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, b,\[l\], m etc., are used to denote the coefficients. If the coefficient is a number, then it is called the numerical coefficient.

- Algebraic expression: A combination of constants and variables connected by some or all of the four fundamental operations +, -, x and - is called an algebraic expression.

- Here, 3 is the coefficient of\['y','y'\] is the variable and -14 is the constant.

- Terms of an algebraic expression: The different parts of the algebraic expression separated by the sign + or -, are called the terms of the expression.

- Equation: A statement of equality of two algebraic expressions involving one or more variables is called an equation.

- Solution of an equation: The value of the variable, which when substituted in the given equation, makes the two sides [L.H.S. (Left Hand Side) and R.H.S. (Right Hand Side)] of the equation equal is called the solution of the equation.

- Trial and error method: This method is used to find the solution of an equation. In this method, we give different values to the variable and check if they satisfy the equation. We continue the process of giving values to the variable until we find a value that satisfies the equation.

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 interchanged. The order of terms in a ratio is important.

- To express two terms in a ratio they should be in the same units of measurement.

- When two ratios are equal they are said to be in proportion. The symbol for proportion is:: and is read as 'is as to'.

- The two terms in the middle of a proportion are called means and the first and last terms are called extremes.

- If two ratios are to be equal or to be in proportion, their product of means should be equal to the product of extremes.

- If a : b :: c : d then the statement ad = be is true.

- If a : b and b: c are in proportion such that b2 = ac then b is called the mean proportional of a : b and b : c.

- We can get equivalent ratios by multiplying or dividing the antecedent and consequent of a ratio by the same number.

- Unitary method: The method in which we find the value of one unit first and then the value of required number of units is called the unitary method.

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.

Figure | Number of lines of symmetry |

Angle | 1 |

Scalene triangle | 0 |

Isosceles triangle | 1 |

Equilateral triangle | 3 |

Parallelogram | 0 |

Rhombus | 2 |

Isosceles trapezium | 1 |

Circle | Infinitely Many |

Semicircle | 1 |

Regular pentagon | 5 |

Regular hexagon | 6 |

- A line symmetry is closely related to mirror reflection. When dealing with mirror reflection, we have to take into account the left right changes in orientation.

- A figure may have a vertical or a horizontal line of symmetry.

- Of the digits 0 to 9, only 1, 3 and 8 have a horizontal line of symmetry, 8 has vertical line of symmetry also.

- Alphabets of English, A to...... Z have different lines of symmetry.

Practical Geometry

- We use the following mathematical instruments to construct geometrical shapes.

- Using a ruler and compasses, we can construct the following:

- A line has no definite length.

- An unlimited number of lines can be drawn, passing through a given point.

- On a single line, there exist infinite number of points.

- Intersecting Sines: If there is a point P common to two lines I and m, we say that the two lines intersect at the point P and this point P is called the point of intersection of the given lines.

- Parallel lines: The lines which do not intersect each other and do not have any point in common are called parallel lines.

- Concurrent lines: When three or more lines pass through a single point, they are called concurrent lines and the point is called the point of concurrence of the given lines.

- Collinear points: Three or more points in a plane are said to be collinear if they lie on the same line and this line is called the line of collinearity for the given points.

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.
Introduction
Raman, a student of class VI lives
in a multi-storeyed building in New Delhi. Every morning, the milkman visits
their house to deliver milk and a vendor drops newspaper at their door step.
Soon after, Bitti bai arrives. Bitti bai is a domestic help. Both his parents
are doctors. Raman gets ready for school and his driver Ramesh drops him by
car. Sometimes Raman walks to school. On the way he crosses a market. There are
many shops with shopkeepers selling all kinds of wares and services. Often a
rickshaw puller approaches Raman to offer him his services. Raman crosses the
market road carefully. It is a busy road. Life in a city is busy and fast and
everyone is in a hurry?the office-goers, school children, vendors.
MIGRATION-MOVEMENT FOR LIVELIHOOD
Many towns and cities grow with
time. With the growth of industries and shrinking of agricultural land,
millions of people move to cities and towns to seek employment every year. The
movement of people from rural areas to urban areas is called migration. Often
people are lured to migrate to urban areas as unskilled daily wage earners by
the development projects in urban areas. Having moved to the cities, the
migrants generally settle in the poor areas of the city streets. These
areas?usually lack basic infrastructure facilities?electricity, water and
drainage. In course of time these areas develop into slums. Thus, slum dwellers
are the urban poor?the daily wage workers, casual labourers, domestic servants,
rickshaw pullers, hotel boys, etc. At the same time, highly skilled and
educated people also move from one city to another in order to get better
opportunities. They are mostly well paid too. Thus, movement is there in
skilled and unskilled segment. Sometime high officials are placed in rural
areas for looking after their projects or industries there. But mostly people
tend to move from rural area to urban area in search of a better life and
livelihoods.
Migration of more...

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,
masonry, carpentry, and handicraft like pottery, basket making and weaving.
6.
People in tertiary rural occupations include
teachers, doctors, rickshaw pullers, drivers, shopkeepers, sweepers, water
bearers, toddy tappers, washermen, hair dressers, etc.
Introduction
Some people work in offices, some
in hospitals or courts, and yet others run businesses of their own. Your
parents go to work every day They do this to earn money so that they can feed
you well, educate you, and give you all the necessities of life. Means of
livelihood are different in rural areas. People do different kinds of jobs to
earn money and lead their life.
The means by which you earn money
is called livelihood. The method you adopt to earn a living is your occupation.
Thus, occupation is the means to earn a livelihood. There are various types of
occupations.
Q. What is the occupation of your
parent(s)?
TYPES OF OCCUPATIONS
The various occupations may be
classified into three sectors. These are?Primary Sector, Secondary Sector and
Tertiary Sector.
PRIMARY SECTOR
The primary sector consists of
those activities concerned with the direct extraction of materials from nature.
In this sector, people are engaged in agriculture, fishing, dairy farming and
poultry farming, mining, forestry, etc. All these occupations are related to
obtaining raw materials from the earth directly and hence are primary
occupations.
SECONDARY SECTOR
The secondary sector includes
industries that process, transform and assemble raw materials into products.
For example, the cotton textile industry makes cloth from the cotton plant; a
bakery makes bread, cakes, pizzas and biscuits from wheat; the steel industry converts
iron ore into steel. All manufacturing industries also come in this sector. The
secondary sector is dependent on the 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 the
problems related to the ward he represents.
5.
Municipal elections are held every five years.
6.
The Mayor, Deputy Mayor and Municipal Commissioner
have the authority to take decisions.
7.
The functions of the municipal bodies relate to
public health, welfare, public safety, public infrastructure works and
development activities.
8.
The municipal bodies levy different taxes such as
property tax, water tax and entertainment tax to collect funds for carrying out
their functions.
Introduction
'Urban' means pertaining to city
or town. The urban scenario is quite different from the rural one. Unlike
villages, cities are large and densely populated. Cities have modern civic
amenities like well-developed communication and transport system, water supply,
electricity, etc. However, cities are constantly grappling with problems today.
Concentration of population in urban areas has resulted in chaos like
mushrooming of slums with inhuman surroundings, degradation of the environment
leading to air, water and noise pollution, traffic jams, power cuts, crowded
markets and spread of diseases like dengue and swine flu etc. Who takes care of
such problems and ensures that the city runs smoothly? Whom do we approach when
we need help to get rid of the mosquito menace or the overflowing garbage?
Here, in this chapter, we will look at the working of the local government in
urban areas.
COMPOSITION OF URBAN
ADMINISTRATION
Cities of India have a local
government that provides necessary community services and civic amenities for
its people. The urban local governments are of three kinds and organized
according to the size of the city: Municipal Corporation or Nagar Nigam,
Municipal Council or simply Municipality or Nagar Palika and Town Committee or
Nagar Panchayat. A Municipal Corporation or Nagar Nigam administers a city that 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 at the tehsil level.
5.
The District Collector is the head of the revenue
department in a district.
6.
The Hindu Succession Amendment Act (HSAA) which came
into force in September 2005 gave the Hindu sons and daughters equal right to
ancestral property.
Introduction
Villages in India are mainly
clusters of small huts and most of the people residing here are farmers. Around
three-fourth of Indians population live in villages. This is why Gandhi at the
beginning of 20th century said, ?The soul of India lives in its villages?.
Villagers own pieces of land and grow crops in them. The local government
maintains proper records of the size of the lands and their produce. It
maintains peace and settles disputes over their land. This is how rural
administration works.
1. From the above story what
impression do you get of a patwari in a village?
2. When villagers are in trouble,
who helps them to resolve their problems?
Let us understand the Police and
Patwari and their roles to answer the above questions.
ADMINISTRATION IN A VILLAGE
Two rural government officials
play an important role in administering the villagers during conflicts: the
patwari and the police. The patwari is the land record officer, whose job is to
visit agricultural lands and maintain record of ownership and yield. The local
police solve the quarrels and are in-charge of maintaining law and order in the
village.
THE POLICE
You have seen how the police
helped Ramu, a villager. Villages are divided into areas and put under
different police stations. Each police station is responsible for maintenance
of law and order of 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.
5.
The members of the Gram Panchayat are called Panchs
and their head is called the Sarpanch.
6.
The Nyaya Panchayat is a system of dispute resolution
at village level.
7.
The responsibilities of the Panchayati Raj include
implementing development programmes and government schemes and ensuring the
welfare of the villagers, and resolve disputes.
8.
The Panchayati Raj has one-third or 33 per cent of
its seats reserved for women.
Introduction
?Independence must begin at the
bottom. Thus, every village will be a republic or Panchayat having full powers.
It follows, therefore, that every village has to be self-sustained and capable
of managing its affairs even to the extent of defending itself against the
whole world. It will be trained and prepared to perish in the attempt to defend
itself against any onslaught from without. Thus, ultimately, it is the
individual who is the unit.? ?Mahatma Gandhi
PANCHAYATI RAJ
Panchayati Raj is the first tier
or the lowest level of administration in the Indian democracy. The word
'Panchayat' means 'assembly (yat) of five' (panch). Traditionally, the
Panchayat was an assembly of five chosen elders of the village community who
settled disputes among individuals and villages. Panchayats have been the
backbone of the Indian villages.
In 1947, India became free and
chose the democratic way of governance. Mahatma Gandhi believed that India's
independence must begin from the bottom or at the grass root level. Every
village ought to be responsible for its own affairs and governance. He advocated
Panchayati Raj as the foundation of India's political system.
He called this political more...

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 alternative government available in case the electorate
desires a change.
5.
People express their opinion about government
policies through media or by organizing rallies and hartals, thus making
government accountable to the public.
6.
Equality and Justice are the two elements that make a
democracy successful.
Introduction
The idea of
democracy is not simple. To say it is "the rule by the people? tells very
little about it. What we call ?democracy? is a complex idea, and to understand
it we must explore a range of ideas that underlie it. So let us read about the
elements of democracy in an attempt to understand it better.
First of all we
must know that democracy is of two types: direct democracy and representative
democracy. Direct democracy is a form of governance in which people
collectively make decisions for themselves, rather than having their off airs
decided by representatives. Direct democracy is classically termed 'pure
democracy?. Switzerland has practised direct democracy for 150 years. However,
most of us would find this practice quite\[dauntin{{g}^{1}}\]. Surely it would
lead to chaos if it is a big nation. Hence, large nations like India,
Australia, Canada, the United Kingdom and South Africa opt for representative
democracy. Here decisions are made by the representatives who are elected by
the people. In this chapter, we will read about 'representative democracy',
this is what we mean by democracy today and most of the modern-day democracies
are representative democracies.
KEY ELEMENTS OF A
DEMOCRACY
Key elements of a
democracy include:
? Participation
and Accountability
? Resolution of
Conflicts
? Equality and
Justice
Know a Little
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