# 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.

If A, B, C and D are four points in a plane such that no three of them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, then the closed figure made up of these four line segments is called a quadrilateral with vertices A, B, C and D.

### Medians of a Triangle

A line joining a vertex to the mid point of the opposite side of a triangle is called its median. Three medians can be drawn in a triangle.

### Altitudes of a Triangle

Perpendicular drawn from a vertex of a triangle to the opposite side is called its altitude. There are three vertices in a triangle, so you can draw three of its altitudes.

### Perpendicular Bisectors of Sides of a Triangle

A line which bisects a side of a triangle at right angle is called the perpendicular bisector of the side. Since a triangle has three sides, you can draw three perpendicular bisectors in a triangle.

### Angle Bisectors of a Triangle

A line which bisects an angle of a triangle is called an angle bisector of the triangle. Since a triangle has three angles, you can draw three angle bisectors in it.

### Concurrent Lines

Two lines in a plane can either be parallel or intersecting. Three lines in a plane may:

### Congruence of Triangles

Two figures, which have the same shape and same size are called congruent figures and this property is called congruence. Congruent figures, when placed one over another, exactly coincide with one another or cover each other. In other words, two figures will be congruent, if parts of one figure are equal to the corresponding parts of the other.

### Types of Triangle

Triangle is the simplest polygon of all the closed figures formed in a plane by three line segments. It is a closed figure formed by three line segments having six elements - three angles (i) ∠ABC or ∠B (ii) ∠ACB or ∠C (iii) ∠CAB or ∠A and three sides - (iv) AB (v) BC (vi) CA.

### Pair of Angles

Each pair has a common vertex O and a common side OA in between OB and OC. Such a pair of angles is called a pair of adjacent angles.

### Angle

An angle is a figure consisting of two rays starting from a common point. An angle is measured in degrees.

### Point

If you press the tip of a pen or pencil on a piece of paper, you get a fine dot, which is called a point. A point is used to show the location and is represented by capital letters - A, B, C.

### Law of Exponents

If a is a rational number, multiplied by itself m times, it is written as am. a is called the base and m is called the exponent.

### Irrational Numbers

A decimal expansion which is neither terminating nor is repeating represents an irrational number.

### Decimal Form of Rational Number

The process of expressing a rational number into decimal form is to carry out the process of long division using decimal notation.

### Integration by Partial Fractions

If the integrand (the expression after the integral sign) is in the form of an algebraic fraction and the integral cannot be evaluated by simple methods, the fraction needs to be expressed in partial fractions before integration takes place.

### Sets

A set is well defined collection of distinct objects (also called as elements). Sets are conventionally denoted with capital letters. The elements of the sets are denoted by small letters. Sets A and B are equal if and only if they have precisely the same elements.

### Sequence and Series

A sequence is an arrangement of a number in a definite order according to some rule. A sequence containing a finite number of terms is called a finite sequence. Let a1, a2, a3, ... be the sequence, then the sum expressed as a1+a2+a3+ ... is called series.

### Exponents and Powers

Very large numbers are difficult to read, understand, compare and operate upon. To make all these easier, you can use exponents, converting many of the large numbers in a shorter form.

### Real Numbers

All real numbers can be classified into two types: Rational and Irrational.

### Plane & Solid Geometry

Plane Geometry is about flat shapes (1D and 2D) like lines, circles and triangles. Solid Geometry is about three dimensional (3D) objects like cubes, prisms, cylinders and spheres.

### Ratio

The ratio of two qualities a and b in the same units, is the fraction a/b and we write it as a:b. In the ratio, a:b, we call a as the first term of antecedent and b, the second term consequent. For example, the ratio 5:9 represents 5/9 with antecedent 5 and consequent 9.

### Statistics

Statistics is the area of study dealing with the presentation, analysis and interpretation of data. Facts or figures, collected with a definite purpose, are called data. Data can be presented graphically in the form of bar graphs, histograms and frequency polygons.

### Algebraic Expressions

Expressions are formed from variables and constants. Terms are added to form expressions. Expressions that contain exactly one, two and three terms are called monomials, binomials and trinomials respectively. In general, any expression containing one or more terms with non-zero coefficients (and with variables having non-negative exponents) is called a polynomial.

### Mensuration: Areas & Volumes

Perimeter is the distance around a closed figure while area is the part of plane or region occupied by the closed figure.

### Simple and Compound Interest

When you borrow money, you have to return the amount within a specific period, along with some extra money. This extra money is called Interest. The rate at which the interest is calculated on the principal is called Rate of Interest.

### Factorial Notation

Let n be positive integer.Then factorial n denoted by n! is defined as n! = n(n-1)(n-2). . . . . . . .3.2.1.

### Basics of Fractions OR Chain Rule

When a fraction has its numerator greater than the denominator, its value is greater than one. It is called greater fraction. Whenever a number (say x) is multiplied by a greater fraction, it gives a value greater than itself.

### Logarithms

If ax = b, you want to write x in terms of a & b, x = logab. It is read as log b to the base a.

### Fractions and Decimals

A fraction is a part of the whole (object, thing, region). For example, 5/12 is a fraction. Here 12 is the number of equal part into which the whole has been divided, is called denominator and 5 is the number of equal parts which have been taken out, is called numerator.