Yearly Archives: 2022

Magnetism:

It the force of attraction or repulsion that act at a distance because of presence of magnetic
field.
Magnetic field is caused or generated by moving electrically charged particles or it is inherent
in magnetic objects such as magnet.
Magnets:
• A magnet has two ends termed as poles. North Pole and South Pole.
• Like poles repel, Opposite poles attracts
• Every magnet creates invisible area around it , called as Magnetic field
• Earth itself act as giant magnet, North pole of magnet indicates north pole of earth
• If you cut the bar magnet at center , you get another two bar magnets
• Magnetization can be brings about in non-magnetic material such as iron nail by
simply running a magnet over it.
Magnetic Field:
The magnetic field is nothing but imaginary area around a magnet in which there
is magnetic force.
It is invisible magnetic field that describes the magnetic influence that extends all around
them.
Electromagnet:

Electromagnet are those temporary magnets in which , the strength of their magnetic field
can easily be controlled just by changing the amount of electric current that flows through it.

Laws of Magnetism:

1. Like poles repel each other whereas unlike pole attracts each other
2. Poles are opposite to each other but equal in magnitude or strength
3. Poles are inseparable, means on cutting of bar magnet new magnets are formed with
   new poles.
4. Long bar magnet can retained magnetism longer than short bar magnets due to the
   less demagnetizing action of poles. (Horse-shoe magnet retained more than bar
   magnet)
5. On Magnet demagnetization as well as remagnetization can be performed. Short Notes
   Class 7 IGS
6. Application of magnets and electromagnets:
7. • Electromagnets are used in numerous of electrical devices such as electrical bell,
8. telephone, radio, transistor, loudspeaker etc.
9. • It is also used in fan, motor, mixers as well as room cooler.
10. • Used in compass needle
11. • Common use big electromagnets are used for removing iron objects from scrap.
12. The branch of physics which deals with the relationship between electricity and magnetism
13. termed as “Electromagnetism”
14. Electrical bell :
15. It is made of an electromagnet and work on its application where there is presence of bell
16. (metal shaped cup like structure), soft iron strip which act as a hammer and contact screw.
17. The shape of device is somewhat cup-shaped, ultimately made up of metal.
18. A soft iron strip works as a small hammer.
19. Working :
20. • Whenever the switched is on then the current is passed through the circuit and the
21. electromagnet acts like a temporary magnet and start attracting the iron strip.
22. • The iron strip that is hammer, which is elastic in nature, strikes the bell.
23. • At the same moment, its contact with the screw is lost , which turn out to be the
24. breaking of circuit and the current stops flowing through the electromagnet.
25. • In fraction of seconds of interval, the iron strip returns to its original position, and
26. quickly the current passes through the electromagnet.
27. This repeated process happens many times in a second, and as the hammer strikes the bell,
28. the sound is heard clearly.
29. The bell rings till the circuit has been switched off temporarily.
30. The electric bell is used in alarms and bells is schools, offices, homes and industries.
31. Electrical current:
32. It is defined as the amount of charge flowing per second through a cross sectional part of
33. conductor.
34. SI unit is Ampere (A).
35. In a conductor the passage of electric current is only due to the flow of electrons as atoms
36. sticks to their position.

Potential Difference:

It is the difference in the amount of energy which tend to act like carriers of charge between
two points in a circuit.
It is required for maintaining the flow of charges in the conductor
It is measured by “Voltmeter” The SI unit for electrical potential is volt (v).
o Combination of two or more cells is consider as battery
o In the circuit diagram the zigzag line indicate the Resistor which is generally made
from metallic alloys namely nichrome , eureka , tungsten , manganin etc.
Electrical Circuit Diagram:
A circuit diagram also known as elementary diagram or may be sometimes as electronic
schematic is nothing but the graphical or symbolic representation of an electrical circuit on
paper.
It is easier to use a circuit diagram rather than show the actual circuit elements.
Following conditions are maintained to ensure current is flowing from circuit:

1. A closed path for flow of current
2. Cell or battery that responsible for production of desire potential difference
   Conductors are those material such as iron, copper, graphite which easily allow flow of
   charges through them.
   Insulators are those such as dry wood, glass, rubber , do not allow flow of charges through
   them.
   • Series circuit:
   In a series circuit, all components such as resistor, voltmeter , battery are connected as
   name suggest that is in series or end-to-end, resulting in a single path for current flow.
   In this case the resistance is increases as the number of appliances connected.
   • Parallel circuit:
   In a parallel circuit, as name suggests all components are connected across each other.
   Which result in the formation of exactly two different sets of electrically common points.
   In this having additional components does not increase resistance unlike the series.
   The malfunctioning in one device in reality does not affect the working of other devices.
   

A battery is a source of energy which provides a push that is a voltage of energy to maintain
the flow of current in the circuit.
When two cells are kept side by side then there is special arrangement to connect the
positive and negative terminal of cell.
The right way to do so , as there is flow of current from neighboring cells , the positive end of
one cell should be connected to negative end of another cell.
Considering many cells are in arrangement of one by one then , they should be connected
direct contact that is one cell follow by other with respect to maintaining positive terminal
attach to negative terminal of consecutive cell.
And in box shaped battery compartment when they place side by side parallel way then the
common metal strip should run over all negative terminals be in touch to ensure the
condition for passage of current and for same as that of positive terminal

Motion

• The movement of an object or the tendency of an object to move from its place with respect to time is called motion 
• For example Movement of the pendulum of a clock is a motion, falling of leaves from trees is a motion etc.

There are two types of motions 

1. Uniform Motion: If an object moves in a straight line at a constant speed i.e., speed is not changing over time, then the motion is uniform motion.
2. Non-Uniform Motion: If an object moves in a straight line and the speed of an object changes over time, then the motion is a non-uniform motion.

Speed

• The distance covered by an object per unit time is called speed. Thus,

S=DTS=DT  where SS represent the speed of an object, DD represent the distance covered by an object and TT represent the time taken by the object.

• SI unit of speed is m/sm/s.

Measurement of Time

• In earlier periods, the shadow of objects cast by the sun was used to measure time.
• Simple Pendulum: It is a type of clock used to measure time and is the best example of periodic motion.
• Periodic or oscillatory motion is the to and fro movement of an object.
• Oscillation: The process of moving back and forth.
• The time taken by the pendulum to complete one complete oscillation is called the time period.
• The basic or SI unit of time is seconds denoted by ss

Measuring Speed:

• Speedometer: It is a device used to measure the speed of a vehicle is Km/hrKm/hr 
• Odometer: It is a device used to measure the distance covered by a vehicle.

Distance-Time Graph 

• It is used to study the motion of an object. 
• The distance is represented on the Y-axis and time is represented on the X-axis.
• The motion is uniform when the distance-time graph is a straight line.
• If the distance-time graph is moving upwards then the speed of the object is increasing. 
•  If the distance-time graph is moving downwards then the speed of an object is decreasing
• The object is said to be at rest if the distance-time graph is parallel to the X-axis.
• The object’s speed is determined by the slope of the distance-time graph.
• If there is a curve in the distance-time graph then the speed of the object is changing

Motion

Distance is the absolute path that is covered by an object in a given time interval. Displacement is the shortest distance that is covered by the object in a given time interval. Distance is calculated as the product of speed and time. The distance is represented in meters, kilometres. 

An object stays in motion if its position changes concerning time, like when a car moves on the road. An object is at rest if it does not change its position concerning time. Like when a person stands on the ground.

As a standard, distance is measured in meters, the unit of time in seconds, and the unit of speed is meter/second.

The Types of Motion

Motion is of three types. These are rectilinear motion or translatory motion, circular motion, and period or oscillatory motion.

The rectilinear or translatory motion is where the body moves in a straight line without it changing its direction. Like when a car moves on a straight road.

A circular motion is where the body moves in a circular shape about a fixed point and on a fixed radius, like the motion of the planets around the sun.

A period or oscillatory motion is when the body’s motion repeats after a fixed time interval. Like, the to and fro movement of the pendulum.

A periodic or an oscillatory motion is where the motion of the body gets repeated after a fixed interval of time. This is like the pendulum moving. The car’s motion in a circular path of the motion of the planet around the sun.

The Oscillation of a Simple Pendulum

When the bob of the pendulum moves from A to B and then back to A again, it is considered one complete oscillation. The time period is the total time taken by the pendulum to complete one oscillation.

Time and Speed

Speed or the average speed is the total distance that the object covers in a particular time interval. Speed is the distance travelled divided by the time taken. Speed is calculated as the distance travelled to the time taken. The unit of speed is measured in meters per second or kilometres per hour.

A motion could be uniform or non-uniform. A uniform motion is when the object moves along in a straight line, and with constant speed, the object is in a uniform motion. Like when a car moves in a straight line with constant speed. A non-uniform motion is when an object moves on a straight line, and it changes its speed with time. Like when a train is in motion.

Time is usually measured in sends, hours, or minutes. The period is the total amount of time taken by an object to complete one full oscillation.

Heat:

• We know that many things around us can be hot or cold, like tea or boiling water is hot, and ice or ice cream is cold. 
• This is not just a sensation but a form of energy called heat energy. Heat can be termed as an energy which makes you feel hot or warm or we can say scientifically that it is a form of energy where the transfer of energy from a hot to a cooler object takes place. 
• The differentiation of hot and cold comes from the difference in their temperatures. Hence temperature is a measure of the degree of hotness of an object. 

Measuring Temperature:

• The device that measures the temperature is known as a thermometer. There are various kinds of thermometers depending on the purpose or usage of the same. 
• The various kinds of thermometers are as follows:

1. Clinical Thermometer:

• This type of thermometer is used to measure the body temperature only and is used in hospitals by doctors and also at home. 
• A clinical thermometer generally consists of a long narrow glass tube with a bulb at one end that contains mercury. A thread of shining mercury is seen along the scale indicated on the thermometer, which helps in taking the reading. 
• The scale used in India is the Celsius scale and is indicated by the symbol ∘C∘C. 
• The normal human body temperature is 37∘C37∘C, and so the range of this thermometer is from 35∘C35∘C to 42∘C42∘C. To take the reading, the bulb of the thermometer is kept below the tongue for a minute. 
• Nowadays due to the toxic nature of mercury and issues of the thermometer being broken and spilling it, digital thermometers are in use which are safe and do not contain mercury. 

2. Maximum-Minimum Thermometers:

• These are used to measure the maximum and minimum temperatures of a day.
• They are U-shaped parallel glass tubes. It is used to record the temperatures at a place. 

3. Laboratory Thermometer: 

• This thermometer is used to measure the temperature of all objects other than a human body. 
• It consists of a long glass tube without a kink and has a bulb containing mercury at the end of the tube. 
• This is generally used in laboratories for checking the boiling points, freezing points etc. Hence the range of this thermometer is from −10∘C−10∘C to 110∘C110∘C.

Transfer of Heat:

• We know that heat is the transfer of energy from a hotter object to a cooler object, like if a spoon is left in a bowl of hot soup, then the heat from the soup is transferred to the spoon and it becomes hot. 
• This transfer of heat can occur in different ways. They are:

1. Conduction:

• This is a process of heat transfer where the heat is transferred from the hot part to the cold part of the object. Example – The handle of a pan gets hot when the pan becomes hot and so a wooden or plastic handle is made for them. 
• The substances that allow the heat to pass through them are termed as conductors. Example – iron, copper, etc. 
• The substances that do not allow the heat to transfer through them are called insulators or poor conductors. Example – wood, plastic.

2. Convection:

• This  is the form of heat transfer in liquids and gases where the heat is transferred by the movement of the heated molecules within them. Example – boiling of water. 
• The molecules of the fluid or gas near the source of heat become hot and rise up and this is replaced by the colder molecules in the fluid or air. They also get heated up and rise till the entire fluid or air is heated. 
• This is the principle behind the interesting feature in the coastal areas called the sea and land breeze.

1. Sea Breeze: 

• In the coastal regions, the land gets heated up faster during the day time. And as the land gets hotter, the hot air rises up. 
• At that time the cool air from the sea blows in to take its place and the warm air from the land moves to the sea to complete the cycle. This cool breeze flowing from the sea to the land is termed as the sea breeze. 

2. Land Breeze: 

• The opposite of this happens at night. The land cools faster than the water at night, so the cool air moves towards the sea to replace the warm air of the sea. 
• The cool air moving from the land towards the sea is termed as land breeze. 

3. Radiation: 

• This is the form of heat transfer where a medium like air or liquid is not required to transfer the heat energy. Example – Heat from the sun, a hot utensil becomes cool after some time by transfer of heat to surroundings this way. 
• All the hot bodies are capable of radiating heat.

Absorption of Heat:

• The heat that is radiated  by the objects is reflected, absorbed. 
• The heat increases the temperature of the object. 
• Dark-colours are capable of absorbing heat. So, we feel comfortable wearing them in winters and we use a black umbrella to go out in the sun. 
• Light colours reflect heat and so we feel comfortable wearing them in summers. 
• We use woollen clothes in winters. Though wool is a poor conductor of heat, it can trap air (again a bad conductor of heat) in between the fibres which does not allow the heat from the body to escape into the surroundings and thus keeping us warm.

Highlights of Chapter 4 Science Class 7 Note

• Temperature Breeze
• Conduction
• Convection
• Radiation

Students can know more about the above topics in CBSE Class 7 Science Chapter 4 Heat Notes.

How Different Colours Absorb Different Amounts of Heat?

In Heat Chapter Class 7 Ncert Notes, absorption of different colours by varied amounts of heat has been demonstrated. This is one of the first activities of the chapter. Below are the steps mentioned to conduct this activity:

• Arrange two tin cans of the same size.
• Paint both the cans in two different colours, preferably black and white.
• Now as mentioned in class 7 Chapter 4 Science Notes, the cans should be filled with an equal volume of water.
• Leave the cans in the mid-noon sun for about an hour. Follow the precise instructions in Heat and Its Effects Class 7 Notes.
• Measure the temperature of the water in the cans after half an hour.

After this, you may find that the water in the black can is comparatively hotter than the water in the white can.

Production of Biogas in Biogas Plant

Biogas can be produced in a biogas plant from raw materials like municipal waste, sewage, agricultural waste, plant waste, and food waste or green waste. It primarily consists of carbon dioxide and methane.

Four elements that are essential for the formation of biogas, as per the Class 7 Science Ch 4 Notes, are:

1. Carbon dioxide
2. Methane
3. Hydrogen sulphide
4. Water vapour

What is the Difference Between Heat and Temperature?

As mentioned in NCERT Class 7 Science Heat Notes, heat has been referred to as the energy stored inside an object whereas the temperature is the measurement of hot and coldness of an object. The heat of an object is dependent upon the mass, temperature, material whereas the temperature of an object depends upon the kinetic energy of its particles and molecules

• Light is a naturally occurring substance that enhances vision and makes objects visible. Light follows a straight path.
• A mirror can be made out of any polished or gleaming surface. 
• A true image is one that can be obtained on a computer screen. It’s made up of light rays that pass through the screen.
• A virtual image is an image that cannot be obtained on a screen. It’s made up of light rays that appear to travel right through the screen.
• A planar mirror produces an erect picture. It’s a virtual object that’s the same size as the real thing. The picture behind the mirror is the same size as the object in front of it.

The left side of an object appears on the right side of an image generated by a mirror, and the right side of the object appears on the left side of the picture. 

• A true and inverted image can be created via a concave mirror. The picture generated when the object is put very close to the mirror is virtual, erect, and enlarged.
• A convex mirror is one that curves outwards and has a convex reflecting surface. The image that is created is virtual, upright, and shrunk. A convex mirror creates an image that is upright, virtual, and smaller in size than the object.

(Image will be Uploaded Soon)

• A concave lens is one that has a thinner centre than it has at the edges. It’s a convergent lens. The resulting image is imaginary, erect, and shrunken.
• A convex lens can create both a true and a distorted image. The image generated when the object is put very close to the lens is virtual, erect, and enlarged. The convex lens is known as a magnifying glass when it is used to magnify objects.

(Image will be Uploaded Soon)

• White light is made up of seven different colours.
• Properties of Light: 

1. Rectilinear Propagation of Light: The quality of light that allows it to move in a straight line in any direction. The direction in which light travels to form a ray.
2. Light Reflection: This is the phenomenon of light rebounding back after striking an object’s surface. Smooth, gleaming surfaces reflect nearly all of the light.
3. Dispersion: The breaking of white light into its seven colours is referred to as dispersion. Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR) hues make up white light.

Plane Figures and Solid Shapes:

• Plane figures are flat or 22-Dimension figures, they have no thickness.  
• For example: Squares, rectangles, circles, triangles etc. 
• Solid Shapes are 33-Dimension shapes, and they occupy space and have volume.
• For example: Cube, cuboid, sphere, cone, hemisphere etc.

Faces, Edges and Vertices of 3D3D Shapes:

• A 3D3D shapes is not flat therefore it has 33 dimensions and these are faces, edges, and vertices.
• Faces: It is simply the face of a 3D3D shape or the flat surface of the 3D3D shape
• For example: The number of faces of a cube is 66.

• Edges: They are the line segments which join one vertex to another vertex. 
• For example – Edges in a cylinder are 22 and are shown below.

• Vertices: Points where two or more edges meet between faces are known vertices of any 3D3D shape or the corners of 3D3D shape. 
• For example: The cube has 88 vertices and is shown below

Net for building 3D3D Shapes:

• Net is used for making 3D3D shapes.
• It is a basic skeleton outline in 22-Dimensions i.e., it is a flat 33-Dimensional shape which can be folded and joined together with the help of glue.
• Nets for building some shapes are shown below

Drawing Solids on a Flat Surface: 

• There are two ways of drawing solids on a flat surface

1. Oblique Sketches:

• It is an easy way of representing the 3D3D objects in pictorial form. 
• These sketches are intended to show the perspective of 3D3D object and are drawn on a sheet by freehand.
• It does not talk about the measurement of 3D3D object
• Oblique sketch of cube is shown below

2. Isometric Sketches: 

• It is also the pictorial representation of a 3D3D objects, but it also meets with measurements of the 3D3D object to be drawn.
• It is drawn on isometric sheets.
• Isometric sketch of cube is shown below and the dotted sheet on which the sketch is made is known as isometric sheet

Viewing Different Sections of a Solid

• There are many methods to view different sections of a solid.

1. Slicing and Cutting: It gives the cross-sectional view of a solid. 
2. Shadow Casting: It gives 2D2D view of an 3D3D object.
3. Viewing Solid from Different Angle: The front-view, the side-view and the top-view are the most common ways to view a solid; it can provide a lot of information about the shape

Solid: An object that occupies space and has a fixed space is called solid.

Some of the characteristics of a solid are:

• Solids have length, breadth and height. It is a three-dimensional figure.
• Solid objects have only three main views.

• Top view.
• Side view.
• Front view.

Cuboid:

Cuboid is solid or hollow which has 6 rectangular faces.

• It is a three dimensional solid.
• A cuboid has 12 edges.
• A cuboid has 8 vertices. 

Cube:

Cube is a symmetrical three-dimensional shape, either solid or hollow contained by six equal squares.

• Each face of a cube is square.
• Cube has 6 faces.
• Cube has 12 edges.
• Cube has 8 corners.

Cylinder:

Cylinder is a solid or hollow geometrical figure with a curved side and two identical circular flat ends.

• Cylinder has  2 edges, 3 faces but no vertex.

Sphere:

Sphere is a round solid or hollow figure with every point on its surface equidistant from its centre.

• A sphere is a 3D figure with no vertex, no edges and only1 surface.

Cone:

Cone is a solid or hollow object which tampers from a circular base to a point.

• Cone is a 3D figure with 1 vertex, 1 edge and 2surfaces.

Prism:

Prism is a solid geometrical figure whose two ends are similar, equal and parallel rectilinear figures and whose sides and faces are either parallelograms or rectangles.

• It has 3 faces,9 edges, and 6 vertices.
• Prism is a solid whose side faces are ||gm and whose end basses are two parallel and congruent polygons.

Pyramid:

Pyramid is a solid whose base is a plane rectilinear figure such as triangle and whose side faces are triangles with a common vertex.

• If the base of the pyramid is quadrilateral then it is called a quadrilateral pyramid.
• If the base of the pyramid is triangle then it is called a triangular pyramid.

Euler’s formula:

For a 3-D solid,

• V stands for the number of vertices.
• E stands for the number of edges.
• F stands for the number of faces.

Euler’s formula is V + F – E = 2.

Drawing a cube:

• The two types of sketches for drawing a cube are oblique and isometric.
• An isometric paper has dots or lines, marked on it dividing the paper into small equilateral triangles.

Cube:

Steps:

1. Take a squared paper.
2. Draw the front face.
3. Draw the opposite face of the same size.
4. Join the corresponding corners.
5. Draw the figure with hidden edges dotted.

a. Line segment: A line with definite end points is called a line segment. It is denoted as AB¯¯¯¯¯¯¯¯AB¯.

b. Line: A line segment when extended infinitely from both ends, we get a line. It is denoted as AB←→AB↔.

c. Ray: A line with one endpoint is called a ray. It is denoted by AB−→−AB→.

d. Angle: When two lines or line segments intersect or meet at a common point, an angle is formed. For example, in the figure below, we can see the angles formed by the lines PQ←→PQ↔ and RS←→RS↔ are ∠POS,∠SOQ,∠QOR∠POS,∠SOQ,∠QOR and ∠ROP∠ROP.

(Image will be Uploaded Soon)

Related Angles:

a. Complementary angles: Two angles having the sum of their measures equal to 90∘90∘ are called complementary angles. When two angles are complementary, one angle is called the complement of another angle. An example has been shown below.

(Image will be Uploaded Soon)

b. Supplementary angles: Two angles having the sum of their measures equal to 180∘180∘ are called supplementary angles. When two angles are complementary, one angle is called the supplement of another angle. An example has been shown below.

(Image will be Uploaded Soon)

c. Adjacent angle: The pair of angles present next to each other such that they have a common vertex, one common arm and the non-common arm lies on either side of the common arm. In the diagram given below, ∠1∠1 and ∠2∠2 are adjacent angles.

(Image will be Uploaded Soon)

d. Linear pair: The adjacent angles who are supplementary to each other are called the linear pairs. The non-common arms of these angles are rays moving in opposite directions. In the diagram given below, ∠1∠1 and ∠2∠2 are linear pair angles.

(Image will be Uploaded Soon)

e. Vertically opposite angles: Two lines that cross each other, four angles are formed as shown in the diagram below.

(Image will be Uploaded Soon)

Here, ∠1&∠3∠1&∠3 and ∠2&∠4∠2&∠4 are vertically opposite to each other.

Pairs of Lines:

a. Intersecting lines: two lines when crosses each other at only one point, then they are called the intersecting lines and that point is called the point intersection. As in the diagram below, ll and mmare intersecting lines with their point of intersection AA.

b. Transversal: When two or more distinct lines are intersected by a common line, then that line is called a transversal. As in the figure below, lines ll and mm are intersected by a common line pp which is the transversal. This transversion creates eight angles.

(Image will be Uploaded Soon)

The relation between the eight angles have been tabulated below.

Interior angles	∠3,∠4,∠5,∠6∠3,∠4,∠5,∠6
Exterior angles	∠1,∠2,∠7,∠8∠1,∠2,∠7,∠8
Pairs of corresponding angles	∠1&∠5,∠2&∠6,∠3&∠7,∠4&∠8∠1&∠5,∠2&∠6,∠3&∠7,∠4&∠8
Pairs of alternate interior angles	∠3&∠6,∠4&∠5∠3&∠6,∠4&∠5
Pairs of alternate exterior angles	∠1&∠8,∠2&∠7∠1&∠8,∠2&∠7
Pairs of interior angles on the same side of transversal	∠3&∠5,∠4&∠6∠3&∠5,∠4&∠6

Traversal of Parallel Lines:

When a pair of parallel lines ll and mm are intersected by a line tt, then following properties can be observed.

(Image will be Uploaded Soon)

1. Each pair of corresponding angles are equal. e.g., ∠7=∠8,∠1=∠2∠7=∠8,∠1=∠2, etc.

2. Each pair of alternate interior angles are equal. e.g., ∠3=∠8,∠1=∠6∠3=∠8,∠1=∠6, etc.

3. Each pair of interior angles on the same side of the transversal are supplementary to each other. e.g., ∠1+∠8=180∘∠1+∠8=180∘, etc

• Data collection, recording, and presentation assist us in organising and concluding from our experiences.
• We need to know what we are going to do with the data before we start collecting it. The information gathered should be organised in a table that is easy to grasp and analyse.
• The average of a set of numbers can be calculated by finding the sum of the numbers divided by the total numbers of values (n)(n) in the set. 
• The mean, median and mode of a data set are collectively known as measures of central tendency.  
• One of the representative values of data is the arithmetic mean.Mean = sum of all observationsnumber of all observationsMean = sum of all observationsnumber of all observations
• Another type of central tendency or representative value is mode. The most common observation in a group of observations is called the mode. If each value in a data set occurs only once, then all of the values are in mode.
• We sometimes refer to this data as having no mode because none of them occurs frequently.
• The median is a type of representative value as well. It’s the value in the middle of the data set, with half of the observations above it and the other half below it.

Median = 12[n2th observation + (n2+1)th observation]Median = 12[n2th observation + (n2+1)th observation].

• A bar graph is a visual representation of numbers made up of uniformly sized bars. Double bar graphs make it easy to compare two sets of data at once.
• Double bar graphs make it easy to compare two sets of data at once. In our lives, there are events that are certain to occur, some that are impossible to occur, and still others that may or may not occur.
• The situation, which may or may not occur, has a possibility to occur.
• Probability is an area of mathematics that may be used to calculate the probability of an event occurring (in percentage terms). If you have ten likelihoods and want to determine the probability of one event occurring, you might say that the probability is 110110or the event has a 10%10% chance of occurring.
• Events with multiple possibilities can have a probability ranging from 00 to 1.1..

Congruence

• Two object is said to be congruent if and only if their shape and size are same.
• The relation between two congruent object is called congruence. 
• Congruence is denoted by symbol ≅≅ 

Congruence of Plane Figures

• Two plane figures are said to be congruent when two plane figures superpose each other i.e., when one figure is placed on another figure they coincide. 
• Suppose a plane P1P1 is congruent to plane P2P2 then it is written or denoted as P1≅P2P1≅P2 

Congruence Among Line Segments

• Two lines are said to be congruent if they have equal length.
• Conversely, if two lines are congruent, they are of equal length.
• Suppose a line AB¯¯¯¯¯¯¯¯AB¯ is congruent to plane CD¯¯¯¯¯¯¯¯CD¯ then it is written or denoted as AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯AB¯≅CD¯

Congruence of Angle

• Two angles are said to be congruent if they have equal measure. 
• Conversely, if two angles are congruent, they are of equal measure. 
• Suppose an angle ∠ABC∠ABC is congruent to angle ∠CDE∠CDE then it is written or denoted as ∠ABC≅∠CDE∠ABC≅∠CDE

Congruence of Triangle

• Two triangles are said to be congruent if they have corresponding vertices, corresponding sides and corresponding angles equal.
• Let us suppose two triangles ΔABCΔABC and ΔPQRΔPQR has correspondence as 

A↔PA↔P

B↔QB↔Q

C↔RC↔R

It can be written as ABC↔PQRABC↔PQR which implies that ΔABC≅ΔPQRΔABC≅ΔPQR 

• In the above case if we denote it as ΔABC≅ΔPRQΔABC≅ΔPRQ then it is not possible since vertex BB is corresponding to vertex QQ not RR 
• Therefore, congruence should be denoted in proper way since the order of the letters in the names of congruent triangles displays the corresponding relationships.

Criteria For Congruence of Triangle 

• There are four criteria for congruence of triangle and these are

1. SSS Congruence Criteria

• If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
• For example:

(Image will be uploaded soon)

In triangles ΔABCΔABC and ΔPQRΔPQR

AB=PQAB=PQ

BC=QRBC=QR

AC=PRAC=PR

Then by SSS congruency ΔABC≅ΔPQRΔABC≅ΔPQR

2. SAS Congruence Criteria

• If under a correspondence, two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.
• For example

(Image will be uploaded soon)

In triangles ΔABCΔABC and ΔPQRΔPQR

AB=PQAB=PQ

∠BAC=∠QPR∠BAC=∠QPR

AC=PRAC=PR

Then by SAS congruency ΔABC≅ΔPQRΔABC≅ΔPQR

3. ASA Congruence Criteria

• If under a correspondence, two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle, then the triangles are congruent.
• For example

(Image will be uploaded soon)

In triangles ΔABCΔABC and ΔPQRΔPQR

AB=PQAB=PQ

∠BAC=∠QPR∠BAC=∠QPR

∠ABC=∠PQR∠ABC=∠PQR

Then by ASA congruency ΔABC≅ΔPQRΔABC≅ΔPQR

4. RHS Congruence Criteria

• If under a correspondence, the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, then the triangles are congruent.
• This criterion is applicable on right angle triangles only.
• For example

(Image will be uploaded soon)

In triangles ΔABCΔABC and ΔPQRΔPQR

AC=PRAC=PR

BC=QRBC=QR

Then by RHS congruency ΔABC≅ΔPQR

Line of Symmetry

• When a shape coincides with another shape completely then they are said to have symmetry.
• Symmetry can also be observed within a shape. When one part of a shape coincides with another part then they are said to have symmetry within a shape.
•  The line which divides a shape into two identical parts is called a line of symmetry.
• For Example: In the figure below the dotted line is the line of symmetry and left and right part looks identical or symmetrical.

(Image will be Uploaded Soon)

Lines of Symmetry for Regular polygon

• Regular polygons are those polygons whose length of all sides and measure of angles are equal. 
• In regular polygons lines of symmetry are equal to the sides of regular polygons.
• For Example: 

1. Triangle has three sides and three lines of symmetry.
2. Square has four sides and four lines of symmetry.
3. Regular pentagon has five sides and five lines of symmetry.
4. Regular hexagon has six sides and six lines of symmetry.

Rotational Symmetry

• When a shape is rotated at some angle about its axis clockwise or anticlockwise and after rotation if the shape looks exactly the same as it was before then it is called rotational symmetry.
• The fixed point through which the shape is rotated is called centre of rotation.
• The angle at which rotational symmetry occurs is called angle of rotation.
• The number of times a shape looks the same on rotation is called order of rotational symmetry. 

For Example: Order of rotational symmetry of square is 4

Line Symmetry and Rotational Symmetry

• There are some shapes which have line as well as rotational symmetry.
• Circle is the perfect example of this type; it has infinite line symmetry and can be rotated around its centre through any angle i.e., it has rotational symmetry at any angle.
• There are some alphabets also which show both line and rotational symmetry such as H, O, I and X.

1. Exponents:

Exponents are used to convey huge numbers in a more readable, understandable, comparable, and manipulable format.

2. Expressing Large Numbers in the Standard Form:

• Any number between 1.01.0 and 10.010.0 (including 1.01.0) multiplied by a power of ten can be expressed as a decimal number between 1.01.0 and 10.010.0(including 1.01.0).
• The standard form of a number is also known as scientific motion.

3. Large numbers are difficult to read, comprehend, compare, and manipulate. 

4. We use exponents to make all of this easier by transforming many of the enormous numbers into a shorter form.

5. What are some examples of exponential forms of numbers?

100=102100=102 (It can be read as 1010 raised to 22)

512=83512=83

243=35243=35

Here, 10, 810, 8 and 33 are the bases, whereas 2, 32, 3 and 55 are their respective exponents.

We also can say that

100100 is the 2nd2nd power of 1010 , 

512512 is the 3rd3rd power of 88 , 

243243 is the 5th5th power of 33 , etc.

6. For any non-zero integers aa and bb, and whole numbers mm and nn, numbers in exponential form obey the following laws:

a. am × an = am+nam × an = am+n

b. am ÷ an = am-n , m  nam ÷ an = am-n , m  n

c. (am)n = amn(am)n = amn

d. am × bm = (ab)mam × bm = (ab)m

e. am ÷ bm = (ab)mam ÷ bm = (ab)m

f. a0 = 1a0 = 1

g. (-1)^{(even number)} = 1

h. (-1)^{(odd number)} = -1Is this page helpful?Related QuestionsIf xa=yxa=y,yb=zyb=zand zc=xzc=x, then prove that abc=1abc=1

Prove that the following equation is correct 3−3×62×98−−√52×125−−−√3×(15)−43×313=282–√