6th Class

 Algebra      
  • Algebra is a branch of mathematics in which Arithmetic is generalised.
 
  • We use lower case English alphabets called literals to represent quantities instead of particular numbers. Literals are also used for representing unknown quantities.
 
  • Literals take different values according to the problem. So, they are called variables.
 
  • Constant: A symbol having a fixed value is called a constant. Usually all numbers are constants. But sometimes, 'c', 'k' etc., are used as symbols to denote constant.
 
  • Coefficient: In the product of a variable and a constant, each is called the coefficient of the other. Sometimes, letters such as a, more...

Ratio and Proportion        
  • Ratio is a method of comparing two quantities of the same kind by division.
 
  • The symbol used to represent a ratio is: and is read as 'is to'.
 
  • A ratio can be expressed as a fraction.
 
  • A ratio is always expressed in its simplest form.
 
  • A ratio does not have any unit, it is only a numerical value.
 
  • A ratio consists of two terms. The first term is called the antecedent and second term is called the consequent.
 
  • A ratio can be written in its simplest form by dividing the antecedent and consequent by their H.C.F.
 
  • The antecedent and consequent of a ratio cannot be more...

 Symmetry        
  • A figure has a line symmetry if a line can be drawn dividing the figure into two identical parts. The line is called a line of symmetry.
 
  • A line segment is symmetrical at its perpendicular bisector.
 
  • A figure may have no line of symmetry, only one line of symmetry, two lines of symmetry or multiple lines of symmetry.
  more...
 Practical Geometry      
  • We use the following mathematical instruments to construct geometrical shapes.
(i)   A graduated ruler or scale    (ii) The compasses      (iii) The divider   (iv) Set - squares                 (v) The protractor  
  • Using a ruler and compasses, we can construct the following:
(i) A circle of a given radius. (ii) A line segment of a given length. (iii) A copy of a given line segment. (iv) A perpendicular to a line through a point (a) on the line.                (b) not on the line. (v) The perpendicular bisector of a line segment of given length. (vi) An angle of a given measure. (vii) A copy of a given angle. (viii) The bisector of a more...

  Urban Livelihoods   Summary   1.            With the growth in industries and the shrinking of agricultural income, people are migrating from rural areas to urban areas. 2.            About a quarter of India's population is urban as there are many opportunities for jobs here. 3.            People in towns and cities are involved in manufacturing and in selling and service sectors, i.e. in secondary and tertiary occupations and in primary occupation like farming. 4.            Urban people are either self-employed, fixed monthly salaried or daily wage earners.   Rural Livelihoods   Summary   1.            Occupation is of three types: primary occupation, secondary occupation and tertiary occupation. 2.            Farming, animal husbandry and fishing are primary rural occupations. 3.            A farmer grows crops in the fields, manages orchards or vineyards, and is of four types: large farmers, medium farmers, marginal farmers and landless farmers. 4.            Poultry and dairy farmers breed and raise livestock for eggs, meat and milk. 5.            Secondary rural occupations include brick making, more...

  Urban Administration   Summary   1.            Urban local administrative units provide basic infrastructure and services in cities. 2.            They are classified into three major categories: Nagar Nigam governing large cities, Nagar Palika governing smaller cities and Nagar Panchayat governing small towns. 3.            The area under a Nagar Nigam which is also called Municipal Corporation and is further divided into Wards, which may be grouped together into Ward Councils. 4.            Each ward elects its representative for the Municipal Corporation. This representative is called Ward Councillor. He looks after more...

  Rural Administrations   Summary   1.            Two rural government officials administer a village - the patwari and the police. 2.            The in-charge of the police station of an area is the Station House Officer (SHO). He solves cases of burglary, quarrels, etc., in that area. 3.            The patwari is the village accountant who maintains land records by visiting agricultural lands, preparing land maps, writing records of land ownership and crop grown in every harvest, etc. 4.            The patwari reports to the tehsildar who is the revenue officer more...

  Panchayati Raj   Summary   1.            Panchayati Raj is the three-tier structure working as the Gram Panchayati at the village level, the Block Samiti at the block level and the Zila Parishad at the district level. 2.            The Panchayati system at village level consists of Gram Panchayat, Gram Sabha and Nyaya Panchayat. 3.            Gram Panchayat is a body of elected representative governing at village level.    4.            The Gram Sabha is the electorate of Gram Panchayat.   Key Elements of a Democratic Government   Summary   1.            Democracy is the government run by the people. 2.            There are two types of democracies - direct democracy and representative democracy. Switzerland has a direct democracy. India has a representative democracy. 3.            The main features of a representative democracy are: free and fair elections, Adult Franchise, rule of constitutional law and protection of citizen?s rights.  4.            In India, the general election is held every five years and there is an more...


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Figure Number of lines of symmetry
Angle   1
Scalene triangle 0