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The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 7 Let’s Cultivate and Reap Goodness Important Questions ensure conceptual clarity.

Let’s Cultivate and Reap Goodness Extra Questions and Answers Class 8 Basic Science Chapter 7 Kerala Syllabus

Let’s Cultivate and Reap Goodness Class 8 Important Questions

Question 1.
Choose the correct answer.
Statement 1: Statement 1: Vertical farming is an innovative agricultural method in which crops are grown in vertically stacked layers.
Statement 2: Vertical farming can be implemented even in urban areas with limited space.
(a) Statements 1 and 2 are correct.
(b) Statements 1 and 2 are wrong
(c) Statement 1 is true and Statement 2 is false
(d) Statement 1 is false and Statement 2 is true
Answer:
(a) Statements 1 and 2 are correct

Question 2.
Which one is isolated? Write the common characteristic of the others.
Potassium, zinc, copper, manganese
Answer:
Potassium, others are micronutrients

Question 3.
Complete the statement.
The taste, colour, smell, and nutritional value of the products will vary depending on the characteristics of the land where they are cultivated. Based on this, agricultural products produced in certain regions receive …………………..
Answer:
Geographical indication status

Question 4.
Identify and match the word pairs. Also, write the relationship between the word pairs.
Azospirillum: Biofertiliser:: Urea: ……………………..
Answer:
Artificial fertiliser, fertilisers and their characteristics.

Question 5.
Complete the table.

Irrigation method	Peculiarity
Drip irrigation	………….(a)……………
………….(b)…………..	A method of directly supplying water to the roots of plants through a cotton cloth filter from a water source is called wick irrigation. It requires less water than drip irrigation.

Answer:
(a) This is an irrigation method using pipes and valves to water the roots in drops. By doing this, the loss of water is reduced to maximum. Another significance of this method is that the availability of water to all plants is ensured.

(b) Wick Irrigation

Question 6.
Which are the correct pairs?
a) Pod borer – Legume
b) Leaf-rolling Caterpillar – Brinjal
c) Stem Borer – Okra
d) Pod borer – Brinjal
e) Leaf-rolling Caterpillar – Okra
Answer:
(a), (e).

Question 7.
Which pair is correct?
a) Online system – Disease and pest information collection, solution – Up-to-date knowledge about climate change – Market opportunities
b) Family members – financial assistance to farmers, procurement, marketing
c) Local self Government Institutions – Financial Assistance, Employment Assistance, Psychological Support.
d) Cooperative societies – Use of barren lands – Approval – Government assistance
e) Krishi Bhavan – Distribution of best planting materials – Scientific guidance and training programs for agriculture
Answer:
(a), (e).

Question 8.
Select and write down the possibilities of overcoming space constraints from those given below.

Sack fanning, smart farming, aquaponics, greenhouse, vertical farming, terrace farming, tissue culture, mulching

Answer:
Sack farming, aquaponics, vertical farming, and terrace farming.

Question 9.
Observe the picture and answer the questions below.

(a) Which farming method is shown in the picture?
(b) What is the advantage of this farming method?
Answer:
(a) Pet bottle farming
(b) To maximise the use of space

Question 10.
Select the ones related to artificial fertilisers from the ones given below.
a) Does not harm soil structure or decomposers.
b) A much smaller amount is sufficient compared to other fertilisers.
c) Plants can easily absorb it.
d) Urea is an example
e) Plants get the nutrients released from these bio residues by the decomposers.
f) It is artificially produced and used to increase the nutrient value of the soil.
g) Excessive fertilizer application can harm soil structure and decomposers.
h) Microorganisms are added to the soil to help fix nitrogen and phosphorus.
Answer:
(c), (d), (f), (g)

Question 11.
Observe the newspaper article and answer the questions below.

GM crops as hope for farmers… Kochi – GM crops are reaching farmers to increase their income…..

(a) What are GM crops?
(b) Write examples of GM crops?
Answer:
(a) GM crops are genetically modified crops. Genetic engineering allows for the incorporation of new traits into crops by altering their genetic structure.

(b) Examples of such crops include cotton, which is resistant to pests, soybeans, which are resistant to herbicides, and rice, which is rich in vitamin A.

Question 12.
What is tissue culture?
Answer:
This is a technology that helps produce large numbers of plants with the same characteristics as the parent plant. Seedlings are produced by separating tissues from suitable parts of the plant and growing them in a special nutrient medium.

Question 13.
Differentiate between drip irrigation and wick irrigation.
Answer:
Drip irrigation – This is an irrigation method that uses pipes and valves to deliver water in droplets to the root zone. This minimises water loss and ensures that all plants receive the same amount of water.
Wick irrigation – This method delivers water directly from the water source to the root zone of plants using a cotton wick. It requires less water than drip irrigation.

Question 14.
(a) What are the characteristics of the following agricultural products?

Palakkadan Matta rice, Malabar pepper, Kuttiyattur mango

(b) On what basis are such agricultural products special?
Answer:
(a) They have been granted geographical indication status.

(b) Depending on the characteristics of the land where it is cultivated, the taste, colour, smell, and nutritional value of the products will vary. Based on this, agricultural products produced in certain regions are given Geographical Indication status.

Question 15.
What is the role of the following in making agriculture a success story?
(a) Online system
(b) Family members
(c) Local self-government bodies
Answer:
(a) Online system – disease and pest information collection, solutions, real-time information on climate change, market opportunities
(b) Family members – Financial assistance – Employment assistance – Psychological support
(c) Local self-government bodies – Use of barren lands, approval, government assistance.

Question 16.
List the following. Give a title to the list.
Magnesium, chlorine, nickel, sulfur

………………………………….	……………………………………

Answer:

Macronutrients	Micronutrients
Magnesium, Sulfur	Chlorine, Nickel

Question 17.
Write the similarities and differences.
• Nano fertilisers
• Artificial fertilisers
Answer:
Similarity – Both are artificial fertilisers. They can be easily absorbed by plants.

Difference – Nano fertilisers: Artificial fertilisers in the form of nanoparticles. Much smaller amounts are required compared to other fertilisers. They do not change the chemical composition of the soil like artificial fertilisers.

Artificial fertilisers: Excessive application of fertilisers can harm the soil structure and disrupt the activities of decomposers.

Question 18.
If there is a mistake in the underlined part of the statements given below, correct it and write it down.
(a) Nanofertilisers added microorganisms to the soil that help in the fixation of nitrogen and phosphorus.
(b) When using organic fertilisers, plants receive nutrients that decomposers release from them.
(c) Organic fertilisers are sufficient in very small quantities compared to other fertilisers.
(d) Ammonium sulphate is an artificial fertiliser.
(e) Excessive application of biofertilisers can harm soil structure and decomposers.
Answer:
(a) Biofertilizers are fertilizers that add microorganisms to the soil that help fix nitrogen and phosphorus.
(c) Nano-fertilisers are only needed in very small quantities compared to other fertilisers.
(e) Excessive application of artificial fertilisers can harm soil structure and decomposers.

Question 19.
Native varieties are beneficial for the environment. Justify the statement.
Answer:
Native varieties are adapted to the local environment and can be grown in harmony with it. They are naturally resistant to pests and diseases in the area, which reduces the use of pesticides. They also help maintain the ecological balance by supporting local pollinators. They also require less fertiliser, which can reduce costs.

Question 20.
A farmer raises cattle, chicken, duck, fish, and rice.
(a) What is this fanning method known as?
(b) What are the advantages of this fanning method?
Answer:
(a) Integrated farming

(b) Multiple sources of income – Farmers can earn money from multiple activities, not just from one crop. Even if one crop fails, they can earn income from other crops.
Efficient use of land and resources – Waste from one activity can be used for another by doing different activities in the same area.

Question 21.
Complete the illustration.
Answer:
(a) By sharing images and information related to crops, you can find solutions to problems with the help of artificial intelligence.

(b) Plants are grown in nutrient solutions, and with the help of sensors, the amount of nutrients is detected and provided as needed.

(c) Aeroponics

Question 22.
What is the government aiming to achieve by giving agricultural awards to children?
Answer:
The government gives such awards to encourage children to develop an interest in agriculture and understand the importance of agriculture in our lives. Such agricultural awards /make children proud of learning and participating in agriculture. Recognise children who farm at school or at home and motivate them to do more farming. It helps students understand why agriculture is important for food and the environment. Young minds may have new and creative ideas for agriculture. Awards help encourage such ideas. It teaches teamwork, responsibility, patience, and care for nature. Agriculture is a part of our culture and heritage. These awards help children appreciate it.

Question 23.
What are some agricultural awards in Kerala?
Answer:

• Karshakottama Award for the best farmer
• Karshaka Tilakam Award for the best woman farmer
• Kerakesari Award for the best coconut farmer
• Samashakti Award for the best agricultural worker
• Yuva Karshaka Award for young farmers
• Karshaka Pratibha Award for the best student farmer

Question 24.
What are the government-led programs to help new entrepreneurs?
Answer:
Government of India:

• Startup India
  Objective – Supporting new business ideas
• Pradhan Mantri Mudra Yojana
  Objective – Providing financial assistance to start small enterprises.
• Atal Innovation Mission
  Objective – Encouraging creative and innovative ideas among children in schools and colleges.
• Made in India
  Objective – Developing India as a manufacturing hub.

Government of Kerala

• Kerala Start-up Mission
  Aim – To make Kerala a start-up friendly state
• Young Innovators Program
  Aim – To identify and encourage innovative ideas among school and college students
• Kudumbashree Mission
  Aim – Women empowerment

Question 25.
What are the Various farming methods to maximise the use of space for farming?
Answer:
Sack farming, aquaponics, Pet bottle farming, vertical farming, pot cultivation, and terrace farming.

Question 26.
What are the limitations and possibilities of various farming methods to maximise the use of land for agriculture?
Answer:

• Sack farming: Potential: Helps grow vegetables in small spaces using old sacks.
  Limitations: Requires regular watering, cannot grow crops with deep roots.
• Aquaponics: Potential: Grows plants and fish together, saves water and space.
  Limitations: Requires technical knowledge and regular maintenance.
• Pet bottle farming: Potential: Reuses waste bottles to grow small plants in limited spaces.
  Limitations: Only suitable for small plants with shallow roots.
• Vertical Farming: Potential: Grows more crops in less space using vertically stacked layers.
  Limitations: Requires proper sunlight or artificial lighting. Costs more
• Pot farming: Potential: An Easy way to grow vegetables and flowers at home.
  Limitations: Limited soil and space can reduce plant growth.
• Terrace Farming: Potential: Converts rooftops into mini-farms for farming.
  Limitations: There is a possibility of water stagnation on the terrace. The ground should be provided with a drainage system.

Question 27.
Prepare a note on vertical farming.
Answer:
Vertical farming uses shelves or stacked layers to grow plants upwards, allowing more crops to be grown in a smaller space. The plants are arranged in such a way that all layers receive sufficient sunlight. Since water drips from the top layer to the ones below, many plants reuse the same water, which saves water.

Question 28.
A vertical farming model that can be built at school and home at low cost.
Answer:
Arrange 4 – 5 used plastic bottles or grow bags vertically on a wooden frame or hanging ropes. Make holes in each bottle for water to drain. Fill the bottle with soil and compost. Grow small plants like mint, spinach, coriander, and chili.

Question 29.
What are the different fertilisation methods?
Answer:
Some fertilisers are spread on the field before or after planting. Others are applied near the roots of plants. Liquid fertilisers are sprayed on the leaves, while others are mixed with water and sprayed on the crops. Using different methods, depending on the type of crop and soil, ensures better yields.

Question 30.
What are the different types of fertilisers used in agriculture?
Answer:
Organic fertilisers, artificial fertilisers, nano fertilisers, and biofertilisers.

Question 31.
What are the benefits of biofertiliser?
Answer:
Microorganisms that help in the fixation of nitrogen and phosphorus are added to the soil. They do not harm the soil structure and decomposers. Examples include Rhizobium, Azospirillum, and Mycorrhiza.

Question 32.
What are the characteristics of organic fertilisers?
Answer:
They are Bio-residues. It will not harm either the texture of the soil or the decomposers. Plants get the nutrients released from these bioresidues by the decomposers. Nutrients may be less, and the process of decomposition takes a long time.

Question 33.
What are the characteristics of nano-fertilisers?
Answer:
They are artificial fertilisers in the form of nanoparticles. They can be easily absorbed by plants. They are required in very small quantities compared to other fertilisers. They do not change the chemical composition of the soil like artificial fertilisers. Examples of nano-fertilisers include nano-urea, nano-phosphate, and nano-magnesium sulfate.

Question 34.
Prepare a note on artificial fertilisers.
Answer:
Artificial fertilisers are artificially produced and used to increase the nutrient value of the soil. These can be easily absorbed by plants. Excessive application of fertilisers can also harm the soil structure and decomposers. Ammonium phosphate, urea, and ammonium sulfate are examples of artificial fertilisers.

Question 35.
What is the importance of indigenous varieties?
Answer:
Indigenous varieties are those that are adapted to the local environment. They are naturally resistant to pests and diseases in the area, so the use of pesticides can be reduced. They also help maintain ecological balance by supporting local pollinators. They also require less fertiliser and reduce costs.

Question 36.
What are the various methods of producing improved varieties of planting material?
Answer:
Grafting, budding, layering and tissue culture are used to produce seedlings with the same characteristics as the parent plant.

Question 37.
What would be the advantage of a rice plant that produces rice containing many nutrients?
Answer:
This will be very helpful as this rice plant can provide a complete diet. This means that, especially for people who cannot afford to buy a variety of foods, all the nutrients like proteins, vitamins, minerals, and energy can be obtained only from rice. This will reduce malnutrition, help keep people healthy, and make agriculture more useful. Scientists are already working on crops that contain vitamin A, such as golden rice.

Question 38.
Gather additional information about tissue culture.
Answer:
Uses
To grow large numbers of plants quickly. To produce exact copies (clones) of a healthy plant. To preserve rare or endangered plants. To grow disease-free plants.

Varieties
In agriculture – crops such as bananas, sugarcane, and orchids
In horticulture – for flowers and ornamental plants.
In forests – to grow more trees quickly.
In medicine and research – to study plant diseases and develop drugs.

Advantages
Rapid production of thousands of plants. All plants have the same quality, making it possible to grow plants even in places with limited space. Can be done all year round regardless of weather conditions.

Limitations
Requires a separate lab and trained people. The cost of setting up a lab is high.

Question 39.
How do GM crops threaten indigenous crops?
Answer:
GM crops can spread rapidly and take over farmland, reducing the number of traditional crops. This can lead to a loss of biodiversity. Native plants and their natural resistance to local pests or conditions may be lost over time.

Question 40.
How does a greenhouse help in agriculture?
Answer:
This system helps in cultivating crops in both the rainy season and summer. The greenhouse is made of sheets like plastic, nylon, and polyethene. It also helps in reducing the incidence of pests and diseases as it is covered on all sides.

Question 41.
What is the advantage of drip irrigation?
Answer:
This is an irrigation method that uses pipes and valves to help water drip down to the root zone. Doing this minimises water loss and ensures equal water availability to all plants.

Question 42.
What is wick irrigation?
Answer:
This is a method of delivering water directly from the water source to the root zone of plants using a cotton wick. It requires less water than drip irrigation.

Question 43.
How does mulching help farms?
Answer:
This is the traditional method of covering the soil in the fiejds using dry leaves, hay, etc, to reduce water loss due to evaporation. Through this method, it is possible to reduce the growth of weeds and to enrich the soil.

Question 44.
Prepare a note on Integrated Pest Management.
Answer:
PEST CONTROL

• Although there are different methods for pest control, the population density of pests and the nature off the crops should be taken into account when choosing the pest control methods.
• Farmers do not want to kill all the pests, but rather control their growth in a way that does not damage the crops.
• Integrated pest control is a method that minimises the use of pesticides through automated pest control methods using various types of nets and traps, friendly insects, and the cultivation of seeds that are resistant to pests.

Question 45.
What is integrated farming?
Answer:
Agriculture is the cultivation of birds, fish, and animals along with plant care. Thus, integrated farming is the care of diverse organisms together.

Question 46.
Prepare a note on smart farming.
Answer:
Smart farming is the effective use of modern technologies in agriculture.

• Artificial intelligence: By sharing images and information related to crops, you can find solutions to problems with the help of artificial intelligence.
• Internet of Things (IoT): With the help of sensors, moisture, fertility, and pest infestations are identified, and a problem-solving system is prepared using machines.
• Hydroponics: Plants are grown in nutrient solutions, and with the help of sensors, the amount of nutrients is detected and proyided as needed.
• Aeroponics: Water and nutrients are delivered to the roots that grow into the air in a timely manner . with the help of sensors.

Question 47.
How to make agricultural product marketing smart?
Answer:
In this era of online marketing, agricultural marketing also needs to become smart. By providing a system that allows consumers to see everything from sowing to harvesting, the reliability and market value of the products can be increased. This can be easily achieved through sensors, drones, and AI cameras in the fields. This can also help deliver products directly to consumers worldwide. This can also increase the global marketing potential of products that have been granted geographical indication status.

Question 48.
Prepare a note on geographical indication.
Answer:
The Ministry of Commerce and Industry has to approve the geographical indication status. Depending on the characteristics of the land in which it is cultivated, there will be differences in the taste, colour, smell and nutritional value of the products. On the basis of this, agricultural products produced in certain areas are given geographical indication status. Such products get added value in the market.

Question 49.
What are some agricultural products that have received Geographical Indication status?
Answer:
Palakkadan Matta rice, Malabar pepper, Kuttiattoor Mango, Kodungallur pottuvellari, Tirur Vettila,
Benganapally mango, Kashmiri saffron, Nagpur orange, Jeeraksala rice, Arunachal orange.

Question 50.
What are the advantages of mobile apps for farmers?
Answer:
There are apps that provide weather alerts, pest and disease warnings, expert advice on agriculture, market price levels, and information about benefits for farmers. If such facilities are implemented properly, the agriculture sector will become stronger.

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 6 Metals and Non Metals Important Questions ensure conceptual clarity.

Metals and Non Metals Extra Questions and Answers Class 8 Basic Science Chapter 6 Kerala Syllabus

Metals and Non Metals Class 8 Important Questions

Question 1.
Which metal has the highest malleability?
a) Aluminium
b) Iron
c) Copper
d) Gold
Answer:
d) Gold

Question 2.
Which of the following metals is the most electrically conductive?
a) Aluminium
b) Silver
c) Copper
d) Gold
Answer:
b) Silver

Question 3.
Find the odd one out
a) Aluminium
b) Sodium
c) Potassium
d) Lithium
Answer:
a) Aluminium (Others are soft metals)

Question 4.
Find and fill in the relationship
The shining of metal surfaces: Metallic lustre
The ability to produce sound when struck on the surface: ____________
Answer:
Sonority

Question 5.
What is the basic substance formed when magnesium oxide dissolves in water?
Answer:
Magnesium Hydroxide

Question 6.
Why do iron appliances in houses near the sea rust quickly?
Answer:
Iron rusts quickly due to the presence of salt (sodium chloride) in the air.

Question 7.
What metal is present in haemoglobin in the blood?
Answer:
Iron

Question 8.
Which of the following metals is subject to corrosion the fastest?
a) Gold
b) Aluminium
c) Iron
d) Sodium
Answer:
d) Sodium

Question 9.
Generally metals can be hammered and flattened into thin sheets. This characteristic property of metals is known as _____________ .
Answer:
Malleability

Question 10.
Write aluminium, copper, gold, and silver in the order of decreasing electrical conductivity.
Answer:
Silver > Copper > Gold > Aluminium

Question 11.
Metals can be drawn and stretched into wires. This property is called ductility. Write any two cases where ductility is used.
Answer:

• Filament of bulb
• Electric wires
• Gold ornaments

Question 12.
Which properties of metals are utilised in the following cases?
a) Iron is used to make weapons.
b) Aluminium is used to make food packaging.
Answer:
a) Hardness
b) Malleability

Question 13.
Give examples of non-metals that are added to metals to make alloys.
Answer:

1. Carbon
2. Phosphorous

Question 14.
Alloys generally have high melting points. Give examples of metals with low melting points.
Answer:

1. Gallium
2. Caesium

Question 15.
Which properties of metals are used in the following situations?
a) Copper is used to make bells.
b) Tungsten is used to make the filament of a light bulb.
Answer:
a) Sonority – the ability to produce a specific sound when struck with a hard object.
b) Ductility – the ability to be formed into very thin wires.

Question 16.
What factors increase the corrosion of iron?
Answer:

• Presence of air
• Presence of moisture
• Presence of salt

Question 17.
Copper nails are used instead of iron nails in coastal areas. Why?
Answer:
In coastal areas, there is a presence of salt in the air. Iron rusts quickly in the presence of air and moisture. Therefore, copper nails are used instead of iron nails.

Question 18.
Classify the following as metals or non-metals.
• Carbon
• Phosphorous
• Sulphur
• Gallium
• Helium
• Sodium
• Caesium
Answer:

Metals	Non-Metals
Sodium Gallium Caesium Calcium	Carbon Sulphur Phosphorous Helium

Question 19.
Magnesium reacts with oxygen in the air to form magnesium oxide.
a) Write the chemical equation for this reaction.
b) What is the product of magnesium oxide dissolved in water?
Answer:
a) 2Mg + O₂ → 2MgO
b) Magnesium Hydroxide

Question 20.
Write any two metals found in the human body and their importance.
Answer:
Iron – is an important component of haemoglobin in the blood.
Calcium – strengthens bones and teeth. Regulates blood pressure.

Question 21.
Compare and list any three properties of metals and non-metals.
Answer:

Metals	Non metals
Generally, they are hard.	Generally, they are less hard.
They exhibit sonority.	They don’t exhibit sonority.
Generally, they are electrically conductive.	Not thermal conductors.

Question 22.
What are the properties of gold that make it suitable for making jewellery?
Answer:
a) Gold is used to make jewellery by alloying it with copper or silver.
b) Malleability, metallic lustre, corrosion resistance, ductility.

Question 23.
Give reasons for the following:
a) The handles of electrical tools and cooking utensils are made of non-metals.
b) Metals like sodium, potassium etc. are stored in kerosene.
c) Pickles and curds are not stored in metal containers.
Answer:
a) Electric tools and cookware are made of metals. Metals are good conductors of electricity and heat. Therefore, their handles are made of non-metals such as wood, plastic, rubber, etc. to ensure safe handling without injury.

b) Sodium and potassium are very reactive metals. They react rapidly with air and moisture and are destroyed. They are stored in kerosene to avoid contact with the environment.

c) Acids are present in sour foods like pickles and curd. Acids can react with metals to form other substances and can corrode metal containers.

Question 24.
a) What is an alloy?
b) What are the benefits of alloying metals?
c) Give examples of alloys.
Answer:
a) Metals are combined with other metals or non-metals to make alloys.

b) It is done to obtain materials with desirable properties and to resist corrosion. A very small amount of non-metals like carbon, phosphorus, etc., are also added to such alloys.

c) Stainless steel, brass, bronze

Question 25.
a) What is corrosion of metals?
b) Suggest ways to prevent corrosion of metals
Answer:
a) Metals react with various elements in the atmosphere to form compounds. This process is palled corrosion.

b)

• Paint metal surfaces.
• Apply oil and grease.
• Apply non-metallic coatings such as rubber and plastic.
• Convert into alloys.

Question 26.
Take three test tubes. Put a rust-free and shiny iron nail in each of them. Place a wet cloth in the first test tube, and add a cloth soaked in salt water to the second test tube.. Iron nails should be fully immersed in these three test tubes. Take anhydrous calcium chloride or quicklime in the third test tube. All three test tubes should be closed immediately with a cork after adding the materials.
What will be the observation after a few days? Write the reason for the observation in each test tube.
Answer:
Test tube 1: The nail in the test tube is rusty
This is due to the presence of air and moisture in the test tube.
Test tube 2: The nail in the test tube is rustier. In addition to the presence of air and moisture, the presence of salt increases the rate of rusting.
Test tube 3: The nail in the test tube is not rusty. The nail absorbs the moisture inside the test tube. In the absence of moisture, the rusting process does not take place.

Question 27.
Observe the picture.

Calcium chloride is taken in a test tube. A smooth iron nail is moistened and passed through a cork and the test tube is closed.
a) What will be the observation after a few days?
b) Write the reason for the observation.
c) What is the conclusion drawn from this?
Answer:
a) The part of the nail inside the test tube is not rusted. The part of the nail outside the test tube is rusted. The calcium chloride absorbs the moisture inside the test tube. Therefore, the iron does not rust.
b) The presence of water and moisture outside the test tube causes the iron to rust rapidly.
c) The presence of water and air affects the rusting of iron.

Question 28.
a) How is soda water made?
b) Write the chemical equation for this reaction.
c) What is observed when blue litmus paper is dipped in soda water? What is the reason?
Answer:
a) Soda water is made by dissolving carbon dioxide in water under high pressure.
b) CO₂ + H₂O → H₂CO₃
c) Soda water is carbonic acid. The presence of acid turns blue litmus red.

Question 29.
Observe the diagram of the electric circuit.

a) Which of the following objects will make the bulb light up if you connect it to the part marked PQ?
• Rolled aluminum foil
• Rubber band
• Glass rod
• Plastic wire
• Iron nail
• Silver necklace
b) What is the reason for this difference?
Answer:

Bulb Glows	The bulb does not glow
Rolled Aluminium foil Iron nail Silver necklace	Glass rod Rubber band Plastic wire

b) Aluminium, iron, and silver are electrical conductors. Glass, rubber, and plastic are not electrical conductors.

Question 30.
Select and arrange the items from columns B and C that match those in section A.

A	B	C
Aluminium	Sonority	Filaments
Tungsten	Thermal Conductivity	Church Bells
Copper	Ductility	Cooking utensils

Answer:

A	B	C
Aluminium	Thermal Conductivity	Cooking utensils
Tungsten	Ductility	Filaments
Copper	Sonority	Church bells

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 5 Elements and Compounds Important Questions ensure conceptual clarity.

Elements and Compounds Extra Questions and Answers Class 8 Basic Science Chapter 5 Kerala Syllabus

Elements and Compounds Class 8 Important Questions

Question 1.
All matter is made up of minute particles called _____________ .
a) Atom
b) Molecule
c) Element
d) Compound
Answer:
a) Atom

Question 2.
____________ discovered that water could be split into hydrogen and oxygen by passing electricity through it.
a) Mendeleev
b) Henry Moseley
c) Cavendish
d) Humphry Davy
Answer:
d) Humphry Davy

Question 3.
Cr is the symbol for which element?
a) Calcium
b) Chromium
c) Chlorine
d) Carbon
Answer:
b) Chromium

Question 4.
Who invented the modern periodic table?
Answer:
Henry Moseley

Question 5.
An ammonia molecule contains one nitrogen atom and three hydrogen atoms. How would you represent five ammonia molecules?
Answer:
5NH₃

Question 6.
Find the relation and fill up the blanks.
Sodium – (Na): Natrium – Latin name
Potassium – (K): ______________ .
Answer:
Kalium – Latin name

Question 7.
Find the monoatomic element from the following.
a) Hydrogen
b) Helium
c) Oxygen
d) Chlorine
Answer:
b) Helium

Question 8.
Find the Odd one out.
a) Rutherfordium
b) Nobelium
c) Rubidium
d) Einsteinium
Answer:
Rubidium (Others are synthetic elements)

Question 9.
Which group is not included in Dobereiner’s triads?
a)

Li, Na, k

b)

He, Ne, Ar

c)

Ca, sr, Ba

d)

CI, Br, I

Answer:
b)

He, Ne, Ar

Question 10.
Give an example of a polyatomic element.
Answer:
Phosphorous (P₄)
Sulphur (S₈)

Question 11.
a) What is the white powder formed when magnesium burns in air?
b) Write its chemical formula.
Answer:
a) Magnesium Oxide
b) MgO

Question 12.
a) Which substances are obtained when sugar is heated strongly in a dry boiling tube?
b) Which of these is an element? Which is a compound?
Answer:
a) Carbon – water
b) Element – Carbon
Compound – Water

Question 13.
What is the basis for naming the elements given below?
a) Mendelevium
b) Rubidium
Answer:
a) From the name of the scientist Mendeleev
b) From the basis of red colour

Question 14.
Write the names of two elements that are found in liquid state at normal temperature.
Answer:
Mercury, Bromine

Question 15.
How do elements and compounds differ?
Answer:
Elements are pure substances made up of the same type of atoms. They cannot be further divided into components through chemical reactions.

Compounds are pure substances formed by the combination of atoms of two or more elements in a fixed ratio. These can be dissociated into constituent elements through chemical reactions.

Question 16.
The symbol for the element hydrogen is H. What is the difference between 2H and H₂?
Answer:
2H refers the two atoms of Hydrogen.
H₂ refers to a nitrogen molecule formed by two atoms.

Question 17.
Find the number of molecules and the total number of atoms in the following.
a) O₂
b) 5F₂
Answer:
a) No. of molecules – 1
Total no. of atoms – 2

b) No. of molecules – 5
Total no. of atoms – 10

Question 18.
It is said that oxygen is an element and carbon dioxide is a compound. Why?
Answer:
In an oxygen molecule, there are only the same type of atoms.
In carbon dioxide, there is the combination of atoms of the elements oxygen and carbon in a fixed ratio.

Question 19.
a) What are the components of water?
b) How can we separate the components of water?
Answer:
a) Hydrogen, Oxygen
b) Water can be split into its components by passing electricity through it.

Question 20.
a) What are periods and groups in the periodic table?
b) How many of these are there in the modern periodic table?
Answer:
a) The horizontal rows in the table are called periods and the vertical columns are called groups. Elements in a group show similar chemical properties.

b) Periods – 7
Groups – 18

Question 21.
When the element carbon burns in air, it combines with oxygen to form carbon dioxide gas.
a) Write what are the reactants and products in this reaction.
b) Write the chemical equation for this reaction using symbols and chemical formulas.
Answer:
a) Reactants: – Carbon (C)
Oxygen (O₂)
Products – Carbon dioxide (CO₂)
b) C + O₂ → CO₂

Question 22.
Classify the following into elements and compounds and list them.
• Carbon
• Carbon dioxide
• Ammonia
• Sodium chloride
• Oxygen
• Sodium
Answer:

Elements	Compounds
• Carbon • Oxygen • Sodium	• Carbon dioxide • Ammonia • Sodium Chloride

Question 23.
Write any three ideas in John Dalton’s atomic theory.
Answer:

• All matter is made up of minute particles called atoms.
• An atom is the smallest particle that can participate in a chemical reaction.
• An atom cannot be divided during a chemical reaction.
• An atom cannot be created or destroyed.
• All atoms of an element are of the same size, property and mass.
• Atoms of different elements differ in their size, property and mass, (any three)

Question 24.
The molecular formula of a compound is H₂SO₄.
a) What elements are contained in this compound?
b) Find the total number of molecules contained in 5H₂SO₄ and also the total number of atoms.
Answer:
a) Hydrogen (H)
Sulphur (S)
Oxygen (O)

b) Number of molecules = 5
Total number of atoms = 35
(H = 10, S = 5, O = 20)

Question 25.
What are the advantages of the periodic table prepared by Mendeleev?
Answer:

• Mendeleev arranged the 63 elements known till that day in ascending order of their atomic masses and prepared a table.
• Blank spaces were left for elements to be discovered and their properties were predicted.
• Elements with similar properties were grouped together to simplify the study of elements and their compounds.

Question 26.
What are the limitations of Mendeleev’s periodic table?
Answer:

• The order of atomic mass was not strictly followed in the case of all elements. Hydrogen could not be given an exact position.
• Elements with very different properties had to be placed in the same group.

Question 27.
The names of some scientists and their contributions are given in the table. Write them in the correct order.

A	B
Splitting of water by passing electricity through it	Henry Moseley
Representation of elements by letters	Sir Humphry Davy
Modern Periodic table	Berzelius

Answer:

A	B
Splitting of water by passing electricity through it	Sir Humphry Davy
Representation of elements by letters	Berzelius
Modern Periodic table	Henry Moseley

Question 28.
Sugar is heated strongly in a dry boiling tube.
a) What will be the observation?
b) What products are formed?
c) What are the elements in sugar?
Answer:
a) Observation – A black substance remains in the boiling tube.
b) Carbon (C), Water (H₂O)
c) Carbon (C), Hydrogen (H), Oxygen(O)

Question 29.
Below are some statements related to early attempts at element classification. Match the statements with the ones in brackets that match them.
(Mendeleev, Dobereiner, Berzelius, Lavoisier, Newlands, Henry Moseley)
a) Classified the then-known elements into metals and non-metals.
b) Classified the elements of similar properties into groups of three.
c) Arranged the elements in ascending order of their atomic masses.
Answer:
a) Lavoisier
b) Dobereiner
c) Mendeleev

Question 30.
The names, nomenclature, and symbols of some elements are given in A, B, C columns. Match these in the correct order and write them.

A Element	B Nomenclature	C Symbol
Chromium	From the Latin name	Cr
Copernicium	From the Greek word, which means colour	Cn
Copper	From the name of a scientist	Cu

Answer:

A Element	B Nomenclature	C Symbol
Chromium	From the Greek word, which means colour	Cr
Copernicium	From the name of a scientist	Cn
Copper	From the Latin name	Cu

 

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 4 Chemistry of Changes Important Questions ensure conceptual clarity.

Chemistry of Changes Extra Questions and Answers Class 8 Basic Science Chapter 4 Kerala Syllabus

Chemistry of Changes Class 8 Important Questions

Question 1.
Burning of wax is a ……………………… change.
(Chemical change / Physical change)
Answer:
Chemical change

Question 2.
What is the form of energy exchanged during the state transition of matter?
Answer:
Heat energy

Question 3.
The amount of space required for matter to exist is …………………………
Answer:
Volume

Question 4.
What gas is produced when magnesium reacts with hydrochloric acid?
a) Chlorine
b) Hydrogen
c) Oxygen
d) Nitrogen
Answer:
b) Hydrogen

Question 5.
An example of a substance that undergoes sublimation is:
a) Water
(b) Talc
(c) Wax
(d) Camphor
Answer:
(d) Camphor

Question 6.
Find the relationship and complete.
Gas that aids combustion: Oxygen
Gas that burns: _____________
Answer:
Hydrogen

Question 7.
What is the energy change that occurs in a Dry cell?
Answer:
Chemical energy is converted into electrical energy.

Question 8.
What is the chemical product formed when electricity is passed through water containing a small amount of acid?
Answer:
Hydrogen and Oxygen

Question 9.
Which solution is used for electroplating copper onto an iron nail?
Answer:
Copper sulphate solution

Question 10.
To gold-plate a copper bangle, what should be connected to the positive terminal of the battery?
Answer:
Gold

Question 11.
Select the correct statements related to gases from the ones given below:
a) Less distance between particles.
b) More energy of particles.
c) Higher speed of particle movement.
d) More attractive force between particles.
Answer:
b) More energy of particles. and c) Higher speed of particle movement.

Question 12.
When a candle burns, both chemical and physical changes occur. What are these?
Answer:
Chemical Change: Burning of a candle
Physical Change: Melting of a candle

Question 13.
Magnesium is taken in a test tube, and a liquid is added to it. A vigorous chemical reaction occurs, and a gas is released. If a burning splinter is shown to the gas, it burns with a “pop” sound.
a) Identify the probable liquid added to the test tube.
b) Which gas was produced?
Answer:
a) Dilute Hydrochloric acid
b) Hydrogen

Question 14.
What is the energy change occurring in the following?
a) Combustion of fuel
b) Photosynthesis
Answer:
a) Chemical energy is converted into heat energy
b) Light energy is converted into chemical energy.

Question 15.
Classify the following into chemical changes and physical changes:
a) Wax melts
b) Wax burns
c) Milk turns into curd
d) Milk thickens (or solidifies) on cooling
Answer:

Chemical changes	Physical changes
Wax burns	Wax melts
Milk turns into curd.	Milk thickens (or solidifies) on cooling.

Question 16.
Two processes are given below:
Quicklime is produced by strong heating limestone (or shells).
Slaked lime is produced by adding water to quicklime.
a) Which of these is an endothermic reaction?
b) Which is an exothermic reaction?
Answer:
a) Quicklime is produced by strong heating limestone (or shells)
b) Slaked lime is produced by adding water to quicklime.

Question 17.
What are the suitable solutions for electroplating the metals given below?
a) Silver
b) Gold
Answer:
(a) Sodium cyanide + Silver cyanide
(b) Sodium cyanide + Gold cyanide

Question 18.
What are the forms of energy associated with chemical reactions?
Answer:
Heat, Light, Electricity

Question 19.
What are the main properties of matter
Answer:
It occupies space
It has mass

Question 20.
Quicklime is taken in a steel cup. A little water is added to it.
(a) What is the substance formed when water is added to quicklime?
(b) Why do people handling quicklime wear gloves?
Answer:
a) When water is added to quicklime (calcium oxide), slaked lime (calcium hydroxide) is formed.

b) The reaction of quicklime with water is highly exothermic. If quicklime comes into contact with moisture on the skin, it will react and release a lot of heat. This can cause severe burns to the skin.

Question 21.
Suggest an experiment to prove that matter requires space to exist.
Answer:
Aim: To demonstrate that matter occupies space.
Materials: Beaker, water, and a small stone.
Procedure & Observation:

1. Fill a beaker partially with water and note the initial water level.
2. Carefully lower the stone into the water.
3. Observe that the water level rises.

Conclusion: The rise in water level proves that the stone, being matter, takes up space (has volume)

Question 22.
Write what type of chemical reaction each of the following is:
a) Fireflies emit light.
b) When zinc and copper nails are inserted into a lemon and connected to an LED through a copper wire, the LED glows.
c) Ammonium chloride decomposes when heated strongly.
Answer:
a) Bioluminescence
b) Electrochemical Reaction
c) Thermochemical reactions

Question 23.
Complete the following chemical reaction

Answer:
(a) Silver (Ag)
(b) Chlorine gas (Cl₂)
(c) Water (H₂O)
(d) Oxygen (O₂)
(e) Water (H₂O)
(f) Slaked lime (Ca(OH)₂)

Question 24.
A substance is strongly heated in a test tube. When a burning incense stick was held near the mouth of the test tube, the incense stick flared up.
a) What caused the incense stick to flare up?
b) What might be the substance that was heated?
c) What type of chemical reaction is this?
Answer:
a) When a substance is heated, oxygen gas is released. Oxygen is a gas that aids in burning/combustion.
b) Potassium permanganate
c) Endothermic reaction

Question 25.
What is the reason for the following?
a) Water kept in the freezer turns into ice.
b) Silver salts are stored in colored bottles.
c) Some specific types of medicines are stored in refrigerators.
Answer:
a) Water turns into ice in a freezer due to the cooling/freezing process (Phase Transition). When water is cooled below its freezing point (0°C), its molecules lose kinetic energy and arrange themselves into a more ordered, crystalline structure. This change of state from liquid to solid is a physical process that occurs when enough heat energy is removed from the water.

b) Silver salts (like silver bromide, silver chloride) are stored in colored or opaque bottles because they are sensitive to light and undergo photochemical reactions when exposed to it. Light energy can decompose silver salts into elemental silver, causing them to blacken or lose their intended properties. Colored or opaque bottles block out light, preventing this decomposition and preserving the integrity of the silver salts.

c) Some specific types of medicines are stored in refrigerators because their chemical stability and efficacy are temperature-dependent. Many ingredients in these medicines are sensitive to heat. Higher temperatures can cause them to degrade, lose their potency, or even become toxic. Refrigeration slows down these chemical degradation processes, maintaining the medicine’s effectiveness and ensuring its safety for use throughout its shelf life.

Question 26.
Define the following
a) Thermochemical Reactions
b) Photochemical Reactions
c) Electrochemical Reactions
Answer:
a) The reactions in which heat energy is liberated or absorbed are known as thermochemical reactions.
b) The reactions in which light energy is absorbed or liberated are known as photochemical reactions
c) If electrical energy is absorbed or produced during a chemical reaction, it is known as an electrochemical reaction.

Question 27.
a) What is electrolysis?
b) Write any practical application of electrolysis.
Answer:
a) The process of dissociation of a substance by absorbing electrical energy is known as electrolysis.
b) Electroplating

Question 28.
Draw a diagram of the setup for electroplating gold onto a copper bangle and label its parts
Answer:

Question 29.
A picture of the arrangement of copper plating on an iron bangle is drawn. What are the mistakes in this?

Answer:
Copper should be connected to the positive terminal of the battery.
The iron bangle should be connected to the negative terminal of the battery. Copper sulphate solution should be used as the electrolyte (or solution).

Question 30.
Match the following

A	B	C
Sublimation	Chemical energy is converted into electrical energy.	Naphthalene
Firefly	Change of state	Photochemical reaction
Dry cell	Bioluminescence	Electrochemical reaction

Answer:

A	B	C
Sublimation	Change of state	Naphthalene
Firefly	Bioluminescence	Photochemical reaction
Dry cell	Chemical energy is converted into electrical energy.	Electrochemical reaction

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 3 Pressure Important Questions ensure conceptual clarity.

Pressure Extra Questions and Answers Class 8 Basic Science Chapter 3 Kerala Syllabus

Pressure Class 8 Important Questions

Question 1.
Which of the following is the unit of atmospheric pressure?
(N, parsec, kg/m³, bar)
Answer:
bar

Question 2.
It is possible to drink juice using a straw because of ……………………
Answer:
Atmospheric pressure

Question 3.
Correct the following. As the number of particles increases, gas pressure decreases.
Answer:
As the number of particles increases, gas pressure increases.

Question 4.
The instrument used to measure atmospheric pressure is a ………………………
Answer:
Barometer.

Question 5.
The pressure exerted on an area of 10 m² by a force of 50 N is ………………….. .
(5 N, 5 N/m², 0.2 N/m², 0.2 N)
Answer:
5 N/m²
P = F/A, F = 50 N, A =10 m²
P = 50 /10 = 5 N/m²

Question 6.
The instrument used to measure liquid pressure is ……………………. .
Answer:
Manometer

Question 7.
Choose the correct equation of pressure.
Answer:
(P = F × A, P = A/F, P = F/A)
Answer:
P = F/A

Question 8.
Observe the diagram

Water flowing down through the holes P, Q and R on a bottle is depicted.
a) Which is the correct figure? i/ii/iii
b) What is the reason for this inference?
Answer:
a) Figure iii is correct

b) As depth of liquid increases pressure increases. So the water flowing from the hole R will have the greatest force and covers more distance.

Question 9.
Observe the picture below. Both beakers contain the same volume of water.

a) Which beaker experiences maximum pressure at the bottom?
b) Justify your answer.
Answer:
a) Beaker A experience maximum pressure at the bottom.

b) The height of liquid column (or depth) is more in beaker A than beaker B. So more pressure is experienced at the bottom of beaker A.

Question 10.
Liquids also exert pressure. Write down any two factors that influence liquid pressure. (Term II, 2022)
Answer:

1. Height of the liquid column
2. Density of the liquid

Question 11.
The weight of the air column over unit area of earth’s surface is atmospheric pressure.
a) What is standard atmospheric pressure?
b) Name the instrument used to measure atmospheric pressure. (Annual 2022)
Answer:
a) Atmospheric pressure at sea level is known as standard atmospheric pressure. It is defined as the weight of a mercury column that is 0.76 m high, with a unit cross sectional area, exerting a pressure of 1 atm.

b) Barometer.

Question 12.
Two identical balloons one filled with water and other with kerosene of equal quantity.

a) Identify the balloon filled with water.
b) Why is the expansion of balloons appear different in figures (a) and (b)? (Annual 2022)
Answer:
a) Figure (b)

b) Water has higher density than kerosene. As density increases, liquid pressure increases. So the balloon which is expanded has water filled in it and the other balloon which is small in size has kerosene filled in it.

Question 13.
Check whether the given statement is correct or wrong. Correct the wrong statement.
(i) Atmospheric pressure increases as height from the Earth’s surface increases.
(ii) The porters in railway stations place a piece of cloth before carrying luggage on head to decrease the area of contact between luggage and head to reduce the pressure felt on their head.
Answer:
(i) Statement is wrong
Corrected statement: Atmospheric pressure decreases as height from the Earth’s surface increases.

(ii) Statement is wrong
Corrected statement: The porters in railway stations place a piece of cloth to increase the area of contact between luggage and head to reduce the pressure felt on their head.

Question 14.
Calculate the force exerted by atmospheric pressure on a table surface of area 3 m². Atmospheric pressure is 101325 Pascal.
Answer:
Force = Pressure × Area
= 1 Pa × 3 m² = 101325 × 3
= 303975 N

Question 15.
The thrust acting per unit area by a liquid is the liquid pressure.

a) Three points A, B and C are marked on a cylindrical glass vessel filled with water as shown in figure. If three identical inflated balloons are placed on these points inside the cylinder, which one will be the largest in size? Justify your answer.
b) Do you expect any change in size to the balloons, if the water is replaced with kerosene? Explain.
Answer:
a) The balloon placed in the position A will be the largest in size. As depth decreases liquid pressure also decreases. The pressure experienced at position A is the least compared to positions B and C and so the balloon with largest size occupies position A.

b) Yes, when kerosene is replaced with water the size of the balloons become comparatively larger than in water because kerosene has low density than water. When density decreases liquid pressure also decreases. So when the pressure experienced is less, the size of balloons (volume of balloons) is comparitively larger.

Question 16.
When area increases, pressure decreases. Find three situations where this principle is applied.
Answer:
a) We can walk easily through a muddy place by placing a plank over it.
b) Ducks walk easily over mud.
c) Constructing dams with wider basements.

Question 17.
Write down reasons for the following statements.
a) Astronauts wear specially designed suits.
b) Sewing needles are made with sharp tips.
c) Connecting the wheels of tanks and other such vehicles using wide chains.
Answer:
a) The suit helps us to maintain the pressure between the dress and the body equal to the atmospheric pressure.

b) Sharp tips have less surface area of contact. As area of contact decreases, pressure increases so that sewing needles can pierce into the materials to be stitched easily.

c) Connecting wheels of tanks and other such vehicles using wide chains helps in making more surface area of contact with the ground to exert less pressure over it. This ensures its smooth motion.

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 2 Motion and Force Important Questions ensure conceptual clarity.

Motion and Force Extra Questions and Answers Class 8 Basic Science Chapter 2 Kerala Syllabus

Motion and Force Class 8 Important Questions

Question 1.
SI unit of force is ……………………….
Answer:
newton(N)

Question 2.
A child is standing in a field. With respect to the ground, the child is in a state of ……………………. (rest / motion).
Answer:
rest

Question 3.
If a body in motion covers equal distance in equal intervals of time, the body is said to have ………………………….. (uniform speed / non uniform speed).
Answer:
uniform speed

Question 4.
Cheetah is the fastest animal on land. Its speed is given in different ways. Which among these is correct?
a) 25 metre per s
b) 25 m/s
c) 25 m/s²
d) 25 M/S
Answer:
b) 25 m/s

Question 5.
Examine the figure below.

A man starts from A and reaches D through the points B and C. Find the distance travelled from A to D.
Answer:
Distance travelled from A to D = 4 + 3 + 4 = 11 km

Question 6.
Motion of four different objects are stated below. Choose the odd one. Also state the reason for choosing it.
(A train starting from the station, A stone thrown up, The motion of a ball rolling down a hill, The motion of a coconut falling from a coconut tree)
Answer:
A train starting from the station.
Because the other three (stone thrown up, ball rolling down a hill, and coconut falling) move mainly because of gravitational force.

Question 7.
The moving parts of machines experience wear and tear. Why?
Answer:
Due to frictional force

Question 8.
The solid substance used as a lubricant is ………………………
Answer:
Graphite

Question 9.
Bearings are used in motor vehicles. Why?
Answer:
Because rolling friction is less than that of sliding friction.

Question 10.
Define the term streamlining?
Answer:
The method of reducing friction by changing the shape is called streamlining.

Question 11.
“Overspeed of vehicles result in accidents”
Write two messages to be written on an awareness board in your school premises to minimise road accidents.
Answer:
Speed thrills but kills, Don’t mix drink with drive, Better late than never, Wear helmets while driving motor cycles.

Question 12.
The paths of two cars are as shown below. Car A started from P and reached R through Q and car B started from P and reached R through S.

a) What is the total distance covered by the car A?
b) What is the total distance covered by car B?
Answer:
a) Total distance covered by car A = 500 + 600 = 1100 m
b) Total distance covered by car B = 400 + 600 = 1000 m

Question 13.
Analyse the table given below and find which force is felt in each situation.

Situation	Force
A coconut falling from a coconut tree	Gravitational force
Magnet attracts an iron nail	…………a)………….
Hammering a nail	……………b)…………..

Answer:
a) Magnetic force
b) Muscular force

Question 14.
A book on a table is in a state of rest.
a) Identify the reference body for the above statement?
b) Considering the Sun as reference body, the book is in a state of (motion/rest)
Answer:
a) Reference body: Table
b) With respect to Sun, the book is in a state of motion

Question 15.
The conversation between two students standing on the road side about a person inside a moving bus is given below.
Student 1 “That person is at state of rest”
Student 2 “No, he is in motion”
Explain the possibilities of the correctness of these statements based on the concept of a reference body.
Answer:

• Reference body: Bus
  That person with respect to the bus: State of rest
  Student 1 – Statement is correct
• Reference body: Road
  That person with respect to the road: State of motion
  Student 2 – Statement is correct

Question 16.
A person starts from A, moves through B, C and reaches D in 30 s.
a) Calculate the distance.
b) Find out the speed.

Answer:
a) Distance covered from A to D = 10 + 10 + 10 = 30 m
b) Speed = \(\frac{\text { Distance }}{\text { Time }}\) = \(\frac{30 \mathrm{~m}}{30 \mathrm{~s}}\) = 1 m/s

Question 17.
a) Choose the appropriate reference body from the given list so that a passenger sitting in a moving train can said to be in motion, (train, Another passenger next to him in the train, objects outside the train)
b) What is meant by the term ‘reference body’?
Answer:
a) The correct reference body is: Objects outside the train
Because the passenger is moving when seen from outside the train.

b) The object taken to determine the state of motion or the state of rest of a body is called the reference object.

Question 18.
What is frictional force? Point out two disadvantages of friction in our daily life and suggest remedy for overcoming it?
Answer:
When a surface moves or tries to move over another surface, a parallel force is produced between them against their relative motion. This force is called frictional force.

• Difficulty to draw water from the well.
  Remedy – Apply oil in the pulley.
• Chains of bicyles sometimes does not move due to friction.
  Remedy – Apply grease on it.

Question 19.
Figure shows a device used in motor vehicles.

a) Name the device.
b) How much time will it take for a vehicle to cover a distance of 90 km at 60 km/h rate?
Answer:
a) Speedometre

b) Speed = \(\frac{\text { distance travelled }}{\text { time taken }}\)
distance travelled = 90 km
speed = 60 km/h
Time taken = \(\frac{90}{60}\) = 1.5 h

Question 20.
Observe the depiction of the path taken by a person as he moves from A to C through B.

Find out his speed?
Answer:
Speed = \(\frac{\text { distance travelled }}{\text { time taken }}\)
distance travelled = 20 m + 60 m = 80 m
Time taken = 4 s + 6 s = 10 s
Speed = \(\frac{80}{10}\) = 8 m/s

Question 21.
Complete the table suitably.

Measurement	Unit
Time	…………..a)…………..
…………..b)…………..	m
Speed	…………..c)…………..

Answer:
a) s
b) Distance
c) m/s

Question 22.
Classify the following situations into contact and non-contact forces.
a) Applying break in a bicycle.
b) The earth revolving around the sun.
c) The speed of a ball rolling on ground is reduced.
Answer:
Contact forces
a) Applying brake in a bicycle
c) The speed of a ball rolling on ground is reduced.
Non-Contact force
b) The earth revolving around the sun.

Question 23.
The following figure is of a traffic sign board placed near school for road safety.

a) What does the board indicate?
b) A motor bike rider travels 180 km in 2 hours through the road near the school. Calculate his speed. Does he cross the speed limits as per Kerala Road Safety Rules.
c) Which is the device used to find the speed in vehicles.
Answer:
a) Speed limit around this school area is 30 km/h

b) Speed = \(\frac{\text { distance travelled }}{\text { time taken }}\) = \(\frac{180}{2}\) = 90 km/h
Yes, The bike travelled in overspeed,

c) Speedometer

Question 24.
Classify the following situations as contact force and non-contact force.
a) A magnet attracting a nail
b) Pushing a wall
c) An apple falling from an apple tree
Answer:
a) A magnet attracting a nail – Non-contact force
b) Pushing a wall – Contact force
c) An apple falling from an apple tree – Non-contact force

Question 25.
A child starts from A and reaches C through B in 1 s.

a) What is the total distance travelled by the child?
b) Calculate the speed of the child?
Answer:
Total distance travelled by the child = 4 m + 3 m = 7 m
Speed = \(\frac{\text { distance travelled }}{\text { time taken }}\) = \(\frac{7}{1}\) = 7 m/s

Question 26.
Why are airplanes and boats made in special shapes?
Answer:
Airplanes and boats are made in special shapes to reduce friction. Smooth, streamlined designs help them move easily through air and water, making travel faster and easier by decreasing the resistance they face.

Question 27.
Bus A covered 75 m in 5 s. Bus B covered 169 m in 13 s.
a) Which bus covered a greater distance?
b) Which bus has a higher speed?
Answer:
a) Bus B covered greater distance (169 m).
b) Speed of bus A = \(\frac{75 \mathrm{~m}}{5 \mathrm{~s}}\) = 15 m/s
Speed of bus B = \(\frac{169 \mathrm{~m}}{13 \mathrm{~s}}\) = 13 m/s
Bus A has higher speed.

The comprehensive approach in SCERT Class 8 Basic Science Textbook Solutions Chapter 1 Measurement and Units Important Questions ensure conceptual clarity.

Measurement and Units Extra Questions and Answers Class 8 Basic Science Chapter 1 Kerala Syllabus

Measurement and Units Class 8 Important Questions

Question 1.
Find out the odd one from following units and write it down.
a) m
b) g
c) kg
d) mg
Answer:
a) m
All others are the units of mass.

Question 2.
How much time does light take to travel 3 lakh kilometre in vacuum?
(1s, 1/2s, 2s, 3s)
Answer:
1s

Question 3.
Find out the correctly written unit from those given below.
(Volt, pascal, Kelvin, Ampere)
Answer:
pascal

Question 4.
SI unit of force is ………………………
Answer:
newton (N)

Question 5.
Imagine that the distance from school to your friend’s house is 2250 m. State this in kilometres.
Answer:
2250 m = 2250/1000 km = 2.250 km

Question 6.
Find the odd one.
cm³ kg/m³; mm, m³
Answer:
mm, All others are derived units.

Question 7.
Choose the derived unit from the following.
(m, kg, N, s)
Answer:
N

Question 8.
Select the odd one. State reason.
(m², m³, m, kg/m³)
Answer:
m. m is a fundamental unit. Others are derived units.

Question 9.
Identify the relation in first word-pair and complete the second one.
Volume : m³
Density : ………………………
Answer:
kg/m³

Question 10.
Write the appropriate unit for expressing the distance between planets in the solar system.
a) m
b) nm
c) AU
d) km
Answer:
c) AU

Question 11.
Pick out the correct representation of units from the following data.
a) 37.65 m
b) 37 m 65 cm
c) 10 Pa
d) 20 Kg
Answer:
Correct representations are a) 37.65 m and c) 10 Pa

Question 12.
Which of the following does not belong to the group?
(km, kg, mm, cm)
Answer:
kg, others are units of length.

Question 13.
A child measures the total thickness of the papers of his science diary having 200 sheets and finds it to be 2 cm. Find the thickness of one of these papers in SI unit.
Answer:
Thickness of one paper = Height of the pile of papers /No. of papers.
Thickness of one paper = 2 cm/200 = 1/100 cm = 0.01 cm
Thickness of paper in SI unit = 0.01 cm/100 = 0.0001 m

Question 14.
Write down the following units in descending order of their values.
a) 2 cm, 2 m, 2 km, 2 mm
b) 5 g, 5 mg, 5 quintal, 5 kg
Answer:
a) 2 km > 2 m > 2 cm > 2 mm
b) 5 quintal > 5 kg > 5 g > 5 mg

Question 15.
Write down the following units in the ascending order of their values.
a) mm, nm, cm, μm
b) 1 m, 1 cm, 1 km, 1 mm
Answer:
a) nm < μm < mm < cm
b) 1 mm < 1 cm < 1 m < 1 km

Question 16.
Complete the table.
Quantity – SI Units
Length – ………………….
Time – ………………….
Area – ………………….
Density – ………………….
Answer:
Length – metre (m)
Time – second (s)
Area – square metre (m²)
Density – kilogram per cubic metre (kg/m²)

Question 17.
Complete the table.

Unit	Symbol
Newton	(a) …………………..
Kelvin	(b) ……………………
Ampere	(c) ……………………
Metre	(d) …………………..
Kilogram	(e) ……………………
Second	(f) …………………….

Answer:
(a) N
(b) K
(c) A
(d) m
(e) kg
(f) s

Question 18.
Classify the physical quantities given in the box as fundamental quantities and derived quantities.

Length, density, area, mass

Fundamental quantities	Derived quantities

Answer:

Fundamental quantities	Derived quantities
Length, mass	Density, area

Question 19.
1 mm is the least count of a metre scale.
a) What do you mean by least count?
b) Arrange the following units in ascending order of their values.
(μm, km, nm, cm) (Annual 2022)
Answer:
a) The smallest value that can be measured using an instrument is called its least count.
b) nm < μm < cm < km

Question 20.
Based on the fundamental physical quantity length, write down the following questions. (Term 1, 2023)
a) In which unit is the thickness of plastic carry bags expressed?
b) How many kilometres make one astronomical unit?
Answer:
a) micrometre
b) 15 crore kilometre (150 million kilometre)

Question 21.
We know about fundamental units and derived units.
a) What is meant by derived units?
b) Based on which fundamental unit is area expressed?
c) Write down the unit of density.
Answer:
a) Derived units are units that can be stated using fundamental units or that depend on fundamental units.

b) Area (m²) is expressed in terms of the fundamental unit length.

c) Density = mass/volume
The unit of density is kg/m³

Question 22.
Convert the following units into SI units without changing their values.
a) 3500 g
b) 2.5 km
c) 2 h
Answer:
a) 3500 g = 3500/1000 kg = 3.5 kg
b) 2.5 km = 2.5 × 1000 m = 2500 m
c) 2 h = 2 × 60 × 60 s = 7200 s.

Question 23.
State whether the following symbol are right or wrong. Correct them if wrong.
a) m/s/s
b) kilogram per cubic metre
c) 100 n
d) 20 kgs
e) 3M
f) 1 kg 500 g
Answer:
a) Wrong, m/s² is the correct form.
b) Right
c) Wrong. 100 N is the correct form.
d) Wrong. 20 kg is the correct form.
e) Wrong. 3 m is the correct form.
f) Wrong. 1.5 kg or 1500 g is the correct form

Students often refer to Kerala State Syllabus SCERT Class 8 Maths Solutions and Class 8 Maths Chapter 5 Solutions of Equations Questions and Answers Notes Pdf to clear their doubts.

SCERT Class 8 Maths Chapter 5 Solutions Solutions of Equations

Class 8 Kerala Syllabus Maths Solutions Chapter 5 Solutions of Equations Questions and Answers

Solutions of Equations Class 8 Questions and Answers Kerala Syllabus

Adding and Subtracting (Page No. 79)

Question 1.
“Six more marks and I would have gotten a hundred out of a hundred in my math exam”, Rajan thought sadly. How much did he score?
Answer:
The mark is 6 less than 100.
Present mark is 94.

Question 2.
“5 more years, and I would be 18. I can vote”, Lissy calculated. How old is she now?
Answer:
The present age is 5 less than 18.
Her current age is 13 years.

Question 3.
What should be added to 123 to make it 321?
Answer:
Number to be added is 321 – 123 = 198

Question 4.
What should be subtracted from 432 to get 234?
Answer:
Number to be subtracted is 432 – 234 = 198

Textbook Page No. 80

Question 1.
Gopalan bought a bunch of bananas. 7 of the bananas had begun to rot, and he removed them. Now there are 46. How many bananas were there in the bunch?
Answer:
The number of good fruits is 46.
Including spoiled fruits total is 46 + 7 = 53.

Question 2.
Vimala bought some things for 163 rupees, and now she has 337 rupees left. How much did she have at first?
Answer:
The total amount in hand is the sum of the balance amount and the amount for purchasing goods.
It is 337 + 163 = 500 rupees

Question 3.
What number becomes 321 on subtracting 123?
Answer:
The subtraction should be done from the number 123 more than 321.
Number is = 321 + 123 = 444

Multiplication and Division (Page No. 80)

Question 1.
The salary of the manager of an office is five times the salary of a peon. The manager gets 75000 rupees a month. How much does the peon get?
Answer:
Peon’s salary is \(\frac {1}{5}\) of Manger’s salary
Peon’s salary is \(\frac {1}{5}\) × 75000 = 15000 rupees

Question 2.
Some friends went for a trip and decided to divide equally among them the 12500 rupees they had spent. Each had to pay 2500 rupees. How many were there in the group?
Answer:
We have to find out the number of 2500s that make 12500.
This will be the number of members
It is 12500 ÷ 2500
Number of members = \(\frac {12500}{2500}\) = 5

Question 3.
A number multiplied by 12 gives 756. What is the number?
Answer:
12 times a number is 756.
Number is \(\frac {1}{12}\) part of 756
Number = \(\frac {1}{12}\) × 756 = 63

Question 4.
A number divided by 21 gives 756. What is the number?
Answer:
\(\frac {1}{21}\) part of a number is 756.
The number is 21 times 756.
Number = 21 × 756 = 15876

Different Kinds of Change (Page No. 82, 83)

Question 1.
The perimeter of a rectangle is 50 metres and the length of one side is 5 metres. What is the length of the other side?
Answer:
Sum of two adjacent sides is 50 ÷ 2 = 25
One side is 5.
Other side 25 – 5 = 20 cm

Question 2.
When Anita and her friend bought 5 pens together, they got a reduction of 3 rupees in the price. The total cost was 32 rupees. Had they bought the pens individually, how much would it have cost each?
Answer:
If there is no reduction in price, the price of 5 pens is 35 rupees
Price of a pen = 35 ÷ 5 = 7 rupees

Question 3.
In each of the problems below, the result of doing some operations on a number is given. Find each number:
(i) Three added to two times the number gives 101
(ii) Two added to three times the number gives 101
(iii) Three subtracted from two times the number gives 101
(iv) Two subtracted from three times the number gives 101
Answer:
(i) Without adding three, twice the number = 101 – 3 = 98
Number is \(\frac {1}{2}\) part of 98.
Number = \(\frac {1}{2}\) × 98 = 49

(ii) Three times the number 101 – 2 = 99
Number is \(\frac {1}{3}\) of 99.
Number = \(\frac {1}{3}\) × 99 = 33

(iii) Twice the number = 101 + 3 = 104
Number is \(\frac {1}{2}\) of 104.
Number is \(\frac {1}{2}\) × 104 = 52

(iv) 3 times the number is 103.
Number is \(\frac {103}{3}\)

Question 4.
The sum of 6 times a number and 4 is 100. What is the number?
Answer:
If 4 is not added, 6 times the number = 100 – 4 = 96
Number is \(\frac {1}{6}\) of 96.
Number = \(\frac {1}{6}\) × 96 = 16

Question 5.
4 times the sum of a number and 6 gives 100. What is the number?
Answer:
6 added to \(\frac {1}{4}\) part of 100.
6 added to the number is 25
Number is 25 – 6 = 19.

Multiple and Part (Page No. 84)

Question 1.
The sum of 2 times a number and 7 times the same number is 27. What is the number?
Answer:
When 2 times a number and 7 times that number are added, we get 9 times that number.
9 times the number is 27.
Number = \(\frac {27}{9}\) = 3

Question 2.
99 added to 12 times a number gives 21 times the number. What is the number?
Answer:
When 12 times a number is subtracted from 21 times that number, we get 99.
9 times the number is 99.
\(\frac {1}{9}\) of 99 is 11.
Number = \(\frac {1}{9}\) × 99 = 11

Textbook Page No. 85

Question 1.
A third of a piece of rope cut away leaves 10 metres. What was the original length?
Answer:
When \(\frac {1}{3}\) is removed results \(\frac {2}{3}\) of length.
It is 10 m.
Length of rope is 10 × \(\frac {3}{2}\) = 15

Question 2.
Half the milk in a can and a third of the remaining was used up, and now there are 5 litres remaining. How many litres did it originally contain?
Answer:
Half of the amount remains \(\frac {1}{3}\) of this is \(\frac {1}{6}\) of the first amount
Used, \(\frac{1}{2}+\frac{1}{6}\). This is \(\frac {4}{6}\) part
Amount remains \(\frac {2}{6}\) part.
It is 5 L.
Amount in the beginning is 5 times \(\frac {6}{2}\).
It is 5 × \(\frac {6}{2}\) = 15L

Algebraic Methods (Page No. 89)

Question 1.
The perimeter of a rectangle is 80 metres, and its length is one metre more than twice the width. What are its length and width?
Answer:
Sum of length and breadth 40
Width = x, length = 2x + 1
∴ x + 2x + 1 = 40
⇒ 3x + 1 = 40
⇒ 3x = 39
⇒ x = 13
∴ Width = 13, Length = 2 × 13 + 1 = 27 cm

Question 2.
When a hundred-rupee note was changed to twenty-rupee and ten-rupee notes, seven notes were obtained. How many of each?
Answer:
Number of 20 rupee notes x, ten rupee notes 7 – x.
∴ 20x + 10(7 – x) = 100
⇒ 20x + 70 – 10x = 100
⇒ 20x – 10x + 70 = 100
⇒ 10x + 70 = 100
⇒ 10x = 100 – 70
⇒ 10x = 30
⇒ x = 3
∴ Number of 20 rupee notes = 3
∴ Number of 10 rupee notes = 4

Question 3.
The price of a book is 4 rupees more than the price of a pen. The price of a pencil is 2 rupees less than the price of this pen. A person bought 5 books, 2 pens, and 3 pencils and paid 54 rupees for them. What is the price of each?
Answer:
The price of a book and a pencil can be written as follows.
Price of pen = x
price of book = x + 4
price of pencil = x – 2
∴ 5(x + 4) + 2x + 3(x – 2) = 54
⇒ 5x + 20 + 2x + 3x – 6 = 54
⇒ 10x + 14 = 54
⇒ 10x = 40
⇒ x = 4
Price of pen 4 rupees, price of book 8, price of pencil 2.

Question 4.
A square containing four numbers in a calendar is marked, and the sum of these numbers is 80. What are the numbers?
Answer:

∴ x + x + 1 + x + 7 + x + 8 = 80
⇒ 4x + 16 = 80
⇒ 4x = 64
⇒ x = 16
Numbers are 16, 17, 23, 24.

Textbook Page No. 92

Question 1.
The age of Appu’s mother is now 9 times that of Appu. After nine years, it will be three times Appu’s age. What are their ages now?
Answer:
If Appu’s age is x, then the mother’s age is 9x
After 9 years ages are x + 9, 9x + 9
∴ (x + 9) × 3 = 9x + 9
⇒ 3x + 27 = 9x + 9
⇒ 18 = 6x
⇒ x = 3
∴ Appu’s age = 3, mother’s age = 27

Question 2.
A class has the same number of girls and boys. On a day when eight boys were absent, the number of girls was twice the number of boys. What are the number of girls and the number of boys?
Answer:
Let the number of boys be x, number of boys x.
When number of boys is x – 8, x = 2(x – 8)
⇒ x = 2(x – 8)
⇒ x = 16

Question 3.
In a class of girls and boys, 50% of the children are girls. When 10 more girls were admitted to this class, this became 60%. How many children were in the class at first?
Answer:
50% denotes the half.
Let the number of boys and the number of girls be x.
There are 2x students.
When 10 girls are added, the number of girls becomes x + 10
∴ x + 10 = 2x × \(\frac {60}{100}\)
⇒ x + 10 = \(\frac {6x}{5}\)
⇒ x = 50
There are 100 students in the class.

Question 4.
Another problem from folk-math. Some lotus flowers have bloomed in a pond. A flock of birds sat on the flowers to rest. First, one bird sat on each flower, but one bird didn’t have a flower to sit on. Then two birds sat on each flower, and there was one flower extra. How many lotuses and how many birds?
Answer:
Let x be the number of lotus flowers.
Number of birds = x + 1
∴ x + 1 = 2(x – 1)
⇒ x = 3
Number of lotus flowers 3, number of birds 4.

Class 8 Maths Chapter 5 Kerala Syllabus Solutions of Equations Questions and Answers

Class 8 Maths Solutions of Equations Questions and Answers

Question 1.
One third of a number is 10 less than the number. Which of the following is the number?
(a) 30
(b) 15
(c) 10
(d) 27
Answer:
\(\frac {2}{3}\) of the number is 10.
Number is \(\frac {3}{2}\) times 10.
Number = 10 × \(\frac {3}{2}\) = 15

Question 2.
The sum of two numbers is 39, difference is 15. Numbers are
(a) 17, 22
(b) 26, 13
(c) 27, 12
(d) 28, 11
Answer:
x, x + 15
∴ 2x + 15 = 39
⇒ 2x = 4
⇒ x = 12
Numbers = 12, 27

Question 3.
Two sides of a triangle are equal. Small angle is 30°. What is one of the equal angles?
(a) 100°
(b) 75°
(c) 70°
(d) 50°
Answer:
Angle sum = 180°
The smallest is 30°.
The sum of the equal angles is 150°
Equal angle is 75°.

Question 4.
When 3 is added to \(\frac {1}{4}\)th of a number gives 15. Find the number.
Answer:
\(\frac {1}{4}\)th of the number is 12.
Number is 4 × 12 = 48

Question 5.
When \(\frac {2}{3}\) of a number is subtracted from a number, we get 13. What is the number?
Answer:
\(\frac {1}{3}\) of the number is 13.
Number is 3 × 13 = 39

Question 6.
The sum of two numbers is 60. One number is four times the other. Find the number.
Answer:
When the number and four times the number are added, we get five times the number.
Number is \(\frac {1}{5}\) part of 60.
The number is 12.

Question 7.
The sum of two consecutive natural numbers is 63.
(a) If the smaller is x, then what is the other number?
(b) Write the equations and find the numbers.
Answer:
(a) x, x + 1 are the numbers.
(b) 2x + 1 = 63
⇒ 2x = 62
⇒ x = 31
Numbers are 31, 32.

Question 8.
Ammu’s mother is four times her mother’s age. After 20 years, mother’s age will be twice Ammu’s age.
(a) If Ammu’s age is x, then write the equation.
(b) Find the age of Ammu and her mother.
Answer:
(a) Ammu’s age x, Mothers age 4x
(b) 20 years hence
Ammu’s age = x + 20
mothers age = 4x + 20
∴ 4x + 20 = 2(x + 20)
⇒ 4x + 20 = 2x + 40
⇒ x = 10
Ammu’s age is 10, Mother’s age is 40.

Question 9.
A man’s age after 15 years will be twice his age before 15 years.
(a) If the present age is x, then write the equation.
(b) Find the present age?
Answer:
(a) Age after 15 years is x + 15
Age before 15 years is x – 15
∴ 2(x – 15) = x + 15
⇒ 2x – 30 = x + 15
⇒ x = 45
(b) Present age = 45 years

Question 10.
The perimeter of a rectangle is 50 cm. Length is 5 cm more than breadth.
(a) What is length + breadth?
(b) If x is the length, then write the equation.
(c) Find the sides.
Answer:
(a) 25 cm
(b) x + x + 5 = 25
⇒ 2x + 5 = 25
⇒ 2x = 20
⇒ x = 10
(c) Sides are 10 cm, 15 cm

Question 11.
The sum of two numbers is 90. The large number is 15 more than twice the small number. Write the equations and find the numbers.
Answer:
Smaller number = x
Larger number = 2x + 15
∴ x + 2x + 15 = 90
⇒ 3x = 75
⇒ x = 25
Numbers are 25, 65.

Question 12.
The sum of the digits of a two-digit number is 10. On reversing the digits, it is found that the number decreases by 36. Find the number.
Answer:
Digit in ten’s place is x.
Digit in one’s place is 10 – x.
Number is 10x + 10 – x
When the digits are reversed number becomes 10(10 – x) + x
It is given that 10(10 – x) + x = 10x + 10 – x – 36
⇒ 100 – 10x + x = 9x – 26
⇒ 100 – 9x = 9x – 26
⇒ 126 = 18x
⇒ x = 7
∴ Number is 73

Question 13.
Length of a bridge is 60 metres longer than \(\frac {1}{3}\) of its length. What is the length of the bridge?
Answer:
If x is the length of the bridge.
∴ \(\frac {2x}{3}\) = 60
⇒ x = 90

Question 14.
In a class of 52 students, the number of boys is \(\frac {6}{7}\) of the number of girls. How many are boys?
Answer:
Number of boys = x
Number of girls = 52 – x
∴ x = \(\frac {6}{7}\) × (52 – x)
⇒ 7x = 6(52 – x)
⇒ 7x = 312 – 6x
⇒ 13x = 312
⇒ x = 24
∴ Boys = 24, Girls = 28

Question 15.
The sum of three consecutive odd numbers is 63.
(a) If the smallest among them is x, then what are the other numbers?
(b) Find the numbers.
Answer:
(a) x, x + 2, x + 4 are the numbers.
(b) 3x + 6 = 63
⇒ 3x = 57
⇒ x = 19
∴ Numbers are 19, 21, 23.

Class 8 Maths Chapter 5 Notes Kerala Syllabus Solutions of Equations

→ Price of 5 pens and 3 pencils is 34 rupees. The price of 3 pens and 5 pencils is 30 rupees. What is the total price of a pen and a pencil together?

→ 64 rupees are needed for 8 pens and 8 pencils. So 8 rupees is needed for a pen and a pencil.

→ 5 pens and 3 pencils cost 34 rupees. 5 pens 5 pencils cost 40 rupees. Note the increased amount is for 2 pencils.

→ The price of 10 pens and 10 pencils is 80 rupees.

→ Three times \(\frac {1}{3}\) of a number is that number itself. So six times \(\frac {1}{3}\) of that number is two times that number.

→ Eight times \(\frac {1}{4}\) of a number is twice that number.

→ What is the sum of eight times \(\frac {1}{4}\) of a number and six times \(\frac {1}{3}\) of that number?

→ Let x be a number. Three times x is 18. This can be written as an equation. 3x = 18 is the equation \(\frac {1}{3}\) of a number is 18. What is the number?
That means, three times that number is 18.
3x = 18
x = \(\frac {1}{3}\) × 18
x = 6

→ 1 more than two times a number is 5.

→ If 1 is not added, two times the number is 4. The number is 2.

Problems that can be solved by simple logic are common in our daily lives. But some problems cannot be solved by simple logic. In mathematics, we use algebra to solve certain problems. The word algebra is derived from the Arabic word Al-Jabr, which means to join together.

Adding and Subtracting
Finding solutions in the form of equations,
x + a = b, x – a = b
Here, only addition and subtraction are needed to find the solutions. The reverse process is the easiest method.

Worksheet – 1

Question 1.
Babu has 600 rupees with him. He went to a shop and purchased some goods. Now he had 301 rupees left with him. How much did he spend?
Answer:
600 – 301 = 299

Question 2.
If we add 54 to a number, we will get 250. What is the number?
Answer:
250 – 54 = 196

Question 3.
Malini had 78 stamps with her. She gave some of them to her friend. Now she has 46 stamps with her. How many stamps did she give to her friend?
Answer:
78 – 46 = 32

Question 4.
When 164 is subtracted from a number, it makes it 235. What is the number?
Answer:
235 + 164 = 399

Multiplication and Division
Finding solutions in the form \(\frac {x}{a}\) = b and ax = b.
Here, only multiplication and division are needed to find the solution.
The reverse process is the easiest method here also.

Worksheet – 2

Question 1.
The price of 4 shirts is 720 rupees. What is the price of one shirt?
Answer:
720 ÷ 4 = 180

Question 2.
The age of Raju’s father is 9 times that of Raju. If the father’s age is 36 years, what is Raju’s age?
Answer:
36 ÷ 9 = 4

Question 3.
A number when multiplied by 14 gives 1008. What is the number?
Answer:
1008 ÷ 14 = 72

Question 4.
A number when divided by 41 gives 215. What is the number?
Answer:
215 × 41 = 8815

Different Kinds of Change
Here we discuss the changes in the form
ax + b = c, ax – b = c, \(\frac {x}{a}\) + b = c
First, we will adopt the method of reverse process, then only the algebraic method.

For example: One added to three times a number gives 100. What is the number?
Here, the last mathematical calculation done on a number is adding ‘1’.
So first we will subtract ‘1’ from the result 100.
So 100 – 1 = 99.
Then the next calculation is multiplying by three, so we will divide 99 by 3.
So the number = \(\frac {99}{3}\) = 33

Worksheet – 3

Question 1.
The double of 3 less than a number is 97. What is the number?
Answer:
3 less than, so add 3
97 + 3 = 100
Double, so half = \(\frac {100}{2}\) = 50

Question 2.
Two less than 3 times a number is 100. What is the number?
Answer:
2 less, so add 2
100 + 2 = 102
3 times, so divide by 3
\(\frac {102}{3}\) = 34

Question 3.
10 is added to half of a number, giving 100. What is the number?
Answer:
10 added, so subtract 10
100 – 10 = 90
Half of a number, so double it.
90 × 2 = 180

Question 4.
Alia has 150 rupees, which is 8 rupees more than twice what Adhil has. How much has Adhil?
Answer:
8 rupees more, so subtract 8
150 – 8 = 142
twice, so half of 142
\(\frac {142}{2}\) = 71

Multiple and Part
If 3 times a number and 2 times the same number added together make 100. What is the number?
Answer:
3 times any number and 2 times the same number make 5 times the number.
That means 5 times the number is 100.
So the number is \(\frac {1}{5}\) of 100.
Number = \(\frac {100}{5}\) = 20

Algebraic Methods
Now we will discuss the algebraic method of solving these word problems. Here, we will take the unknown number as x, then form an equation. Solving is based on the reverse process itself.

For example, the perimeter of a rectangle is 46 cm. The length is 5 cm more than the breadth. What are its length and breadth?
Here, the length is given as 5 more than the breadth.
Breadth is completely unknown.
So it is better to take breadth as ‘x’, which means length is x + 5
∴ Perimeter = 2(length + breadth)
⇒ 2(x + 5 + x) = 46
⇒ x + 5 + x = 23
⇒ 2x + 5 = 23
⇒ 2x = 23 – 5
⇒ 2x = 18
⇒ x = 9
∴ Length = 9 + 5 = 14

Worksheet – 4

Question 1.
Raju has 75 rupees more than Rani. If both of them together have 725 rupees, what are the amounts with Raju and Rani?
Answer:
Rani has ‘x’ rupees
Raju has 75 + x rupees
∴ x + 75 + x = 725
⇒ 2x + 75 = 725
⇒ 2x = 725 – 75
⇒ 2x = 650
⇒ x = 325
Raju has 325 + 75 = 400 rupees

Question 2.
The second angle of a triangle is double the first. The third angle is 40 degrees less than the first. Find the three angles.
Answer:
First angle = x
Second angle = x + x = 2x
Third angle = x – 40
∴ x + 2x + x – 40 = 180°
⇒ 4x – 40 = 180
⇒ 4x = 180 + 40
⇒ 4x = 220
⇒ x = 55°

Students often refer to Kerala State Syllabus SCERT Class 8 Maths Solutions and Class 8 Maths Chapter 3 Square Identities Questions and Answers Notes Pdf to clear their doubts.

SCERT Class 8 Maths Chapter 3 Solutions Square Identities

Class 8 Kerala Syllabus Maths Solutions Chapter 3 Square Identities Questions and Answers

Square Identities Class 8 Questions and Answers Kerala Syllabus

Squares of Sums (Page No. 40)

Question 1.
Calculate the squares below in your head:
(i) 15²
(ii) 25²
(iii) 33²
(iv) \(\left(5 \frac{1}{2}\right)^2\)
(v) \(\left(10 \frac{1}{2}\right)^2\)
(vi) \(\left(25 \frac{1}{2}\right)^2\)
(vii) \(\left(5 \frac{1}{5}\right)^2\)
Answer:
(i) 15² = 10² + 5² + 2 × 10 × 5 = 225
(ii) 25² = 20² + 5² + 2 × 20 × 5 = 625
(iii) 33² = 30² + 3² + 2 × 30 × 3 = 1089
(iv) \(5 \frac{1^2}{2}=5^2+5+\frac{1}{2^2}=30 \frac{1}{4}\)
(v) \(10 \frac{1}{2}^2=10^2+10+\frac{1}{2^2}=110 \frac{1}{4}\)
(vi) \(25 \frac{1}{2}^2=25^2+25+\frac{1}{2^2}=650 \frac{1}{4}\)
(vii) \(5 \frac{1}{5}^2=5^2+2+\frac{1}{5^2}=27 \frac{1}{25}\)

Question 2.
In the general identity on the square of a sum of two numbers, what special case do we get by taking one of the numbers as 2? Do the calculations below in your head, using this:
(i) What is 22²?
(ii) What is 52²?
(iii) 25² = 625; What is 27²?
Answer:
(x + 1)² = x² + 2 × x × 2 + 2² = x² + 4x + 4
(i) 22² = (20 + 2)²
= 20² + 2 × 20 × 2 + 2²
= 400 + 80 + 4
= 484

(ii) 52² = (50 + 2)²
= 50² + 2 × 50 × 2 + 2²
= 2500 + 200 + 4
= 2704

(iii) 25² = 625
27² = (25 + 2)²
= 25² + 2 × 25 × 2 + 2²
= 625 + 100 + 4
= 729

Question 3.
43² = 1849
(i) What is 44²?
(ii) What is 46²?
Answer:
43² = 1849
(i) 44² = (43 + 1)²
= 43² + 2 × 43 × 1 + 1²
= 1849 + 86 + 1
= 1936

(ii) 46² = (43 + 3)²
= 43² + 2 × 43 × 3 + 3²
= 1849 + 258 + 9
= 2116

Textbook Page No. 45

Question 1.
Calculate the squares of some odd numbers and check the following statement. Explain why they are true:
(i) The square of any odd number is odd.
(ii) The square of any odd number leaves a remainder of 1 on division by 4.
(iii) The square of any odd number leaves a remainder of 1 on division by 8.
Answer:

(i) Let the odd number be, 2n + 1 where n = 0, 1, 2, 3,…..
(2n + 1)² = 4n² + 4n + 1 = 2(2n² + 2n) + 1
∴ The square of an odd number is of the form 2n + 1, which is an odd number.

(ii) (2n + 1)² = 4n² + 4n + 1 = 4(n² + n) + 1
That means the square of an odd number is 1 more than a multiple of 4.
∴ It leaves a remainder of 1 on division by 4.

(iii) (2n + 1)² = 4n(n + 1) + 1
Among the two consecutive numbers n and n + 1, one is always even.
So n(n + 1) is always even.
Thus, 4n(n + 1) is divisible by 8.
Hence, the square is of the form multiple of 8 + 1.
That means it leaves a remainder of 1 on division by 8.

Question 2.
Calculate the remainders on dividing the squares of some natural numbers by 4. Explain why the Statements below are true:
(i) The square of any natural number divided by 4 leaves a remainder of 0 or 1.
(ii) Any natural number that leaves a remainder of 2 or 3 on division by 4 is not a perfect square.
Answer:
The natural numbers on division by 4 are of the form 4n, 4n + 1, 4n + 2, 4n + 3, where n = 0, 1, 2,…
The possible remainders are 0, 1, 2, 3.
(i) Even natural numbers can be written as 2n
Squaring it gives (2n)² = 4n²
Here, the remainder is 0.
Odd natural numbers can be written as 2n + 1
Squaring it gives,
(2n + 1)² = 4n² + 4n + 1 = 4(n² + n) + 1
Here, the remainder is 1.
∴ The square of any natural number divided by 4 leaves a remainder of 0 or 1.

(ii) The square of any natural number divided by 4 leaves a remainder of 0 or 1.
∴ Any natural number leaving a remainder of 2 or 3 when divided by 4 is not a perfect square.

Question 3.
See this pattern:
3 = 2² – 1²
5 = 3² – 2²
7 = 4² – 3²
Check whether some other odd numbers can also be written as the difference of two perfect squares. Explain why all odd numbers greater than 1 can be written like this.
(Hint: Recall the general form of an odd number seen in class 7).
Answer:
All odd numbers greater than 1 can be written as the difference of two perfect squares.
Specifically, the difference of the squares of two consecutive natural numbers.
That is, (n + 1)² – n² = 2n + 1, always an odd number.
So, for any odd number n, it can be written as (n + 1)² – n².

Question 4.
Give reasons for the fact that the square of any number ending in 1 also ends in 1. What about numbers ending in 5? And numbers ending in 6?
Answer:
The last digit of a square is determined by the last digit of the original number.
The numbers ending in 1, 5, or 6 will have squares ending in 1, 5, or 6, respectively.
Because their last digits, when multiplied by themselves, result in the same digit.

Squares of Differences (Page No. 50)

Question 1.
Calculate the squares below in your head:
(i) 29²
(ii) 38²
(iii) 999²
(iv) \(\left(9 \frac{1}{2}\right)^2\)
(v) (9.7)²
Answer:
(i) 29² = (30 – 1)²
= 30² – 2 × 30 × 1 + 1²
= 900 – 60 + 1
= 841

(ii) 38² = (40 – 2)²
= 40² – 2 × 40 × 2 + 2²
= 1600 – 160 + 4
= 1444

(iii) 999² = (1000 – 1)²
= 1000000 – 2000 + 1
= 998001

(iv) \(\left(9 \frac{1}{2}\right)^2=9 \times 10+\frac{1}{4}=90 \frac{1}{4}\)
Or
\(\left(9 \frac{1}{2}\right)^2=\left(10-\frac{1}{2}\right)^2=10^2+\left(\frac{1}{2}\right)^2-10=90 \frac{1}{4}\)

(v) (9.7)² = (10 – 0.3)²
= 10² + (0.3)² – 2 × 10 × 0.3
= 100 + 0.09 – 6
= 94.09

Question 2.
See these computations:
3² – (2 × 3) = 3 = 2² – 1
4² – (2 × 4) = 8 = 3² – 1
5² – (2 × 5) = 15 = 4² – 1
Explain the general principle of these using algebra.
Answer:
3² – (2 × 3) = 3 = 2² – 1
4² – (2 × 4) = 8 = 3² – 1
5² – (2 × 5) = 15 = 4² – 1
…………………………………..
…………………………………..
n² – (2 × n) = (n – 1)² – 1

Textbook Page No. 53, 54

Question 1.
See these computations:
\(\left(\frac{1}{2}\right)^2+\left(1 \frac{1}{2}\right)^2=2 \frac{1}{2}\); 2 = 2 × 1²
\(\left(1 \frac{1}{2}\right)^2+\left(2 \frac{1}{2}\right)^2=8 \frac{1}{2}\); 8 = 2 × 2²
\(\left(2 \frac{1}{2}\right)^2+\left(3 \frac{1}{2}\right)^2=18 \frac{1}{2}\); 18 = 2 × 3²
(i) Write the next two lines following this pattern.
(ii) Explain the general principle of these using algebra.
Answer:

Question 2.
Some natural numbers can be written as the difference of two perfect squares in two different ways. For example
24 = 7² – 5² = 5² – 1²
32 = 9² – 7² = 6² – 2²
40 = 11² – 9² = 7² – 3²
Write the next few multiples of 8 as the difference of two perfect squares in two different ways. Explain algebraically how we can do this for all multiples of 8 starting with 24.
Answer:
The next few lines are:
48 = 13² – 11² = 8² – 4²
56 = 15² – 13² = 9² – 5²
64 = 17² – 15² = 10² – 6²
Algebraic explanation is: 8x = (2x + 1)² – (2x – 1)² where x is 3, 4, 5,……….

Question 3.
See how some numbers are written as the difference of two perfect squares in two different ways:
15 = 8² – 7² = 4² – 1²
21 = 11² – 10² = 5² – 2²
35 = 18² – 17² = 6² – 1²
(i) What are the different ways in which the numbers 15, 21, and 35 can be written as the product of two factors?
(ii) Find two more numbers of this type, which can be written as the difference of two perfect squares in two different ways.
(iii) What general result can we form from this?
Answer:
(i) 15 = (8 – 7) × (8 + 7) = 1 × 15
15 = (4 – 1) × (4 + 1) = 3 × 5
21 = (11 – 10) × (11 + 10) = 1 × 21
21 = (5 – 2) × (5 + 2) = 3 × 7
35 = (18 – 17) × (18 + 17) = 1 × 35
35 = (6 – 1) × (6 + 1) = 5 × 7

(ii) 45 = 9² – 6² = 7² – 2²
65 = 33² – 32² = 9² – 4²

(iii) a² – b² = (a – b)(a + b)

Question 4.
Compute the following products by writing them as the difference of two squares.
(i) 78 × 22
(ii) 301 × 299
(iii) \(2 \frac{1}{3} \times 1 \frac{2}{3}\)
(iv) 10.7 × 9.3
Answer:

Question 5.
Find the largest of each of the following pairs of products, without actual multiplication:
(i) 75 × 25; 76 × 24
(ii) 76 × 24; 74 × 26
(iii) 10.6 × 9.4; 10.4 × 9.6
Answer:

Differences of Squares (Page No. 58, 59, 60)

Question 1.
Do the computations below in your head:
(i) 68² – 32²
(ii) \(\left(3 \frac{1}{2}\right)^2-\left(2 \frac{1}{2}\right)^2\)
(iii) 3.6² – 1.4²
Answer:
(i) 68² – 32² = (68 – 32)(68 + 32)
= 36 × 100
= 3600

(ii) \(\left(3 \frac{1}{2}\right)^2-\left(2 \frac{1}{2}\right)^2=\left(\frac{7}{2}\right)^2-\left(\frac{5}{2}\right)^2=\left(\frac{7-5}{2}\right)\left(\frac{7+5}{2}\right)\)
= 1 × 6
= 6

(iii) 3.6² – 1.4² = (3. 6 – 1.4)(3.6 + 1.4) = 11

Question 2.
Note the pattern in the computations below:
3² – 2² = 5 = 3 + 2
4² – 3² = 7 = 4 + 3
5² – 4² = 9 = 5 + 4
(i) Write the next two computations following these.
(ii) Write the general principle in these as an algebraic equation.
(iii) Write this general principle in ordinary language.
Answer:
(i) 6² – 5² = 11 = 6 + 5
7² – 6² = 13 = 7 + 6

(ii) n² – (n – 1)² = 2n – 1 = n + (n – 1)

(iii) The difference between the square of an integer and the square of the preceding integer is equal to the sum of those two integers.

Question 3.
In a calendar sheet, take a square containing nine numbers and mark the numbers on the left and right, top, and bottom of the middle number:

Calculate the products of the left and right numbers and the top and bottom numbers, and also their difference
8 × 10 = 80
2 × 16 = 32
80 – 32 = 48
Do this for other squares of nine numbers. Explain using algebra why the difference is 48 in all cases.
(Hint: It is convenient to take the middle number as x)
Answer:
Let the middle number be x.
The number to the left is x – 1.
The number to the right is x + 1.
The number on top is x – 7.
The number on the bottom is x + 7.
Since, in a calendar, the numbers in a row differ by 1, and the numbers in a column differ by 7.
Product of left and right numbers be (x – 1)(x + 1) = x² – 1
Product of top and bottom numbers be (x – 7)(x + 7) = x² – 49
Difference = (Product of left and right) – (Product of top and bottom)
= (x² – 1) – (x² – 49)
= x² – 1 – x² + 49
= 48
Therefore, the difference between the product of the left and right numbers and the product of the top and bottom numbers is always 48.

Question 4.
As in the previous problem, mark a square of nine numbers in a calendar. Mark the four numbers in the corners:

Calculate the products of the diagonal pairs of numbers and find their difference:
15 × 3 = 45
1 × 17 = 17
45 – 17 = 28
Do this for other squares of nine numbers. Explain using algebra why the difference is 28 in all cases.
Answer:
Let the middle number be x.
The number to the top left is x – 8.
The number to the top right is x – 6.
The number on the bottom left is x + 6.
The number on the bottom right is x + 8.
Product of first diagonal part = (x – 8)(x + 8) = x² – 64
Product of second diagonal part = (x – 6)(x + 6) = x² – 36
Difference = (x² – 36) – (x² – 64)
= x² – 36 – x² + 64
= 28
Therefore, the difference between the products of the diagonal pairs of numbers is 28.

Question 5.
A square has a perimeter of 20 centimetres. A rectangle has one side 2 centimetres longer and one side 2 centimetres shorter than a side of this square.
(i) What is the perimeter of the rectangle?
(ii) What are the areas of the square and the rectangle?
Answer:
Perimeter of the square = 20 cm
One side = \(\frac {20}{2}\) = 5 cm
(i) One side of the rectangle = 5 + 2 = 7 cm
∴ Other side = 5 – 2 = 3 cm
Perimeter of the rectangle = 2 × (7 + 3)
= 2 × 10
= 20 cm

(ii) Area of the square = side²
= 5²
= 25 cm²
Area of the rectangle = 7 × 3 = 21 cm²

Question 6.
One side of a rectangle is longer than the side of a square, and the other side is equally shorter than the side of the square.
(i) What can we say about the perimeters of the square and the rectangle?
(ii) Which has the larger area, the square or the rectangle?
Answer:
Let the side of the square be x cm
One side of the rectangle = x + a
Other side = x – a (where a > 0)
(i) The perimeter of the square = 4x
Perimeter of the rectangle = 2[(x + a) + (x – a)]
= 2(2x)
= 4x
∴ The perimeter of the rectangle is equal to the perimeter of the square.

(ii) Area of the square = x²
Area of the rectangle = (x + a)(x – a) = x² – a²
Here x² – a² < x²
∴ The square has the larger area.

Class 8 Maths Chapter 3 Kerala Syllabus Square Identities Questions and Answers

Class 8 Maths Square Identities Questions and Answers

Question 1.
Calculate the squares below in your head:
(i) 101²
(ii) 9.2²
Answer:
(i) 101² = 100² + 2 × 100 × 1 + 1²
= 10000 + 200 + 1
= 10201

(ii) 9.2² = (9 + 0.2)²
= 9² + 2 × 9 × 0.2 + 0.2²
= 81 + 3.6 + 0.04
= 84.64

Question 2.
23² = 529
(i) What is 24²?
(ii) What is 26²?
Answer:
23² = 529
(i) 24² = (23 + 1)²
= 23² + 2 × 23 × 1 + 1²
= 529 + 46 + 1
= 576

(ii) 26² = (23 + 3)²
= 23² + 2 × 23 × 3 + 3²
= 529 + 138 + 9
= 676

Question 3.
\(\left(1 \frac{1}{2}\right)^2+\left(3 \frac{1}{2}\right)^2+\left(5 \frac{1}{2}\right)^2\) = _____________
Answer:

Question 4.
Find the value of \(\left(1 \frac{1}{2}\right)^2+\left(2 \frac{1}{2}\right)^2+\left(3 \frac{1}{2}\right)^2+\left(4 \frac{1}{2}\right)^2\)
Answer:

Question 5.
\(\left(19 \frac{1}{2}\right)^2+\left(20 \frac{1}{2}\right)^2\) = _____________
Answer:

Question 6.
101² – 100²
Answer:
101² – 100² = 101 + 100 = 201

Question 7.
99999² – 99998²
Answer:
99999² – 99998² = 99999 + 99998 = 199,997

Question 8.
\(\left(99 \frac{1}{2}\right)^2+\left(100 \frac{1}{2}\right)^2\) = _____________
Answer:

Question 9.
From the following, which of the numbers will be the sum of the digits in the ones and tens place of a square of a number that ends in 5?
(a) 2
(b) 5
(c) 7
(d) 3
Answer:
(c) 7

Question 10.
If the square of a number ending in 5 is of the form 56xy. Then y – x = _____________
Answer:
y – x = 5 – 2 = 3

Question 11.
If the square of a number ending in 5 is of the form 110pq. Then p × q = _____________
Answer:
p × q = 2 × 5 = 10

Question 12.
10² + 2² = 100 + 4 = 104. By using this, write 208 as the sum of the two perfect squares.
Answer:
208 = 2 × 104
= 2(10² + 2²)
= (10 + 2)² + (10 – 2)²
= 12² + 8²

Question 13.
3² + 2² = 9 + 4 = 13.
By using this, write 26 as the sum of the two perfect squares.
Answer:
26 = 2 × 13
= 2(3² + 2²)
= (3 + 2)² + (3 – 2)²
= 5² + 1²

Question 14.
11² + 10² = 121 + 100 = 221.
By using this, write 442 as the sum of the two perfect squares.
Answer:
442 = 2 × 221
= 2(11² + 10²)
= (11 + 10)² + (11 – 10)²
= 21² + 1²

Class 8 Maths Chapter 3 Notes Kerala Syllabus Square Identities

→ The square of the sum of two numbers is equal to the sum of the squares of these numbers and twice their product.

→ (x + y)² = x² + y² + 2xy for all numbers x and y.

→ To get the square of one more than a number, we need only add the square of the number, twice the number, and one.

→ (x + 1)² = x² + 2x + 1 for all numbers x.

→ The square of the difference of two numbers is twice their product subtracted from the sum of their squares.

→ (x – y)² = x² + y² – 2xy for all numbers x and y.

→ The product of any two numbers is the difference of the squares of half their sum and half their difference.

→ The difference of the squares of two numbers is the product of the sum and difference of the numbers.

→ x² – y² = (x + y)(x – y) for all numbers x and y.

→ Sum of digits of a perfect square is either 1 or 4 or 7, or 9.

→ The difference of the squares of two consecutive natural numbers is their sum.

In the first chapter, we discussed the problems related to finding the squares of a number. But in this chapter, ‘Square Identities’, we are going to discuss the algebraic formulas used to simplify expressions that involve the squares of numbers. These identities follow a particular pattern, making it easier to expand without doing lengthy multiplication each time. In this chapter, we are going to discuss squares of sums, squares of differences, and differences of squares.

Squares of Sums
We have seen a method to calculate the squares of many numbers in the section Squares.

How do we find the square of 36?
Answer:

36² = (30 + 6)²
= 30² + (2 × 30 × 6) + 6²
= 900 + 360 + 36
= 1296
Here we wrote 36 as the sum of 30 + 6 to calculate its square.
So the square of 36 can be written as (30 + 6)² = 30² + (2 × 30 × 6) + 6²

In general, we can say that the square of the sum of two numbers is equal to the sum of the squares of these numbers and twice their product.
In algebraic form, we can write it as (x + y)² = x² + y² + 2xy for all numbers x and y.
We can see it geometrically as a result of areas:

Worksheet – 1

Question 1.
1. 42²
2. 56²
3. 73²
4. 84²
5. 93²
Answer:
1. 42² = 40² + 2 × 40 × 2 + 2²
= 1600 + 160 + 4
= 1764

2. 56² = 50² + 2 × 50 × 6 + 6²
= 2500 + 600 + 36
= 3136

3. 73² = 70² + 2 × 70 × 3 + 3²
= 4900 + 420 + 9
= 5329

4. 84² = 80² + 2 × 80 × 4 + 4²
= 6400 + 640 + 16
= 7056

5. 93² = 90² + 2 × 90 × 3 + 3²
= 8100 + 540 + 9
= 8649

To get the square of one more than a number, we need only add the square of the number, twice the number, and one.
In general, (x + 1)² = x² + 2x + 1 for all numbers x

For example, find 31²?
Answer:
31² = 30² + 2 × 30 + 1²
= 900 + 60 + 1
= 961

Find 21²?
Answer:
21² = 20² + 2 × 20 + 1²
= 400 + 40 + 1
= 441

Find 51²?
Answer:
51² = 50² + 2 × 50 + 1²
= 2500 + 100 + 1
= 2601

Find 61²?
Answer:
61² = 60² + 2 × 60 + 1²
= 3600 + 120 + 1
= 3721

Find 71²?
Answer:
71² = 70² + 2 × 70 + 1²
= 4900 + 140 + 1
= 5041

Find 101²?
Answer:
101² = 100² + 2 × 100 + 1²
= 10000 + 200 + 1
= 10201

Suppose take y as \(\frac {1}{2}\), we get
(x + \(\frac {1}{2}\))² = x² + x + \(\frac {1}{4}\) for all numbers x
It can also be written in the form, (x + \(\frac {1}{2}\))² = x(x + 1) + \(\frac {1}{4}\)

For example, Find \(1 \frac{1^2}{2}\)?
Answer:
\(\mathbf{1} \frac{1}{2}^{\mathbf{2}}=1^2+1+\frac{1}{4}=2 \frac{1}{4}\) = 2.25

Find \(9 \frac{1^2}{2}\)?
Answer:
\(9 \frac{1^2}{2}=9 \times 10+\frac{1}{4}=90 \frac{1}{4}\) = 90.25

Find \(10 \frac{1^2}{2}\)?
Answer:
\(10 \frac{1}{2}^2=10 \times 11+\frac{1}{4}=110 \frac{1}{4}\) = 110.25

Find \(19 \frac{1^2}{2}\)?
Answer:
\(19 \frac{\frac{1}{2}^2}{2}=19 \times 20+\frac{1}{4}=380 \frac{1}{4}\) = 380.25

Find \(6 \frac{1^2}{2}\)?
Answer:
\(6 \frac{1}{2}^2=6^2+6+\frac{1}{4}=42 \frac{1}{4}\) = 42.25

Find \(12 \frac{1^2}{2}\)?
Answer:
\(12 \frac{1^2}{2}\) = 12² + 12 + \(\frac {1}{4}\)
= 144 + 12 + \(\frac {1}{4}\)
= 156\(\frac {1}{4}\)
= 42.25

For any non-zero number x, we get
\(\left(x+\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}+2\)

For example, Find \(3 \frac{1}{3}^2\)?
Answer:
\(3 \frac{1}{3}^2=\left(3+\frac{1}{3}\right)^2=3^2+\frac{1}{3^2}+2=9+\frac{1}{9}+2=11 \frac{1}{9}\)

Find \(4 \frac{1}{4}^2\)?
Answer:
\(4 \frac{1}{4}^2=\left(4+\frac{1}{4}\right)^2=4^2+\frac{1}{4^2}+2=16+\frac{1}{16}+2=18 \frac{1}{16}\)

Find \(10 \frac{1}{10}^2\)?
Answer:
\(10 \frac{1}{10}^2=\left(10+\frac{1}{10}\right)^2=10^2+\frac{1}{10^2}+2=100+\frac{1}{100}+2=102 \cdot \frac{1}{100}\)

Worksheet – 2

Question 1.
1. \(\left(5 \frac{1}{5}\right)^2\)
2. \(\left(30 \frac{1}{30}\right)^2\)
3. \(\left(100 \frac{1}{100}\right)^2\)
4. \(\left(3 \frac{1}{2}\right)^2+\left(3 \frac{1}{3}\right)^2\)
5. \(\left(10 \frac{1}{2}\right)^2+\left(10 \frac{1}{3}\right)^2\)
Answer:

Square of a number ending in 5:
The square of any number with the last digit (the digit in the one’s place) 5 has 25 as the last two digits.
The last digit of any number is the remainder on division by 10.
So a number ending in 5, divided by 10, leaves a remainder of 5.
The general form of such a number is 10n + 5.
The square of a number in this form is:
(10n + 5)² = (10n)² + (2 × 10n × 5) + 5²
= 100n² + 100n + 25
= 100(n² + n) + 25
= 100n(n + 1) + 25
The last two digits of 100n(n + 1) are zeroes.
∴ The last two digits of 100n(n + 1) + 25 is 2 and 5

For example: Find 35²?
Answer:
35² = 100 × 3 × 4 + 25 = 1225

Find 55²?
Answer:
55² = 100 × 5 × 6 + 25 = 3025

Remainders on dividing natural numbers by 3:
If we consider any number, it will be a multiple of 3 or the number that leaves a remainder of 1 or 2 on division by 3.
That means, the general form of a number which is not a multiple of 3 is 3n + 1, where n = 0, 1, 2, 3,… or 3n + 2, where n = 0, 1, 2, 3,……….

The square of any non-multiple of 3 leaves a remainder of 1 on division by 3.
That means, (3n + 1)² = 9n² + 2 × 3n × 1 + 1
= 9n² + 6n + 1
= 3(3n² + 2n) + 1
= multiple of 3 + 1
Here, the remainder is 1.
(3n + 2)² = 9n² + 12n + 4
= 3(3n² + 4n) + 4
= 3(3n² + 4n) + 3 + 1
= 3(3n² + 4n + 1) + 1
= multiple of 3 + 1
Here also the remainder is 1.
Any perfect square leaves a remainder of 0 or 1 on division by 3.
Any number that leaves a remainder of 2 on division by 3 is not a perfect square.

Worksheet – 3

Question 1.
Calculate
(i) 45²
(ii) 205²
(iii) 555²
Answer:
(i) 45² = (100 × 4 × 5) + 25
= 2000 + 25
= 2025

(ii) 205² = (100 × 20 × 21) + 25
= 42000 + 25
= 42025

(iii) 555² = (100 × 55 × 56) + 25
= 308000 + 25
= 308025

Squares of Differences
The square of the difference of two numbers is twice their product subtracted from the sum of their squares.
If x and y are any two numbers.
Then, (x – y)² = x² + y² – 2xy for all numbers x and y.

For example: Compute 58².
Answer:
58² = (60 – 2)²
= 60² – 2 × 60 × 2 + 2²
= 3600 – 240 + 4
= 3364

If the equations of squares of sums and differences are added together, we get (x + y)² + (x – y)² = 2(x² + y²)
Therefore, 2(x² + y²) = (x + y)² + (x – y)²
The differences of this two identities is, 4xy = (x + y)² – (x – y)²
That means xy = \(\left(\frac{x+y}{2}\right)^2-\left(\frac{x-y}{2}\right)^2\)

The product of any two numbers is the difference of the squares of half their sum and half their difference.
If all the multiples of 4 starting with 8 can be written as the difference of two perfect squares.

For example: Compute 125 × 75.
Answer:
125 × 75 = \(\left(\frac{125+75}{2}\right)^2-\left(\frac{125-75}{2}\right)^2\)
= 100² – 25²
= 9375

Worksheet – 3

Compute the following.
(i) 112 × 12
(ii) 144 × 14
(iii) 17²
(iv) 39²
Answer:
(i) 112 × 12 = \(\left(\frac{112+12}{2}\right)^2-\left(\frac{112-12}{2}\right)^2\)
= 62² – 50²
= 1344

(ii) 144 × 14 = \(\left(\frac{114+14}{2}\right)^2-\left(\frac{114-14}{2}\right)^2\)
= 79² – 65²
= 2016

(iii) 17² = (20 – 3)²
= 20² – 2 × 20 × 3 + 3²
= 400 – 120 + 9
= 289

(iv) 39² = (40 – 1)²
= 40² – 2 × 40 × 1 + 1²
= 1600 – 80 + 1
= 1521

Differences of Squares
The difference of the squares of two numbers is the product of the sum and difference of the numbers.
x² – y² = (x + y)(x – y) for all numbers x and y.
If we take y as 1, then we get the equation as x² – 1 = (x + 1)(x – 1)

For three consecutive natural numbers, the product of the first and the last is one less than the square of the middle number.

For example: Compute 68² – 32²?
Answer:
68² – 32² = (68 + 32)(68 – 32)
= 100 × 36
= 3600

Worksheet – 4

Question 1.
Calculate
(i) 42² – 17²
(ii) \(\left(10 \frac{1}{2}\right)^2-\left(9 \frac{1}{2}\right)^2\)
Answer:
(i) 42² – 17² = (42 + 17)(42 – 17)
= 59 × 25
= 1475

(ii) \(\left(10 \frac{1}{2}\right)^2-\left(9 \frac{1}{2}\right)^2=\left(10 \frac{1}{2}+9 \frac{1}{2}\right)\left(10 \frac{1}{2}-9 \frac{1}{2}\right)\)
= 20 × 1
= 20

Students often refer to Kerala State Syllabus SCERT Class 8 Maths Solutions and Class 8 Maths Chapter 1 Squares Questions and Answers Notes Pdf to clear their doubts.

SCERT Class 8 Maths Chapter 1 Solutions Squares

Class 8 Kerala Syllabus Maths Solutions Chapter 1 Squares Questions and Answers

Squares Class 8 Questions and Answers Kerala Syllabus

Perfect Squares (Page No. 11)

Question 1.
Calculate the squares given below.
(i) 64²
(ii) 35²
(iii) 47²
(iv) 53²
(v) 88²
Answer:
(i) 64²
64² = 60² + (2 × 60 × 4) + 4²
= 3600 + 480 + 16
= 4096

(ii) 35²
35² = 30² + (2 × 30 × 5) + 5²
= 900 + 300 + 25
= 1225

(iii) 47²
47² = 40² + (2 × 40 × 7) + 7²
= 1600 + 560 + 49
= 2209

(iv) 53²
53² = 50² + (2 × 50 × 3) + 3²
= 2500 + 300 + 9
= 2809

(v) 88²
88² = 80² + (2 × 80 × 8) + 8²
= 6400 + 1280 + 64
= 7744

Decimal Squares (Page No. 13)

Question 1.
Find the squares of the numbers below:
(i) 2.3
(ii) 8.7
(iii) 10.1
(iv) 12.5
(v) 15.7
Answer:
(i) 2.3² = 2² + 2 × 2 × 0.3 + (0.3)²
= 4 + 1.2 + 0.09
= 5.29

(ii) 8.7² = 8² + 2 × 8 × 0.7 + (0.7)²
= 64 + 11.2 + 0.49
= 75.69

(iii) 10.1² = 10² + 2 × 10 × 0.1 + (0.1)²
= 100 + 2 + 0.01
= 102.01

(iv) 12.5² = 12² + 2 × 12 × 0.5 + (0.5)²
= 144 + 12 + 0.25
= 156.25

(v) 15.7² = 15² + 2 × 15 × 0.7 + (0.7)²
= 225 + 21 + 0.49
= 246.49

Class 8 Maths Chapter 1 Kerala Syllabus Squares Questions and Answers

Class 8 Maths Squares Questions and Answers

Calculate the squares given below.

Question 1.
70² = _____
Answer:
70² = 70 × 70
= 7 × 10 × 7 × 10
= 7 × 7 × 10 × 10
= 49 × 100
= 4900

Question 2.
71² = _____
Answer:
71² = 70² + 2 × 70 × 1 + 1²
= 4900 + 140 + 1
= 5041

Question 3.
72² = _____
Answer:
72² = 70² + 2 × 70 × 2 + 2²
= 4900 + 280 + 4
= 5184

Question 4.
75² = _____
Answer:
75² = 7 × 8 | 25 = 5625

Question 5.
8.5² = _____
Answer:
8.5² = 8 × 9 + \(\frac {1}{4}\)
= 72 + 0.25
= 72.25

Question 6.
7.4² = _____
Answer:
7.4² = 7² + 2 × 7 × 0.4 + (0.4)²
= 49 + 5.6 + 0.16
= 54.76

Question 7.
7.62 = _____
Answer:
7.6² = 7² + 2 × 7 × 0.6 + (0.6)²
= 49 + 8.4 + 0.36
= 57.76

Question 8.
75.4² = _____
Answer:
75.4² = 75² + 2 × 75 × 0.4 + (0.4)²
= 5625 + 60 + 0.16
= 5685.16

Question 9.
8.25² = _____
Answer:
8.25² = 8² + \(\frac {8}{2}\) + 0.0625
= 64 + 4 + 0.0625
= 68.0625

Question 10.
10.25² = _____
Answer:
10.25² = 10² + \(\frac {10}{2}\) + 0.0625
= 100 + 5 + 0.0625
= 105.0625

Question 11.
6.25² = _____
Answer:
6.25² = 6² + \(\frac {6}{2}\) + 0.0625
= 36 + 3 + 0.0625
= 39.0625

Question 12.
100.25² = _____
Answer:
100.25² = 100² + \(\frac {100}{2}\) + 0.0625
= 10000 + 50 + 0.0625
= 10050.0625

Class 8 Maths Chapter 1 Notes Kerala Syllabus Squares

→ The digit in the ones place of a perfect square can only be any of these numbers: 0, 1, 4, 5, 6, or 9.

→ If a number ends in 5. The digit in the ones place of its square should be 5, and the digit in its tens place should be 2.

→ The square of an even number is always even.

→ The square of an odd number is always odd.

→ The number of factors of a perfect square is odd.

→ In the first 100 natural numbers, there are 10 perfect squares, and in the first 1000 natural numbers, there are 31 perfect squares.

A perfect square is a number that is obtained by multiplying a natural number by itself. For example, when we multiply 4 by 4, we get 16. So 16 is called the perfect square. Perfect squares are easy to recognize and have many unique patterns and properties. They are always positive, and their square roots are always natural numbers. These numbers appear frequently in mathematics, especially in geometry, like calculating the area of a square, and in algebra. In this chapter, you will learn how to find the square of an integer. And also discuss how to find the square of a decimal number.

Perfect Squares
The squares of natural numbers 1, 2, 3, … are called perfect squares.

Multiplication of two-digit numbers.
11 × 11

In another form,

11 × 11 = 100 + (10 + 10) + 1
That means,
11² = 10² + 2 × 10 + 1² = 121
Similarly, the square of 12
12 × 12

12 × 12 = 100 + 20 + 20 + 4
= 10² + 2 × 20 + 2²
= 144
Without drawing the cells, we can write them like this,
13² = 10² + 2 × 30 + 3² = 169
14² = 10² + 2 × 40 + 4² = 196

Square of 20 = 20 × 20
= 2 × 10 × 2 × 10
= 2 × 2 × 10 × 10
= 4 × 100
= 400

Square of 212

212² = 200² + 2 × 200 × 12 + 12²
= 40000 + 4800 + 144
= 44944

Square of 386
386² = 300² + 2 × 300 × 86 + 86²
= 90000 + 51600 + 7396
= 148996

Worksheet – 1

Calculate the squares given below.
(i) 24
(ii) 56
(iii) 76
(iv) 35
(v) 91
(vi) 101
(vii) 211
(viii) 912
Answer:
(i) 576
(ii) 3136
(iii) 5776
(iv) 1225
(v) 8281
(vi) 10201
(vii) 44521
(viii) 831744

Square of 30 = 30 × 30
= 3 × 10 × 3 × 10
= 9 × 100
= 900

Square of 40 = 4 × 4 × 100
= 16 × 100
= 1600

Square of 25

25 × 25 = 20² + 2 × 20 × 5 + 5²
25² = 400 + 200 + 25
25² = 625

52 × 52 = 50² + 2 × 50 × 2 + 2²
52² = 2500 + 200 + 4
52² = 2704

87 × 87 = 80² + 2 × 80 × 7 + 7²
87² = 6400 + 1120 + 49
87² = 7569

Simplest method to calculate the square of integers that end in 5:
For example:
35² = 30² + 2 × 30 × 5 + 5²
= 900 + 300 + 25
= 1225
In this answer 1225, if we remove the last two digits 25 we get the remaining as 12.
12 | 25
The 12 is 3 × 4.
We can check this in other numbers also.
For example:
4 | 5² = 20 (4 × 5) | 25
6 | 5² = 6 × 7 | 25 = 4225
9 | 5² = 9 × 10 | 25 = 9025
105² = 10 × 11 | 25 = 11025
295² = 29 × 30 | 25 = 87025
1005² = 100 × 101 | 25 = 1010025

The square of the integer ending in 5 is the multiple of the number of tens (the number obtained after removing 5 from it), with the next natural number, and joining the square of 5 with this.

Decimal Squares
Square of 15 is 15² = 225
Then 1.5 × 1.5 = \(\frac{15}{10} \times \frac{15}{10}\)
= \(\frac {225}{100}\)
= 2.25

If the length of the side of a square is 2.3 metres. Find its area.
Answer:
Area = side × side
= 2.3 × 2.3
= \(\frac{23^2}{100}\)
= \(\frac {529}{100}\)
= 5.29 sq.m
This multiplication can also be considered as a rectangle math problem

3.7² = 3.7 × 3.7
= 3² + 2 × 3 × 0.7 + (0.7)²
= 9 + 4.2 + 0.49
= 13.69

4.3² = 4.3 × 4.3
= 4² + 2 × 4 × 0.3 + (0.3)²
= 16 + 2.4 + 0.09
= 18.49

Worksheet – 2

Calculate the squares given below.
Question 1.
6.8²
Answer:
6.8² = 6.8 × 6.8
= 6² + 2 × 6 × 0.8 + (0.8)²
= 36 + 9.6 + 0.64
= 46.24

Question 2.
12.3²
Answer:
12.3² = 12.3 × 12.3
= 12² + 2 × 12 × 0.3 + (0.3)²
= 144 + 7.2 + 0.09
= 151.29

Question 3.
30.5²
Answer:
30.5² = 30.5 × 30.5
= 30² + 2 × 30 × 0.5 + (0.5)²
= 900 + 30 + 0.25
= 930.25

Simplest method to calculate the square of a number with the decimal part 0.5:
3.5² = 3.5 × 3.5
= 3² + 2 × 3 × 0.5 + (0.5)²
= 9 + 3 + 0.25
= 12.25

7.5² = 7² + 2 × 7 × 0.5 + (0.5)²
= 72 + 7 + 0.25
= 56.25

10.5² = 10² + 10 + 0.25 = 110.25

50.5² = 50² + 50 + 0.25 = 2550.25

We can see this in another form,
3.5² = 3 × 4 + 0.25 = 12.25
7.5² = 7 × 8 + 0.25 = 56.25
10.5² = 10 × 11 + 0.25 = 110.25

If the decimal part is 0.25:
For example:
2.252 = 22 + 2 × 2 × 0.25 + (0.25)2
= 4 + 1 + 0.0625
= 5.0625

3.252 = 32 + 2 × 3 × 0.25 + (0.25)2
= 9 + 1.5 + 0.0625
= 10.5625

If we consider the right side first,
Square of the integer + half of the integer + square of 0.25

Worksheet – 3

Question 1.
Find the square of 12.25.
Answer:
12.25 = Square of 12 + half of 12 + 0.0625
= 144 + 6 + 0.0625
= 150.0625

Question 2.
Square of 30.25.
Answer:
30.25 = Square of 30 + half of 30 + 0.0625
= 900 + 15 + 0.0625
= 915.0625