Class 7 Science and Maths Notes Free

Chapter 1 Nutrients in plants


- Plants and animals are two main types of organisms found in the natural world.

- Plants are autotrophic, meaning they can produce their own food, whereas animals are heterotrophic and depend on other organisms for nutrition.

Mode of Nutrition in Plants:

- Plants use a process called photosynthesis to obtain energy from sunlight and convert it into usable forms of food.

- Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to synthesize glucose and oxygen.

- It occurs in the chloroplasts of plant cells, specifically in the green pigments called chlorophyll.

- The glucose produced during photosynthesis is used as a source of energy to carry out various metabolic processes in the plant.


- Photosynthesis is a chemical reaction that takes place in the leaves of green plants.

- It involves the conversion of light energy into chemical energy in the form of glucose.

- This process requires sunlight, water, and carbon dioxide.

- Sunlight is absorbed by chlorophyll in the chloroplasts, which powers the reaction.

- Water is taken up from the roots and transported to the leaves through specialized tissues called xylem.

- Carbon dioxide is obtained from the surrounding air through tiny pores called stomata.

- The end product of photosynthesis is glucose, which is either used immediately by the plant or stored as starch for later use.

Heterotrophic Nutrition:

- Unlike plants, animals cannot perform photosynthesis and rely on other organisms for their nutrition.

- Heterotrophic nutrition refers to the mode of nutrition in which organisms obtain their food from external sources.

- There are different types of heterotrophic nutrition, including herbivores, carnivores, omnivores, and scavengers.

- Herbivores: These animals primarily consume plants and plant-based materials.

- Carnivores: These animals mainly feed on other animals.

- Omnivores: These animals have a mixed diet, consuming both plants and animals.

- Scavengers: These organisms feed on decaying organic matter to obtain their nutrition.

Types of Heterotrophic Nutrition:

i. Holozoic

ii. Parasitic

iii. Saprophytic

Digestion in Human Beings:

- In humans, digestion is a process that breaks down ingested food into smaller, absorbable molecules.

- It involves mechanical and chemical processes that occur in the digestive system.

- The digestive system consists of various organs, including the mouth, esophagus, stomach, small intestine, large intestine, and accessory organs such as the liver and pancreas.

- Mechanical digestion begins in the mouth through chewing and mixing food with saliva, while chemical digestion starts with the enzyme amylase found in saliva.

- Food is then swallowed and passed through the esophagus into the stomach, where further breakdown and digestion occur, aided by stomach acid and enzymes.

- The partially digested food then moves into the small intestine, where additional enzymes from the pancreas and bile from the liver break down nutrients into smaller molecules.

- Absorption of these molecules occurs in the small intestine through its large surface area.

- The indigestible components and water then move into the large intestine, where water absorption takes place, and the remaining waste is formed into feces for elimination.

Chapter 2 Nutrition in Animals


- Nutrition is the process by which organisms acquire and utilize food for growth, development, and maintenance of their body functions.

- Ingestion, digestion, absorption, and assimilation are the four main steps involved in the process of nutrition.

Nutrition Ingestion, Digestion, Absorption, Assimilation:

- Ingestion refers to the intake of food into the body through the mouth.

- Digestion involves the breakdown of complex food molecules into simpler forms that can be absorbed by the body.

- Absorption occurs when the digested nutrients are taken up by the bloodstream and transported to different cells and tissues.

- Assimilation is the process by which the absorbed nutrients are utilized by cells for energy, growth, and repair.

Heterotrophic Nutrition, Omnivores, Decomposers:

- Heterotrophic nutrition is a type of nutrition in which organisms obtain their food from other organisms.

- Omnivores are organisms that consume both plant and animal matter as their source of nutrition.

- Decomposers are organisms that feed on dead organic matter and help in the breakdown and recycling of nutrients in an ecosystem.

Nutrition in Humans - Mouth, Teeth, Stomach:

- The process of nutrition in humans begins in the mouth, where food is mechanically broken down by the action of teeth and mixed with saliva.

- Teeth play a crucial role in the initial breakdown of food by chewing and grinding it into smaller pieces, increasing its surface area for better digestion.

- The chewed food, now called a bolus, is mixed with saliva in the mouth, which helps in lubrication and contains enzymes to initiate the digestion of carbohydrates.

Salivary Glands:

- Salivary glands, including the parotid, sublingual, and submandibular glands, produce saliva.

- Saliva contains enzymes like salivary amylase that begin the digestion of complex carbohydrates (starch) into simpler sugars (such as glucose).


- The liver is an important organ that plays many roles in the process of digestion and overall metabolism.

- It produces bile, which is stored in the gallbladder and released into the small intestine to aid in the digestion and absorption of fats.

- The liver also detoxifies harmful substances, stores vitamins and minerals, and regulates blood sugar levels.


- The pancreas is both an endocrine and exocrine gland involved in digestion.

- It produces digestive enzymes, including pancreatic amylase, lipase, and proteases, which are released into the small intestine to break down carbohydrates, fats, and proteins, respectively.

- The pancreas also produces insulin and glucagon, hormones involved in the regulation of blood glucose levels.

Digestion in Small Intestine:

- The small intestine is where most of the digestion and absorption of nutrients occur.

- It receives bile from the liver and digestive enzymes from the pancreas to aid in the breakdown of carbohydrates, proteins, and fats.

- The inner lining of the small intestine is covered in tiny finger-like projections called villi, which increase the surface area for better absorption of the digested nutrients into the bloodstream.

Digestion in Large Intestine:

- The large intestine primarily functions in the absorption of water, electrolytes, and some vitamins produced by the gut bacteria.

- It also houses beneficial bacteria that aid in the final breakdown of undigested food and the production of certain vitamins,

- The waste material, called feces, is formed in the large intestine and eventually eliminated from the body through the rectum and anus.

Chapter 3 Fiber to Fabric

1. Animal Fibre:

- Animal fibers are natural fibers that come from animals. They are different from plant fibers because they are produced by animals and not plants.

- Animal fibers are commonly used in making fabrics and textiles. They are valued for their warmth, softness, and durability.

2. Wool and Animals that Yield Wool:

- Wool is a type of animal fiber that comes from the fleece or coat of certain animals.

- The main animal that yields wool is sheep. Other animals that produce wool include goats (cashmere, mohair), rabbits (angora), and muskoxen (qiviut).

3. Rearing of Sheep and Obtaining Wool:

- Rearing sheep involves taking care of them so that they can produce good quality wool.

- In India, there are various breeds of sheep that yield wool, such as the Merino, Rambouillet, and Nali breeds.

- Sheep are reared by providing them with proper food, water, and shelter. They are also protected from diseases and pests.

- The process of obtaining wool starts by shearing the sheep, which means removing their fleece or coat. This is done by skilled workers using special scissors or electric clippers.

4. Processing Wool from Fiber:

- After shearing, the wool goes through several steps to be processed and made into usable fibers.

- The first step is scouring, which involves washing the wool to remove any dirt, grease, or impurities. This is done using warm water and mild detergent.

- Next, the wool is sorted based on its quality and fineness. The fibers are separated into different grades.

- After sorting, the wool is carded. Carding involves combing the fibers to align them in one direction. This makes the wool easier to spin into yarn.

- The carded wool can then be spun into yarn, which is done by twisting the fibers together. This can be done using a spinning wheel or a machine.

- The final steps include dyeing the yarn with different colors, weaving or knitting it into fabrics, and finishing the fabric to give it the desired texture and appearance.

5. Silk and Life History of Silk Moth:

- Silk is another type of animal fiber that comes from the cocoons of silk moths.

- The life history of a silk moth starts with the female moth laying eggs. These eggs hatch into tiny silkworm larvae.

- The larvae feed on mulberry leaves and grow rapidly. They molt or shed their skin several times as they continue to eat and grow.

- After molting several times and reaching their maximum size, the silkworms form a protective covering called a cocoon around themselves.

- Inside the cocoon, the silkworm undergoes metamorphosis and transforms into a pupa.

- Inside the pupa, the process of turning into a moth takes place. The pupa secretes a liquid that hardens and forms a silk thread, which is used to create the cocoon.

- Finally, the fully transformed moth breaks out of the cocoon and emerges as an adult silk moth.

6. From Cocoon to Silk and Rearing Silkworms and Processing Silk:

- To obtain silk, the cocoons are collected before the moth can break out. This is done carefully to ensure the silk thread remains intact.

- The collected cocoons are then soaked in hot water to soften the silk fibers.

This makes it easier to unwind the silk thread without breaking it.

- The unwound silk threads are then spun together to form a single thread, which is called raw silk.

- The raw silk is further processed to remove impurities and make it more lustrous and smooth. This involves reeling, twisting, and weaving the silk into fabrics.

- The final step is finishing the silk fabric by adding colors, designs, and textures using various techniques like dyeing, printing, and embroidering.

Chapter 4 Heat


- Hot and cold are relative terms used to describe the level of temperature or heat.

- When something has a high temperature, we consider it hot. On the other hand, when something has a low temperature, we consider it cold.

- The sensation of hotness or coldness can vary from person to person, as it is subjective.


- Temperature is measured using a device called a thermometer.

- A thermometer consists of a long, narrow glass tube with a bulb at one end containing mercury or alcohol.

- To measure the temperature, the bulb is placed in contact with the object whose temperature is to be measured.

- As the temperature changes, the mercury or alcohol expands or contracts, indicating the temperature on a calibrated scale.


Step 1: Hold the thermometer by the top end and give it a gentle shake to make sure the mercury or alcohol level is below the scale.

Step 2: Place the bulb of the thermometer in contact with the object or substance whose temperature you want to measure.

Step 3: Wait for a few minutes until the mercury or alcohol settles and stops moving. Make sure to keep the thermometer steady during this time.

Step 4: Look at the scale and read the temperature indicated by the height of the mercury or alcohol level on the calibrated scale.

Precautions for Clinical Thermometer:

- A clinical thermometer is used to measure body temperature.

- It should be disinfected before and after every use to prevent the spread of germs.

- The mercury level should be brought below 35°C (95°F) before using it to avoid incorrect readings.

- It should be held properly and not shaken vigorously to prevent mercury breakage.

- The thermometer should be wiped clean and stored properly after use.

Precautions of Laboratory Thermometer:

- Laboratory thermometers are used for measuring temperatures in scientific experiments.

- Handle the laboratory thermometer with care to prevent breakage.

- Avoid direct contact with corrosive or harmful substances, as it may damage the thermometer.

- Calibrate the thermometer regularly to ensure accurate readings.


- Heat is a form of energy that can transfer from one object to another.

- Conduction is the transfer of heat through direct contact between objects.

For example, if you touch a hot pan, heat transfers through conduction.

- Convection is the transfer of heat through the movement of hot fluids (liquids or gases). For example, boiling water or warm air rising.

- Radiation is the transfer of heat in the form of electromagnetic waves. For example, feeling the warmth of the sun's rays.


- Sea breeze is a phenomenon that occurs during the day near coastal areas.

- During the day, the land heats up faster than the sea, creating a temperature difference.

- The warm air above the land rises and creates a low-pressure zone. The cool air from the sea moves towards the land to fill the vacuum and create a cool breeze.


- Land breeze is a phenomenon that occurs during the night near coastal areas.

- At night, the land cools down faster than the sea, creating a temperature difference.

- The cool air above the land descends and creates a high-pressure zone. The relatively warmer air from the sea moves towards the land to fill the vacuum and create a breeze.


- In winter, we wear thick clothes that provide insulation and keep us warm.

- Common winter clothes include sweaters, jackets, coats, scarves, gloves, and hats.

- These clothes trap air, creating a layer of insulation that helps retain our body heat and protect us from the cold weather.

- In summer, we wear light and breathable clothes that allow air circulation and help us stay cool.

- Common summer clothes include t-shirts, shorts, skirts, dresses, and sandals.

- These clothes are made from fabrics that allow sweat to evaporate quickly, keeping our bodies cool and comfortable during hot weather.

Chapter 5 Acids and Salts

Acids and Bases:

1. Acids are a group of substances that have certain properties. They taste sour, can cause burns, and turn blue litmus paper red.

2. Bases, on the other hand, taste bitter, feel slippery, and turn red litmus paper blue.

3. Acids and bases are found in various everyday substances like lemon juice, vinegar, and soap.

4. Acids release hydrogen ions when dissolved in water, while bases release hydroxide ions.

5. The strength of an acid or base is determined by its concentration, with stronger acids/bases having a higher concentration of ions.

Indicators like Natural Indicator and China Rose Indicator:

1. Indicators are substances that help us determine whether a substance is acidic or basic by showing color changes.

2. Natural indicators are substances obtained from nature, like turmeric, red cabbage, or beetroot juice. These indicators change color in the presence of acids or bases.

3. China rose indicator is a commonly used natural indicator made from the petals of the China rose flower. It turns acidic solutions red and basic solutions green.

Neutral Substances:

1. Neutral substances are neither acidic nor basic. They have a pH value of 7, which is considered neutral.

2. Examples of neutral substances include water and table salt (NaCl). Water is essential for life and has a pH value close to 7. Table salt is a compound formed from a reaction between an acid and a base and does not show acidic or basic properties.


1. Neutralisation is a chemical reaction between an acid and a base, resulting in the formation of a neutral substance, usually water and a salt.

2. This reaction is often used to neutralize the effects of an acid or a base. For example, if you get stung by an ant, applying a base like baking soda (sodium bicarbonate) can relieve the pain caused by the acidic ant venom.

3. Neutralisation is also used to treat indigestion. Antacids are medicines that contain bases and help neutralize excess stomach acid.

4. In agriculture, neutralisation is an important process used for soil treatment. Acidic soils can be treated with bases like lime to bring the pH to a neutral level, which enables better plant growth.

5. Additionally, neutralisation is employed in dealing with factory wastes. Industries often generate acidic or basic wastes, which need to be neutralized before they can be safely disposed of to prevent environmental damage.

Chapter 6 Physical and Chemical Changes

Types of Changes:

1. Physical Change:

- It refers to a change in which the substance does not transform into a new substance with different properties.

- In physical changes, the molecules remain the same, but their arrangement or state may alter.

- Examples include changing the shape, size, or state of matter without altering its chemical composition. For instance:

- Cutting a piece of paper into smaller parts.

- Melting an ice cube to obtain water.

- Freezing water to form ice.

2. Chemical Change:

- It involves the transformation of one or more substances into completely new substances with different properties.

- In chemical changes, the molecules undergo a rearrangement, leading to the formation of new substances.

- Examples include reactions that result in the formation of new products. Two common examples are:

- Burning magnesium ribbon: When magnesium ribbon is ignited, it reacts with the oxygen in the air to form magnesium oxide. The magnesium ribbon disappears, and a white powder (magnesium oxide) is produced.

- Dissolving magnesium ash in water: When you dissolve magnesium ash in water, a chemical reaction occurs, forming magnesium hydroxide. The initial solid ash disappears and a new substance is formed.

Difference between Physical and Chemical Changes: 1. Physical Changes:

- No new substances are formed.

- The chemical composition remains the same.

- Reversible in most cases.

- Examples include changes in size, shape, or state of matter without altering the substance's chemical properties.

2. Chemical Changes:

- New substances are formed.

- The chemical composition changes.

- Irreversible in most cases.

- Examples include combustion, oxidation, and decomposition reactions. Copper Sulphate (CuSO4) Reaction:

- Copper Sulphate is a compound containing copper and sulphur.

- When heated strongly, copper sulphate loses its water molecules and turns into anhydrous copper sulphate.

- The blue crystals change into a white powder due to this chemical change.

Rusting and Protection from Rusting:

- Rusting is a type of chemical change that occurs when iron or steel reacts with oxygen and water in the presence of air moisture.

- The iron or steel slowly converts into hydrated iron(III) oxide, commonly known as rust.

- To prevent rusting, various methods are used: 1. Applying a coat of paint or oil: This acts as a barrier, preventing oxygen and water from reaching the iron or steel surface.

2. Galvanization: Coating iron or steel with a layer of zinc prevents rusting. Zinc acts as a sacrificial anode and corrodes before iron or steel.

3. Using alloys: Mixing iron or steel with other metals like chromium creates stainless steel, which is more resistant to rusting.


- Crystallization is a process where highly ordered crystalline solid forms from a solution, melt, or gas.

- It occurs due to the slow evaporation of a liquid or a decrease in temperature, causing the solute particles to come together and form an organized solid structure.

- Examples of crystallization include the formation of snowflakes, salt crystals when seawater evaporates, and sugar crystals when a sugar solution cools down slowly.

Chapter 7 Wheater, Climate and Adaptations of Animals

Polar Region:

1. The polar region refers to the areas around the Earth's North and South Poles.

2. It is characterized by extremely cold temperatures, icy landscapes, and long periods of darkness.

3. The polar region is home to unique wildlife and is mainly inhabited by polar bears, penguins, seals, and walruses.

Adaptive Features of Polar Bears:

1. Polar bears have a thick layer of fat called blubber that helps them to insulate their bodies and keep warm in the freezing temperatures of the polar region.

2. They also possess a dense fur coat that provides excellent insulation and helps them blend with the snowy surroundings.

3. Polar bears have large, strong claws that enable them to grip the slippery ice and catch their prey, mainly seals.

4. Their keen sense of smell helps them locate seals from long distances, even when they are hidden beneath the ice.

5. Polar bears also have a streamlined body shape and strong limbs for efficient movement both on land and in water.

Adaptive Features of Penguins:

1. Penguins have a layer of fat and dense feathers that provide insulation and keep them warm in the cold temperatures of the polar region.

2. Their feathers are waterproof, allowing them to glide through water efficiently and stay dry.

3. Penguins have streamlined bodies and wings adapted into flippers that enable them to swim swiftly, helping them catch fish, squid, and krill, which are their main food sources.

4. They possess strong bones that help them withstand the pressure in deep dives while hunting for food.

5. Penguins have a unique adaptation called the "huddle," where they gather closely together to keep warm during harsh weather conditions.

Adaptive Features of Animals in the Tropical Rainforest:

1. Rainforests are characterized by high temperatures, heavy rainfall, and dense vegetation that provide a diverse habitat for various animals.

2. Many animals in the tropical rainforest have adaptations to help them thrive in this environment.

3. Some animals, like jaguars and tree-dwelling monkeys, have developed strong limbs and muscular bodies to navigate through the dense vegetation.

4. Many rainforest animals have evolved the ability to climb trees, such as tree frogs with adhesive toe pads and sloths with long, curved claws.

5. Animals in the rainforest often have bright and vibrant colors as a means of camouflage or to communicate with others. Examples include poison dart frogs and toucans.

6. Some animals, like tapirs and anteaters, have long snouts and tongues to help them reach food sources, such as fruits, insects, and nectar found in the rainforest.

7. Animals in the rainforest often possess sharp teeth or beaks to adapt to their specific diets, such as the sharp beaks of toucans for feeding on fruits or the long, thin beaks of hummingbirds for sipping nectar.

Chapter 8 Winds, Stroms and Cyclones

• Air exerts pressure:

- Air is made up of particles that are constantly moving and colliding with each other and with surfaces around them.

- These collisions create a force, known as air pressure.

- Air pressure is the weight of the air pushing down on a given area.

- The pressure of air decreases as we go higher up in the atmosphere because there is less air above.

• Air expands on heating:

- When air is heated, the particles in the air gain energy and move faster.

- As the particles move faster, they spread out and take up more space, leading to expansion.

- This expansion causes the air to become less dense.

- Hot air rises because it is lighter than the colder air around it.

• Wind currents generated due to uneven heating:

- Wind is the movement of air from areas of high pressure to areas of low pressure.

- Uneven heating of the Earth's surface creates regions of different air temperatures.

- The equator receives more direct sunlight, so it heats up more compared to the poles.

- This temperature difference creates variations in air pressure, leading to the formation of wind currents.

- Additionally, uneven heating of land and water bodies also contributes to the generation of wind.

• Thunderstorms and cyclones:

- Thunderstorms are intense weather phenomena that include lightning, thunder, heavy rain, and strong winds.

- Cyclones, also known as hurricanes or typhoons, are large-scale weather systems characterized by low-pressure centers and high-speed winds.

- Cyclones can cause widespread destruction due to their strong winds, torrential rainfall, storm surges, and tornadoes that are sometimes associated with them.

• Safety measures for cyclones:

- Staying informed about weather updates and warnings through reliable sources like meteorological departments.

- Identifying safe areas in your home or community, such as basements or designated storm shelters.

- Securing loose objects and reinforcing doors and windows.

- Having emergency kits ready with essentials like food, water, first aid supplies, and flashlights.

- Evacuating to higher or safer grounds if instructed to do so by authorities.

• Action taken by people:

- People should follow evacuation orders given by local authorities to ensure their safety.

- Clearing and securing outdoor objects that could become projectiles during strong winds.

- Staying indoors until the cyclone has passed and it is safe to venture outside.

- Assisting neighbors and those who need help, especially the elderly and disabled.

• Precautions for cyclone-prone areas:

- Constructing buildings with cyclone-resistant designs and materials.

- Developing efficient drainage systems to prevent flooding.

- Planting windbreaks, such as trees or hedges, to reduce the impact of strong winds.

- Educating communities about cyclone preparedness and conducting drills.

- Regular maintenance and inspection of infrastructure to ensure it can withstand cyclonic conditions.

• Help from advanced technology:

- Advanced technology plays a crucial role in monitoring and predicting cyclones.

- Weather satellites provide real-time data, helping meteorologists track cyclones and issue timely alerts.

- Doppler radar systems can detect the movement and intensity of cyclones, aiding in accurate forecasting.

- Advanced computer models simulate the behavior of cyclones, assisting in predicting their paths and potential impacts.

- Communication technologies enable quick dissemination of cyclone warnings and emergency information to affected populations.

Chapter 9 Soil

Introduction with humus and weathering:

- Humus is the dark, organic material that forms in soil when plant and animal matter decompose. It is rich in nutrients and helps improve soil fertility.

- Weathering refers to the breaking down of rocks, minerals, and organic materials on the Earth's surface. It plays a crucial role in the formation of soil. Soil profile with A, B, C, and D horizon:

- Soil profile is a vertical section of the soil showing the different layers or horizons.

- The topsoil or A horizon is the uppermost layer, rich in organic matter, minerals, and nutrients.

- The B horizon or subsoil is relatively less fertile and contains minerals and nutrients washed down from the topsoil.

- The C horizon is the layer of weathered rock fragments.

- The D horizon is the bedrock, which lies beneath the soil layers.

Soil types with examples of sandy, clayey, and loamy soil:

- Sandy soil is composed of larger particles and drains quickly. It doesn't hold water or nutrients well. Cacti and carrots grow well in sandy soil.

- Clayey soil consists of tiny particles that pack tightly together. It retains moisture but doesn't drain well. Rice and wheat thrive in clayey soil.

- Loamy soil is a balance of sand, silt, and clay particles, making it ideal for plant growth. Many vegetables, fruits, and flowers flourish in loamy soil.

Properties of soil with percolation rate:

- Percolation rate measures how quickly water drains through the soil. Sandy soil has a high percolation rate, meaning water moves through rapidly. Clayey soil has a low percolation rate, causing water to stay longer in it.

Soil and crops with four crops grown on four types of soil:

- Carrots, which prefer sandy soil with good drainage.

- Rice, which thrives in clayey soil that retains water.

- Tomatoes, which grow well in loamy soil with balanced drainage and water retention.

- Maize (corn), which can adapt to different soil types but prefers loamy soil.

Crops and their two types (Rabi and Kharif) with examples:

- In India, Rabi crops are planted in winter and harvested in spring. Examples include wheat, barley, mustard, and peas.

- Kharif crops are sown at the beginning of the monsoon and harvested in autumn. Examples include rice, maize, millet, and cotton.

Basic crop production practices with examples of food items and their nutrients:

- Crop production practices involve activities like plowing, sowing, irrigation, weeding, and harvesting.

- Examples of food items: Wheat (carbohydrates and fiber), spinach (vitamins and minerals), lentils (proteins), and oranges (vitamin C).

Factors leading to soil pollution:

- Use of chemical fertilizers and pesticides in excessive amounts.

- Improper disposal of industrial waste containing harmful chemicals.

- Urbanization and construction activities leading to soil erosion.

- Mining activities and improper waste management practices.

- Oil spills and accidental release of toxic substances.

Chapter 10 Respiration in Organisms

1. Cellular Respiration:

- Cellular respiration is the process by which cells convert nutrients into energy in the form of ATP (adenosine triphosphate).

- It takes place in the mitochondria, which are the powerhouse of the cell.

- The three main steps of cellular respiration are glycolysis, the Krebs cycle, and oxidative phosphorylation.

- During cellular respiration, glucose (a type of sugar) is broken down and combined with oxygen to produce carbon dioxide, water, and energy in the form of ATP.

2. Two Types of Respiration:

- There are two types of respiration: aerobic respiration and anaerobic respiration.

- Aerobic respiration requires oxygen and is the most common type of respiration.

- It occurs in the presence of oxygen and involves the complete breakdown of glucose into carbon dioxide and water, releasing a large amount of energy.

- Anaerobic respiration, on the other hand, occurs in the absence of oxygen.

- It involves the incomplete breakdown of glucose and releases less energy compared to aerobic respiration.

- Examples of anaerobic respiration include fermentation in yeast and bacteria.

3. Breathing and Exchange of Gases:

- Breathing is the process of taking in oxygen-rich air (inhalation) and releasing carbon dioxide-rich air (exhalation).

- Inhalation occurs when we breathe in; the diaphragm contracts, and the ribcage expands, allowing air to enter the lungs.

- Exhalation takes place when we breathe out; the diaphragm relaxes, and the ribcage returns to its original position, pushing air out of the lungs.

- During breathing, oxygen is taken in and carbon dioxide is released, allowing for the exchange of gases in the lungs.

4. Respiration in Plants:

- Plants also require energy, and they obtain it through a process called respiration.

- Plant respiration occurs in the cells of leaves, stems, and roots.

- During respiration, plants take in oxygen from the air through tiny pores called stomata, mainly found in the leaves.

- They release carbon dioxide as a byproduct of respiration.

- Unlike animals, plants can also perform photosynthesis, a process that allows them to produce glucose using sunlight, water, and carbon dioxide.

5. Respiration in Microorganisms:

- Microorganisms, such as bacteria and fungi, also respire to generate energy.

- Like other living organisms, they break down organic molecules to release energy in the form of ATP.

- Some microorganisms perform aerobic respiration, requiring oxygen for their energy production.

- Others carry out anaerobic respiration in the absence of oxygen.

- Certain microorganisms are capable of surviving in extreme environments where oxygen is limited, and they have adapted to perform anaerobic respiration to meet their energy needs.

Chapter 11 Transportation in Animals and Plants

1. Circulatory System:

- The circulatory system is a network of organs and blood vessels that transports blood and other essential substances throughout the body.

- Its main function is to deliver oxygen, nutrients, hormones, and other necessary substances to the body's cells while removing waste products.

- The circulatory system consists of the heart, blood vessels, and blood.

2. Blood and Functions of Blood:

- Blood is a fluid connective tissue that plays a vital role in the circulatory system.

- It carries oxygen from the lungs to the body's tissues and carbon dioxide back to the lungs for elimination.

- Blood also transports nutrients, hormones, and waste materials.

- It helps regulate body temperature and pH balance, and it contains cells and components that assist in fighting infections and clotting to prevent excessive bleeding.

3. Composition of Blood:

- Blood comprises red blood cells (carry oxygen), white blood cells (fight infections), platelets (help in clotting), and plasma (liquid portion that carries cells and nutrients).

- Red blood cells contain a protein called hemoglobin that binds oxygen and gives blood its red color.

- White blood cells help defend the body against harmful microbes and foreign substances.

- Platelets are responsible for forming blood clots to prevent excessive bleeding.

- Plasma is a yellowish fluid that carries cells, nutrients, hormones, and waste products throughout the body.

4. Lymph:

- Lymph is a clear fluid that circulates through the lymphatic system, which complements the circulatory system.

- It contains white blood cells and helps remove toxins, waste materials, and excess fluid from tissues, playing a crucial role in the immune system.

- Lymph is filtered in lymph nodes, where harmful substances are trapped and destroyed.

5. Blood Vessels with Arteries, Veins, and Capillaries:

- Arteries carry oxygenated blood away from the heart to various parts of the body, delivering oxygen and nutrients.

- Veins bring deoxygenated blood back to the heart, allowing waste materials, like carbon dioxide, to be eliminated.

- Capillaries are tiny, thin-walled blood vessels that connect arteries and veins. They facilitate the exchange of oxygen, nutrients, and waste products between the blood and the body's cells.

6. Heart:

- The heart is a muscular organ located in the chest that pumps blood throughout the body.

- It has four chambers: two atria (upper chambers) and two ventricles (lower chambers).

- The heart contracts and relaxes in a rhythmic pattern called the cardiac cycle, which allows blood to flow smoothly in one direction.

7. Excretory System with Excretion, Kidneys, and Dialysis:

- The excretory system eliminates waste products from the body, maintaining a balance of fluids and electrolytes.

- Kidneys are the main organs of the excretory system. They filter waste products and excess water from the blood to produce urine.

- Dialysis is a medical procedure used when the kidneys are not functioning properly. It involves using a machine to remove waste and excess fluids from the body artificially.

8. Transport in Plants with Transport of Food and Water:

- Plants have a complex network of vessels called xylem and phloem that transport water, nutrients, and sugars throughout the plant.

- Xylem vessels transport water and dissolved minerals from the roots to the rest of the plant.

- Phloem vessels transport food materials, such as sugars, produced in the plant's leaves to other parts, including the roots.

9. Excretion in Plants:

- Plants eliminate waste materials through special structures like stomata (tiny holes on leaves) and lenticels (small openings on stems and barks).

- Stomata allow plants to release excess water and oxygen while taking in carbon dioxide during photosynthesis.

- Lenticels facilitate gas exchange and the release of volatile waste products from plant tissues.

Chapter 12 Reproduction in Plants

1. What is reproduction?

- Reproduction is the biological process by which living organisms produce offspring or create new individuals of the same species.

- It ensures the continuity of a species and helps in maintaining genetic diversity.

2. Two modes of reproduction:

a) Sexual Reproduction in Plants:

- Sexual reproduction involves the fusion of male and female gametes (reproductive cells) to produce offspring.

- In plants, sexual reproduction can occur through bisexual and unisexual means.

- Bisexual reproduction occurs when a single flower possesses both male and female reproductive parts, enabling self-fertilization. Examples include hibiscus, sunflower, and rose.

- Unisexual reproduction occurs when male and female reproductive flowers are present on separate plants. Examples include watermelon (pumpkins), papaya, and date palms.

b) Asexual Reproduction:

- Asexual reproduction doesn't involve the fusion of gametes and produces offspring identical to the parent.

- Various types of asexual reproduction exist, including:

(i) Vegetative reproduction: This occurs when new individuals develop from vegetative parts of the parent, such as stems, roots, or leaves. Examples include potato, mint, and strawberry plants. (ii) Budding: It is a form of asexual reproduction in which a small bud grows on the parent organism and eventually detaches to form a new individual. Examples include yeast, hydra, and some flowering plants like Bryophyllum. (iii) Fragmentation: This type of reproduction happens when a parent organism breaks into fragments, with each fragment being capable of developing into a new individual. Examples include flatworms, sea stars, and some algae. (iv) Spore Formation: Organisms like ferns, mosses, and fungi produce microscopic spores capable of germinating into new individuals. These spores travel through air or water to find suitable conditions for growth.

3. Define pollination and its two types with examples:

- Pollination is the transfer of pollen grains from the male reproductive part (anther) to the female reproductive part (stigma) of a flower, leading to fertilization.

- There are two types of pollination:

a) Self-pollination: In self-pollination, the transfer of pollen occurs within the same flower or between the flowers of the same plant. Examples include pea plants and tomatoes. b) Cross-pollination: Cross-pollination involves the transfer of pollen from the anther of one flower to the stigma of another flower, typically between two different plants of the same species. Examples of plants that rely on cross-pollination include apple trees, sunflowers, and roses.

4. Fertilization and formation of fruits and seeds:

- Fertilization is the process in which the male gamete (in pollen) fuses with the female gamete (in the ovule) to form a zygote, initiating the development of a new individual.

- After fertilization, the ovule matures into a seed, and the ovary develops into a fruit.

- The seed contains the embryo of the new plant, while the fruit helps in seed dispersal through various means.

5. Seed dispersal and two main methods:

- Seed dispersal refers to the scattering or transportation of seeds away from the parent plant to ensure the distribution of plants in different areas.

- Two main methods of seed dispersal are:

a) Wind dispersal: Some seeds have adaptations like wings, hairs, or parachutes that help them be carried by the wind. Examples include dandelions, maple trees, and ferns. b) Animal dispersal: Seeds can attach to animals' fur or feathers and get carried to new locations. Some fruits are also eaten by animals, and the seeds are then excreted elsewhere. Examples include burdock, raspberries, and blackberries.

Chapter 13 Motion and Time

1. What is motion?

• Motion refers to the change in position of an object with respect to time.

• It involves the movement of objects from one place to another.

• Motion can be observed in various forms, such as a car moving on a road, a bird flying in the sky, or a person walking.

Types of Motion:

• Translational Motion: When an object moves along a straight line, it is called translational motion. For example, a car moving on a highway.

• Rotational Motion: When an object spins or rotates around an axis, it is called rotational motion. For example, a spinning top or a merry-go-round.

• Vibrational Motion: When an object vibrates back and forth about a fixed position, it is called vibrational motion. For example, the strings of a guitar or a tuning fork vibrating.

2. What is speed?

• Speed is a measure of how quickly an object moves.

• It indicates how fast or slow an object is traveling.

• Speed is calculated by dividing the distance covered by an object by the time taken to cover that distance.

Types of Speed:

• Uniform Speed: When an object covers equal distances in equal intervals of time, it is said to be moving at uniform speed. For example, a car running at a steady speed of 60 km/h.

• Variable Speed: When an object covers unequal distances in equal intervals of time, it is said to be moving at variable speed. For example, a car in traffic, where it may slow down or speed up.

• Instantaneous Speed: It refers to the speed of an object at a particular moment in time. For example, the speedometer of a vehicle shows the instantaneous speed.

3. Measuring Time:

• Time is a measure of the duration between events.

• It allows us to quantify the sequence and duration of events or actions. Time Measuring Devices:

• Sundial: A device that uses the position of the Sun's shadow to tell time.

• Hourglass: A device with sand that takes a specific amount of time to flow from one bulb to another, indicating the passage of time.

• Clock: A mechanical or electronic device that displays the time, commonly used in our daily lives.

Units to Measure Time and Speed:

• Time is measured in seconds (s), minutes (min), hours (h), days (d), etc.

• Speed is measured in units such as kilometers per hour (km/h), meters per second (m/s), miles per hour (mph), etc.

4. Oscillatory Motion and Time Period of Pendulum:

• Oscillatory motion refers to the repetitive back-and-forth motion of an object about a fixed position.

• A pendulum is a simple example of oscillatory motion, consisting of a mass (bob) attached to a string or rod, which swings to and fro.

Time Period of a Pendulum:

• The time period of a pendulum refers to the time it takes to complete one full swing (back and forth).

• The time period depends on the length of the pendulum and the acceleration due to gravity.

Units to Measure Time and Speed:

• The time period of a pendulum is measured in seconds (s).

5. Define Distance-Time Graph and Finding Speed from Distance-Time Graph:

• A distance-time graph represents how the distance traveled by an object changes over time.

• On the graph, time is represented on the x-axis, while the distance is represented on the y-axis.

Finding Speed from a Distance-Time Graph:

• Speed can be determined from a distance-time graph by calculating the slope (gradient) of the graph.

• The slope represents the speed of the object. A steeper slope indicates a higher speed, while a flatter slope indicates a lower speed.

Chapter 14 Electric Current and it's Effects

1. What is electric current?

- Electric current is the flow of electric charges, usually in the form of electrons, through a conductor.

- It is similar to the flow of water in a pipe, where the water represents the charges and the pipe represents the conductor.

2. Define electronic component, electric circuit, and battery:

- An electronic component is a basic building block used in electronic devices, such as resistors, capacitors, transistors, and diodes.

- An electric circuit is a complete path that allows electric current to flow. It consists of conductors (wires) connecting various electronic components.

- A battery is a device that stores chemical energy and converts it into electrical energy. It provides a source of power for electronic circuits.

3. Electric circuit and two types of circuits: open and closed:

- An electric circuit is a closed loop or pathway through which electric charges flow.

- An open circuit is a circuit that is broken or incomplete, meaning the path for the electric current is interrupted, and charges cannot flow.

- A closed circuit is a complete circuit where the path for the electric current is continuous, allowing charges to flow smoothly.

4. Define heating effect of electric current, MCB, and fuse:

- The heating effect of electric current is the phenomenon where electric current flowing through a conductor produces heat. For example, when electricity passes through a filament in a light bulb, it glows and gives off light due to the heating effect.

- MCB stands for Miniature Circuit Breaker. It is a safety device used in electrical circuits to protect against overcurrents and short circuits. When it detects an abnormal current flow, it automatically breaks the circuit to prevent damage or accidents.

- A fuse is another safety device used in electrical circuits. It contains a thin wire that melts when an excessive current passes through it. This melting breaks the circuit, protecting devices and preventing fires.

5. Magnetic effect of electric current:

- The magnetic effect of electric current is the creation of a magnetic field around a wire when electric current flows through it.

- The strength of the magnetic field depends on the amount of current and the number of turns in the wire.

- This effect is the basis for many electrical devices such as electromagnets and electric motors.

6. Electromagnet and applications of electromagnets:

- An electromagnet is a type of temporary magnet created by passing an electric current through a coil of wire.

When the current flows, it generates a magnetic field. When the current stops, the magnetism disappears.

- Electromagnets have various applications, such as in doorbells, speakers, MRI machines, and cranes. They can be turned on and off by controlling the electric current.

7. Electric bell:

- An electric bell is a device that uses an electromagnet to produce a ringing sound.

- When the electric current flows in the coil, it creates a magnetic field that pulls an iron clapper towards it, striking the bell and producing a sound.

- When the current is interrupted, the magnetic field disappears, allowing the clapper to return to its original position, stopping the sound.

Chapter 15 Light

• What is light? And what is an image?

- Light is a form of energy that enables us to see objects. It is a combination of various colors that form what we perceive as white light. Light travels in straight lines and at a very high speed.

- An image is a representation of an object formed by the light that is reflected or refracted by the object. It allows us to see objects that are not directly in front of us.

Examples of erect and inverted images:

- An erect image is formed when light rays appear to converge, meaning they come together at a point. A simple example is a pencil partially immersed in a glass of water. The portion of the pencil above the water appears to be bent but is still upright.

- An inverted image is formed when light rays appear to diverge or spread out. For example, when we see ourselves in a mirror, our image appears to be upsidedown compared to ourselves.

Examples of left-right inversion of an image:

- When we look at ourselves in a mirror, our reflection appears as if our left side is on the right side and vice versa. For instance, if you have a mole on your left cheek, the mirror image will show it on the right cheek.

• Define reflection of light with examples of incident ray and reflected ray and laws of reflection of light:

- Reflection of light occurs when light rays bounce off a surface after striking it.

- The incident ray is the incoming ray of light that strikes the surface, and the reflected ray is the ray that bounces off the surface.

- The laws of reflection state that the angle of incidence (the angle between the incident ray and the normal) is equal to the angle of reflection (the angle between the reflected ray and the normal).

Examples of incident and reflected rays:

- If we shine a flashlight on a mirror, the light from the flashlight is the incident ray, and the reflected light from the mirror is the reflected ray. • Spherical mirrors with examples of concave and convex mirrors and real and virtual images:

- Spherical mirrors are curved mirrors that have a spherical shape.

- Concave mirrors are curved inward, and convex mirrors are curved outward.

- Concave mirrors can form both real and virtual images. Real images are formed when the reflected light actually converges at a specific point, such as the image formed on a movie screen in a theater. Virtual images, on the other hand, cannot be obtained on a screen because they appear to diverge and do not intersect.

- Convex mirrors always form virtual images that are smaller, upright, and appear further away than the object, such as the side mirrors of a car.

• Lenses and its two types, concave and convex:

- Lenses are transparent curved objects made of glass or plastic that refract light.

- Concave lenses are thinner at the center and thicker at the edges, causing light to diverge when passing through them. They can only produce virtual images, which are smaller and upright.

- Convex lenses are thicker at the center and thinner at the edges, causing light to converge when passing through them. They can produce both real and virtual images depending on the position of the object relative to the lens.

• Rainbow:

- A rainbow is a beautiful natural phenomenon caused by the reflection, refraction, and dispersion of sunlight.

- Rainbow consists of seven colors red,yellow,green,blue,indigo,violet and orange

Chapter 16 Water a Precious Resource

1. How much water is available? And three forms of water:

- Earth is often called the "Blue Planet" because it is covered with a lot of water. Around 70% of the Earth's surface is covered with water.

- Water exists in three main forms: solid, liquid, and gas. The solid form is ice, the liquid form is water, and the gas form is water vapor.

2. Water cycle and seven steps of the water cycle:

- The water cycle is the continuous movement of water on, above, and below the Earth's surface. It is also known as the hydrological cycle.

- The seven steps of the water cycle are:

1. Evaporation: The process of water turning into vapor, aided by the Sun's heat.

2. Transpiration: When plants release water vapor through their leaves.

3. Condensation: The water vapor in the air cools down and turns back into liquid droplets, forming clouds.

4. Precipitation: The release of water from clouds in the form of rain, snow, sleet, or hail, which falls to the ground.

5. Infiltration: The process where water soaks into the ground from the surface.

6. Percolation: The movement of water through the soil and rocks underground.

7. Runoff: The excess water that flows over the ground and collects in rivers, lakes, and oceans, completing the cycle.

3. Define groundwater, infiltration, aquifer, and depletion of water table:

- Groundwater is the water present beneath the Earth's surface, usually in aquifers, and is obtained by drilling wells. It is an important source of freshwater.

- Infiltration is the process by which water gradually seeps into the soil through its surface.

- An aquifer is an underground layer of rock, sand, or gravel that contains water and allows it to flow.

- Depletion of the water table refers to the excessive removal or extraction of groundwater, causing the level of the water table (underground water) to decline. This can lead to a scarcity of water in an area.

4. Water management and reasons for scarcity of water:

- Water management refers to the planning and control of water resources to ensure their sustainable use and distribution.

- Scarcity of water can occur due to several reasons, some of which are:

1. Overpopulation: An increase in the number of people leads to higher water demand, exceeding the available supply.

2. Climate change: Changing weather patterns and global warming can cause irregular rainfall, affecting the availability of water.

3. Pollution: Contamination of water sources makes it unsuitable for use, reducing the amount of safe water available.

4. Wasteful usage: Wasting water through leaky pipes, over-irrigation, or excessive use contributes to water scarcity.

5. Deforestation: Cutting down trees reduces the natural water-holding capacity of an area, impacting the water cycle and availability.

6. Unequal distribution: Water scarcity can also occur when water resources are not distributed equitably among regions, leading to increased competition for limited supplies.

Maths Notes

Chapter 1 Integers

1. Introduction to Integers:

- Integers are a set of whole numbers that include positive, negative, and zero values.

- They are denoted by the symbol "Z" and can be represented on a number line.

2. Positive and Negative Integers:

- Positive integers are numbers greater than zero, denoted as +1, +2, +3, etc.

- Negative integers are numbers less than zero, denoted as -1, -2, -3, etc.

3. Operations on Integers:

- Addition: When adding integers with the same sign, add their absolute values and keep the same sign. When adding integers with different signs, subtract their absolute values and give the sign of the number with the higher absolute value.

- Subtraction: Subtracting an integer is the same as adding its additive inverse. In other words, change the sign of the number to be subtracted and perform addition.

- Multiplication: The product of two positive integers or two negative integers is positive. The product of a positive integer and a negative integer is negative.

- Division: Division of integers follows the same rules as multiplication. The quotient of two positive integers or two negative integers is positive. The quotient of a positive integer and a negative integer is negative.

4. Properties of Integers:

- Closure Property: The sum or difference of two integers is always an integer.

- Commutative Property: Addition and multiplication of integers are commutative, meaning the order of numbers does not affect the result.

- Associative Property: Addition and multiplication of integers are associative, meaning grouping of numbers does not affect the result.

- Identity Property: The additive identity of integers is zero (0), which when added to any integer gives the same integer.

5. Representation of Integers on Number Line:

- Integers can be represented on a number line. Positive integers lie to the right of zero, and negative integers lie to the left of zero.

- Absolute value is the distance of a number from zero on the number line, denoted by "|" symbols.

6. Comparison of Integers:

- Integers can be compared using the greater than (>) and less than (<) symbols. - Larger positive integers are greater than smaller positive integers. For negative integers, larger absolute values are smaller in magnitude. 7. Applications of Integers: - Integers are used in real-life situations such as temperature changes, gaining and losing money, movement above or below sea level, etc.

Chapter 2 Fractions and Decimals

1. Introduction to Fractions:

- Understanding fractions as a part of a whole.

- Numerator, denominator, and fraction representation.

- Proper and improper fractions.

- Equivalent fractions and simplification.

- Mixed fractions and conversion to improper fractions.

2. Types of Fractions:

- Like and unlike fractions.

- Addition, subtraction, multiplication, and division of fractions.

- Fraction-word problems in real-life situations.

- Comparison of fractions using different methods.

3. Decimals:

- Introduction to decimals and place value system.

- Decimal representation and reading decimal numbers.

- Conversion between decimals and fractions.

- Addition, subtraction, multiplication, and division of decimal numbers.

- Word problems involving decimal operations.

4. Comparing and Ordering Decimals and Fractions:

- Comparing decimals and fractions with the same denominator.

- Comparing decimals with different place values.

- Arranging decimals and fractions in ascending or descending order.

5. Operations with Decimals and Fractions:

- Converting fractions to decimals and vice versa.

- Addition, subtraction, multiplication, and division of decimals and fractions.

- Solving word problems involving combined operations.

6. Applications of Fractions and Decimals:

- Decimal and fraction representation in measurement systems.

- Application of fractions and decimals in money calculations.

- Real-life examples of using fractions and decimals for problem solving.

Chapter 3 Data Handling

I. Introduction to Data Handling:

A. Data: It refers to any collection of information, facts, or figures.

B. Organizing Data: It involves arranging data in an orderly manner for analysis and interpretation.

II. Types of Data:

A. Qualitative Data: It describes qualities or characteristics and is non-numerical.

Example: Colors of different flowers in a garden.

B. Quantitative Data: It consists of numerical values and can be further categorized into two types:

1. Discrete Data: It represents distinct values and cannot be subdivided. Example: The number of students in a class. 2. Continuous Data: It represents a range of values and can be subdivided. Example: Height measurements of students in centimeters.

III. Representation of Data:

A. Pictographs: It uses pictures or symbols to represent data values.

Example: Representing the number of apples sold using apple icons.

B. Bar Graphs: It uses rectangular bars to represent data values. Example: Comparing the sales of different fruits using a bar graph.

C. Line Graphs: It uses points connected by lines to show the relationship between two variables.

Example: Displaying the temperature variations throughout a day.

D. Pie Charts: It uses a circular graph divided into sectors to represent data proportions.

Example: Showing the percentage distribution of students in different grades.

IV. Collection of Data:

A. Primary Data: It is collected firsthand by conducting surveys, experiments, or observations.

Example: Collecting data on the favorite sports of students by asking them directly.

B. Secondary Data: It is collected from existing sources, such as books, articles, or databases.

Example: Gathering data about population growth from the census reports.

V. Organization of Data:

A. Raw Data: It is the original, unorganized form of data. Example: A list of students' heights in centimeters without any arrangement.

B. Array: It involves arranging data in ascending or descending order.

Example: Organizing a list of students' test scores from highest to lowest.

C. Frequency Distribution: It represents the tally or count of different data values.

Example: Creating a table to show the frequency of different shoe sizes in a class.

VI. Interpretation of Data:

A. Mean: It is the average obtained by dividing the sum of all values by the total count.

Example: Calculating the mean of test scores to determine the average performance of students.

B. Median: It is the middle value when data is arranged in ascending or descending order.

Example: Finding the median of ages to identify the age group representing the middle value.

C. Mode: It is the value that occurs most frequently in the data set.

Example: Identifying the mode of favorite colors to determine the most common choice.

A. Data handling is crucial for analyzing and interpreting information effectively.

B. Representing data through different graphical forms makes it easier to understand.

C. Collecting and organizing data accurately ensures reliable results.

Chapter 4 Simple Equations

1. Introduction to Simple Equations:

- Simple equation: A mathematical statement that states the equality between two expressions.

- Example: 3x + 4 = 10, where 'x' is the unknown variable.

2. Solving Simple Equations:

a. Balance Method:

- The goal is to isolate the variable on one side of the equation.

- Perform the same operation on both sides to maintain balance.

- Example: Solve the equation 2y - 5 = 11.

Solution: Adding 5 to both sides gives 2y = 16. Dividing by 2 gives y = 8. b. Inverse Operations:

- Use inverse operations to isolate the variable.

- Addition and subtraction are inverses, as are multiplication and division.

- Example: Solve the equation 3a + 7 = 22.

Solution: Subtracting 7 from both sides gives 3a = 15. Dividing by 3 gives a = 5.

3. Word Problems:

- Translate verbal problems into equations and solve them.

- Example: A number is increased by 8; the result is 25. Find the number.

Solution: Let the number be 'n'. The equation will be n + 8 = 25. Solving it gives n = 17.

4. Solving Equations with Variables on Both Sides:

- Sometimes equations have variables on both sides; simplify to get the solution.

- Example: Solve the equation 2x + 5 = 3x - 7. Solution: Move all 'x' terms to one side, 2x - 3x = -7 - 5, giving -x = -12. Dividing by -1 gives x = 12.

5. Checking the Solution:

- After finding the solution, substitute it back into the original equation to verify.

- Example: Check if x = 4 is a solution for the equation 2x + 5 = 13.

Solution: Substitute x = 4 in the equation gives 2(4) + 5 = 13, which is true.

6. Summary:

- Simple equations involve finding the unknown variable in an equality statement.

- Various methods like the balance method and inverse operations can be used for solving.

- Word problems require converting the problem into an equation.

- Equations with variables on both sides need simplification before finding the solution.

- Always check the solution by substituting it back into the original equation.

Chapter 5 Lines and Angles

1. Introduction to Lines and Angles:

- A line is a straight path that extends infinitely in both directions.

- Points on a line are named using capital letters.

- A line segment is a part of a line that has two endpoints.

- An angle is formed when two rays share a common endpoint called the vertex.

- Angles are measured in degrees using a protractor.

2. Types of Angles:

- Acute Angle: An angle smaller than 90 degrees. Example: 30°.

- Right Angle: An angle measuring exactly 90 degrees. Example: 90°.

- Obtuse Angle: An angle greater than 90 degrees but less than 180 degrees. Example: 120°.

- Straight Angle: An angle measuring exactly 180 degrees. Example: 180°.

- Reflex Angle: An angle measuring greater than 180 degrees but less than 360 degrees. Example: 270°.

3. Pairs of Angles:

- Adjacent Angles: Angles that share a common vertex and a common side, but no common interior points. Example: ?ABC and ?CBD.

- Vertical Angles: Pair of non-adjacent angles formed by two intersecting lines. Example: ?ABC and ?DBE.

- Linear Pair: Pair of adjacent angles formed by a straight line, summing up to 180 degrees. Example: ?ABC and ?CBD.

- Complementary Angles: Pair of angles whose sum is 90 degrees. Example: ?ABC and ?DBE forming a 90° angle.

- Supplementary Angles: Pair of angles whose sum is 180 degrees. Example: ?ABC and ?DBE forming a straight angle.

4. Parallel Lines and Transversal:

- Parallel Lines: Two or more lines that will never intersect, no matter how far they are extended. Example: AB || CD.

- Transversal: A line that intersects two or more parallel lines. Example: Line PQ intersects AB and CD.

- Corresponding Angles: Pairs of angles at the same corresponding positions when a transversal intersects two parallel lines. Example: ?1 ? ?5.

- Alternate Interior Angles: Pairs of nonadjacent angles on opposite sides of a transversal and between the two parallel lines. Example: ?3 ? ?6.

- Alternate Exterior Angles: Pairs of nonadjacent angles on opposite sides of a transversal and outside the two parallel lines. Example: ?4 ? ?7.

- Consecutive Interior Angles: Pairs of angles on the same side of the transversal and inside the two parallel lines. Example: ?3 ? ?5.

5. Triangles and Interior Angles:

- Triangle: A polygon with three sides and three angles.

- Sum of Interior Angles: The sum of all interior angles in a triangle is always 180 degrees.

- Types of Triangles: Equilateral (all sides and angles are equal), Isosceles (two sides and angles are equal), Scalene (no sides or angles are equal), Rightangled (one angle is 90 degrees).

Chapter 6 The Triangles and its Properties

1. Triangles:

- Triangle: A polygon with three sides and three angles.

- Types of Triangles based on sides:

- Equilateral Triangle: All sides are equal.

- Isosceles Triangle: Any two sides are equal.

- Scalene Triangle: All sides are different.

- Types of Triangles based on angles:

- Acute Triangle: All angles are less than 90 degrees.

- Right Triangle: One angle is 90 degrees.

- Obtuse Triangle: One angle is greater than 90 degrees.

- Sum of angles in a triangle: The sum of all interior angles of a triangle is 180 degrees.

2. Exterior Angle Property:

- Exterior Angle: Angle formed by any side of a triangle and the extension of its adjacent side.

- The measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.

3. Congruence of Triangles:

- Two triangles are said to be congruent if their corresponding sides and corresponding angles are equal.

- Criteria for Congruence:

- Side-Side-Side (SSS) Congruence: All three sides of one triangle are equal to the corresponding three sides of the other triangle.

- Side-Angle-Side (SAS) Congruence: Two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle.

- Angle-Side-Angle (ASA) Congruence: Two angles and the included side of one triangle are equal to the corresponding parts of the other triangle.

- Right-Angle-Hypotenuse-Side (RHS) Congruence: The hypotenuse and one side of a right-angled triangle are equal to the corresponding parts of the other triangle.

4. Properties of Triangles:

- Pythagoras Theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Example: In triangle ABC, with AB as the hypotenuse, if AC = 3 cm and BC = 4 cm, find the length of AB.

Solution: Using Pythagoras theorem, ABx2 = ACx2 + BCx2 ABx2 = 3x2 + 4x2 ABx2 = 9 + 16 ABx2 = 25 AB = ?25 = 5 cm

- Median of a Triangle: A line segment joining a vertex of a triangle to the midpoint of the opposite side.

- Angle Bisector: A line segment that divides an angle of a triangle into two equal parts.

- Altitude of a Triangle: A line segment drawn from a vertex perpendicular to the opposite side of the triangle.

Chapter 7 Comparing Quantities

1. Ratio: The ratio is a way of comparing two or more quantities that are related. It is expressed in the form of a fraction or using a colon (:). For example, if there are 3 red balls and 5 blue balls, the ratio of red to blue balls is 3:5.

2. Proportion: Proportion is a statement that two ratios are equal. For example, if the ratio of boys to girls in a class is 3:4 and there are 15 boys, then the number of girls can be found by forming a proportion: 3/4 = 15/x.

3. Percentage: Percentage expresses a number as a fraction of 100. For example, 45% means 45 parts out of 100. It is denoted using the symbol "%".

4. Increase and Decrease: To find the increase or decrease in a quantity, we calculate the difference between the new and old value, and express it as a percentage of the old value. For example, if the original price of an item was $100 and it increased to $120, the increase is $20 or 20% of the original price.

5. Discount: A discount is a reduction in the original price of an item. It is usually expressed as a percentage. For example, if an item originally costs $200 and there is a 10% discount, the discounted price would be $200 - (10% of $200) = $180.

6. Sales Tax and Value Added Tax (VAT): Sales tax and VAT are additional charges levied on the selling price of goods or services. It is usually expressed as a percentage. For example, if the selling price of an item is $100 and the VAT rate is 5%, the VAT amount will be $100 x (5/100) = $5, and the total price will be $100 + $5 = $105.

7. Profit and Loss: Profit is the positive difference between the selling price and the cost price, whereas loss is the negative difference. For example, if an item is bought for $50 and sold for $70, there is a profit of $20 ($70 - $50), which can be expressed as a percentage of the cost price.

8. Simple Interest: Simple interest is the amount charged for borrowing or lending money. It is calculated using the formula: Simple Interest = (Principal x Rate x Time) / 100. For example, if $2000 is borrowed at an interest rate of 5% for 2 years, the simple interest will be ($2000 x 5 x 2) / 100 = $200.

9. Compound Interest: Compound interest is the interest calculated on the initial principal as well as the accumulated interest from previous periods. It is usually calculated annually or semi-annually. The formula for compound interest is: A = P(1 + r/n)x(nt), where A is the final amount, P is the principal, r is the rate, n is the number of times interest is compounded per time period, and t is the time period in years.

10. Discounts and Commissions: In business transactions, discounts and commissions are often given or received. These are either a fixed amount or a percentage of the transaction value. For example, if a salesman receives a 5% commission on the total sales of $1000, the commission earned will be $1000 x 5/100 = $50.

Chapter 8 Rational Numbers

I. Introduction to Rational Numbers:

- Rational numbers are the numbers that can be expressed in the form p/q, where p and q are integers and q is not equal to zero.

- Example: 2/3, -7/5, 1/2, etc.

II. Representation of Rational Numbers on Number Line:

- The number line can be used to represent rational numbers.

- Positive rational numbers lie to the right of zero, while negative rational numbers lie to the left.

- Example: Representing 2/3, -7/5, 1/2 on a number line.

III. Equivalent Rational Numbers:

- Equivalent rational numbers have the same value but are expressed with different numerators and denominators.

- To find equivalent rational numbers, we can multiply or divide both the numerator and the denominator by the same non-zero integer.

- Example: 2/3 and 4/6 are equivalent rational numbers.

IV. Operations on Rational Numbers:

a) Addition and Subtraction:

- To add or subtract rational numbers, we need to have the same denominator.

- Example: Add 3/4 and 1/2. b) Multiplication:

- To multiply rational numbers, multiply the numerators and denominators separately.

- Example: Multiply 2/3 and 5/8. c) Division:

- To divide rational numbers, multiply the first number by the reciprocal of the second number.

- Example: Divide 7/8 by 3/4.

V. Properties of Rational Numbers:

a) Closure Property:

- The sum and product of two rational numbers is always a rational number.

- Example: If a = 2/3 and b = 4/5, then a + b = 22/15, which is a rational number.

b) Commutative Property:

- The order of numbers does not affect the result.

- Example: If a = 5/6 and b = 2/3, then a + b = b + a. c) Associative Property:

- The grouping of numbers does not affect the result.

- Example: If a = 3/4, b = 1/2, and c = 2/5, then (a + b) + c = a + (b + c).

d) Distributive Property:

- The product of a rational number with the sum of two other rational numbers is equal to the sum of the products.

- Example: If a = 2/3, b = 4/5, and c = 1/2, then a x (b + c) = (a x b) + (a x c).

VI. Comparing Rational Numbers:

- To compare rational numbers, we can find their decimal representations or convert them into fractions with the same denominator.

- Example: Compare 3/4 and 7/8.

VII. Applications of Rational Numbers:

- Rational numbers are used in various real-life situations, such as measurement, money, and recipes.

- Example: Using rational numbers in measurement conversions.

Chapter 9 Perimeter and Area

1. Introduction:

- Perimeter: It is the distance around the boundary of a closed figure.

- Area: It is the measure of the region enclosed by a closed figure.

- Calculating perimeter and area helps us understand the size and shape of different objects.

2. Perimeter:

- Perimeter of a Rectangle: P = 2(l + b)

Example: Consider a rectangle with length (l) = 6 cm and breadth (b) = 4 cm. The perimeter of the rectangle = 2(6 + 4) = 2(10) = 20 cm.

- Perimeter of a Square: P = 4s (where s is the side length) Example: If the side length (s) of a square is 5 cm, then The perimeter of the square = 4(5) = 20 cm.

- Perimeter of a Triangle: P = a + b + c (where a, b, c are the side lengths)

Example: Let's consider a triangle with sides a = 4 cm, b = 5 cm, and c = 6 cm. The perimeter of the triangle = 4 + 5 + 6 = 15 cm.

3. Area:

- Area of a Rectangle: A = l x b

Example: If length (l) = 8 cm and breadth (b) = 6 cm, The area of the rectangle = 8 x 6 = 48 sq. cm.

- Area of a Square: A = sx2 (where s is the side length)

Example: If the side length (s) of a square is 7 cm, then The area of the square = 7x2 = 49 sq. cm.

- Area of a Triangle: A = (1/2) x b x h (where b is the base and h is the height)

Example: Consider a triangle with base (b) = 5 cm and height (h) = 8 cm. The area of the triangle = (1/2) x 5 x 8 = 20 sq. cm.

4. Related Examples:

a) Find the perimeter and area of a rectangular garden that measures 12 m by 8 m.

Perimeter = 2(12 + 8) = 2(20) = 40 m Area = 12 x 8 = 96 sq. m

b) Calculate the perimeter and area of a square courtyard with side length 9 m. Perimeter = 4(9) = 36 m Area = 9x2 = 81 sq. m

c) Determine the perimeter and area of a triangular field with side lengths 6 m, 8 m, and 10 m.

Perimeter = 6 + 8 + 10 = 24 m Area = (1/2) x 6 x 8 = 24 sq. m

Chapter 10 Algebraic Expressions

1. Algebraic expressions are combinations of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division.

Example: 2x + 3y, 4a - 7b, 5c/2

2. Variables are unknown values represented by letters, while constants are fixed values.

Example: In the expression 3x + 2, 'x' is a variable, and '2' is a constant.

3. Coefficients in an algebraic expression are the numerical part attached to variables.

Example: In the expression 5xy + 3z, '5' and '3' are coefficients.

4. Like terms in an expression have the same variables and exponents. Example: In the expression 4x + 2y - 5x, '4x' and '-5x' are like terms.

5. Unlike terms have different variables, or the same variables but with different exponents.

Example: In the expression 2xy - 3xx2, '2xy' and '-3xx2' are unlike terms.

6. Simplifying an algebraic expression involves combining like terms.

Example: Simplifying 4x + 2y - 5x gives -x + 2y.

7. Expanding an expression involves distributing and multiplying each term.

Example: Expanding 3(x + 4) gives 3x + 12.

8. Factorizing an expression involves finding a common factor and taking it out.

Example: Factorizing 6x + 15 as 3(2x + 5).

9. The commutative property allows us to change the order of terms without affecting the result.

Example: a + b = b + a

10. The associative property allows us to change the grouping of terms without changing the result.

Example: (a + b) + c = a + (b + c)

11. The distributive property states that a(b + c) is equal to ab + ac.

Example: 3(2x + 5) = 6x + 15

12. Addition and subtraction of like terms can be performed by adding or subtracting their coefficients.

Example: 4x + 2y - 5x = (4x - 5x) + 2y = -x + 2y

13. Multiplication of algebraic expressions involves multiplying the coefficients and combining the variables.

Example: (2x)(3y) = 6xy

14. Division of algebraic expressions involves dividing the coefficients and subtracting the exponents of variables.

Example: (6xy)/(3x) = 2y

15. Evaluating an expression means finding its value for given values of the variables.

Example: If x = 3 and y = 2, evaluate 4x + 3y as 4(3) + 3(2) = 12 + 6 = 18.

16. Substituting a value into an expression involves replacing the variable with the given value and simplifying the result.

Example: If x = 2, substitute x in 3x + 4 to get 3(2) + 4 = 10.

17. Like terms can be combined using the addition/subtraction property to simplify an expression.

Example: Simplify 2x + 4y - 2x - 3y + 5z to get 4y - 3y + 5z = y + 5z.

18. Using brackets in expressions helps to group terms and perform operations accurately.

Example: Simplify 2(x + 3) - 4(2x - 1) as 2x + 6 - 8x + 4 = -6x + 10.

19. Algebraic expressions are used extensively in real-life applications such as calculating cost, distance, areas, etc.

Example: If the cost of each mango is 'x' rupees and you buy 'n' mangoes, the total cost would be 'nx' rupees.

20. Practice solving various algebraic expressions to enhance your understanding and problem-solving skills.

Chapter 11 Exponents and Powers

1. Introduction to Exponents: Exponents are used to represent repeated multiplication. A number expressed with an exponent is called a power.

Example: 5x3 means 5 raised to the power of 3, which is 5 × 5 × 5 = 125.

2. Base and Exponent: In expressions like axn, 'a' is the base and 'n' is the exponent.

3. Laws of Exponents:

a) Product of Powers: axm × axn = ax(m + n) Example: 3x2 × 3x3 = 3x(2 + 3) = 3x5 b) Division of Powers: axm / axn = ax(m - n) Example: 6x4 / 6x2 = 6x(4 - 2) = 6x2 c) Power to a Power: (axm)xn = ax(m × n) Example: (2x3)x4 = 2x(3 × 4) = 2x12

4. Zero as an Exponent: Any non-zero number raised to the power of zero is equal to 1.

Example: 5x0 = 1

5. Negative Exponents: ax(-n) = 1 / axn

Example: 2x(-3) = 1 / 2x3 = 1 / 8

6. Scientific Notation: A convenient way of writing very large or very small numbers, using powers of 10.

Example: 2.5 × 10x3 = 2500

7. Laws of Exponents for Multiplication and Division of Powers: Covers the rules for multiplying/dividing numbers with exponents.

Example: (5x2 × 5x3) / (5x4 × 5x1) = 5x(2 + 3 - 4 - 1)

8. Powers of 10: Introduces the concept of powers of 10, their patterns, and how to write them.

Example: 10x0 = 1, 10x1 = 10, 10x2 = 100, ...

9. Standard Form: Expressing a number in the form of 'a' multiplied by 10 raised to the power of 'b'.

Example: 678,000 = 6.78 × 10x5

10. Application of Exponents and Powers: Practical applications of exponents in real-life situations.

11. Exponents with Fractions: Explains how to raise fractions to a power and simplify them.

Example: (3/4)x2 = 3x2 / 4x2 = 9/16

12. Laws of Exponents with Fractions:

13. Perfect Squares and Perfect Cubes: Identifying numbers that are square or cube of integers.

Example: 9 is a perfect square (3x2), and 8 is a perfect cube (2x3).

14. Square and Square Roots: Understanding the concept of squaring a number and calculating square roots.

Example: ?64 = 8

15. Cube and Cube Roots: Understanding the concept of cubing a number and finding cube roots.

Example: ?125 = 5

16. Repeated Division: Finding the square root of a perfect square by repeated division method.

17. Prime Factorization: Factoring a number into its prime factors.

Example: Prime factors of 24 are 2, 2, 2, and 3 (2 × 2 × 2 × 3).

18. Exponents and Radicals: Understanding the connection between exponents and radicals (?).

19. Rational Numbers: Introduction to rational numbers and their representation on the number line.

20. Real-Life Applications: Discussing real-world applications of exponents and powers.

Chapter 12 symmetry

1. Symmetry: Symmetry is the balanced arrangement of parts on opposite sides of a central dividing line or point.

Example: When you fold a piece of paper in half, the two halves are symmetric.

2. Line of symmetry: A line that divides a figure into two identical parts is called a line of symmetry.

Example: The letter 'X' has a line of symmetry passing through its central point.

3. Identifying lines of symmetry: To find the line(s) of symmetry in a figure, you can fold or draw lines through it.

Example: In the figure of a square, there are four lines of symmetry passing through its center.

4. Figures with multiple lines of symmetry: Some figures can have more than one line of symmetry.

Example: A rectangle has two lines of symmetry, one through its length and one through its width.

5. Figures with no lines of symmetry: Irregular shapes usually do not have any lines of symmetry.

Example: A scalene triangle does not have any lines of symmetry.

6. Order of rotational symmetry: The number of times a figure coincides with itself in one full rotation is called the order of rotational symmetry.

Example: A regular hexagon has an order of rotational symmetry of 6.

7. Rotational symmetry in everyday objects: Many objects around us have rotational symmetry, such as wheels or clock faces.

Example: A wheel of a bicycle has a rotational symmetry of multiple orders, as it looks the same after rotating it.

8. Symmetry in letters of the alphabet: Some letters of the alphabet have lines of symmetry.

Example: The letter 'B' has a vertical line of symmetry through its center.

9. Symmetry in digits: Few digits have lines of symmetry. Example: The digits 0, 8, and 6 have lines of symmetry that divide them into two equal parts.

10. Reflection symmetry: Reflection symmetry is also known as mirror symmetry, where one half of a figure is a mirror image of the other half.

Example: The capital letter 'A' has reflection symmetry along a vertical line through its center.

11. Symmetrical objects in nature: Many natural objects exhibit symmetry, such as butterfly wings or flower petals.

Example: A butterfly's wings are usually symmetrical in shape and pattern.

12. Symmetry in geometrical shapes: Various geometric shapes have lines of symmetry.

Example: A regular pentagon has five lines of symmetry passing through each of its corners.

13. Symmetry in architecture: Architects often incorporate symmetry in building designs to create a sense of balance and harmony.

Example: The Taj Mahal in India is an exquisite example of symmetrical architecture.

14. Artists and symmetry: Artists use symmetrical patterns in paintings and other forms of art for aesthetic appeal.

Example: The famous artwork "The Last Supper" by Leonardo da Vinci displays perfect symmetry.

15. Symmetry in kaleidoscopes: Kaleidoscopes use multiple mirrors to create beautiful symmetric patterns.

Example: By rotating a kaleidoscope, you can observe intricate symmetrical designs.

16. Symmetry in tessellations: Tessellations are patterns formed by repeating shapes without any gaps or overlaps.

Example: The honeycomb pattern observed in beehives is an example of a tessellation with hexagonal symmetry.

17. Symmetry in logo design: Companies often use symmetrical logos to create a sense of trust and balance.

Example: The McDonald's logo features a golden 'M' that has reflection symmetry.

18. Symmetry in puzzles: Symmetry puzzles, like spot-the-difference or jigsaw puzzles, often require identifying and matching symmetric parts.

Example: Solving a spot-the-difference puzzle involves identifying the asymmetrical elements.

19. Symmetry in flags: Many national flags incorporate symmetrical designs to represent unity and order.

Example: The flag of Switzerland features a white cross on a red background, exhibiting reflection symmetry.

20. Symmetry and beauty: Symmetry is often associated with beauty and aesthetics across various disciplines and cultures.

Example: The concept of symmetry has been admired in art, nature, and even mathematics due to its pleasing and balanced attributes.

Chapter 13 Visualising Solid Shapes

1. Introduction to Solid Shapes:

- Solid shapes are three-dimensional objects that occupy space.

- They have length, breadth, and height and are not flat like 2D shapes.

- Examples: Cube, cuboid, pyramid, sphere, cone, cylinder, etc.

2. Faces, Edges, and Vertices:

- A face is a flat surface on a solid shape.

- An edge is a line where two faces meet.

- A vertex is a point where three or more edges meet.

- Examples: A cube has 6 faces, 12 edges, and 8 vertices.

3. Types of Polyhedrons:

- A polyhedron is a solid shape with flat faces and straight edges.

- Triangular pyramid: It has a triangular base and three triangular faces.

- Cuboid: It has six rectangular faces, and all edges are at right angles to each other.

4. Nets of Polyhedrons:

- A net is a 2D representation that can be folded to form a 3D solid shape.

- It shows all the faces, edges, and vertices of a solid shape.

- Example: Unfolding a cube creates a net with 6 squares connected by tabs.

5. Euler’s Formula:

- Euler's formula states that for any polyhedron, F + V ? E = 2.

- F represents the number of faces, V represents the number of vertices, and E represents the number of edges.

6. Visualising Solids and Their Projections:

- A projection is a representation of a 3D object on a 2D surface.

- Types of projections: top view, front view, and side view.

- To draw projections, we need to imagine the object from different angles.

7. Drawing Isometric Sketches:

- An isometric sketch is a 3D representation of a solid shape.

- It is drawn using non-parallel lines called isometric lines.

- Isometric sketches give a realistic view of the object.

8. Understanding 3D Figures:

- Different solid shapes have distinct properties.

- For example, a cube has all sides equal in length, and all interior angles are right angles.

9. Volume of Cuboids and Cubes:

- The volume of a cuboid or cube is found by multiplying its length, width, and height.

- Volume (V) = Length × Width × Height

- Example: Find the volume of a cuboid with length 5 cm, width 3 cm, and height 6 cm.

10. Surface Area of Cuboids and Cubes:

- The surface area of a cuboid or cube is found by adding up the areas of all its faces.

- Surface Area = 2(L × W + W × H + H × L)

- Example: Find the surface area of a cube with side length 4 cm.

11. Volume and Total Surface Area of a Cylinder:

- The volume of a cylinder is given by V = ?r²h, where r is the radius and h is the height.

- The total surface area of a cylinder is given by A = 2?rh + 2?r².

- Example: Find the volume and total surface area of a cylinder with radius 4 cm and height 10 cm.

12. Properties of Pyramids and Cones:

- A pyramid has one base and triangular faces that meet at a common vertex.

- A cone has one circular base and a curved face that meets at a point called the apex.

13. Volume of Pyramids and Cones:

- The volume of a pyramid or cone is given by V = (1/3) × Base Area × Height.

- For a cone, the base area is the area of the circular base.

- Example: Find the volume of a cone with a radius of 6 cm and a height of 8 cm.

14. Curved Surfaces and Total Surface Area:

- Curved surfaces of pyramids and cones are regions excluding the bases.

- The total surface area of a pyramid or cone is the sum of the base area and the curved surface area.

- Example: Find the total surface area of a cone with radius 5 cm and slant height 13 cm.

15. Spheres and Hemispheres:

- A sphere is a perfectly round three-dimensional object.

- A hemisphere is a half of a sphere, cut through its center.

- Formulas for the volume and surface area of spheres and hemispheres are provided.

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