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CROP PRODUCTION AND MANAGEMENT | Study
MICROORGANISMS : FRIEND AND FOE | Study
COAL AND PETROLEUM | Study
CONSERVATION OF PLANTS AND ANIMALS | Study
COMBUSTION AND FLAME | Study
REPRODUCTION IN ANIMALS | Study
REACHING THE AGE OF ADOLESCENCE | Study
FORCE AND PRESSURE | Study
FRICTION | Study
SOUND | Study
CHEMICAL EFFECTS OF ELECTRIC CURRENT | Study
SOME NATURAL PHENOMENA | Study
LIGHT | Study
Rational Numbers | Study
Linear Equations in One Variable | Study
Understanding Quadrilaterals | Study
Data Handling | Study
Squares and Square Roots | Study
Cubes and Cube Roots | Study
Comparing Quantities | Study
Algebraic Expressions and Identities | Study
Mensuration | Study
Exponents and Powers | Study
Direct and Inverse Proportions | Study
CROP PRODUCTION AND MANAGEMENT | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage In order to provide food for a large population – regular production, proper management and distribution of food is necessary. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Crop : When plants of the same kind are grown and cultivated… readmore
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In order to provide food for a large population – regular production, proper management and distribution of food is necessary. (Scroll down till end of the page)
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Crop : When plants of the same kind are grown and cultivated at one place on a large scale,
it is called a crop.In India, crops can be broadly categorised into two types based on seasons – Rabi and Kharif crops. Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds are sown after selection of healthy seeds.
Sowing is done by seed drills.
Soil needs replenishment and enrichment through the use of organic manure introduction of new crop varieties.
Basic practices of crop production:
(i) Preparation of Soil: One of the most important tasks in agriculture is to
turn the soil and loosen it.The process of loosening and turning of the soil is
called tilling or ploughing.(ii) Sowing: Sowing of seeds at appropriate depths and distances gives good yield.
Good variety of seeds is sown after selection of healthy seeds. Sowing is done by seed
drills.(iii) Adding Manure and Fertilisers Soil needs replenishment and enrichment through the use of organic manure and fertilisers.
Use of chemical fertilisers
fertilisers has increased tremendously with the introduction of new crop varieties.
Fertiliser: The inorganic compounds containing nutrients such as nitrogen, potassium and phosphorus. They are made in the factories.
Example: ammonium sulphate, potash, etc.
Manure: A natural substance prepared from decomposition of plant and animal wastes (cow dung, animal bones, dead leaves, dead insects and vegetable wastes) by t(he action of microbes.
iv) Irrigation : Supply of water to crops at appropriate intervals is called
irrigation. Method of Irrigation:
(a)Tradition methods of Irrigation: Moat, Chain pump, Dheki, Rahat.(b) Modern methods of Irrigation: Sprinkler system, Drip
(v) Protection from Weeds: Weeding involves removal of unwanted and
uncultivated plants called weeds.(vi) Harvesting: Harvesting is the cutting of the mature crop manually or by
machines.(vii) Storage Proper storage of grains is necessary to protect them from pests
and microorganisms.Harvested food grains normally contain more moisture than
required for storage.Large scale of storage of grains is done in silos and granaries to
pest like rats and insects.Farmers store grains in jute bags or metallic bins.
Food is also obtained from animals for which animals are reared.
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Advanced Tools For Study Assess Interact MICROORGANISMS : FRIEND AND FOE | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Micro-organisms: Micro-organisms are too small and are not visible to the un aided eye. They can survive under all types of environment, ranging from ice cold climate to hot springs and deserts to marshy lands. They are also found inside the bodies of animals including humans.… readmore
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Micro-organisms: Micro-organisms are too small and are not visible to the un aided eye.
They can survive under all types of environment, ranging from ice cold climate to hot springs and deserts to marshy lands.
They are also found inside the bodies of animals including humans. (Scroll down till end of the page)
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Micro-organisms are found in air, water and in the bodies of plants and animals.They may be unicellular or multicellular.
Micro-organisms are classified into four major groups. These groups are bacteria,fungi, protozoa and some algae.
Viruses are quite different from other micro-organisms. They reproduce only inside
Micro-organisms: Friend and Foe
Based on the significance, micro-organisms can be useful or harmful.
Uses Of Microorganisms
Protozoan cause serious diseases like dysentery and malaria.
Some bacteria and blue green algae present in the soil fix nitrogen from the atmosphere and convert into nitrogenous compounds.
Certain bacteria convert compounds of nitrogen present in the soil into nitrogen gas which is released to the atmosphere.
Pathogens: Some of the microorganisms cause diseases animals. Such disease causing microorganisms are called pathogens.
Cleaning of Environment: The microorganisms decompose dead organic waste
of plants and animals converting them into simple substances. These substances are again used by other plants and animals.Microorganisms can be used to degrade theharmful and smelly substances and thereby clean up the environment.
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Advanced Tools For Study Assess Interact COAL AND PETROLEUM | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Natural Resources: Resources include everything provide by the nature. They form the wealth of a country. Types of Natural Resources:(i) Inexhaustible: There are some resources that are present unlimited in nature and will not be exhausted even if used continuously. Example: Sunlight, Air. (Scroll down till… readmore
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Natural Resources: Resources include everything provide by the nature. They form the wealth of a country.
Types of Natural Resources:
(i) Inexhaustible: There are some resources that are present unlimited in nature and will not be exhausted even if used continuously.Example: Sunlight, Air. (Scroll down till end of the page)
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Natural Resources: Resources include everything provide by the nature. They form the wealth of a country.
Types of Natural Resources:
(i) Inexhaustible: There are some resources that are present unlimited in nature and will not be exhausted even if used continuously.Example: Sunlight, Air.
(ii) Exhaustible: These resources are limited and can soon get exhausted because of Coal, petroleum and natural gas are fossil fuels.
Fossil fuels were formed from the dead remains of living organisms millions of yearsago.
Fossil fuels are exhaustible resources.
Coke, coal tar and coal gas are the products of coal.
Petroleum gas, petrol, diesel, kerosene, paraffin wax, lubricating oil are
obtained by refining petroleum.Coal and petroleum resources are limited.
We should use them judiciously.
Petroleum is mixture of various constituents such as petroleum gas, petrol, diesel, lubricating oil, paraffin wax, etc.
Refining: Refining is the process of refracting the various constituents / fractions of petroleum.
It carried out in a petroleum refinery.
Natural Gas: A very important fuel as it easy to transport through pipes and can be compressed and stored under high pressure as Compressed Natural Gas (CNG).
It causes no pollution and has high calorific value.
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Advanced Tools For Study Assess Interact CONSERVATION OF PLANTS AND ANIMALS | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Biodiversity: Occurrence of innumerable types of organisms and the whole range of their varieties (biotypes) adapted to different climates, environments and areas. Wildlife sanctuary, national park and bio-sphere reserve are names given to the areas meant for conservation and preservation of forest and wild animals. (Scroll… readmore
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Biodiversity: Occurrence of innumerable types of organisms and the whole range of their varieties (biotypes) adapted to different climates, environments and areas. Wildlife sanctuary, national park and bio-sphere reserve are names given to the areas meant for conservation and preservation of forest and wild animals. (Scroll down till end of the page)
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Biodiversity refers to the variety of living organisms in a specific area.
Plants and animals of a particular area are known as the flora and fauna of that area.
Endemic species are found only in a particular area.
Endangered species are those which are facing the danger of extinction.
Red Data Book contains a record of endangered species.
Migration is the phenomenon of movement of a species from its own habitat to some other habitat for a particular time period every year for a specific purpose like breeding.
We should save, reuse and recycle paper to save trees, energy and water.
Reforestation is the restocking of destroyed forests by planting new trees.
Flora: Different types of plants belonging to an area.
Example: Silver ferns, sal, teak, mango, etc.
Fauna: All animals found in an area.
Example: dog, frog, insects, bull, jackal, etc.
Endemic Species: Species of plants and animals found exclusively in a particular area.
These are not naturally found anywhere else.
Extinct Species: Species of plants and animals which have already been lost.
Type of Threatened Species:
(ii) Vulnerable Species: A vulnerable species is a species of animals or plants which are likely to become endangered unless something changes.
Example: Chinkara deerand black buck, golden langur, etc
(iii) Rare Species: Species whose population are originally small and scattered in the National Parks: Protective areas reserved exclusively for the betterment of the wildlife. These are established at the approval of legislature.Example: Hazaribagh National Park in Jharkhand, Desert National Park in Rajasthan.
Sanctuaries: Hunting prohibited areas set up by government are known as sanctuaries. These are only for the protection of wild animals.
Example: Jaldapara in Madarihat (West Bengal), Keoladeo Ghana in Bharatpur (Rajasthan)
igration: The regular, periodic, two way movements of birds and some animals from their place of residence to some other place along well defined routes. It is linked to seasonal factors, breeding, shortage of foods, etc.The sanctuary is known for the migratory birds
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Advanced Tools For Study Assess Interact COMBUSTION AND FLAME | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Combustion: The process of burning a substance in the presence of air (oxygen) andundergoes a chemical reaction to produce heat and light. The substances which burn in air are called combustible. Oxygen (in air) is essential for combustion. During the process of combustion, heat and light… readmore
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Combustion: The process of burning a substance in the presence of air (oxygen) andundergoes a chemical reaction to produce heat and light. The substances which burn in air are called combustible.
Oxygen (in air) is essential for combustion. During the process of combustion, heat and light are given out. Ignition temperature is the lowest temperature at which a combustible substancecatches fire.
Types of combustion: The type of combustion differs depending on the type of fuel. (Scroll down till end of the page)
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Based on nature and intensity combustions are classified into three types. They are:
(i) Rapid combustion
(ii) Spontaneous combustion
(iii) ExplosionFlame: It is a zone or burning vapour. The substances which vaporise during
burning give flames.Example: Kerosene oil and molten wax. Inflammable substances have very low ignition temperature. Fire can be controlled by removing one or more requirements essential for producing fire. Water is commonly used to control fires. Water cannot be used to control fires involving electrical equipments or oils.
There are three different zones of a flame – dark zone, luminous zone and non-luminous zone.
Fuel is any material that is burned to obtain energy that can be used to heat or
A good fuel must:Oxides of sulphur and nitrogen produced by the burning of coal, diesel and
petrol cause Acid rain which is harmful for crops, buildings and soil.Be readily
available. Be cheap. Burn easily at a moderate rate.Produce a large amount of heat. • Not leave behind any undesirable
Fuels differ in their efficiency and cost. Fuel efficiency is expressed in terms of its calorific value which is expressed in
units of kilo joule per kg.Types of Fuels:
(i) Solid Fuels: Combustible substances which are solid at room
temperature.Example: coal, coke, wood, charcoal, etc. (ii) Liquid fuels: Volatile liquids which produce combustible vapour. Example:
Petrol,kerosene, alcohol, diesel, etc. (iii) Gaseous fuels: Combustible gases or mixture of combustible gases. Example:
Effects of Burning of Fuels:
(i) Carbon fuels like wood, coal petroleum release un burnt carbon particles. Theseare dangerous pollutants causing respiratory diseases, such as asthma.(ii) Incomplete combustion of carbon fuels gives carbon monoxide which
is apoisonous gas.(iii) Increased concentration of carbon dioxide in the air is believed to cause
globalwarming.(iv) Oxides of Sulphur and nitrogen dissolve in rain water and form acids. Such
rain is Un burnt carbon particles in air are dangerous pollutants causing respiratoryproblems.Incomplete combustion of a fuel gives poisonous carbon monoxide gas. Increased percentage of carbon dioxide in air has been linked to global warming.
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Advanced Tools For Study Assess Interact REPRODUCTION IN ANIMALS | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Reproduction is a process in which the organisms produce the young ones of their own kind. There are two modes by which animals reproduce. These are: (i) Sexual reproduction, and (ii) Asexual reproduction (Scroll down till end of the page) Study Tools Audio, Visual & Digital… readmore
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Reproduction is a process in which the organisms produce the young ones of their own kind. There are two modes by which animals reproduce.
These are: (i) Sexual reproduction, and (ii) Asexual reproduction (Scroll down till end of the page)
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Sexual Reproduction
Reproduction resulting from the fusion of male and female gametes is called sexual reproduction.
The reproductive organs in the female include ovaries, oviducts and uterus.
The reproductive organs in male include testes, sperm ducts and penis.
The ovary produces female gametes called ovum and the testes produce male gametes called sperms. The fusion of ovum and sperm is called fertilization.
zygote: The fertilized egg is called a zygote.
internal fertilization: Fertilization that takes place inside the female body is called internal fertilization. This is observed in human beings and other animals such as hens, cows and dogs.
external fertilization: Fertilization that takes place outside the female body is called external fertilization. This is observed in frogs, fish, starfish, etc.
The zygote divides repeatedly to give rise to an embryo. The embryo gets embedded in the wall of the uterus for further development.
The stage of the embryo in which all the body parts are identifiable is called foetus.
Animals such as human beings, cows and dogs which give birth to young Ones.
Asexual Reproduction: The type of reproduction in which only a single parent is involved is called asexual reproduction. The transformation of the larva into adult through drastic changes is called Asexual Reproduction
budding: In hydra, new individuals develop from buds. This method of asexual reproduction is called budding.
binary fission.: Amoeba reproduces by dividing itself into two. This type of asexual reproduction is called binary fission.
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Advanced Tools For Study Assess Interact REACHING THE AGE OF ADOLESCENCE | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Humans become capable of reproduction after puberty. Puberty sets in between the ages of 11 years and 19 years. These children are called adolescents. The onset of puberty brings about growth of the reproductive organs. Hairs grow at various places on the body. Breasts develop in… readmore
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Humans become capable of reproduction after puberty. Puberty sets in between the ages of 11 years and 19 years. These children are called adolescents.
The onset of puberty brings about growth of the reproductive organs. Hairs grow at various places on the body.
Breasts develop in girls.
Facial hair (moustache and beard) appear in boys.
Voice of boys become hoarse as voice box enlarges during adolescence.
Children gain height during adolescence.
Puberty: It is the time when sex organs begin to work.
It brings about growth in reproductive organs and changes in the body.
Puberty starts at the beginning of adolescence. (Scroll down till end of the page)
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Reaching the age of Adolescence
The onset of puberty starts much earlier in girls, between 8 and 13 years of age, whereas it starts between 10 and 14 years of
age in boys and lasts upto 2 to 4 years.Changes during Puberty:
(i) Increase in Height: The bones of the legs and arms elongate and the individual becomes tall and lanky.(ii) Changes in Body Shape: In boys, the body becomes more muscular, the shoulder becomes wider.
In girls, the body shows curves in certain parts and the region below the waist become wider and broader.
(iii) Change in Voice: In boys, the voice becomes hoarse and heavy due to the extra growth of larynx (voice box).
In girls, the voice becomes high pitched and shriller.
(iv) Sweat and sebaceous glands: They become more active and secrete more.
(v) Emotional aspects develop.
Periodic cycle of 28 days. The onset of puberty and maturity of reproductive parts are controlled by hormones.
Hormones are secretions of endocrine glands which pour them directly into the blood stream.
Pituitary gland secretes hormones which include growth hormone and hormones that make other glands such as the testes, ovaries, thyroids and adrenals, secrete hormones.
Pancreas secretes insulin, thyroid produces thyroxin and adrenals produce adrenalin.
Testosterone is the male hormone and estrogens, the female hormone.
The uterine wall in females prepares itself to receive the developing fertilised egg.
Menstruation: In case there isno fertilisation, the thickened lining of the uterine wall breaks down and goes out of the body along with blood.This is called menstruation.
Sperm and Ovum fuses together to form a zygote.
Sex chromosomes in sperms determine the baby’s gender. Humans have 23 pairs of chromosomes in each cell.
A pair of chromosome forms the sex chromosomes. Males carry XY and females carry XX chromosomes.
If a sperm carrying X fertilises the ovum with X chromosome, then the resulting baby is a girl.
If a sperm carrying Y chromosome fertilises the ovum with X chromosome, then the resulting baby is a boy.
Hence, males are responsible for the gender of the newly formed babies, Not Women.
Reproductive Health:
It is important to eat balanced food and maintain personal hygiene during adolescence.Cleaning of private parts is important to prevent possible infections.
The activity of sweat glands increases in puberty and releases bad odour from the body.
Thus frequent bathing is necessary. Physical exercise keeps the body fit and healthy as it releases lot of sweat.
Peer pressure is best addressed by self-confidence and a healthy lifestyle.
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Advanced Tools For Study Assess Interact FORCE AND PRESSURE | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Force: A push or a pull, that changes or tends to change the state of rest or of uniform motion of an object or changes its direction or shape. A force arises due to the interaction between two objects. Force has magnitude as well as direction.Therefore… readmore
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Force: A push or a pull, that changes or tends to change the state of rest or of uniform motion of an object or changes its direction or shape.
A force arises due to the interaction between two objects.
Force has magnitude as well as direction.Therefore force is a vector quantity.
The SI unit of force is newton (Scroll down till end of the page)
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A change in the speed of an object or the direction of its motion or both implies a change in its state of motion.
Force acting on an object may cause a change in its state of motion or a change in its shape.
Contact Non Contact Forces:
A force can act on an object with or without being in contact with it. Based on Contact the forces are classclassified as Contact Forces and Non Contact Forces.
Contact Forces: The forces act on a body when the source of force touches the body directly.
The point where the force is applied on an object is called the point of application of force (or point of contact).
Examples of Contact Forces:
(i) Muscular Force: The force exerted by the muscles of the body.
We use force acted by muscles of animals like Humans, bullocks, horses and camels to get our activities done.
(ii) Mechanical Force: The force acted by a machine.
Non-Contact Forces:
Non-Contact Forces: Forces which do not involve physical contact between two bodies on which they act.
Examples of Non-Contact Forces:
(i) Magnetic Force: A magnet exerts a non-contact force on objects made of iron, steel, cobalt or nickel.
(ii) Electrostatic Force: The force which result due to repulsion of similar charges or attraction of opposite charges.
(iii) Gravitational Forces: The force that exists between any two bodies by virtue of
Pressure
Pressure: Thrust acting per unit surface area is called pressure.
Thrust
Thrust is the force acting on an object perpendicular to its surface.
In SI system, pressure is measured in newton per square metre which is equal to 1 pascal (Pa).
Like solids, fluids (liquids and gases) also exert pressure.
A solid exerts pressure only in the downward direction due to its weight, whereas liquids and gases exert pressure inall directions.
Hence liquids and gases exert pressure on the walls of their container.
Atmospheric Pressure
Ttmosphere: The thick blanket of air that covers the earth is termed atmosphere.
The pressure exerted by the atmosphere is called atmospheric Pressure.
The tremendous atmospheric pressure surrounding us is not felt by us because the fluid pressure inside our bodies counter-balances the atmospheric pressure around us.
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Advanced Tools For Study Assess Interact FRICTION | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Friction: Friction is the force that resists the motion of one object against another. It is the force felt between two surfaces when one attempts to slide against the other. Causes of Friction: Friction exists between two surfaces due to irregularities on the surfaces of the objects… readmore
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Friction:
Friction is the force that resists the motion of one object against another. It is the force felt between two surfaces when one attempts to slide against the other.
Causes of Friction: Friction exists between two surfaces due to irregularities on the surfaces of the objects in contact, interlocking of micro-level irregularities of the two surfaces and ploughing of harder surfaces into smoother surfaces.
Factors Affecting Friction:
(i) Roughness of the surface.
(ii) The extent to which the two surfaces press against each other.
(iii) Nature of the surface· (Scroll down till end of the page)
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Types of Friction: Friction is classified into three types as: Static Friction, Sliding Friction, Rolling Friction.
(i) Static Friction: When a body is at rest, the force of friction is called the static friction and is always equal and opposite to the applied force.limiting friction: The force of friction which acts when the body is just at the verge of sliding on the surface is called limiting friction.
Motion between two contacting surfaces
(ii) Sliding friction: The friction force which opposes the actual relative sliding motion between two contact surfaces.
Sliding friction is smaller than static friction.
(iii) Rolling Friction: The frictional force that exists between two surfaces when a body rolls over the other.
Rolling friction is smaller than sliding friction.
Static friction > Sliding friction > Rolling friction
Effects of Friction
(i) Friction produces heat.
(ii) Friction causes wear and tear.
(iii) Friction opposes motion.
Advantages of Friction
(i) Friction between pen and paper enables us to write on the paper.
(ii) Friction between our feet and the ground allows our movements like standing, walking and running.
(iii) Friction between the surface of the road and tyres of our vehicles allow the vehicles to move without slipping.
Disadvantages of Friction:
(i) Friction causes moving objects to stop or slow down.
(ii) Friction produces heat causing wastage of energy in machines.
(iii) Friction causes wear and tear of moving parts of machinery, soles of shoes, etc.
Friction is a necessary Evil:
As friction is advantageous to us it is considered as a friend but, due to its disadvantages it is a foe.
Depending on the circumstance, friction can be a help or a hindrance.
Thus it is a necessary evil.
Increasing Friction: By pressing the surfaces together more strongly.
For example, when brakes are applied on a bicycle or car, the brake pads press against a moving part of the wheel and the force of friction increases.
Friction can be increased by increasing the roughness of the surfaces in contact.
For example, treading of shoes and tyres is done to increase friction.
Reducing Friction: Friction between the sliding surfaces of two objects can be reduced by making the surfaces in contact smooth by polishing them.
Sliding friction between the moving parts of vehicles and machinery can be reduced by introducing oil, grease, graphite or any other lubricant.
Lubricant: A lubricant is a substance that reduces friction between surfaces in contact. This reduces the heat generated when the surfaces move. Lubricants can also transmit forces, transport foreign particles, or heat or cool the surfaces.
Rolling friction is less than sliding friction. Hence, sliding friction is replaced by rolling friction by using rollers, like ball bearings between the hub and the axles in the moving parts of machines and vehicles.
Friction is reduced by providing wheels,
Examples: suitcase, school bags of kids, etc.
Streamlined shape: Aeroplanes, boats, fishes and birds which move through fluids have bodies of special shape, called streamlined shape, The streamlined shape reduces the friction due to fluid and reduces the energy usage.
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Advanced Tools For Study Assess Interact SOUND | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Sound: Vibrations that travel through the air or another medium and can be heardwhen they reach a person’s or animal’s ear. Musical Sound: The sound which produce a pleasing effect on the ear. Noise: The sounds which produce a jarring or unpleasant effect Study Tools Types… readmore
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Sound: Vibrations that travel through the air or another medium and can be heard
when they reach a person’s or animal’s ear. Musical Sound: The sound which produce a pleasing effect on the ear.Noise: The sounds which produce a jarring or unpleasant effect
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Types of Sound:
(i) Audible Sound: Vibrations whose frequency lies between 20 Hz to 20,000 Hz (20
kHz) are heard by human ear.(ii) Inaudible Sound: The sounds having frequencies above 20,000 Hz and below
20 Hz cannot be heard by the normal human ear.Low frequency sounds which cannot be heard are called infrasonics.
High frequency sounds which cannot be heard are called ultrasonics.
In human beings, the vibration of the vocal cords produces sound.Sound travels through a medium (gas, liquid or solid). It cannot travel in
vacuum.The eardrum senses the vibrations of sound. It sends vibrations to the inner ear. From
there, the signal goes to the brain.That is how we hear. Higher the frequency of vibration, the higher is the pitch, and shriller is the
sound. Unpleasant sounds are called noise.Excessive or unwanted sounds lead to noise pollution. Noise pollution may pose health problems for human beings. Lack of sleep, hypertension (high bloodpressure), anxiety and many more health disorders may be caused by noise pollution.
A person who is loud sound continuously may get temporary or even permanent impairment of hearing.
Attempts should be made to minimise noise pollution. Silencing devices must be installed in air craft engines, transport vehicles, industrial machines and home appliances. Plantation on the roadside and elsewhere can reduce noise pollution.
Amplitude: The maximum extent of vibration of the vibrating body from its mean position is known as its amplitude.
Time Period: One complete to and fro movement of the pendulum around its mean positionis called one oscillation.
The time taken by the vibrating particle to complete one oscillation is called time period.
Frequency: The number of vibrations made by the vibrating body in one second is known as its frequency. The SI unit of frequency is the hertz (Hz).
Characteristics of Sounds:
(i) Loudness: The sensation produced in the ear which enables us to distinguish between a loud and a faint sound. Larger the amplitude of vibration, the louder is the sound produced. It is proportional to square of the amplitude.(ii) Pitch: The characteristics of sound which distinguishes between a shrill sound and a soft sound.
Higher the frequency of vibration, higher is the pitch and shrillness.
(iii) Quality: Characteristic which enables us to distinguish between musical notes emittedby different musical instruments or voices even though they have the same.
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CHEMICAL EFFECTS OF ELECTRIC CURRENT | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Materials through which electric current can pass through easily are called electric conductors or conductors of electricity. Electrical conductivity Or Electric Conductivity: Electrical conductivity is a measure of the ability of a substance to allow the flow of electric current. Among solids metals and graphite are… readmore
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Materials through which electric current can pass through easily are called electric conductors or conductors of electricity.
Electrical conductivity Or Electric Conductivity: Electrical conductivity is a measure of the ability of a substance to allow the flow of electric current.
Among solids metals and graphite are good conductors which have high electrical conductivity.
Some liquids are also good conductors. (Scroll down till end of the page)
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Pure water or distilled water is a poor conductor of electricity. But the presence of even small amount of impurities(salts and minerals) makes water a good conductor as it contains ions through which conduction takes place.
Hence water from taps, wells, lakes, etc. conduct electricity as they contain impurities.
Most liquids that conduct electricity are solutions of acids, bases and salts.
When electricity is passed through a conducting solution, the molecules of the solution dissociate into ions.
Ions are atoms or group of atoms with a positive or a negative charge.
These ions cause electrical conduction through the liquid.
Electrolyte: A liquid That conducts electricity is called an electrolyte.
Electrolysis:
The process of chemical decomposition compound in a solution when an electric current passes through it is called electrolysis.Electrolysis, is due to the chemical effect of electric current.
electrolytic cell: Two electrodes are inserted in the solution and are connected to the terminals of a battery with a switch in between them.
This arrangement is called an electrolytic cell.
anode: The electrode that is connected to the positive terminal of the battery is called the anode,
cathode: The electrode that is connected to the negative terminal of the battery is called the cathode.
Electrolysis is used in refining, electroplating and extraction of metals from impure samples.
electrorefining: This process of refining and extraction of metals from impure samples is called electrorefining.
electroplating: electroplating is the process of coating a useful metal with another metal.
chemical effect of electric current: The process of passing an electric current through a conducting solution to cause chemical reactions is known as the chemical effect of electric current.
Chemical effects of electric current:
(i) Formation of bubbles of a gas on the electrodes.(ii) Deposition of metal on electrodes.
(iii) Change in colour of solutions.
Electroplating: The process of depositing a layer of any desired metal on another material by means of electricity is called electroplating. The object to be electroplated is made the cathode (negative electrode) by connecting it to thenegative terminal of the battery.The metal which has to be deposited is made the anode (positive electrode) by connecting it to the positive terminal of the battery. Usually a salt solution of the metal to be coated is made as anode.
Application of Electroplating:
(i) Metals that rust are often coated with other metals to prevent rusting.(ii) Chromium plating is found on bath taps, car bumpers, etc. to give a bright attractive appearance and resist scratches and wear.
(iii) Silver plating is done on cutlery and jewellery items.
(iv) Tin cans, used for storing food, are made by electroplating tin onto iron.
Tin is less reactive than iron. Thus, food does not come into contact with iron and is protected from getting spoilt.
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Advanced Tools For Study Assess Interact SOME NATURAL PHENOMENA | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Some objects can be charged by rubbing with otherobjects. There are two kinds of charges — positive charge and negative charge Like charges repel and unlike charges attract each other. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Static Electric… readmore
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Some objects can be charged by rubbing with other
objects. There are two kinds of charges — positive charge and negative charge Like charges repel and unlike charges attract each other. (Scroll down till end of the page)Study Tools
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Static Electric Charges: The electric charges produced due to rubbing are called static electric charges. The electric charges constitute electric current during their motion.
An electroscope may be used to detect whether a body is charged or not.
An electroscope is a deviced used to detect the presence of electric charge.
earthing: The process of transfer of charge from a charged object to the earth is called earthing.
Lightning
Lightning is a sudden, natural and violent phenomenon of creating bright flashes during a thunderstorm.
Lightning occurs due to a high-voltage electric discharge between two clouds or a cloud and the ground, or within a single cloud during a thunderstorm.
The formation of clouds involves friction between water droplets in the atmosphere.
The friction charges the particles in the atmosphere. The negative charges accumulate at the bottom of the cloud and the positive charges at the top.
As the accumulation of the charges increases, the cloud will induce positive charges on the ground nearby.
As the amount of charge increases. This causes an imbalance of charges between a region of a cloud and gorund or another cloud (or in a cloud itself). This imbalance is significant enough to break through air resistance.
Lightning releases an average of one gigajoule of energy.
Lightning strike could destroy life and property.
Protective measures are of utmost importance during lightning strikes.
Taking shelter in interiors (house or other closed places) and vehicles (closed e.g. cars) are the most preferred measures.
Lightning conductors can protect buildings from the effects of lightning.
Earth Quake
A natural phenomenon that cannot be predicted is an earthquake.
The earth consists of three major layers, called the crust, the mantle and the core.
The core is further divided into the inner core and the outer core.
The mantle consists of semi-solid material above which the crust floats.
The crust consists of oceans and continents.
The crust is divided into several parts, called tectonic plates.
The regions where one tectonic plate slides against another are referred to as fault zones, and these are the regions where an earthquake is likely to occur.
Hence, these zones are referred to as seismic zones.
The place in the interior of the earth where an earthquake occurs is the focus, and the region on the surface of the earth that is the closest to focus is likely to experience the largest damage.
This region is called the epicenter of the earthquake.
The instrument that measures the severity of an earthquake is a seismograph.
It basically consists of a drum that rolls and a pendulum with a stylus that traces the waves of an earthquake on a sheet like a graph paper.
The energy released at the focus propagates outwardly in form of waves known as seismic waves. Destructive energy of an earthquake is measured on the Richter scale.
It is a logarithmic scale, ranging from 1 to 10 for indicating the intensity of an earthquake.
The earthquake measuring 7 or more on Richter scale can cause severe damage to life and property. Protective measures for earthquake:
If you are at home:
Take shelter under a table and stay there till shaking stops.Stay away from tall and heavy objects that may fall on you. If you are in bed, do not get up. Protect your head with a pillow.If you are outdoors: Find a clear spot, away from buildings, trees and overhead power lines. Drop to the ground. If you are in a car or a bus, do not come out. Ask the driver to drive slowly to a clear spot. Do not come out till the tremors stop. Moreover, it is advisable to make the structure of buildings simple so that they are ‘Quake Safe’.
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Advanced Tools For Study Assess Interact LIGHT | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Light is the natural agent that stimulates sight and makes things visible. Light is reflected from all surfaces. It is a form of energy. Reflection of Light: Bouncing back of light after striking any surface such as a rough surface, Smooth surfce, shiny surface or polished… readmore
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Light is the natural agent that stimulates sight and makes things visible. Light is reflected from all surfaces. It is a form of energy.
Reflection of Light: Bouncing back of light after striking any surface such as a rough surface, Smooth surfce, shiny surface or polished surface, into the same medium, is called reflection of light. (Scroll down till end of the page)
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luminous objects: Objects that give out light on their own are called luminous objects.
Examples: Flame, Sun, Glowing bulb
Non-luminous objects: Objects that do not give out light on their own are called non-luminous objects.
Examples: Rocks, Plasic Toys, Walls of room.
The Non – Luuminous objects, reflect light that falls on them.
When the reflected light enters into our eyes from the objects we could see them.
Types of Reflection:
(i) Regular Reflection: When a beam of parallel light rays is incident on a smooth and plane surface, the reflected rays will also be parallel. This type of reflection is called Regular Reflection.The reflection from a plane mirror is an example of regular reflection.
(ii) Diffused or Irregular Reflection: When a parallel beam of light is incident upon a rough or uneven surface, it is reflected in many directions due to presence of irregularities on that.
multiple reflections: If a reflected light ray is reflected again on being incident on another surface, it is termed as multiple reflections.
Multiple reflections are used in periscope, kaleidoscope etc.
Periscopes are used in submarines, war tanks and by soldiers in bunkers to see objects.
In a kaleidoscope, beautiful patterns are formed due to multiple reflections.
Laws of reflection of light:
(i) The angle of incidence is equal to the angle of reflection.
(ii) Incident ray, reflected ray and the normal drawn at the point of incidence to the reflecting surface, lie in the same plane.
Lateral inversion: Lateral inversion is the effect produced by a plane mirror in reversing images from left to right.
Example: Our left hand will appear as right and vice versa.
Characteristics of the image formed by a plane mirror
Size the image formed by a plane mirror is equal to the siz of the object.
The image formed by the plane mirror is left-right inverted.
The image formed by the plane mirror erect and virtual formed behind the mirror.
Since the distance of the object in front of the mirror two mirrors inclined to each other give multiple images.
Sunlight: Sunlight, called white light, consists of seven colours.
dispersion: Splitting of light into its constituent colours is known as dispersion.
Human Eye:
A normal eye can see nearby and distant objects clearly.
Visually challenged persons can read and write using Braille system.
Visually challenged persons develop their other senses more sharply to improve their interaction with their environment.
Parts of Human Eye:
(i) Cornea: Transparent bulge on the front surface of the eyeball which protects the eye andhelps in refraction of light.(ii) Iris: Coloured diaphragm behind the cornea which controls the amount of light
entering the eye.(iii) Pupil: Dark hole in the middle of iris through which light enters the eye. (iv) Eye lens: Transparent, crystalline structure behind pupil and iris. (v) Ciliary muscles: Hole the eye lens in position and control the focal length of the eye lens.
(vi) Retina: Surface of the rear part of the eyeball where the light entering the eye is focused.
(vii) Rods and Cones: Rod cells respond to the brightness of light while cone cells.
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Advanced Tools For Study Assess Interact Rational Numbers | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content The operations addition and multiplication are(i) commutative for rational numbers. (ii) associative for rational numbers. The… readmore
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Rational numbers are closed under the operations of addition, subtraction and multiplication, But not in division. (Scroll down till end of the page)
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The operations addition and multiplication are
(i) commutative for rational numbers.(ii) associative for rational numbers.
The rational number 0 is the additive identity for rational numbers.
The additive inverse of the rational number a/b is -a/b and vice- versa.
The reciprocal or multiplicative inverse of the rational number
is if a/b is c/d if (a/b)(c/d) =1Distributive property of rational numbers:
For all rational numbers a, b and c, a(b + c) = ab + ac
and a(b – c) = ab – ac.Rational numbers can be represented on a number line.
Between any two given rational numbers there are countless rational numbers.
The idea of mean helps us to find rational numbers between two rational numbers.
Positive Rationals: Numerator and Denominator both are either positive or negative.
Example: 2/3, -4/-5
Positive Rationals: Numerator and Denominator both are either positive or negative.
Example: -2/3, 4/-5
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Advanced Tools For Study Assess Interact Linear Equations in One Variable | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Linear Equation in One variable: The expressions which form the equation that contain single variable and the highest power of the variable in the equation is one. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Linear Equations in One Variable… readmore
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Linear Equation in One variable: The expressions which form the equation that contain single variable and the highest power of the variable in the equation is one. (Scroll down till end of the page)
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Linear Equations in One Variable
An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side.
The equations we study in Classes VI, VII and VIII are linear equations in one variable. In such equations, the expressions which form the equation contain only one variable. Further, the equations are linear, i.e., the highest power of the variable appearing in the equation is 1.
A linear equation may have for its solution any rational number.
An equation may have linear expressions on both sides. Equations that we studied in Classes VI and VII had just a number on one side of the equation.
Just as numbers, variables can, also, be transposed from one side of the equation to the other.
Occasionally, the expressions forming equations have to be simplified before we can solve them by usual methods. Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.
The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved
using linear equations.
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Advanced Tools For Study Assess Interact Understanding Quadrilaterals | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Practical Geometry Five measurements can determine a quadrilateral uniquely. A quadrilateral can… readmore
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A quadrilateral has 10 parts – 4 sides, 4 angles and 2 diagonals. Five measurements can determine a quadrilateral uniquely. (Scroll down till end of the page)
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Practical Geometry
Five measurements can determine a quadrilateral uniquely.
A quadrilateral can be constructed uniquely if the lengths of its four sides and a diagonal is given.
A quadrilateral can be constructed uniquely if its two diagonals and three sides are
known.
A quadrilateral can be constructed uniquely if its two adjacent sides and three angles
are known.
A quadrilateral can be constructed uniquely if its three sides and two included angles
are given.
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Advanced Tools For Study Assess Interact Data Handling | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Data Handling: Deals with the process of collecting data, presenting it and getting result. Data mostly available to us in an unorganised form is called raw data. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Grouped data can be presented… readmore
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Data Handling: Deals with the process of collecting data, presenting it and getting result.
Data mostly available to us in an unorganised form is called raw data. (Scroll down till end of the page)
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Grouped data can be presented using histogram. Histogram is a type of bar diagram, where the class intervals are shown on the horizontal axis and the heights of the bars show the frequency of the class interval. Also, there is no gap between the bars as there is no gap between the class intervals.
In order to draw meaningful inferences from any data, we need to organise the data systematically.
Frequency gives the number of times that a particular entry occurs.
Raw data can be ‘grouped’ and presented systematically through ‘grouped frequency distribution’.
Statistics: The science which deals with the collection, presentation, analysis and interpretation of numerical data.
Observation: Each entry (number) in raw data.
Range: The difference between the lowest and the highest observation in a given data.
Array: Arranging raw data in ascending or descending order of magnitude. Data can also presented using circle graph or pie chart. A circle graph shows the relationship between a whole and its part.
There are certain experiments whose outcomes have an equal chance of occurring. A random experiment is one whose outcome cannot be predicted exactly in advance. Outcomes of an experiment are equally likely if each has the same chance of occurring.
Frequency: The number of times a particular observation occurs in the given data.
Class Interval: A group in which the raw data is condensed.
(i) Continuous: The upper limit of a class interval coincides with the lower limit of the next class.
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Advanced Tools For Study Assess Interact Squares and Square Roots | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4). If a natural number m can be expressed as n2, where n is also a natural number, then… readmore
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Square: Number obtained when a number is multiplied by itself. It is the number raised to the power 2. 22 = 2 x 2=4(square of 2 is 4).
If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. (Scroll down till end of the page)
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All square numbers end with 0, 1, 4, 5, 6 or 9 at unit’s place. Square numbers can only have even number of zeros at the end. Square root is the inverse operation of square.
There are two integral square roots of a perfect square number.
Positive square root of a number is denoted by the symbol For example, 32=9 gives
Perfect Square or Square number: It is the square of some natural number. If m=n2, then m is a perfect square number where m and n are natural numbers. Example: 1=1 x 1=12, 4=2 x 2=22.
Properties of Square number:
- A number ending in 2, 3, 7 or 8 is never a perfect square. Example: 152, 1028, 6593 etc.
- A number ending in 0, 1, 4, 5, 6 or 9 may not necessarily be a square number. Example: 20, 31, 24, etc.
- Square of even numbers are even. Example: 22 = 4, 42=16 etc.
- Square of odd numbers are odd. Example: 52 = 25, 92 = 81, etc.
- A number ending in an odd number of zeroes cannot be a perferct square. Example: 10, 1000, 900000, etc.
- The difference of squares of two consecutive natural number is equal to their sum. (n + 1)2– n2 = n+1+n. Example: 42 – 32 =4 + 3=7. 122– 112 =12+11 =23, etc.
- A triplet (m, n, p) of three natural numbers m, n and p is called Pythagorean
triplet, if m2 + n2 = p2: 32 + 42 = 25 = 52
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Advanced Tools For Study Assess Interact Cubes and Cube Roots | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Cube number: Number obtained when a number is multiplied by itself three times. 23 = 2 x 2 x 2 = 8, 33 = 3 x 3 x 3=27, etc. Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They can be expressed… readmore
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Cube number: Number obtained when a number is multiplied by itself three times. 23 = 2 x 2 x 2 = 8, 33 = 3 x 3 x 3=27, etc.
Numbers like 1729, 4104, 13832, are known as Hardy – Ramanujan Numbers. They
can be expressed as sum of two cubes in two different ways. (Scroll down till the end of the page).
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Numbers obtained when a number is multiplied by itself three times are known as cube numbers. For example 1, 8, 27, … etc.
If in the prime factorisation of any number each factor appears three times, then the
number is a perfect cube.
The symbol
denotes cube root. For example
Perfect Cube: A natural number is said to be a perfect cube if it is the cube of some natural number. Example: 8 is perfect cube, because there is a natural number 2 such that 8 = 23, but 18 is not a perfect cube, because there is no natural number whose cube is 18.
The cube of a negative number is always negative.
Properties of Cube of Number:
- Cubes of even number are even.
- Cubes of odd numbers are odd.
- The sum of the cubes of first n natural numbers is equal to the square of their sum.
- Cubes of the numbers ending with the digits 0, 1, 4, 5, 6 and 9 end with digits 0, 1, 4, 5, 6 and 9 respectively.
- Cube of the number ending in 2 ends in 8 and cube of the number ending in 8 ends in 2.
- Cube of the number ending in 3 ends in 7 and cube of the number ending in 7
ends in 3.
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Comparing Quantities | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Ratio: Comparing by division is called ratio. Quantities written in ratio have the sameunit. Ratio has no unit. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Equality of two ratios is called proportion. Product of extremes = Product of meansPercentage:… readmore
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Ratio: Comparing by division is called ratio. Quantities written in ratio have the sameunit. Ratio has no unit. (Scroll down till end of the page)
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Equality of two ratios is called proportion. Product of extremes = Product of means
Percentage: Percentage means for every hundred. The result of any division in
whichthe divisor is 100 is a percentage. The divisor is denoted by a special
symbol %, read as percent. Profit and Loss:
(i) Cost Price (CP): The amount for which an article is bought. (ii) Selling Price (SP): The amount for which an article is sold. Additional expenses made after buying an article are included in the cost price
and are known as overhead expenses. These may include expenses like amount
spent onrepairs, labour charges, transportation, etc. Discount is a reduction given on marked price. Discount = Marked Price – Sale
Price. Discount can be calculated when discount percentage is given. DiscountHindi Version Key Terms
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Advanced Tools For Study Assess Interact Algebraic Expressions and Identities | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Expressions are formed from variables and constants. Constant: A symbol having a fixed numerical value. Example: 2,, 2.1, etc. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Variable: A symbol which takes various numerical values. Example: x, y, z, etc.… readmore
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Expressions are formed from variables and constants.
Constant: A symbol having a fixed numerical value.
Example: 2,, 2.1, etc. (Scroll down till end of the page)
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Variable: A symbol which takes various numerical values. Example: x, y, z, etc.
Algebric Expression: A combination of constants and variables connected by the sign
+, -, and is called algebraic expression.
Terms are added to form expressions.
Terms themselves are formed as product of factors.
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.
Like terms are formed from the same variables and the powers of these variables are the same, too.
Coefficients of like terms need not be the same.
While adding (or subtracting) polynomials, first look for like terms and add (or subtract) them; then handle the unlike terms.
There are number of situations in which we need to multiply algebraic expressions: for example, in finding area of a rectangle, the sides of which are given as expressions.
Monomial: An expression containing only one term. Example: -3, 4x, 3xy, etc.
Binomial: An expression containing two terms. Example: 2x-3, 4x+3y, xy-4, etc.,
Polynomial: In general, any expression containing one or more terms with non-zero coefficients (and with variables having non-negative exponents).
A polynomial may contain any number of terms, one or more than one.
A monomial multiplied by a monomial always gives a monomial.
Multiplication of a Polynomial and a monomial:
While multiplying a polynomial by a monomial, we multiply every term in the polynomial by the mononomial.
Trinomial: An expression containing three terms.
Example:
3x+2y+5z, etc.
In carrying out the multiplication of a polynomial by a binomial (or trinomial), we multiply term by term, i.e., every term of the polynomial is multiplied by every term in the binomial (or trinomial).
Note that in such multiplication, we may get terms in the product which are like and have to be combined.
An identity is an equality, which is true for all values of the variables in the equality.
On the other hand, an equation is true only for certain values of its variables.
An equation is not an identity.
The following are the standard identities:
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab +b2
(a + b)(a – b) = a2 – b2
(x + a) (x + b) = x2 + (a + b) x + ab
The above four identities are useful in carrying out squares and products of algebraic expressions.
They also allow easy alternative methods to calculate products of numbers and so on.
Coefficients: In the term of an expression any of the factors with the sign of the term is called the coefficient of the product of the other factors.
Terms: Various parts of an algebraic expression which are separated by + and – signs. Example: The expression 4x + 5 has two terms 4x and 5.
- Constant Term: A term of expression having no lateral factor.
- Like term: The term having the same literal factors. Example 2xy and -4xy are like terms.
(iii) Unlike term: The terms having different literal factors.
Example:
are unlike terms.
and 3xy
Factors: Each term in an algebraic expression is a product of one or more number (s) and/or literals. These number (s) and/or literal (s) are known as the factor of that term. A constant factor is called numerical factor, while a variable factor is known as
a literal factor. The term 4x is the product of its factors 4 and x.
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Advanced Tools For Study Assess Interact Mensuration | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Perimeter: Length of boundary of a simple closed figure. Perimeter of Rectangle = 2(l +b)Perimeter of Square = 4aPerimeter of Parallelogram = 2(sum of two adjacent sides)Area: The measure of region enclosed in a simple closed figure. Area of a trapezium = half of the sum… readmore
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Perimeter: Length of boundary of a simple closed figure.
Perimeter of Rectangle = 2(l +b)
Perimeter of Square = 4a
Perimeter of Parallelogram = 2(sum of two adjacent sides)
Area: The measure of region enclosed in a simple closed figure.Area of a trapezium = half of the sum of the lengths of parallel sides × perpendiculardistance between them.
Area of a rhombus = half the product of its diagonals. (Scroll down till end of the page)
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Advanced Tools For Study Assess Interact Exponents and Powers | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Numbers with exponents obey the following laws of exponents. Very small numbers can be expressed in standard form using negative exponents. (Scroll down till end of the page) Study Tools Audio, Visual & Digital Content Use of Exponents to Express Small Number in Standard form: (iii)… readmore
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Numbers with exponents obey the following laws of exponents.
Very small numbers can be expressed in standard form using negative exponents. (Scroll down till end of the page)
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Use of Exponents to Express Small Number in Standard form:
- Very large and very small numbers can be expressed in standard form.
- Standard form is also called scientific notation form.
(iii) A number written as number such that is said to be in standard form if m is a decimal and n is either a positive or a negative integer.
Examples: 150,000,000,000 = 1.5 x 1011.
Exponential notation is a powerful way to express repeated multiplication of the same number.
For any non-zero rational number ‘a’ and a natural number n, the product a x a x a x x a(n times) = an.
It is known as the nth power of ‘a’ and is read as ‘a’ raised to the power n’.
The rational number a is called the base and n is called exponent.
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Advanced Tools For Study Assess Interact Direct and Inverse Proportions | Study
Mind Map Overal Idea Content Speed Notes Quick Coverage Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down till end of the page) Study Tools Audio,… readmore
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Variations: If the values of two quantities depend on each other in such a way that a change in one causes corresponding change in the other, then the two quantities are said to be in variation. (Scroll down till end of the page)
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Direct Variation or Direct Proportion:
Extra:
Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains
constant. That is if
=k [k is a positive number, then x and y are said to vary directly.
In such a case if y1, y2 are the values of y corresponding to the values x1, x of x
respectively then = .
If the number of articles purchased increases, the total cost also increases. More than money deposited in a bank, more is the interest earned.
Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are
written as
. Symbol
stands for ‘is proportion to’.
Inverse Proportion: Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if xy
= k, then x and y are said to vary inversely. In this case if y1, y2 are the values of y
corresponding to the values x1, x2 of x respectively then
x1, Y1 = x2, y2 or
=
When two quantities x and y are in inverse proportion (or vary inversely), they are
written as x
. Example: If the number of workers increases, time taken to finish
the job decreases. Or If the speed will increase the time required to cover a given distance decreases.
1. Distance and Time
Time (hours) Distance (km) Formula 0 0 1 60 2 120 3 180 2. Cost of Groceries
Number of Apples Total Cost ($) Formula 0 0 1 2 2 4 5 10 3. Cooking Ingredients
Number of Servings Amount of Flour (cups) Formula 0 0 4 2 6 3 8 4 4. Speed and Fuel Consumption
Distance (km) Fuel Consumed (liters) Formula 0 0 15 1 30 2 45 3 5. Salary and Hours Worked
Hours Worked Total Earnings ($) Formula 0 0 1 15 5 75 10 150 Hindi Version Key Terms
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