# Review Concepts

Quick review of important concepts asked in the UPSC exams.

Concepts Index

### Probability

Probability is that branch of Mathematics which deals with the measure of uncertainty in various phenomenon that gives several results or outcomes instead of a particular one.

### Statistics

Statistics is a branch of Mathematics which deals with collection, presentation, analysis, interpretation of data and drawing of inferences or conclusions there from.

### Tigonometry

Trigonometry is that branch of Mathematics which deals with the measurement of the sides and the angles of a triangle and the problems related to angles. Ratios of the sides of a triangle with respect to its acute angles are called trigonometric ratios.

### Mensuration of Solid Figures

Solid figures include cube, cuboid, cylinder, cone, sphere, and hemisphere.

### Mensuration of Plane Figures

Plane figures include triangle, circle, square, rectangle, and parallelogram.

### Circles

A circle is a collection of all points which are at a constant distance from a fixed point. The fixed point is called the centre of the circle. A line segment joining centre of the circle to a point on the circle is called radius of the circle.

Quadrilateral is a plane, closed, geometric figure with four sides. A quadrilateral has four sides - AB, BC, CD and DA, four angles - ∠A, ∠B, ∠C, ∠D, two diagonals - AC and BD, and four vertices - A, B, C and D.

### Properties of Triangles

The angles opposite to equal sides of a triangle are equal. The sides opposite to equal angles of a triangle are equal.

### Concurrent Lines

Two lines can either be parallel or intersecting. Three lines may be parallel to each other, intersect each other in exactly one point, intersect each other in two points (transversal), or intersect each other at most in three points.

### Triangles

Triangles is a a plane figure bounded by three line segments. The sum of the three interior angles of a triangle is 180º.

### Lines and Angles

Line Segment is the portion of the line between two points A and B. A line segment has two end points. Ray is a line segment AB when extended in one direction.

### Arithmetic Progression

Sequence or progression is a group of numbers forming a pattern. Arithmetic Progression (AP) is a progression in which each term, except the first, is obtained by adding a constant to the previous term.

### Linear Equations

Linear polynomial is a polynomial having degree 1. Equation means two expressions separated by sign of equality. Thus, linear equation involves only linear polynomials - An equation in which the highest power of the variable is 1.

### Algebraic Expressions and Polynomials

Algebraic expressions are a combination of constants and variables, connected by any or all of the four fundamental operations (+, -, ×, ÷).

### Number System

Natural Numbers (N) are Counting numbers  - 1, 2, 3, 4, and so on. The smallest natural number is 1. Whole Numbers (W) are Natural numbers including 0 - 0, 1, 2, 3, 4 , and son on. The smallest whole number is 0.

### Governance at State Level

India is a Federation having governments at two levels - State level and Union or Central level. The three branches of government - executive, legislature and judiciary exist and function at both the levels.

### Local Government

Local Government is a government of the local people. Being located nearest to the local people, local government institutions are under constant observation of the society. The Government of India has empowered the institutions by 73rd and 74th Constitutional Amendment Acts 1992, so that they may work for the welfare of the local people in a more effective manner.

### Fundamental Rights and Duties, Welfare State

In a Democratic Country like India certain basic and fundamental rights have been granted to every citizen, but in many parts of the world people are still struggling for these rights.

### Salient Features of Indian Constitution

A Constitution contains basic or fundamental laws of the land and establishes Rule of the Law. Indian Constitution was prepared by a representative body, known as the Constituent Assembly.

### Constitution of India

Constitution is a legal document which determines the structure of the government and direction to which society is to move on. A democratic constitution represents consensus among the people on certain rules, principles, procedures and ideals and guides the social and political institutions.

### Indian National Movement

Anti-Colonial Movement gave rise to a feeling of Nationalism. In 1885 Indian National Congress was founded by A.O. Hume. There were phases of Naram Dal and Garam Dal. The Partition of Bengal in 1905 gave rise to a strong national movement. The Non Cooperation Movement, Civil Disobedience and finally Quit India Movement resulted in Independence of India and of course its partition.

### Resistance to the British Rule

Exploitation of natural and human resources by British led to rise of Popular Resistance Movements mainly by Peasants, Tribals and Sainiks. The most important Popular Resistance to the British rule during the 19th century was the revolt of 1857. There was a sense of self confidence that gave an impact to National Awakening.

### Religious and Social Reformers of 19th Century

In the first half of 19th century, the Indian society was backward due lack of education and subordination of women. This prevented society’s progress. Many reformers came up during this period who contributed to religious and social awakening helped in transforming the society for betterment.

### Impact of British Rule in India

British Rule had a tremendous effect on Indian society, economy and culture. It also gave rise to a sense of nationhood and a spirit of Nationalism arose which resulted in National Awakening and a feeling of revolt against Britishers.

### World Wars I and II

Division of colonies in Asia and Africa created conditions of war. In the last quarter of the 19th century, Germany became the main competitor of England.

### Imperialism and Colonialism

Industrial Revolution brought social and economic changes that transformed the agricultural society to a modern industrial society. The industrialised nations needed raw materials for their industries as well as markets for their finished good. The necessitiated colonization of under developed countries.

### Revolutions of the Modern World

There was a very strong dissatisfaction with political leadership and people started demanding more participation in the affairs of the State.

### Modern World

With the decline of feudalism, the restrictions on peasants become a thing of the past simultaneously, the period witnessed the rise of powerful merchant class, which financed discoveries of new lands. These, with other factors, brought about the Industrial revolution which led a sea change throughout the world. This was the begining of the Modern Age.

### Medieval World

There was transformation of European Society after the downfall of the Roman Empire, and the birth of a new religion called Islam which led to the founding of a vast empire that originated in West Asia and spread out over a large part of the world.

### Ancient World

Human beings emerged about two million years ago. They resembled apes, who lived in caves or on tree tops. Prehistory is the period for which no written records are available. History refers to the period of history for which written records are available.