equation of a plane in the normal form can be determined if normal to the plane as well as the distance ...

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Union and Intersection of Sets

Cardinal Number of a set The number of distinct elements or members in a finite set is known as the ...

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Hyperbolic Functions

In Mathematics, the hyperbolic functions are similar to the trigonometric functions or circular functions. ...

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Equivalent Fractions

The equivalent fractions are a type of fraction which seems to be different (not having the exact numbers) ...

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Unitary Method

Unitary method concepts are covered in this article. In simple terms, the unitary method is used to find ...

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Solve the Linear Equation in Two or Three Variables

Consider the linear equation in one variable 5x = 2x + 3. We can easily figure out x = 1. Now when we ...

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Estimation of Numbers

We involuntarily participate in estimation all our lives. Be it a kid estimating how much chocolate he ...

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Universal Set

In Mathematics, the collection of elements or group of objects is called a Set. There are various types ...

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How to Simplify Fractions?

A fraction is a number representing a part of a single whole object or a group of objects. It is defined ...

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Introduction To Euclidean Geometry

Euclidean geometry is the study of geometry (especially for the shapes of geometrical figures) which ...

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Implication of If-Then Statement

In mathematical reasoning, to infer a conclusion we frequently make use of if-then statements as: P: ...

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How to Find Square Root of a Number

A square has the same length and width. Which means, if the length is equal to 3 then the width should ...

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Euler's Formula and De Moivre's Theorem

Euler’s formula: Euler’s formula states that ‘For any real number \(x\), \(e^{ix}\) = \(cos~x~+~i ...

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Variable

what is a variable in Math? Variable Definition: In rudimentary arithmetic operations, a variable is ...

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Mean Deviation for Ungrouped Data

The basic difference between grouped data and ungrouped data is that in the case of latter the data is ...

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Even and Odd Numbers

Even and Odd Numbers Definition: Normally the even and odd numbers definition is, “Even numbers are ...

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Variance

What is Variance in Statistics? Variance meaning – It is a measure of how data points differ from ...

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How to Draw a Circle?

Everyday we come across different shapes in our day to day life. Many of us are already aware of a couple ...

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Prime, Composite and Even, Odd Numbers

A life without numbers is difficult. Numbers have influenced our daily routine in such a way that almost ...

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Vector algebra

Vector algebra is one of the essential topics of algebra. It studies the algebra of vector quantities. ...

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How to Divide

Learn how to divide a number by another number. The division is a basic arithmetic operation apart from ...

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Exact Differential Equation

Exact Differential Equation Definition The equation P (x,y) dx + Q (x,y) dy=0 is an exact differential ...

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Vectors

Vectors is an object which has magnitude and direction both. It is represented by a line with an arrow, ...

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How Negative Numbers Arise?

We have seen some numbers have  a minus sign. If we take a real life instance, the temperature in some ...

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Experimental Probability

You and your 3 friends are playing a board game. It’s your turn to roll the die and to win the game ...

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Vector Space

A vector space or a linear space is a group of objects called vectors, added collectively and multiplied ...

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Homogeneous Differential Equation

A differential equation of the form f(x,y)dy = g(x,y)dx is said to be homogeneous differential equation ...

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Exponential Function - Logarithmic Function

The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, ...

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Vertically Opposite Angles & Vertical Angles Theorem

Vertical Angles: When two lines meet at a point in a plane, they are known as intersecting lines. When ...

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Hexadecimal Number System

In the hexadecimal number system, the numbers are represented with base 16. It is also pronounced sometimes ...

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Exponents and Powers Class 7

Basically, the exponents state the repeated multiplication of the same number with respect to the number ...

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Vertices, Faces and Edges

In this article, we will discuss the vertices, faces, and edges of solid shapes. We come across a number ...

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Heron's Formula

Heron’s formula is one of the most important concepts used to find the area of a triangle when all ...

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Expression: Term, Factor and Coefficient

An algebraic expression is a mathematical phrase that contains integral or fractional constants (numbers), ...

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Volume of a Combination of Solids

A solid which is bounded by six rectangular faces is known as cuboid and if the length, breadth and height ...

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Height and Distance: Application in Trigonometry

The topic heights and distance is one of the applications of Trigonometry which is extensively used in ...

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Triangles, Exterior Angle Theorem

A polygon is defined as a plane figure which is bounded by finite number of line segments to form a closed ...

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Volume of a Cylinder

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can ...

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HCF - Highest Common Factor

The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor. ...

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Faces, Edges and Vertices: 3D Shapes

A 3D shape or an object is made up of a combination of certain parts. In other words, a solid figure ...

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Volume of a Cone

A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to ...

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Group Theory

Group theory is the study of a set of elements present in a group, in Maths. A group is a collection ...

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Factoring Polynomials: How To Factorize

An expression of the form axn + bxn-1 + cxn-2 + ….+kx+ l, where each variable has a constant accompanying ...

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Volume of Cuboid

A cuboid is a three-dimensional structure having six rectangular faces. These six faces of cuboid exist ...

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Factorisation of Algebraic Expression: Algebra

A number or quantity that when multiplied with another number produces a given number or expression. ...

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Volume of a Pyramid

A pyramid is a polyhedron figure which has only one base. The base of the pyramid is also a polynomial. Pyramid’s ...

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Greater Than and Less Than Symbols

Greater than and less than symbols are used to compare any two numbers.  When a number is bigger than ...

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Factors and Multiples

FACTORS When a number is said to be a factor of any other second number, then the first number must ...

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Weibull Distribution

The Weibull Distribution is a continuous probability distribution used to analyse life data, model failure ...

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Graphing of Linear Equations

Linear Equations in Two Variables Equations of degree one and having two variables are known as linear ...

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Greatest Common Factor

What is Greatest Common Factor? The largest common factor of two or more numbers is called as Greatest ...

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Vector and Scalar Quantities

In mathematics and physics, we have physical quantities which can be categorized in two ways, namely Scalar ...

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Graphical Representation

Graphical Representation is a way of analysing numerical data. It exhibits the relation between data, ...

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Geometric Distribution

In a series of trials, if you assume that the probability of either success or failure of a random variable ...

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Symmetric Matrix & Skew Symmetric Matrix

To understand if a matrix is a symmetric matrix, it is very important to know about transpose of a matrix ...

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Maps: Space Maps - Get Directions

All through these years, we have been dealing with maps viz. world map, regional maps, maps of various ...

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Geometric Progression and Sum of GP

If in a sequence of terms each term is constant multiple of the preceding term, then the  sequence is ...

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Word Problems on Number Operations

A number is a figure or a value to denote the count or quantity of something. The counting numbers or ...

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Geometric Tools: Description and Uses

Geometric tools are the instruments used to draw different types of geometric shapes. In Maths, geometry ...

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Zeros of polynomial

For a polynomial, there could be some values of the variable for which the polynomial will be zero. These ...

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Geometric Shapes

Geometric Shapes are the figures which we have come across in Maths, with different names. Triangle, ...

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Geometry Formulas For Class 10

Formulas, theorems and properties are important in studying Geometry for class 10. If you are studying ...

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Z-Score Table

A standard normal table also called the unit normal table or z-score table, is a mathematical table for ...

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Geometric Mean

In Mathematics, the Geometric Mean is the average value or mean which signifies the central tendency ...

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Geometry Formulas For Class 12

Find the best practice material that covers all important geometry formulas for class 12. So that students ...

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Integers: Word Problems on Integers

An arithmetic operation is an elementary branch of mathematics. Arithmetical operations include addition, ...

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Equation of a Line

The standard forms of the equation of a line are: Slope-intercept form Intercept form Normal form General ...

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Geometry Formulas For Class 9

Geometry is a branch of mathematics that concerned with shapes, points, lines and much more. Geometry ...

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Whole Numbers

The whole numbers are the part of the number system in which it includes all the positive integers from ...

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