Category: CBSE Class 8

On this page, you will find Materials: Metals and Non-Metals Class 8 Notes Science Chapter 4 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 4 Materials: Metals and Non-Metals will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Notes Chapter 4 Materials: Metals and Non-Metals

Materials: Metals and Non-Metals Class 8 Notes Understanding the Lesson

1. Materials can be broadly grouped into two groups metals and non-metals.

2. Substances which are generally hard, lustrous, malleable, sonorous and good conductors of heat and electricity are metals. For example, copper, iron, gold, silver, etc.

3. Substances which are generally soft, dull in appearance, brittle, non-sonorous and bad conductors of heat and electricity are non-metals. For example, oxygen, hydrogen, carbon, sulphur, etc.

4. The property of metals by which they can be beaten into thin sheets is called malleability.

5. The property of metal by which it can be drawn into wires is called ductility.

6. The property of metal of producing ringing sound is called sonority.

7. Chemical properties of metals and non-metals:

(i) Reaction with oxygen: Both metals and non-metals form their oxides when burnt in oxygen. Metals form basic oxides whereas non-metals generally form acidic oxides.
Reactions of metal or non-metal with oxygen are called oxidation reactions.

(ii) Reaction with water: Metals produce their oxides or hydroxides and hydrogen gas on reacting with water. Non-metals do not react with water.

(iii) Reaction with acids: Metals react with acids and produce metal salts and hydrogen gas. Hydrogen gas burns with a ‘pop’ sound, when a burning matchstick is brought near it.
Non-metals generally do not react with acids.

(iv) Reaction with bases: Most of the metals and non-metals generally do not react with bases. Some metals like aluminium, lead and zinc react with strong bases like sodium hydroxide to make complex salts and hydrogen gas. Similarly, sometimes some complex reactions take place between non-metals and bases.

(v) Displacement reactions: Reactions in which more reactive metal displaces the less reactive metal from its salt is called displacement reactions. Certain metals are capable of displacing other metals from their solutions. For example, zinc (Zn) replaces copper from copper sulphate solution. The reaction is as follows:

8. On the basis of reactivity of metals a sequence is formed called reactivity series. Metals on the top of the series are most reactive and those on the bottom are least reactive. Zinc is more reactive than copper and iron. A more reactive metal can replace a less reactive metal but, a less reactive metal cannot replace a more reactive metal.

9. Uses of metals: Metals are used in making machinery, automobiles, aeroplanes, trains, satellites, industrial gadgets, water boilers, utensils, etc. They are also used in making wires and sheets.

10. Uses of non-metals

• All living beings inhale oxygen during breathing, which is a non-metal.
• Non-metals like nitrogen, phosphorus and potassium are used in fertilisers to enhance the growth of plants.
• Non-metal like chlorine is used in water purification process.
• Non-metal is used in the purple coloured solution which is applied on wounds as an antiseptic.
• Non-metals are used in crackers.

Class 8 Science Chapter 4 Notes Important Terms

Atom: An atom is the smallest particle of an element which cannot be further divided by any physical mean.

Conductor: Substance which allow heat and electricity to pass through it is called conductor.

Displacement reaction: Reaction in which more reactive element displaces less reactive element is known as displacement reaction.

Ductility: The property of metals due to which they can be drawn into wires is called ductility. Metals are ductile.

Elements: The substances whose molecules are made up of only one type of atoms are known as elements.

Hardness: It is the property of a substance due to which it cannot be cut easily is called its hardness. Metals possess this property.

Malleability: It is the property of a substance due to which it can be beaten into thin sheets is called malleability. Metals have this property.

Metals: Substances which are generally shiny, hard, malleable, ductile, sonorous and good conductors of heat and electricity are metals.

Metalloid: Substances which possess properties of both metals and non-metals are called metalloids. For example, bismuth, antimony, arsenic and boron.

Non-metals: Materials which are soft, dull in appearance, non-sonorous and poor conductors of heat and electricity are called non-metals. They break down into a powdery mass on tapping with a hammer. They also form negative ions by gaining electrons.

Sonorous: The property due to which metals produce a ringing sound is called sonority. This is why metals are called to be sonorous.

On this page, you will find Synthetic Fibres and Plastics Class 8 Notes Science Chapter 3 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 3 Synthetic Fibres and Plastics will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Notes Chapter 3 Synthetic Fibres and Plastics

Synthetic Fibres and Plastics Class 8 Notes Understanding the Lesson

1. A fabric is the material used for making clothes.

2. Fabrics are made from fibres obtained from natural or artificial source.

3. Beside clothes, fibres are also used for making carpets, sail of boats, parachutes, upholstery and many more items.

4. Fibres can be natural or artificial. Fibres such as cotton, wool, jute and silk are natural fibres whereas rayon, nylon and polyester are artificial fibres.

5. The man-made fibres produced from chemical substances are called synthetic fibres.

6. Synthetic fibres are also known as man-made fibres or artificial fibres.

7. Depending upon the types of chemicals used for manufacturing of the synthetic fibres they are called rayon, nylon, polyester and acrylic.

8. Rayon or artificial silk is made from cellulose obtained from wood pulp.

9. It can be dyed in a wide variety of colours.

10. Nylon was the first synthetic fibre produced by man in 1935.

11. Nylon fibres are strong, elastic, light, lustrous and easy to wash.

12. It is used to make many items like socks, ropes, tents, toothbrushes, car seat belts, curtains, etc.

13. Terylene and dacron are polyester fibres.

14. It is made from two monomers, terephthalic acid and ethylene glycol.

15. It is used for making PET bottles, jars, floppy discs, shirts, hats, etc.

16. Acrylic is the synthetic fibre that resembles wool in its texture and properties.

17. It is used to make sweaters, shawls, socks, etc.

18. They dry up soon, are durable, less expensive, readily available and easy to maintain.

19. A plastic is a synthetic material which can be set into desired shape when soft and then hardened to produce a durable article.

20. Some plastic polymers have linear arrangement of units, whereas in others it is cross-linked arrangement.

21. Thermoplastic is a plastic which gets deformed easily on heating and can be bent easily, e.g., polythene and PVC. These are used for manufacturing toys, combs, containers, etc.

22. Thermosetting plastics is a plastic which when moulded once cannot be softened by heating, e.g., bakelite and melamine.

23. Bakelite is used for making electrical switches, handles of various utensils, etc.

24. Melamine is used for making floor tiles, kitchenware, etc.

25. Plastic is a non-biodegradable substance. So, the articles made of plastics do not rot when they are thrown away after use. This pollute the environment.

26. When the plastic waste materials are burnt, they produce poisonous gases which pollute the air. The 4R principle, Reduce, Reuse, Recycle and Recover should be our basic mantra to minimise the hazards associated with the disposal of plastic wastes.

27. We must think twice before using plastic items.

Class 8 Science Chapter 3 Notes Important Terms

Acrylic: The synthetic fibre that resembles wool in its texture and properties is called acrylic.

Artificial silk: A man-made fibre obtained from chemical treatment of wood pulp which has properties similar to that of silk is called artificial silk.

Nylon: A fully synthetic polymer which is prepared from coal, water and air is called nylon.

Plastic: Those substances which are mostly synthetic in nature, obtained mainly from petrochemical sources and can be moulded into different shapes are called plastics.

Polyester: The synthetic fibre which is used for making PET bottles, home furnishings, etc., and are blended with natural fibres to enhance its properties is called polyester.

Polymer: The compound that are made up of small repeating units, joined together through bonds in a linear pattern is called polymer.

Polythene: The compound obtained from ethylene under high temperature, high pressure and in the presence of a catalyst is called polythene.

Rayon: A man-made fibre which is produced by the chemical processing of wood pulp, which is a natural substance is called rayon.

Synthetic fibres: The fibres which are made by human beings with the help of chemical substances are called synthetic fibres.

Terylene: A common variety of polyester which can be drawn into very fine fibres is called terylene.

Thermoplastics: Those plastics which soften on heating and hardened on cooling are called thermoplastics.

Thermosetting plastics: Those plastics, which when moulded once, cannot be softened again and lose their plasticity are called thermosetting plastics.

On this page, you will find Microorganisms: Friend and Foe Class 8 Notes Science Chapter 2 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 2 Microorganisms: Friend and Foe will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Notes Chapter 2 Microorganisms: Friend and Foe

Microorganisms: Friend and Foe Class 8 Notes Understanding the Lesson

1. Microorganisms or microbes are extremely small living organisms which cannot be seen with the naked eyes.

2. Microorganisms can survive under all types of environment.

3. Microorganisms are broadly classified into four categories bacteria, fungi, protozoa and some algae.

4. Viruses are quite different from other microorganisms. They reproduce only inside the host organisms.

5. Some of the microorganisms are beneficial for us, while some are harmful for us.

6. Microorganisms are used in making curd, cake, bread, beverages, etc.

7. Out of several microorganisms contained in curd, the bacterium, Lactobacillus promote the formation of curd.

8. Yeast is a fungi which is used to convert sugar into alcohol. It reproduces rapidly and produces carbon dioxide during respiration.

9. The process of conversion of sugar into alcohol in the absence of oxygen is called fermentation.

10. Microorganisms are also used for producing antibiotics and vaccines. These antibiotics and vaccines stop the growth of other disease-causing microbes.

11. Some bacteria and blue green algae fixes atmospheric nitrogen into the soil. Thus increases soil fertility.

12. Microbes play the chief role in making of manures, which are useful for nourishment of soil.

13. Pathogens are disease-causing microorganisms that can enter our body through the air we breathe, the water we drink, and through direct contact with an infected person or through carriers.

14. Microbial diseases that can spread from an infected person to a healthy person through air, water, food or physical contact are called communicable diseases.

15. There are some animals and insects that transfer harmful disease-causing microbes from one body to the other, e.g., flies, mosquitoes, etc., These are called carriers.

16. Anthrax is a harmful human and cattle disease caused by a bacterium.

17. Some microorganisms spoil the food items by producing toxic substances on them. These make the food poisonous causing serious sickness and even death.

18. To save the food from the attack of harmful microbes, some chemicals called preservatives are used. Common preservatives used are common salt, sugar, edible oils, vinegar, sodium benzoate, sodium metabisulphite.

19. Milk is pasteurised for killing harmful microbes. It is heated to about 70° C for 15-30 seconds and then suddenly chilled and stored. This prevents the growth of harmful microbes. This process was given by Louis Pasteur. It is called pasteurisation.

20. Nitrogen Cycle: Some bacteria and blue-green algae present in the soil fix nitrogen gas from the atmosphere and convert it into nitrogenous compounds. These useful nitrogenous compounds are then used by plants from the soil with the help of their roots. They help in the synthesis of proteins and other compounds. On the other hand, there are some bacteria that convert some part of nitrogenous compounds into nitrogen gas again and send them back into the atmosphere.

21. Due to this, nitrogen cycle, the percentage of nitrogen gas in the atmosphere remains more or less constant.

Class 8 Science Chapter 2 Notes Important Terms

Algae: Algae is a vast group of simple, unicellular to multicellular, plant-like organisms which are often present in aquatic habitat, e.g., Chlamydomonas, etc.

Antibiotics: A type of medicine that kills or stops the growth of disease-causing microbes is called as antibiotics.

Antibodies: When harmful pathogens enter our body, our defense mechanism produces substance to fight them, which are called antibodies.

Bacteria: Very small single-celled microbes which have cell walls, but don’t have an organised nucleus and other structures.

Carrier: An animal or insect that transmits pathogens from an infected person to a healthy one is called a carrier.

Communicable diseases: The microbial diseases which can be spread from an infected person to a healthy one through air, water, food or physical contact, etc., are called communicable diseases.

Fermentation: The method in which sugar present in the food is converted into alcohol and carbon dioxide by the microorganisms in absence of oxygen is called fermentation.

Fungi: Fungi are vast groups of microbes which do not have chlorophyll and thus don’t photosynthesise, e.g., yeast, moulds, etc.

Lactobacillus: Bacterium present in curd which promotes its formation.

Microorganisms: Organisms which are too small, to be visible with the naked eyes are called as microorganisms. These include virus, bacteria, fungi, protozoa and a few algae.

Nitrogen cycle: The series of processes by which nitrogen and its compounds are interconverted in the environment and in living organisms, including nitrogen fixation and decomposition.

Nitrogen fixation: The process of conversion of atmospheric nitrogen into its usable forms.

Pasteurisation: The process in which the milk is heated to about 70°C for 15 to 30 seconds and then it is chilled suddenly and stored is called pasteurisation.

Pathogens: Pathogens are disease-causing microorganisms.

Preservation: The method used for prevention of spoiling of food by the action of microbes is called food preservation.

Protozoa: Group of single-celled microorganisms, which are also categorised as small animals are called protozoa.

Rhizobium: Bacteria which is present in the root nodules of leguminous plants and fixes atmospheric nitrogen in the soil is called Rhizobium.

Vaccine: Dead or weakened microbes that produces immunity against a disease causing microbe in the living body is termed as vaccine.

Virus: Viruses are microbes which are living only inside another living cell. They are considered intermediate between living and non-living.

Yeast: Yeast are unicellular microbes categorised under fungi are used in fermentation to produce wine, beer and other beverages.

On this page, you will find Crop Production and Management Class 8 Notes Science Chapter 1 Pdf free download. CBSE NCERT Class 8 Science Notes Chapter 1 Crop Production and Management will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Science Chapter 1 Notes Crop Production and Management

Crop Production and Management Class 8 Notes Understanding the Lesson

1. The branch of science that deals with growing plants and raising livestock for human use is called agriculture.

2. When plants of same kind are grown and cultivated at one place on a large scale, it is called a crop.

3. The products obtained from the crops are called produce.

4. The crops grown in India can be classified as kharif and rabi crops.

5. Kharif crops are sown in the rainy season by June/July, and are harvested by September/October. Thus, they are also known as summer season crops. For example, rice, maize, cotton, pulses, etc.

6. Rabi crops are sown in the winter season in October or November and are harvested by March/April. For example, wheat, potato, barley, etc.

7. Agricultural practices are those practices which involve the necessary steps to be taken during production of crops.

8.  Important steps that are taken during crop production are:

• Preparation of soil
• Sowing
• Adding manure and fertilisers
• Irrigation
• Protecting from weeds
• Harvesting
• Storage

9. The preparation of soil is the first step before growing a crop. One of the most important tasks in agriculture is to turn soil and
loosen it.

10. The loosening of soil allows roots to penetrate deep into the soil.

11. The process of loosening and turning of the soil is called tilling or ploughing. Ploughing is either done by a plough or a tractor.

12. Hoe is a simple tool which is used for removing weeds and for loosening the soil.

13. Levelling is the process of breaking down the larger lumps of soil, and then levelling it by using a leveller.

14. Sowing is the most important part of crop production. Before sowing, good quality of seeds are selected.

15. The tool used traditionally for sowing seeds is shaped like funnel. Nowadays the seed drill is used for sowing with the tractors. This tool sows the seeds uniformly.

16. Continuous growing of crops makes the soil poorer in certain nutrients.

17. The substances which are added to the soil in the form of nutrients for the healthy growth of plants are called manure and fertilisers.

18. Manure is an organic substance obtained from the decomposition of plant or animal wastes.

19. Fertiliser is a chemical substance which is rich in a particular nutrient. Fertilisers are produced in factories. Some examples of fertilisers are urea, ammonium sulphates, superphosphate, etc.

20. The use of fertilisers helps farmer to get better yield of crops such as wheat, paddy and maize whereas manure improves soil texture as well as its water retaining capacity.

21. Excessive use of fertilisers makes soil less fertile. Fertilisers also leads to water pollution.

22. The organic manures is considered better than fertilisers.

23. The supply of water to crops at different intervals is called irrigation.

24. The time and frequency of irrigation varies from crop to crop, soil to soil and season to season.

25. The sources of irrigation are wells, tubewells, ponds, lakes, rivers, dams and canals.

26. The various traditional ways for irrigation are:

• moat (pulley-system)
• chain pump
• dhekli
• rahat (lever system)

27. Modern methods of irrigation help us to use water economically. Modern methods of irrigation are sprinkler system and drip system.

28. Sprinkler system is more useful on the uneven land where sufficient water is not available.

29. In drip system the water falls drop by drop just at the position of the roots.

30. The undesirable plants that grow naturally along with the crop are called weeds. Weeds compete with the crop plant for nutrients, space and sunlight.

31. The process of removal of weeds is called weeding.

32. The growth of weeds is controlled by using certain chemicals, called weedicides.

33. Weedicides are sprayed in the field to kill the weeds.

34. The process of cutting of crop after it is mature is called harvesting.

35. Harvesting in our country is either done manually by using sickle or by a machine called harvester.

36. The process of separating the grain seeds from the chaff is known as threshing.

37. The process of threshing is carried out with the help of a machine called combine which is in fact a combined harvester and thresher.

38. Farmers with small holdings of land do the separation of grain and chaff by the process of winnowing.

39. The large scale storage of grains is done in silos and granaries to protect them from pests like rats and insects.

40. Animals reared at home or in farms, have to be provided with proper food, shelter and care. When this work is done at a large scale then the process is called animal husbandry.

Class 8 Science Chapter 1 Notes Important Terms

Agricultural practices: The activities carried out for cultivation of crops over a period of time are known as agricultural practices.

Animal husbandry: Animals reared at home or in a farm, have to be provided with proper food, shelter and care, when this is done on a large scale it is called animal husbandry.

Crop: The same kind of plants which are grown and cultivated at a place are known as crop.

Fertiliser: Fertiliser is a chemical compound which is very rich in plant nutrients like nitrogen, phosphorus and potassium.

Granaries: The storehouse or repository for grain after it has been threshed or husked.

Harvesting: The process of cutting the crop after it is fully mature is called harvesting.

Irrigation: The process of supplying water to crops at appropriate intervals is called irrigation.

Kharifi: The type of crops which are grown in the rainy season, that is from June to September, are called kharif crops.

Manure: The decomposed organic matter obtained from plant or animal wastes is called manure.

Plough: The device which is used for tilling and ploughing is called plough.

Rabii: The type of crops grown in winter season, that is from October to March, are called rabi crops.

Seed: A plant’s fertilised ovule from which a new plant may grow is called seed.

Silo: A tall tower or pit on a farm used to store grains.

Sowing: The process of putting seeds in the soil is known as sowing.

Storage: Storage is a process of keeping crop grain safe from moisture, insect and rats for longer time.

Threshing: The process of separation of grain from the chaff in the harvested plant is called threshing.

Weeds: The unwanted plants that grow along with the crop are known as weeds.

Weedicide: The chemicals sprayed to control the growth of weeds is known as weedicide.

Winnowing: The process of separation of grain and chaff is called winnowing.

On this page, you will find Mensuration Class 8 Notes Maths Chapter 11 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 11 Mensuration will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 11 Notes Mensuration

Mensuration Class 8 Notes Conceptual Facts

1. Area of rectangle
A = Length x Breadth
= a x b sq. units

2. Area of square
A = (side)²
= a² sq. units

3. Area of triangle
A = \(\frac{1}{2}\) x b x h sq.units

4. Area of equilateral triangle
A = \(\frac{\sqrt{3}}{4} a^{2}\) sq.units

5. Area of parallelogram
A = b x h sq. units

6. Area of Circle
A = πr² sq. units

7. Area of trapezium
A = \(\frac{1}{2}\)(a + b) x h sq. units

8. Area of general quadrilateral
A = Area of ΔABC + area of ΔACD
= \(\frac{1}{2}\) (a + b) x AC sq. units

9. Area of rhombus
A = \(\frac{1}{2}\) (d₁ x d₂) sq. units

10. Surface area of cube
A = 6a² sq. units

11. Surface area of cuboid
A = 2 [ab + bc + ca] sq. units

12. Surface area of cylinder
A = 2πrh sq. units

13. Volume of cube V = a³ units

14. Volume of cuboid V = a x b x c cu. units

15. Volume of cylinder V = πr²h

On this page, you will find Visualising Solid Shapes Class 8 Notes Maths Chapter 10 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 10 Visualising Solid Shapes will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 10 Notes Visualising Solid Shapes

Visualising Solid Shapes Class 8 Notes Conceptual Facts

3-D figures: Any shape which occupies space and has three dimensions, i.e., length, breadth and heights is called 3-D solid or a figure.

Parts of a solid objects:

• Face
• Vertex
• Edge

Types of Solids:

(i) Prism:

(ii) Pyramids:

(iii) Other Solid

Euler’s Formula:
Number of faces + Number of vertices – Number of edges = 2

On this page, you will find Algebraic Expressions and Identities Class 8 Notes Maths Chapter 9 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 9 Algebraic Expressions and Identities will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 9 Notes Algebraic Expressions and Identities

Algebraic Expressions and Identities Class 8 Notes Conceptual Facts

1. Algebraic Expression: A combination of numbers which includes literal number connected by the
symbols +, -, x and + is called an algebraic expression.

For example: 5x, 8x -3, 2x + 3y, \(\frac{3}{4}\)x² 4xyz are some algebraic expressions.
Here. 5, 8, 3, 2. and 4 are constants and the literal numbers are x, y and z.

The different parts of the expression are called terms.
5x, 8x, 2x, 3y, \(\frac{3 x^{2}}{4}\) etc., are all the terms.

2. Coefficient: A coefficient is a multiplicative factor in some term of a polynomial. It is usually a number,
but may be only expression along.

For example in 7x² – 3xy + y + 3. The first three terms respectively have coefficient 7, -3 and 3 is a
constant in given polynomial.

3. Monomial: The expression having only one term is called monomial.
For example: 3x, 8xy, 6×2, 11xyz, etc.

4. Binomial: The expression containing two terms is called binomial.
Forexample: 2x +y,x +y, 3xy-5z, \(\frac{1}{2}\) xy + 5, etc.

5. Trinomial: The expression containing three terms is called trinomial.
For example: x + 2y + 3, xy – z +\(\frac{1}{2}\) , \(\frac{1}{2}\) x²+ 2x + 5, etc.

6. Polynomial: Algebraic expression containing one or more terms with non-zero coefficient is called a
polynomial.
For example: 2+3x, x+y+3z-5, \(\frac{1}{2}\) x²+yz -5, etc.

7. Like and Unlike Terms: Algebraic expressions having same combination of literal numbers are called
like terms.
For example: 4xy, -5xy, –\(\frac{17}{3}\) xy, are like terms.

8. Algebraic expressions having different combinations of literal numbers are called unlike terms.
For example: (xy, yz, zx), (2x², – 5xy², 7xyz), (3, – 5x, 7yz) etc.

9. Degree of Algebraic Expression: Highest power of the variable of an algebraic expression is called its degree.
For example: Degree of 3x² – 7x + 5 is 2.

Addition or Subtraction of two or more polynomials:

• Collect the like terms together.
• Find the sum or difference of the numerical coefficients of these terms.

For example:
(i) Add: 2x²y³, -5x²y³ + \(\frac{11}{2}\)x²y^z
Answer:

(ii) Subtract: (3x – 5) from (8x – 25)
Answer:

[Arrange the terms columnwise and change the sign of and add]

Multiplication Rule of Signs:
(+x) x (+y) = (+xy)
(+x) x (-y) = (-xy)
(-x) x (y) = (-xy)
(-x) x (-y) = (+xy)

 

On this page, you will find Comparing Quantities Class 8 Notes Maths Chapter 8 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 8 Comparing Quantities will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 8 Notes Comparing Quantities

Comparing Quantities Class 8 Notes Conceptual Facts

1. In every hundred or per hundred is called as percent. For example: 30% means 30 in every hundred.
To change a percentage to a fraction:
40% \(\frac{40}{100}\)=0.4 , 125% = \(\frac{125}{100}\)=1.25

2. Percentage increase and decrease
Increase 240 by 10% = 240 + \(\frac{10}{100}\) x 240 = 240 + 24 = 264
Decrease 180 by 18% = 180 – \(\frac{18}{100}\) x 180 = 180 – 32.4 = 147.6

3. Profit and Loss
Profit = SP – CP,Loss= CP – SP

4. Profit and Loss are always calculated on CP.

5. Marked Price: The printed or the tagged price of an article is known as marked price or MP.

6. Discount: The deduction allowed on the market price is called Discount. It is generally given in percent.

7. Net Price: The selling price after the discount to an article is called its Net Price.

SP = MP – Discount
\(\mathrm{MP}=\left(\frac{100 \times \mathrm{SP}}{100-\mathrm{Discount} \%}\right)\)

8. Sales Tax: Sales tax is a tax levied by the Government on the selling price of an article at a rate given by the Government.

9. Value Added Tax (VAT): VAT is an extra tax which is levied and collected by State Government in lieu of State Tax.

10. Simple Interest:
\(\mathrm{SI}=\frac{\text { Principal } \times \text { Rate } \times \text { Time }}{100}\)

11. Compound Interest: Cl = Amount – Principal
\(\mathrm{CI}=\mathrm{P}\left(1+\frac{r}{100}\right)^{n}-\mathrm{P}\)

Amount = \(\mathrm{P}\left(1+\frac{r}{100}\right)^{n}\) where n represent time in years.

12. Conversion of Period:

• If interest is calculated half-yearly or semi-annually, then ‘r’ is halved and T is doubled.
• If interest is calculated quarterly, then V’ is one-fourth and T is four times.

On this page, you will find Cubes and Cube Roots Class 8 Notes Maths Chapter 7 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 7 Cubes and Cube Roots will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 7 Notes Cubes and Cube Roots

Cubes and Cube Roots Class 8 Notes Conceptual Facts

• A natural number n is a perfect cube if there exists a natural number m such that m x m x m = n For example: 1, 8, 27 …. are all perfect cubes

Properties of Cubes of Numbers:

• Cubes of all odd numbers are odd. Thus 3³ = 27, 5³ = 125, etc.
• Cubes of all even numbers are even. Thus 2³ = 8, 4³ = 64, 6³ = 216, etc.
• Cubes of all negative numbers are always negative. Thus (-1)³ = -1, (-2)³ = -8, (-3)³ = -27, etc.
• \(\left(\frac{a}{b}\right)^{3}=\frac{a^{3}}{b^{3}}\)

Properties of Cube Roots:

(i) \(\sqrt[3]{-a^{3}}=-a\)

(ii) \(\sqrt[3]{a b}=\sqrt[3] a^{a} \sqrt[3]{b}\)

(iii) \(\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}, b \neq 0\)

A Pattern of Cube:

1³ = 1
2² = 8 = 3 + 5
3³ = 27 = 7 + 9 + 11
4³ = 64 = 13 + 15 + 17 + 19
5³ = 125 = 21 + 23 + 25 + 27 + 29

 

On this page, you will find Squares and Square Roots Class 8 Notes Maths Chapter 6 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 6 Squares and Square Roots will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 6 Notes Squares and Square Roots

Squares and Square Roots Class 8 Notes Conceptual Facts

1. If a number is multiplied by itself, the product that we get is called the square of the number.
For example:
4 x 4 = 4² = 16                                                                 (16 is square of 4)
20 x 20 = 20² = 400                                                         (400 is square of 20)
\(\frac{3}{5} \times \frac{3}{5}=\left(\frac{3}{5}\right)^{2}=\frac{9}{25}\) \(\left(\frac{9}{25} \text { is square of } \frac{3}{5}\right)\)

2. Square of a number is represented as the number raised to the power 2.

3. A perfect square is a number that can be expressed as the product of two equal integers.
For example: 1, 4, 9, 16, 25, …, are all perfect square numbers.

4. Properties of square numbers:
(i) No square number ends with the digits 2, 3, 7 or 8 at its unit places.

(ii) The square numbers must end with the digits 0, 1, 4, 5, 6, 9 but the number ending with 0, 1, 4, 5, 6, 9 may or may not be a perfect number.
For example: 36 is a perfect square but 56 is not.
256 is a perfect square but 346 is not.

(iii) Square of even number is always an even and the square of odd number is odd.
For example:
4² = 16(even)
5² = 25(odd)

(iv) A perfect square can never be a negative number.

(v) For every natural number n, (n + 1)² – n² – (n + 1) + n
For example: 14² -13² = (13 + 1) + 13 = 14 + 13 = 27
26² – 25² = (25 + 1) + 25 = 26 + 25 = 51

5. Pythagorean Tripletr: A triplet (m, n,p) is called a Pythagorean triplet if m² + n² = p²
For example: (3, 4, 5), (8, 15, 17) and (20, 21, 29)
Product of two consecutive even or odd natural numbers:
Example:
11 x 13 = 143 – 12² – 1 (product of odds)
13 x 15 = 195 = 14² – 1 (product of odds)
44 x 46 = 2024 = 45² – 1 (product of evens)

Some Patterns in square numbers:

 

On this page, you will find Data Handling Class 8 Notes Maths Chapter 5 Pdf free download. CBSE NCERT Class 8 Maths Notes Chapter 5 Data Handling will seemingly help them to revise the important concepts in less time.

CBSE Class 8 Maths Chapter 5 Notes Data Handling

Data Handling Class 8 Notes Conceptual Facts

1. Data: Collection of information as numerical facts about the objects or events is called Data.

2. Types of Data: Discrete and continuous.

3. Frequency: The number of times each score occurs is called frequency.

4. Range: The difference between the greatest and the least observations is called the Range.

5. Relative Frequency: The ratio of the frequency of each item to the sum of all frequencies is called Relative frequency.
\(\text { Relative frequency }=\frac{\text { Frequency of an object }}{\text { Total frequency }}\)

6. Class-size: Difference between upper and lower limits of a class interval is called class-size.

7. Class-mark: Mid value of class interval is called its class-mark.
\(\text { Class-mark }=\frac{\text { Upper limit }+\text { Lower limit }}{2}\)

8. Class-frequency: The frequency of a particular class-interval is called class-frequency.

9. Bar Graph: Horizontal and vertical Histogram: Horizontal and vertical

10. Pie chart: Pie chart is a way of representing the data in the form of sectors of a circle.
Central angle for a sector = \(\left(\frac{\text { Value of the component }}{\text { Total value }} \times 360\right)^{\circ}\)