Maths

Mathematics is the base of human civilization. From cutting vegetables to arranging books on the shelves, from tailoring clothes to motion of Planets - Mathematics applies everywhere.

Calculus | Probability | Trigonometry | Coordinate Geometry

  1. Number System
  2. Algebra & Arithmetic
  3. Geometry & Mensuration
Fundamental Operations on Rational Numbers

Four fundamental operations on rational expressions are performed in exactly the same way as in case of rational numbers.

Read more ...
Basic Geometry

The term ‘Geometry’ is the English equivalent of the Greek word ‘Geometron’. ‘Geo’ means Earth and ‘metron’ means Measurement. According to historians, the geometrical ideas shaped up in ancient times, probably due to the need in art, architecture and measurement. These include occasions when the boundaries of cultivated lands had to be marked without giving room for complaints.

Read more ...
Means of Progressions

Arithmetic Mean

A is called the arithmetic mean of the numbers a and b if and only if a, A, b are in AP.

Read more ...
Harmonic Progression

A sequence of non-zero numbers is said to be in harmonic progression (HP) if their reciprocals are in AP.

Read more ...
Geometric Progression

A geometric progression (GP) is a sequence of numbers in which the first term is non-zero and each term, except the first, is obtained by multiplying the term immediately preceding it by a fixed non-zero number. This fixed number is called the common ratio and it is denoted by r.

Read more ...
Arithmetic Progression

An arithmetic progression (AP) is a sequence of numbers in which each term, except the first, is obtained by adding a fixed number to the immediately preceding term. This fixed number is called the common difference, which is generally denoted by d.

Read more ...
Binomial Theorem

A Binomial is an algebraic expression of two terms which are connected by the operation: + or −.

Read more ...
Principle of Mathematical Induction

Induction is the process of inferring a general statement from the truth of particular cases.

Read more ...
Combinations

The word combination means selection. Suppose you are asked to make a selection of any two things from three things: a, b and c.

Read more ...
Circular Permutations

A circular permutation is one in which the things are arranged along a circle. It is also called closed permutation.

Read more ...
Permutations When Objects Can Repeat

The number of permutations of n different things, taken r at a time, when each may be repeated any number of times in each arrangement, is nr.

Read more ...
Permutations of Objects Not All Distinct

The number of mutually distinguishable permutations of n things, taken all at a time, of which p are alike of one kind, q alike of second such that p + q = n, is n!/p! q!.

Read more ...
Scalar or Dot Product

The scalar product of two vectors is a scalar quantity. Therefore, the product is called scalar product.

Read more ...
Direction Ratios

Any three numbers proportional to direction cosines of a vector are called its direction ratios.

Read more ...
Direction Cosines

Let P(x, y, z) be any point in space with reference to a rectangular coordinate system O (XYZ). Let α, β and γ be the angles made by OP with the positive direction of coordinate axes OX, OY, OZ respectively. Then cos α, cos β, cos γ are called the direction cosines.

Read more ...
Resolution of Vector

If P is a point in a two dimensional plane which has coordinates (x, y).

Read more ...
Addition of Vectors

Triangle Law of Addition of Vectors

Triangle Law of Addition of vectors states that, if two vectors are represented in magnitude and direction by the two sides of a triangle taken in the same order, then their sum is represented by the third side taken in the reverse order.

Read more ...
Types of Vectors

Zero or Null Vector

A vector whose initial and terminal points are coincident is called a zero or null or a void vector. The zero vector is denoted by .

Read more ...
Introduction To Vectors

Physical quantities are divided into two categories: Scalar quantities and Vector quantities.

Read more ...
Inverse Trigonometrical Functions

The quantities sin−1x, cos−1x, tan−1x are called inverse circular functions. sin−1x is an angle θ, whose sine is x.

Read more ...
Solution of Triangles

A triangle has six parts or elements - the sides a, b, c and the angles A, B, C.

Read more ...
Triangle Area Formula

In any triangle ABC, area of the triangle is

Read more ...
Projection Formula

In any triangle ABC,

Read more ...
Cosine Formula

In any triangle ABC,

Read more ...
Napier’s Formula

In any triangle ABC,

Read more ...
Sine Formula

In any triangle ABC,

a/sinA = b/sin B = c/sinC = 2R

Read more ...
Equation of the Form: a cosθ + b sinθ = c

a cosθ + b sinθ = c where c2 ≤ a2 + b2 

Divide each term by √(a2 + b2)

Read more ...
General Solutions of sin θ = 0, cos θ = 0, tan θ = 0

sin θ = 0

The general solution of sin θ = 0 is given by

θ = nπ, n ∈ Z where Z is the set of all integers.

Read more ...
Trigonometrical Equations

An equation involving trigonometrical function is called a trigonometrical equation. To solve these equations, you are required to find all replacements for the variable θ that make the equations true.

Read more ...
Trigonometric Multiple Angle Identities

Identities involving sin 2A, cos 2A, tan 3A, etc. are called multiple angle identities. To derive these identities you can use sum identities.

Read more ...
Trigonometric Compound Angles: A + B and A − B

The relation f(x+ y) = f(x) + f(y) is not true for all functions of a real variable. All the six trigonometric ratios do not satisfy this relation.

Read more ...
Properties of Trigonometric Functions

Periodic Functions

A function f(x) is said to be a periodic function with period α if f(x + α) = f(x). The least positive value of α is called the fundamental period of the function.

Read more ...
Six Trigonometrical Ratios

In the co-ordinate plane, consider a point A on the positive side of x-axis. Let this point revolve about the origin in the anti-clockwise direction through an angle θ and reach the point P.

Read more ...
Quadrants, Angles & Measurement

Angle and Measurement

An angle is defined as the amount of rotation of a revolving line from the initial position to the terminal position. Counter-clockwise rotations are called positive and the clockwise are called negative.

Read more ...
Roots of Complex Number

A number ω is called an nth root of a complex number z, if ωn = z.

Read more ...
De Moivre’s Theorem

For any rational number n, cos nθ + i sin nθ is the value or one of the values of (cos θ + i sin θ)n.

Read more ...
Cube Roots of Unity

Let x be the cube root of unity, then

x = (1)1/3

x3 = 1

Read more ...
Exponential Form of Complex Number

The symbol e or exp (iθ) (called exponential of iθ) is defined by

Read more ...
Polar Form of Complex Number

Let (r, θ) be the polar co-ordinates of the point.

P = P(x, y) in the complex plane corresponding to the complex number z = x + iy.

Read more ...
Geometrical Representation of Complex Number

If real scales are chosen on two mutually perpendicular axes X′OX and Y′OY (called the x axis and y axis respectively), you can locate any point in the plane determined by these lines, by the ordered pair of real numbers (a, b) called rectangular co-ordinates of the point.

Read more ...
Modulus of Complex Number

Let z = a + ib be a complex number. The modulus or absolute value of z denoted by |z| is defined by

Read more ...
Conjugate of Complex Number

If z = a + ib, then the conjugate of z is denoted by  and is defined by

Read more ...