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Integers | Study
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English Version Integers | Speed Notes
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Whole Numbers The numbers 1,2, 3, ……which we use for counting are known as natural numbers. If you add 1 to a natural number, we get its successor. If you subtract 1 from a natural number, you get its predecessor. (Scroll down to continue …)
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Integers
Definition
Integers are the set of whole numbers that include positive numbers, negative numbers, and zero. The set of integers can be represented as: Integers={…,−3,−2,−1,0,1,2,3,…}Integers={…,−3,−2,−1,0,1,2,3,…}
Key Properties of Integers
- Closure Properties:
- Addition: The sum of any two integers is an integer.
- Examples:
- 2+3=52+3=5
- −1+4=3−1+4=3
- −2+(−3)=−5−2+(−3)=−5
- Examples:
- Subtraction: The difference between any two integers is an integer.
- Examples:
- 5−3=25−3=2
- −2−1=−3−2−1=−3
- 0−(−4)=40−(−4)=4
- Examples:
- Multiplication: The product of any two integers is an integer.
- Examples:
- 3×2=63×2=6
- −4×5=−20−4×5=−20
- −3×−2=6−3×−2=6
- Examples:
- Addition: The sum of any two integers is an integer.
- Identity Elements:
- Additive Identity: The integer 0 is the identity element for addition.
- Examples:
- 7+0=77+0=7
- −5+0=−5−5+0=−5
- 0+0=00+0=0
- Examples:
- Multiplicative Identity: The integer 1 is the identity element for multiplication.
- Examples:
- 4×1=44×1=4
- −3×1=−3−3×1=−3
- 0×1=00×1=0
- Examples:
- Additive Identity: The integer 0 is the identity element for addition.
- Inverse Elements:
- Additive Inverse: For every integer a, there exists an integer −a such that a+(−a)=a+−a=0.
- Examples:
- The additive inverse of 5 is -5: 5+(−5)=5+−5=0
- The additive inverse of -3 is 3: −3+3=0
- The additive inverse of 0 is 0: 0+0=0
- Examples:
- Multiplicative Inverse: Integers do not have multiplicative inverses within the set of integers (except for 1 and -1).
- Additive Inverse: For every integer a, there exists an integer −a such that a+(−a)=a+−a=0.
- Commutative and Associative Properties:
- Commutative Property:
- Addition: a+b = b+a
- Examples:
- 2+3=3+2
- −1+4 = 4+(−1) = 4-1 = 3
- 0+5 = 5+0 = 5
- Examples:
- Multiplication: a×b=b×a
- Examples:
- 3×4 = 4×3 = 12
- −2×1 = 1×−2 = -2
- 0×5 = 5×0 = 0
- Examples:
- Addition: a+b = b+a
- Associative Property:
- Addition: (a+b)+c = a+(b+c) = (a+c)+b
- Examples:
- (1+2)+3 = 1+(2+3) = (1+3)+2
- [0+(−4)]+2 = 0+[−4+2] = [(0+2)+(-4)]
- [-2+(−3)]+(-1) = -2+[−3+(-1)] = [-2+(−1)]+(-3)
- Examples:
- Multiplication: (a×b)×c=a×(b×c)(a×c)×b
- Examples:
- (2×3)×4 = 2×(3×4) = (2×4)×3
- (0×−1)×5 = 0×(−1×5) = (0×5)×−1
- (−2×3)×−1 = −2×(3×−1) = (−2×-1)×3
- Examples:
- Addition: (a+b)+c = a+(b+c) = (a+c)+b
- Commutative Property:
- Distributive Property:
- Multiplication distributes over addition:
- Example: a×(b+c)=(a×b)+(a×c) Or a×(b+c)=a×b+a×c
- Examples:
- 2×(3+4) = (2×3)+(2×4) = 6+12 = 14 Or (2×7) = 14
- −3×(1+2) = (−3×1)+(−3×2) = -3-6 = -9 Or −3×3 = −9
- 0×(5+7) = (0×5)+(0×7) = 0×(5+7) = 0×5+0×7 = 0+0 =0
- Examples:
- Example: a×(b+c)=(a×b)+(a×c) Or a×(b+c)=a×b+a×c
- Multiplication distributes over addition:
Ordering of Integers
- Integers can be ordered on a number line, where:
- Negative integers are to the left of 0.
- Positive integers are to the right of 0.
- Examples of ordering:
- …−3<−2<−1<0<1<2<3−3<−2<−1<0<1<2<3…
- −5,−2,0,4,3−5,−2,0,4,3 arranged in order: −5<−2<0<3<4−5<−2<0<3<4
Absolute Value
- The absolute value of an integer is its distance from zero on the number line, regardless of direction.
- Notation: ∣a∣∣a∣
- Examples:
- ∣3∣=3∣3∣=3
- ∣−3∣=3∣−3∣=3
- ∣0∣=0∣0∣=0
Conclusion
Understanding integers and their properties is fundamental in mathematics. They play a critical role in various areas, including algebra, number theory, and real-world applications. Mastery of integer operations is essential for higher-level mathematics.
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- Closure Properties:
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GETTING TO KNOW PLANTS | Study
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English Version Getting to know Plants | Speed Notes
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Plants are usually grouped into herbs, shrubs, trees, creepers and climbers.
From where does a plant come?
A plant comes from a seed. A seed is covered with seed coats.,The seed coats protect the seed. The seed has a baby plant inside. (Scroll down to continue …)Study Tools
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The baby plant has a tiny root towards the outer side. The tiny root is termed as radicle.
The baby plant has a tiny shoot towards the inner side. The tiny shoot is termed as plumule.
Classification of Plants Based On The of Growth Habit:
(a) Herbs: Have soft, green and weak stems.Example: rice, wheat, maize, sunflower, mint,etc.
(b) Shrubs: They are bushy and have hard stems that do not bend easily.
These are plants with the stem branching out near the base. Example: lemon, China rose, jasmine, Nerium, etc.
(c) Trees: These are big plants which have a tall and strong stem (trunk).
Stems have branches in the upper part, much above the ground. Live for many years. Example: mango,neem, banyan, coconut, etc.
(d) Climbers: Have weak stems and cannot stand erect. They take the support of other treesand climb on them. Example: pea, grape, vine, etc.
(e) Creepers: Plants which creep on the ground and spread out. Example: pumpkin and watermelon.
Classification of plants on the basis of their Life Cycle:
(a) Annuals: Plants whose life cycle is completed in the one season. These are generallyherbs.
Example: wheat and mustard.
(b) Biennials: Plants whose life cycle requires two seasons for completion. They aregenerally
herbs and rarely shrubs.Example: carrot, radish, and potato.
(c) Perennials: Plants whose life cycle runs for more than two seasons example: guava, Babul, and palm trees. Parts of a Plants:
(a) Root system: The root and its branches make up the root system of a plant. Root is the underground art of a plant body.It is non-green. The root grows into the soil and away from the light.(i) Tap Root: It is formed by the baby root (radicle) which comes out from a germinating seed.
It is the main primary root arises from the lower end of the stem.
A number of tiny branches called secondary roots. Example: mustard, neem, rose, etc.
(ii) Fibrous Root: A bunch of roots arises from the base of the stem. Example: wheat, maize, etc. Functions of root system:
(i) Roots absorb water and nutrients from the soil.(ii) Roots help the plant to stand erect.
(iii) Roots check soil erosion.
(iv) Roots store food.
(v) Prop roots offer extra support.
MODIFIED ROOTS:
Roots may show certain changes in their shape, size or structure for performing special functions. These roots are called the modified root.1. Roots modified for the storage of food: – We find such roots in carrots, radish, turnip, beetroot, sweet potato and some other plants.
2. Roots modified to provide support to the plant: – In a banyan tree, you might have noted root like roots coming out from the branches and hanging downwards.
These roots give support to the branches. They are called the supporting roots or the prop roots.
3. Root modified to bear nodules: On the roots of the gram and other pulses.
Rhizobium, a nitrogen-fixing bacteria makes its home in the form of small are termed as nodules.
(b) Shoot system: The part of the plant which grows above the soil.
It includes The stem, The leaves,The buds, The branches,The flower, The fruits, The seeds.
(ii) Leaf: A leaf is a flat and green structure on a plant, coming out from a node on the stemand always bearing a bud in its axil. Parts of leaf:
(a) Petiole: Stalk of the leaf with which it joined to the stem.(b) Leaf lamina: The flat green portion of the leaf. (c) Veins: These are the network of small, narrow, tube-like structures on both sides The function of Leaf:
(i) Transpiration: Process of losing water by the leaves of a plant.(ii) Preparation of food by the process of photosynthesis.
(iii) Flower: It is the reproductive organ of the plant.
The function of Flowers:
(i) Help in reproduction.
(ii) These become fruits that store food and seeds.
(iii) Modified flowers like cauliflower, broccoli are rich sources of vitamins. ·
Parts of Flower:
(i) Pedicel: Stalk of the flower through which the flower is joined to the branch. It has joinedto the branch.
(ii) Sepal: Small green leaf-like structures on the thalamus. They protect the flower.
(iii) Petals: Brightly colored leaf-like structures present inside the sepals. Petals attract the insects and help in the process of reproduction.
(iv) Stamens: These are long, thin and needle-like structures. These are male organs of the flower. It consists of two parts: Anther, Filament.
(a) Anther: The swollen tip of each stamen that encloses in it a small powdery
(b) Filament: Long stalk-like structure that joins the anther with thalamus.(v) Carpel: It is a flask-shaped organ in the center of the flower. It is the female organ of the flower. It consists three parts: Style, Stigma, and Ovary.
(a) Style: a Long thin tube-like structure which is swollen at the base.
(b) Stigma: Small, round and sticky part of the carpel at the top of the style the
traps thepollen grains.(c) Ovary: Swollen part of carpel that contains ovules. The Bud : A bud is a compact or a condensed shoot. It encloses future stem, nodes and leaves. Axillary bud Terminal bud floral bud
(i) Stem: Stem forms the central axis of the plant body.Gives rise to a number of branches that bear leaves. The stem bears leaves, flowers, and fruits.
The function of Stem:
(i) It provides support to plant.(ii) It bears important plant parts.
(iii) It helps in transportation of water and food.
(iv) Underground stems store food.
(v) Thick and fleshy stems make food.
(vi) Stem modified into tendrils give extra support for Some Extra Points:
The pattern of veins on the leaf is called venation. It can be reticulate or parallel.Leaves give out water vapor through the process of transpiration.
Green leaves make their food by the process of photosynthesis using carbon dioxide and water in the presence of sunlight.
Roots absorb water and minerals from the soil and anchor the plant firmly in the soil.
Roots are mainly of two types: taproot and fibrous roots.
Plants having leaves with reticulate venation have tap roots while plants having leaves with parallel venation have fibrous roots.
The stem conducts water from roots to the leaves (and other parts) and food from leaves to other parts of the plant.
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BODY MOVEMENTS | Study
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English Version Body Movements | Speed Notes
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Locomotion in the human body:
(i) Human skeleton:It forms a framework that gives shape and support to the body.
It consists of 206 bones.
It protects internal organs. (Scroll down to Continue …)
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Locomotion:
Movement of organisms from place to place.
The human skeleton has two parts: They are The axial skeleton system and Appendicular skeleton system.
- The axial skeleton system: It includes the skull, vertebral column and the chest
bones or the rib-cage. - Appendicular skeleton system: – It includes shoulder and hip girdles and the limbs
( two hands and two legs ). - Bones: – Bone is the unique combination of flexibility and stiffness. Cartilages: – It is a flexible bone which gives support to body parts like ears and nose.
- It also connects bones together. Tough fibers, the tendons: – Tendons are strong, white cords made from collagen.
- They attach to bones.
- Collagen: – Bones in a just born baby are made from soft fibres of a protein
called ‘ collagen ‘. - Ligaments: – Ligaments may be in the form of cords or sheets.
The human skeleton is made of:
(a) Skull: It protects the brain. It is a rigid box made up of plates of bone firmly
joined together. The skull is bony, forming cranium or the brain-case and the face. Twenty-two small flat big bones join to form the skull. Eight flat bones are fitted together forming a protective box for the brain. Fourteen bones of different shapes fuse together to form the face.(b) Rib cage: It is a flexible case of ribs. Each rib curves round the side of the chest from the backbone and is joined in front to a plate of bone called sternum.
Ribs are connected to one another by the muscles. Two lowermost pairs of ribs are called
‘floating ribs’.(c) Backbone or the vertebral column: It is also called the spine or vertebral column. Backbone is made from 33 rings like pieces.
Each piece is called a vertebra. It is a chain of small bones called vertebrae. It protects the spinal cord, which carries messages between the brain and body.
It also supports the skull, ribs and limbs. (d) Limbs: It is made up of long bones with joints that allow them to move. They are mainly for support.
(i) Arms: fore-arms is made up of two bones and hands have several small bones. Shoulder
bones have a pair of collarbones in front and a pair of shoulder blades.(ii) Legs: Lower leg is made up of two bones and feet have several small bones. Hip
bones or griddles bear the weight of the body and are attached to thigh bones.(iii) Joints: The point where two bones meet. Allow movement to take place. Bones
are held together by ligaments.(a) Movable Joints: It allows movement between bones and has cartilage between
them. Type of movable joints are:
(i) Hinge Joints: It allows movement only in one plane backwards and forwards. Example:
elbow joints, knee joints and the joint between phalanges of fingers and toes. (ii) Ball and Socket Joints: It permits a circular movement.Example: the shoulder.
(iii) Gliding Joints: It allows bones to slide a little. Example: bones inside wrists and
feet.(iv) Pivotal Joints: Joint where the neck joins the head. It allows the head to move
backwards and forward and turn to the right and left.(b) Immovable or Fixed Joints: The bones cannot move at these joints. Example:
bones in skull, joint between upper jaw and rest of skull. Locomotion in other animals:
(i) Fish: Locomotion achieved by lateral contractions of the muscular body with a
final thrust by the tail. Fish swim by forming loops alternately on two sides of the
(ii) Birds: When the large flight muscles contract, they pull the wings
down.(iii) Snails: The muscular foot helps in locomotion.
(iv) Earthworms: Move by stretching out the body in front and keeping the hind end
fixed to the ground.The bones are moved by alternate contractions and relaxation of two sets of
muscles.The bone joints are of various kinds depending on the nature of joints
and direction ofmovement they allow. Strong muscles and light bones work together to help the birds fly. They fly by flapping their wings. Snakes slither on the ground by looping sideways. A large number of bones and associated muscles push the body forward.The body and legs of cockroaches have hard coverings forming an outer skeleton. Themuscles of the breast connected with three pairs of legs and two pairs of wings help the cockroach to walk and fly.
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- The axial skeleton system: It includes the skull, vertebral column and the chest
THE LIVING ORGANISMS — CHARACTERISTICS AND HABITATS | Study
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English Version The Living Organisms and Their Surroundings | Speed Notes
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The surroundings where plants and animals live are called their habitat. Several kinds of plants and animals may share the same habitat.
The presence of specific features and habits, which enable a plant or an animal to live in a particular habitat, is called adaptation. (Scroll down to continue …)
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There are many types of habitats, however, these may be broadly grouped as terrestrial (on the land) and aquatic (in water). There is a wide variety of organisms present in different habitats.
Characteristics of living things:
The living things need food, air and water to grow and for the other ife processes.
The young ones grow into adults.
They respire.
Animals breathe in oxygen and breathe out carbon dioxide.
Plants take incarbon dioxide and give out oxygen.
They respond to changes in the surrounding (stimuli).
They all get rid of wastes produced in the body (excretion).
They reproduce their own kind.
They have a definite life span.
Habitat: Habitat is the place where an organism finds comfort, safety, food, water, air, shelter and suitable conditions for breeding and survival.
It has two components biotic (living things like plants and animals) and abiotic (non-living things like rocks, soil, air and water).
BIOTIC COMPONENTS
AUTOTROPHS
AUTOTROPHS MAKE THEIR OWN FOOD ( AUTO MEANS SELF; TROPH MEANS NUTRITION.)
green plants are autotrophs.HETEROTROPHS ( HETERO MEANS DIFFERENT OR OTHERS; TROPH MEANS NUTRITION ) .
Herbivores: Plants and grass eating animals.
Carnivores: flesh or meat eating animals
Omnivores: eat both, plants and flesh or meat of animals.
Habitat provides almost everything to an organism which is needed by it.
ABIOTIC COMPONENTS
Light, temperature, water, humidity and rain, soil, air and wind, height of a place-plains or hills.
Type of Habitat:
(a) Terrestrial Habitat: Plants and animals live on land.
some terrestrial habitats are seashore or the coastal area.
Examples: lants like mangroove and coconut palm are common on the bank of Ponds and lakes.
Examples: Frog, turtle, alligator, crocodile, duck etc.
Life on land.
Examples: cat, deer, lion,tiger, cow.
Plants growing on land under normal conditions of moderate temperature and availability of water are the mesophytes desert habitat on land.
Examples: cactus, euphorbia, aloe, lizards, snake, camel.
Underground habitats:
Examples: moles, beetle, cricket, termite, milliped, ant.
Plants and animals living on hills and mountains.
Example: yak, bear, hill goat, flying fox.
Plants in hills are mostly conical in shape and evergreen.
They bear deep growing roots.
The stem is woody, bearing needle-like leaves.
Plants are mostly xerophytes.
Examples: Apple, pear, plum, apricot, walnut, almond.
High snowy peaks and polar regions.
Examples: Polar bear (white bear), penguin.
(b) Aquatic Habitat: Plants and animals live in water.
Example: ponds, swamps, lakes, rivers and oceans.
Plants growing in water are called hydrophytes.
Adaptations: Plant body is covered with a slippery substance called Adaptations.
Presence of specific features or certain habitats which enable an organism to live in its surrounding.
Adaptation helps an organism in acquiring certain characteristics which helps it in being able to live in the habitat of its choice.
The adaptation may be:
(i) related to the habitat, or
(ii) related to its body structure.
Terrestrial:
(a) Deserts: Small animals stay in burrows deep in sand during the day, and come out at night.
In plants, leaves are either absent or very small as spines;
Stem has a thick waxy coating;
Roots go deep into the soil.
(b) Mountains: Animals have thick skin or fur.
Mountain goat has strong hooves.
Trees are cone shaped having sloping branches.
Leaves are needle like.
(c) Grasslands: Animals are light brown in colour.
Lion: a Long clause in front legs that can be withdrawn inside the toes.
Eyes in front of face.
Deer: Srong teeth, long ears, eyes on the sides of head.
Aquatic:
(a) Ponds:
Plants with roots fixed in soil:Stems are long, hollow and light.
leaves float on water.
Plants with roots submerge: Leaves are narrow and thin ribbon-like.
(b) Oceans: organisms living in sea are called the marine plants and marine animals.
Animals have streamlined body.
Gills to respire (dolphins and whales have blowholes).
Animals like squids and octopus do no have streamlined body and stay deep in the oceans.
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MOTION AND MEASUREMENT OF DISTANCES | Study
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REST: The objects which remain stationary at a place and do not change their position are said to be at rest.
Different modes of transport are used to go from one place to another.
In ancient times, people used the length of a foot, the width of a finger, the distance of a step as units of measurement.
This caused confusion and a need to develop a uniform system of measurement.
We use International System of Unit ( SI unit). This is accepted all over the world.
Meter is the unit of length in SI unit.
Rectilinear motion: Motion in a straight line is called rectilinear motion.
Circular motion: Motion of an object such that its distance from a fixed point is constant.
Periodic motion: Motion that repeats itself after some period of time, is called periodic motion.
Measurement: The comparison of an unknown quantity with some known quantity of the same kind is called measurement.
Measurement of an object consists of:
(i) The unit of measurement.(ii) The number of units the object.
Conventional Methods of Measurement:
Conventional measurements have only been approximate measurement. They differ from person to person and lack precision.Hand span: Length between the tip of the thumb and little finger.
Cubit: Length between the tip of middle finger and elbow.
Arm length: Length from shoulder to the tip of middle finger.
Footstep: It is the distance covered by a step.
Needs for standard units of measurement:- Units such as hand span, foot, footstep, cubit, etc., vary.
They depend upon the size of an individual’s hand, foot,etc., hence such units cause confusion in measurements.
Standard Units of Measurement: Standard Units of Measurement: is a unit to measure any quantity completely and uniformly.
Standard units for measuring, length-metre, mass-kilogram, time-Second.
‘The system International of ‘Units’ or better known as ‘S.I. UNITS.
RULES FOR WRITING SYMBOLS OF UNITS
Symbols for units are usually written in small letters.Symbols is not given in plural form.
Symbols for a unit is not to be followed by a full stop unless it is at the end of a sentence.
Rest: When the position of a body does not change with the passage of time, the body is said to be at rest.
Motion: When the position of a body changes with the passage of time, the body is said to be in motion.
Types of motion:
(a) Linear Motion:
Linear motion is further classified into two types as Straight line motion or Rectilinear Motion and
Curvilinear Motion.
Straight line motion or Rectilinear Motion: Object moves from one position to another along a straight line.
Example: A stone droped from a height.
2. Curvilinear Motion:
Object moving along curved lines.
Example: a car moving along a curve at a turning.
(b) Random Motion: When an object moves from one position to another and changes direction in an irregular manner.Example: butterfly, flies randomly in the
(c) Circular Motion: Object moves in a circular manner in relation to its own axis or arounda fixed centre.
An object remains at the same distance from a fixed point which is the centre of the path of the motion.
Two types of circular motion: (i) Revolution, taking rounds around a fixed point.
Object moves as a whole around a fixed centre.
Example: Earth revolving around the sun in a definite orbit.
(ii) Rotation or spinning motion: Object moves in a circular path in relation to its own fixed axis.
Example: Blades of a moving fan, windmill, etc.
Rotation is restricted to the central axis. The extended parts attached to the rotating axis are in revolutionary motion.
(d) Vibratory Motion: Object moves to and fro very fast. Example: strings of a guitar when plucked.
(e) Oscillatory motion: Object oscillates to and fro along the same path again and again and with the same speed. Time taken by an object to complete one oscillation is same, no matter how many oscillations the object takes. Example: heartbeat, a pendulum of a clock.
(f) periodic motion: – The motion which repeats at regular intervals of time is a periodic motion.
Ex. heartbeat, pendulum o clock, hands of a clock.
(g) Non-periodic Motion: Object does not repeat motion at regular intervals of time.
Ex. Earthquake, the eruption of a volcano, landslide, storm.
(h) Mixed motion: – more than one type of motion at the same time.
Ex. A cricket ball bowled shows linear as well spin motion.
(i) Resultant motion: – one kind of motion resulting in another kind of motion is a resultantmotion.
Ex. wheels of a bicycle rotate about its axis resulting in the linear motion of the bicycle on the road.
(j) Random motion: – The motion without any sequence or direction is random motion.
Ex. A buzzing bee, A player of a football on the field.
(k) Uniform Motion:
When the body covers the equal distance in equal time interval.
Motion of a clock hand.
(l) Non-uniform
Motion: Motion in which the body covers the unequal distance in equal inter of time, the motion of a bus.
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LIGHT, SHADOWS AND REFLECTIONS | Study
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Light is the natural agent that stimulates sight and makes things visible.
Its path is only visible when it is scattered by dust particles present in the atmosphere. Light is a form of invisible energy.
Light itsel is not visible .
It makes other objects visible.
Light and the eyes both are necessary to see the things.
The sensation which helps us to see things is called Sight or the Vision.
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SOURCES OF LIGHT
Light is classified into two:
(i) Emission of light: Classifying objects on the basis of emission of light.
LUMINOUS OBJECT: objects which emit their own light are called luminous objcts.
Ex. A candle, electric torch.
NON-LUMINOUS OBJCTS: Objects which do not have their own light and are seen by the light scattered by them are called non-luminous objects.. Example: moon, chair, table, etc.
Optical Media: Any substance which allows ligt to pass through it either partially or wholly is calle an otical media.·
Transparent: All substances that allow light to pass freely through them and through Sun, stars electric torch, candle flame.
Light, Shadows and Reflections
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which objects can clearly be seen are called transparent substances.
Example: Glass, water, air, etc.
Translucent: A substance that allows light to ass through it only partially is calle a translucent medium or substance.
Example: butter paper, tissue paper, etc.
Opaque: Objects that do not allow light to pass through them.
Example: book, brick, etc.
Shadow: A shadow is the ‘region of absence of light’. Light from a source is cut off by an obstacle and shadow is formed.
Opaque object cast a dark shadow. Translucent objects produce a weak shadow.
Transparent objects do not cast a shadow at all.
Types of shadow:
The kind of shadow depends upon the size of he source of light.
Due to smaller (point) light source: Only one dark shadow is formed and this is known as Umbra.
Due to larger(extended) light source: Two shadows are formed-a dark one in the centre and a light one on the outside. Dark shadow is called umbra and the faint or lighter shadow is called penumbra.
The size of umbra decreses and penumbra increses as the the screen is moved away from the object.
Colour of shadow: Whatever be the colour of the opaque objcet , the shadow formed is always of the same colour, that is , black.
LENGTH OF THE SHADOW:- The length of the shadow differs depends upon the angle at which light falls on a body.
Eclipse: A shadow formed in space that makes the sun or the moon invisible for some time.Eclips is the overshading of a bright obect.
(ii) Reflection of light: The process of sending back the light rays whichafall on the surface of an object. Silver metal is one of the best reflector of light.
Solar eclipse: The moon comes between the sun and the earth, so that the earth (in the shadow) darkens during the day.
The solar eclips occurs only on a ‘NEW MOON DAY’.
Lunar eclipse: The moon and the sun are in a straight line such that the earth is in the between the sun and the moon, the shadow of the earth falls on moon and the moon cannot be seen.
The lunar eclips occurs on a ‘FULL MOON ‘ NIGHT.
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ELECTRICITY AND CIRCUITS | Study
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English Version Electricity | Speed Notes
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Electric Circuit: Connecting wires, bulb, switch and electric cell is used in Torch, Battery, LED (Light Emitting Diode), etc.
Electric current is carried by Conductor.
Conductor: Materials that allow electic current to pass through them.
All metals are good conductors of electricity. Carbon is the only non-metal which is a good conductor of electricity.
Electric current is stopped by Insulators.
Insulators: Materials which do not allow electric current to pass through them.
Example: Plastic, rubber, wood, glass, polythene, PVC, etc.
Electricity can give us magnetism
Electricity is a form of energy which helps us with, heating effect, light effect , and magnetic effect.
:- It is a flow of electic current.
SOURCES OF ELECTRICAL ENERGY :- Electrical energy is available to us from electric power houses,domestic generators, batteries, and dry cells. (Scroll down to continue …)
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Electric Current :- The Electic current is a flow of elcetric charges ( electron ). Electric current flows in one direction only.
Electric Circuit: The complete ath from one terminal of the cell ( say positive ) through the bulb and back to the other terminal of the cell ( say negative ) is calle an electric circuit .
CLOSED CIRCUIT :- An unbroken path travelled by electrIcity is known as a CLOSED CIRCUIT.
OPEN CIRCUIT :- A broken path is known as an OPEN CIRCUIT.
Circuit Diagram: It is a symbolic representation of the electric circuit and the electrical parts (electrical components).
Component of Electricity:
Connecting wires: Help to conduct the electric current and complete the circuit. A metalic wire used for connections in an circuit is also called a ‘lead’.
Bulb: Lights up when an electric current flows through it. An electric bulb has a filament that is connected to its terminals. An electric bulb glows when electric current passes through it. The filament of an electric bulb is made of a tiny , coiled tungsten wire.
Battery :- A series combination of two or more cells.
Switch: Switch is a simple device that is used to either break the electric circuit or to complete it. When a switch is on, a gap in the circuit is bridge by a conducting material through which the current flows.
Electric cell or dry cell : An electric cell has two terminals; one is called positive (+ ve) while the other is negative (– ve).Inside the electric cell the electric charges flows from
negative (- ive ) terminal to the positive ( + ive ) terminal.
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FUN WITH MAGNETS | Study
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English Version FUN WITH MAGNETS | Speed Notes
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Magnets: Materials that attract iron, nickel and cobalt.
Natural magnet is called Iodestone or magnetite.
Magnetite is a natural magnet.
Magnet attracts materials like iron, nickel, cobalt. These are called magnetic materials.
Materials that are not attracted towards magnet are called non-magnetic
Examples: aer, glass, cloth, lastic, rubber etc. (Scroll down to continue …)
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Magnetic force : The force by means of which a magnet attracts objects towards itself
Poles of a magnet :- The ends of the magnet where maximum iron filings get collected are called the poles.
North pole :- The end pointing towars north is called the north seeking end or the North pole.
South pole :-The end pointing towards south is calle the south seeking or the South pole.
A freely suspended magnet always aligns in N-S direction.
Like poles repel , and unlike poles attract each other.
DIFFERNT TYPES AND SHAPE OF MAGNETS
Bar magnet Ball-ended magnet (Dumb-bell)
Horseshoe magnet
Cylindrical magnet
Magnetic needle Artificial magnet
Loadstone ( natural magnet)
ring or disc shape magnet
Fun with Magnets
Revision Notes
Temporary magnets :- Temporary magnets last or a short time.( Iron bar magnets)
Permanent magnets :- Permanent magnets last for a long time. They are made from a steel
or an alloy known as AlNiCo, a combination of aluminium,nickel an cobalt.
Classification of substances based on attraction to magnets:
Magnetic Substances: Materials which get attracted towards magnets. Example: copper, iron, nickel, etc.
Non-magnetic Substances: Materials which do not get attracted towards magnets.
Example: wood, paper, plastic and most metals.
Single Touch Method: When a magnet is used to rub an iron object along it’s length, the starting from one end to another end like combing one’s hair, the iron object gets magnetised.
Double Touch Method: When an iron bar ( object ) is rubbed by two powerfull bar magnets of equal strength with their opposite poles at the centre, in opposite direction , the bar or the object becomes a magnet.
Using Electric Current: The bar to be magnetized is placed inside the coils of a
conductor and current is passed through these coils of wire.
Properties of Magnet:
A magnet has two poles – north pole and south pole. Similar poles repel each other.
Opposite poles attract each other. Magnetic poles always exist in pairs.
There is no magnet like monopolar magnet. magnet is always bipolar.
Applications of Magnet:
Compass needle: The compasss is a small glass case containing a magnetised neele pivoted on an aluminium nail.
The needle is free to rotate.
It points north-south because the earth is.
Methods to make your own Magnet:
Also a giant magnet.
The compass lines up with the earth’s magnetic field.
Used in factories for lifting heavy masses of iron like scrap iron.
Call bells an door chimes use elctromagnet.
Loudspeaker have parmanent magnet.
Used by surgeons in hospitals to remove steel splinters from the wounds.
Used in the construction of telephones, electric bells, etc.
Used to separate iron and steel from non-magnetic materials.
DEMAGNETISATION, loss of magnetic proprty
A magnet may lose its magnetic property when it is:
hammered heated, or
dropped with a force and it strikes against a hard substance.
When two bar magnets are not stored with their like oles pointing in the same direction, each pole will destroy the other by induction.
TAKING CARE OF MAGNETS
When not in use the magnets should be stored in boxes made from non-magnetic materials like cardboard or wood. magnets should be protected with ‘keepers ‘.
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AIR AROUND US | Study
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English Version Air Around Us | Speed Notes
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Air: The invisible gaseous substance surrounding the earth, a mixture mainly of oxygen and
nitrogen.
The blanket of air that surround the earth is called atmosphere. Air is found everywhere. We cannot see air, but we can feel it. Air in motion is called wind.
Air occupies space. (Scroll down to continue …)
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Air is present in water and soil.
Air is a mixture of nitrogen, oxygen, carbon dioxide, water vapour and a few other gases. Some dust particles may also be present in it.
Atmosphere is essential for life on earth.
Aquatic animals use dissolved air in water for respiration.
Plants and animals depend on each other for exchange of oxygen and carbon dioxide from air.
Different Layers of Atmosphere
Troposphere Stratosphere Mesosphere
Thermosphere
Constituent of Air
Air contains mostly nitrogen and oxygen . Nitrogen is nearly 78% of the air.
Oxygen is nearly 21% of the air.
Rest 1% is carbon dioxide, water vapour, dust particles and some other gases.
The composition of gases in air changes from place to place.
Nitrogen : Plants need nitrogen to grow.
Oxygen : Used by all living things to respire and help to burn things.
Carbon dioxide: Plants and animals consume oxygen and produce carbon dioxide during respiration. It is used by green plants for photosynthesis. It is released on burning.
Water Vapour: Formed due to evaporation of water. Amount of water vapour present in the air is called humidity. Varies from place to place and also in the same place during day and night.
Dust and Smoke: Smoke contains a few gases and fine dust particles. It is very harmful.
Presence of dust particles in air varies from time to time and from place to place.
Importance of Air
Air aids burning.
Air is needed for breathing.
Plants need air to make food.
Birds fly in air.
Aeroplane also go up in the air because of air pressure.
Moving air is called wind.
The wind makes the windmill rotate.
Air help in quick evaporation of sweat that helps in keeping us cool.
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COMPONENTS OF FOOD | Study
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English Version Components of Food | Speed Notes
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Nutrients: Food substances that provide nourishment to the body are called nutrients.
The major nutrients in our food are carbohydrates, proteins, fats, vitamins and minerals. In addition, food also contains dietary fibres and water. Carbohydrates and fats mainly provide energy to our body. (Scroll down to continue …)
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Carbohydrates: Carbohydrates are energy-giving compounds.
Cellulose, starch and sugar are the examples of carbohydrates.
There may be simple carbohydrates or complex carbohydrates.
Fats: Fats are very high energy-giving compounds. They produce greater amount of energy than carbohydrates.
Sources of fats: animal fats and vegetable fats.
Carbohydrates and fats are Energy giving food.
Minerals: minerals are the elements required by the body in small amounts. Minerals are essential for growth and development of bones, teeth and red blood cells.
Proteins: These are body-building foods. They help in growth of the body.
Vitamins: These are organic substances that protect the body from diseases.
Roughage: It is the dietary fibre present in the food. It facilitates regular movement of the bowels and prevents constipation.
Note: Dietary fibre and water are not food.
Balanced diet: It provides all the nutrients that our body needs, in right quantities, along with adequate amount of roughage and water.
Deficiency Diseases: These are the diseases cause due to the lack of required nutrients for a long period in the diet.
Malnutrition: when a person eats enough of food but his diet is unbalanced, it isknown as malnutrition.
Undernutrition: A person not eating sufficient food to maintain good health suffers from undernutrition.
Some Nutrients Deficiency Diseases:
Protein: Kwashiorkar – Stunted growth, thinning of legs, protruding belly.Protein and Carbohydrates – Marasmus – Complete/partial arrest of growth, lack of energy.
Vitamin D and calcium: Rickets – Bowed legs, bent spine, deformed bones are joints.
Vitamin C: Scurvy – Bleeding and swelling of gums, weakness.
Iodine: Goitre – Enlargement of thyroid gland, retarded growth.
Iron – Anaemia – Fatigue, loss of appetite, pale skin.
Vitamin K: Bleeding disease- delay in blood clotting leads to excess bleeding.
Beri-beri: Vitamin B1 – weakness in muscles, little energy to do work, paralysis
Night blindness – Vitamin A – No vision at night or in dim light.
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SORTING MATERIALS INTO GROUPS | Study
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English Version Sorting Material into Groups | Speed Notes
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Material: A material is a substance which is used for making things.
A given material could be used to make a large number of objects.
It is also possible that an object could be made of a single material or of many different types of materials. (Scroll down to continue …)
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GENERAL PRPERTIES OF MATRIAL
(A) Apearance : Shiny ( luster or luster ) or Roughness ( non-lustrous ) All metals are lustrous , some are more and some are less.
wood, rubber or a piece of rock is non-lustrous.
(B) Hardness: Hard and soft Rocks, iron and many metals are hard.
Hard materials may be:
1. Brittle :- Which break into samller pieces or are powdered when hammered.Example: rock, glass, salt.
Malleable: Which spread into sheets when beaten. metals are malleable.
Ductile:- they can be drawn into thin and long wires. metals are ductile.
Materials like wood, rubber and fibres are soft.
(C) Visibility:-
Transarent :- object through which light passes .
Examples: glass some plastis, sugar and salt solution in water etc.
Transluscent:- object through which light passes partially.
Example: Butter paper, etc.
Opaque: object through which light does not pass.
Examples: wood, metals, rock and wall etc.
(D) Good and bad conductor of electricity:-
Good conductors of electricity:- Material through which electric current can pass easily are the good conductors of electricity.
Examples: metals are good conductors of electricity.
Bad conductors of electricity:- Material through which electric current do not can pass are the bad conductors of electricity.
Examples: wood, plastic, rubber, cork and certain materials are bad conductors of electricity.
(D) Good and bad conductor of heat:- All metals are good conductors of heat.
Examples: wood are bad conductors of heat.
(E) combustible substances:- The materials which catch fire on heating are combustible substance.
wood, plastic, fibre and paper are combustible substance.
(F) SOME MATERIAL MAY FLOAT AND SOME SINK IN WATER.
material which sinks in water is denser than water. material which floats on water is less dense than water.
(G) SOLUBILITY O A SUBSTANCES IN WATER.
The substnces like salt and sugar , which disappear in water , are said to be soluble.
The substances which remain as such and do not disappear in water are said to be
(H) Miscible and Immiscible Liquid:- when two liquids are mixed and they do nort mixed well, they are said to be immiscible.
The liquids which mix well with water are said to be miscible.
GROUPING OF MATERIALS. Things made from wood
Things made from metal
Things made from ceramic
Things made from glass
Things made from plastic
Things made from rubber
things that are liquids such as oil.
Materials are grouped together on the basis of similarities and differences in their properties.
Things are grouped together for convenience and to study their properties.
Advantages of classification:
(a) Helps in identification of objects.(b) Helps in sorting of objects.
(c) Helps in locting things.
(d) Makes study of different objects easy and more meaningful rather than studying each other separately. (e) Helps to understanding similarities and dissimilarties among
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SEPARATION OF SUBSTANCES | Study
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PURE SUBSTANCES: The substances which contain only one kind of particles are called pure substances. Elements and compounds are pure substances.
ELEMENT: A substance made from identical particles of one material.
COMPOUND: A substance formed as a result of chemical combination of two or more elements in a fixed ratio.
Solution: A solution is a homogeneous mixture of two substances.
Solvent: The substance in larger quantity is the solvent.
The substance other than the solvent present in the solution is/are is the solute/solutes.
IMPURE SUBSTANCES: The substances which contain more than one kind of particles are called impure substances.
NEED FOR SEPARATING COMPONENT OF A MIXTURE
Removing harmful or unwanted components, and obtaining useful and desire component in pure form.Methods of separation are Threshing, winnowing, handpicking, sieving, magnetic separation, floating and sinking method, filtration.
separation to immiscible liquids, churning to separate cream from milk, sublimation.
(i) Separation of solid from other solids:
(a) Threshing: The process of separating grain from husk or chaff is called threshing.
Chaff: The waste material of agriculture processes such as pieces of straw are called chaff.
(b) Winnowing: The process of separation of heavier and lighter components of a mixture by wind or blowing air.
(c) Hand-picking: The process of picking the undesirable components from desirable material with hand is called Hand-picking.
(d) Sieving: The process of separating the solid constituents of different sizes in a mixture using a sieve is called sieving.
Sieve: A sieve is a device with many small holes in it , which allow the smaller particles to pass through and stops the bigger particles in it is called a sieve.
(e) Magnetic separation: Process of seperating the magnetic material by moving a magnet over a mixture of magnetic and non-magnetic substances is called magnetic seperation. In this process the magnetic material sticks to the magnet are removed.
(ii) Separation of water soluble solids or separating solute dissolved in solvent:
(a) Evaporation: Process of converting a liquid into its gaseous state by placing in open air without heating is called evaporation.
(b) Condensation: Process of converting a gaseous material into its liquid state by cooling it is called condensation.
(iii) Separation of insoluble solids from Liquids:
(a) Sedimentation: The process of settling down of heavier and insoluble component from mixture is called sedimentation.
Examples: sand, water.
(b) Decantation: The process of transferring clean liquid without disturbing the sediment, is called decantation
(c) Loading: The methods by which finer particles are made to settle faster by dissolving a small quantity of alum.
(d) Filtration: In this process the impurities are passed through a filter.
Filter: The filter has pores in it that allow only liquids to pass through the pores but stops the suspended particles or solid particles.
Therefore, the filter separates the suspended particles or solid particles.
The clear liquid so obtained in filtration is called the filtrate.
residue: The left over material on the filter paper due to filtration is known as residue.
(iv) Separation of Immiscible Liquids:
IMMISCIBLE: The liquids which donot mix well with one another are called immiscible liquids.
Example: Mixture of oil and water are immiscible liquids.
immiscible liquids are sepreated by centrifugation, churning etc. methods.
(b) Centrifugation: The method in which mixture containing suspended particles is rotated at a high speed in a centrifuge and heavier particles settle down.
Example: Cream is separated from milk, using centrifugation method.
(c) Churning: The method which is used for separating lighter particles of solid suspended in.
SEPARATING SOLUTE NOT SOLUBLE IN A SOLVENT
Flotation and sinking methods:- This method is used when the components are not soluble in water and one of the component of a mixture is lighter than water and the other is heavier than water.SUBLIMATION:- The changing of a solid directly to vapour, without coming to liquid state is called sublimation.
Husk and stones could be separated from grains by handpicking.
· Husk is separated from heavier seeds of grain by winnowing.
· A saturated solution is a solution in which no more solute could be dissolved.
· More of a substance can be dissolved in a solution by heating it.
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[ultimatemember form_id=”26482″]Motion and Time | Study
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English Version Motion and Time | Speed Notes
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Motion: The action or process of moving or being moved.
The distance moved by an object in a unit time is called its speed.
Speed of objects help us to decide which one is moving faster than the other.
The speed of an object is the distance travelled divided by the time taken to cover that distance.
Its basic unit is mere per second (m/s). (Scroll down to continue …).
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Periodic events are used for the measurement of time.
Periodic motion of a pendulum has been used to make clocks and watches.
Motion of objects can be presented in pictorial form by their distance-time graphs.
The distance-time graph for the motion of an object moving with a constant speed is a straight line.
Uniform Motion ANd Non – Uniform Motion:
- Uniform motion: An object moving with a constant speed is said to be in uniform motion. The average speed is the same as the actual speed.
- Non-Uniform motion: If the speed of a moving object keeps changing, the object is said to be in non-uniform motion.
Speed: It is the distance covered by an object in a unit time.
Speed = Total distance/ Total Time
Basic unit of speed is m/s.
Distance-Time Graph: Motion of objects can be presented in pictorial form by their distance-time graphs.
The distance-time graph for the motion of an object moving with a constant speed is a straight line.
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INTEGERS | Study
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English Version Integers | Speed Notes
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We haveseen that there are times whenwe need touse numbers witha negative sign. This is when we want to go below zero on the number line. These are called negative numbers. Some examples of their use can be in temperature scale, water level in lake or river, level of oil in tank etc. (Scroll down to continue …)
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They are also used to denote debit account or outstanding dues. The collection of numbers…, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, … is called integers. So, – 1,– 2, – 3, – 4, … called negative numbers are negative integers and 1, 2, 3, 4, … called positive numbers are the positive integers. We havealso seen howone more thangiven number givesa successor andone less than given number gives predecessor. We observe that (a) When we havethe same sign,add and putthe same sign. (i) When two positive integers are added, we get a positive integer [e.g.. (+3) + (+2) = + 5]. (ii) When two negative integers are added, we get a negative integer [e.g.. (–2) +(–1)= – 3]. (b) When one positive and one negative integers are added we subtract them as whole numbers by considering thenumbers without their sign and thenput the signof the bigger number with the subtraction obtained. The bigger integer is decided by ignoring thesigns of theintegers [e.g.. (+4)+ (–3) =+ 1 and(–4) + (+3)= – 1]. (c) The subtraction ofan integer isthe same asthe addition ofits additive inverse. We have shownhow addition andsubtraction of integers can also beshown on a number line.
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FRACTIONS | Study
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English Version Fractions | Speed Notes
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What havewe discussed? A fraction is a number representing a partof a whole. The whole maybe a single object or agroup of objects. (Scroll down to continue …)
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Whenexpressing a situation of counting partsto write a fraction, itmust be ensured that allparts are equal.
In5/7, 5 iscalled the numerator and 7 iscalled the denominator.
Fractions can beshown on a number line.
Every fraction has a point associated with it onthe number line.
In a proper fraction, the numerator is less than the denominator.
Thefractions, where the numerator is greater than the denominator are called improper fractions.
An improper fraction can be written as a combination of a whole and a part, and such fraction then called mixed fractions.
Each proper or improper fraction has many equivalent fractions.
To find an equivalent fraction of a given fraction, we may multiply or divide boththe numerator andthe denominator ofthe given fraction by the samenumber.
A fraction issaid to bein the simplest (or lowest) formif its numerator and the denominator haveno common factor except 1.
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DECIMALS | Study
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English Version Decimals | Speed Notes
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To understand the parts of one whole (i.e. a unit) we represent by a block divided into 10 eaual parts means (1/10) th of a unit. (Scroll down to continue …)
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Addition of Decimals: Decimalscan be added by writingthem with equal number of decimals places.Example: add 0.005,6.5 and 20.04.
Solution: Convert the given decimals as 0.005, 6.500 and 20.040. 0.005+ 6.500 + 20.040 = 26.545
Subtraction of Decimals: Decimalscan be subtracted by writingthem with equalnumber of decimalplaces.
Example: Subtract the given decimals as 5.674 and 12.500 12.500– 5.674 = 6.826
ComparingDecimals: Decimalsnumberscanbecompare The givendecimals have distinctwhole number part, so we compare wholenumber part only. The whole number part of 45.32 is greater than 35.69. Therefore, 45.32>35.69.
Using Decimals: Many dailylife problems can be solvedby converting different units of measurements such as money,length, weight, etc. in the decimal form.
Money:
100 paise = 1 Rupee
1 paise = 1/100 Rupee = 0.01 Rs. 5 paise = 5/100 Rs. = 0.05 Rs.
105 paise = 1 Rs. +5 paise = 1.05 Rs.
7 Rs. 8 paise= 7 Rs. + 0.08 Rs = 7.08 Rs.
7 Rs. 80 paise = 7 Rs. + 0.80 Rs. = 7.80 Rs.
Length:
10 mm = 1 cm
1mm = 1/10 cm = 0.1 cm 100 cm = 1 m
1 cm = 1/100 m = 0.01 m 1000 m = 1 km
1 m = 1/1000 km = 0.001km
Weight:
1000 g = 1 kg
1 g = 1/1000kg = 0.001 kg
25 g = 25/1000kg = 0.025 kg
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DATA HANDLING | Study
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English Version Data Handling | Speed Notes
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Data: A collection of numbers gathered to give someinformation. Recording Data:Data can becollected from different sources. Pictograph: The representation of data through pictures of objects. It helps answer the questions onthe data ata glance. (Scroll down to continue …)
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Bar Graph: Pictorial representation of numerical datain the formof bars (ractangles) of equal width and varying heights. We have seen that data is a collection of numbers gathered to give some information.
To get a particular information from the givendata quickly, thedata can be arranged ina tabular formusing tally marks. We learnt how a pictograph represents data in the formof pictures, objects or parts ofobjects.
We have also seen how to interpret a pictograph and answer the related questions.
We havedrawn pictographs using symbols to represent a certain number of items orthings.
We havediscussed how torepresent data byusing a bardiagram or abar graph.
Ina bar graph, bars of uniform width are drawn horizontally or vertically with equal spacing between them.
Thelength of eachbar gives therequired information.
To do this we also discussed the process of choosing a scale for the graph. For example, 1unit = 100students.
We havealso practised reading a given bargraph.
We have seen howinterpretations from thesame can bemade.
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MENSURATION | Study
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English Version Mensuration | Speed Notes
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Perimeter is the length of the boundary of the geometric shape.
In other words the distance covered along theboundary forming aclosed figure whenyou go round the figure once.
(a) Perimeter of arectangle = 2 × (length + breadth) (b) Perimeter of a square = 4 × length ofits side. (Scroll down to continue …)
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Mensuration
Perimeter is the length of the boundary of the geometric shape.
In other words the distance covered along theboundary forming aclosed figure whenyou go round the figure once.
(a) Perimeter of arectangle = 2 × (length + breadth)
(b) Perimeter of a square = 4 × length ofits side
(c) Perimeter of anequilateral triangle =3 × length of a side
(d) Perimeter of a regular pentagon has five equal sides = 5 × length of a sides Figures in which all sides and angles are equal are called regular closed figures.
The amount of surface enclosed by a closed figure is called its area. To calculate the area of a figure using a squared paper, the following conventions are adopted :
(a) Ignore portions ofthe area thatare less thanhalf a square.
(b) If more than half a square is in a region. Count it as one square
(c) If exactly half the square is counted, take its area as
Area of a rectangle = length × breadth Area of a square = side × side
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ALGEBRA | Study
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Algebra: A generalization of arithmetic in which letters representing numbers are combined according to the rules of arithmetic.
We looked at patterns of making letters and other shapes using matchsticks.
We learnt how to write the general relation between the number of matchsticks required for repeating a given shape. (Scroll down to continue …)
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The number of times a given shape is repeated varies;
it takes on values 1,2,3, It is a variable, denoted by some letter like n.
A variable takes on different values, its value is not fixed.
The length of a square can have any value.
It is a variable.
But the number of angles of a triangle has a fixed value 3.
It is not a variable.
We may use any letter a, b, c … x, y, z etc., to show a variable.
A variable allows us to express relations in any practical situation.
Variables are numbers, although their valueis not fixed.
We can do the operations ofaddition, subtraction, multiplication and division on them just as in the case of fixed numbers.
Using different operations we can form expressions with variables like x –3, x +3, 2n, 5m, 3p, 2y + 3, 3l – 5, etc.
Variables allow us to express many common rules in both geometry and arithmetic in a general way.
For example, the rule that the sum of two numbers remains the same if the order in which thenumbers are taken is reversed canbe
expressed as a + b = b +a.
Here, the variables a and b stand for any number, 1, 32, 1000– 7, – 20, etc.
An equation is a condition on a variable.
It is expressed by saying that an expression with avariable is equal to a fixed number, e.g. x– 3 =10.
An equation has twosides, LHS and RHS, between them is the equal (=) sign.
Solution of an Equation: The value ofthe variable inan equation which satisfies the equation.
For getting thesolution of anequation, one method is the trial and error method.
In this method, we give somevalue to the variable and check whether it satisfies the equation.
We go on giving this way different values to the variable until we find the right which satisfies the equation.
The LHS of an equation is equal to its RHS only for a definite value of the variable in the equation.
We say that this definite value of the variable satisfies the equation.
This value itself is called the solution of the equation.
For getting the solution of an equation, one method is the trial and error method.
In this method, we give some value to the variable and check whether it satisfies the equation.
We goon giving this way different values to the variable` until we find the right value which satisfies the equation.
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RATIO AND PROPORTION | Study
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English Version Ratio and Proportion Comparison By Taking Difference | Speed Notes
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CHAPTER 12 Ratio and Proportion Comparison by taking difference: For comparing quantities of thesame type, wecommonly use themethod of taking difference between thequantities. Some times thecomparison by difference does not makebetter sense thanthe comparison by division. (Scroll down to continue)
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Comparison by Division: In many situations, a more meaningful comparison between quantities is made byusing division, i.e.. by seeing how many times one quantity is to the other quantity. This method is known ascomparison by ratio. The comparison of two numbers or quantities bydivision is knownas the ratio. Symbol ‘:’is used todenote ratio. For comparison by ratio, thetwo quantities mustbe in thesame unit. Ifthey are not,they should beexpressed in thesame unit before the ratio istaken. For example, Isha’s weight is25 kg andher father’s weight is 75 kg.We say thatIsha’s father’s weight and Isha’s weight are in theratio 3 : 1
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CBSE 6 | Mathematics – Study – Free
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[ultimatemember form_id=”26482″]PLAYING WITH NUMBERS | Study
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English Version PLAYING WITH NUMBERS | Speed Notes
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We have discussed multiples, divisors, factors and have seenhow to identify factors and multiples. We have discussed and discovered thefollowing: (a) A factor of a number is an exactdivisor of thatnumber. (Scroll down to continue …)
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(b) Every number is a factor of itself. 1 is a factor ofevery number.
(c) Every factor ofa number isless than or equal tothe given number.
(d) Every number isa multiple ofeach of itsfactors.
(e) Every multiple ofa given number is greater thanor equal tothat number.
(f) Every number is a multiple of itself.
We have learnt that – (a) The number otherthan 1, withonly factors namely 1 and thenumber itself, isa prime number. Numbers that have more than two factors are called composite numbers. Number 1is neither prime nor composite.
(b) The number 2is the smallest prime number andis even. Every prime number other than 2 isodd.
(c) Two numbers withonly 1 asa common factor are called co-prime numbers.
(d) If a number is divisible byanother number thenit is divisible by each of the factors of that number.
(e) A number divisible by two co-prime numbers is divisible by their product also.
We have discussed how we can find just by looking at a number, whether it is divisible by small numbers 2,3,4,5,8,9 and 11.
We have explored the relationship between digits of thenumbers and theirdivisibility by different numbers.
(a) Divisibility by 2,5and 10 canbe seen byjust the lastdigit.
(b) Divisibility by 3and 9 ischecked by finding the sum ofall digits.
(c) Divisibility by 4 and 8is checked bythe last 2and 3 digits respectively.
(d) Divisibility of11 is checked by comparing thesum of digits at odd andeven places.
We have discovered that if twonumbers are divisible by a number then their sum and difference are also divisible by that number.
We have learnt that – (a) The Highest Common Factor (HCF) of two ormore given numbers is the highest of their common factors.
(b) The Lowest Common Multiple (LCM) of two ormore given numbers is the lowest of their common multiples.
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