Data is a collection of raw facts and figures that give you information.
Recording Data
Recording of data depends upon the requirement of the data. Everybody has different ways to record data.
If we have to compare the choice of the people about certain movies then we have to collect the data of the survey which tells the choice of the people about those movies.
Organization of Data
Raw data is difficult to read, so we have to organize it in such a way so that we can use it in need.
Data can be organized in a tabular form.
Data is represented in a tabular form using frequency distribution and the tally marks.
Frequency tells the number of times the particular observation happened.
Tally marks are used to show the frequency of the data.
Tally marks are represented as
Example
There are 30 students in a class. They have to choose one sport each for the sports period.5 took badminton, 10 took cricket, 4 took football, 1 took hockey, 3 took tennis and 7 went for volleyball. Represent this data in the frequency distribution table.
Solution
To make a frequency distribution table-
Make a table with three columns.
Write the name of sports in the first column.
Write the respective frequencies in front of each sport.
Mark the tally marks according to the frequency given.
Pictograph
If we represent the data with the pictures of objects instead of numbers then it is called Pictograph. Pictures make it easy to understand the data and answer the questions related to it by just seeing it.
We can easily answer the questions like who has a maximum number of toys, who has the least number of toys etc.
Interpretation of a Pictograph
In the pictograph, we have to understand it and get the information from the pictures given.
If we have to represent more number of items then we can use the key which represents more numbers with one picture.
Example
The number of cars parked in a parking lot every day is given in the pictograph.
Find the day when the highest number of cars are parked and how many?
When the least number of cars did park?
Solution
In the above pictograph one car represent 5 cars.
As there is the maximum number of cars is shown on Tuesday so the highest number of cars was parked on Tuesday.
Hence, 40 cars were parked on Tuesday in the parking lot.
Least number of cars were parked on Monday as there are only 4 pictures of cars are shown on that day.
Drawing a Pictograph
Drawing a pictograph is an interesting task but it may be difficult to draw some difficult pictures repeatedly as we had used cars in the above example so we can use easy symbols to draw a pictograph.
We must use a proper key of the symbols so that it could be easily understood by anyone.
Example
The following table shows the choice of the fruits of the 35 students of class 3.represent the data in a pictograph.
Name of fruit
Number of students
Mango
5
Apple
12
Guava
3
Litchi
7
Grapes
8
Solution
Bar Graph
As the pictograph is a very time-consuming process, so we can use another way to represent data.
If we use the bars of the same width with equal spacing to represent the data in which the length of the bars represent the frequency is called Bar Graph or Bar Diagram.
Interpretation of a Bar Graph
Example
The following graph tells the favourite colours in a class of 30 students.
Answer the following questions:
Which colour is liked by the maximum number of students?
Which colour is liked by the same number of students?
Solution
The graph shows that the pink colour is liked by 9 students so it is the favourite colour of the maximum number of students.
Blue and green colour bars are equal in length and both are liked by 6 students.
Drawing a Bar Graph
Drawing a bar graph is an interesting task, but we must choose an appropriate scale to draw the bar graph. It depends upon our own choice that what we are taking for the scale.
Example
The daily sale of mobile phones in Vicky production is given below. Draw the bar graph to represent the data.
Days
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
No. of phones sold
25
13
32
14
42
55
Solution
Steps to make a bar graph-
Draw two lines, one horizontal and one vertical in L shape.
Mark days on the horizontal line and no. of phones on the vertical line.
Take a suitable scale for the number of phones and mark on the vertical line. Let 1 unit = 10 phones.
Use the bars of equal width and draw them with the frequency given at the same distance.
The height of the bars tells the sale of the mobile phones in Vicky production.
This same bar graph can be made by interchanging the positions of the days and the number of phones.
When we use dots to write some numbers then that dot is the decimal point. This is used to show the part of a whole number.
Tenths
As we know that 1 cm = 10 mm, so if we have to find the opposite then
1mm = 1/10 cm or one-tenth cm or 0.1 cm.
Hence, the first number after the decimal represents the tenth part of the whole.
This reads as “thirty-four point seven”.
Representation of Decimals on Number Line
To represent decimals on the number line we have to divide the gap of each number into 10 equal parts as the decimal shows the tenth part of the number.
Example
Show 0.3, 0.5 and 0.8 on the number line.
Solution
All the three numbers are greater than 0 and less than 1.so we have to make a number line with 0 and 1 and divide the gap into 10 equal parts.
Then mark as shown below.
Fractions as Decimals
It is easy to write the fractions with 10 as the denominator in decimal form but if the denominator is not 10 then we have to find the equivalent fraction with denominator 10.
Example
Convert 12/5 and 3/2 in decimal form.
Solution
Decimals as Fractions
Example
Write 2.5 in a fraction.
Solution
Hundredths
As we know that 1 m = 100 cm, so if we have to find the opposite then
1 cm = 1/100 m or one-hundredth m or 0.01 m.
Hence, the second numbers after the decimal represent the hundredth part of the whole.
It reads as “thirteen point nine five”.
Decimal in the hundredth form shows that we have divided the number into hundred equal parts.
Example
If we say that 25 out of 100 squares are shaded then how will we write it in fraction and decimal form?
Solution
25 is a part of 100, so the fraction will be 25/100.
In the decimal form we will write it as 0.25.
Place Value Chart
This is the place value chart which tells the place value of each digit in the decimal number. It makes it easy to write numbers in decimal form.
Example
With the given place value chart write the number in the decimal form.
Hundreds (100)
Tens (10)
Ones (1)
Tenths (1/10)
Hundredths (1/100)
4
6
3
8
5
Solution
According to the above table-
Comparing Decimals
1. If the whole number is different.
If the whole numbers of the decimals are different then we can easily compare them .the number with the greater whole number will be greater than the other.
Example
Compare 532.48 and 682.26.
Solution:
As the whole numbers are different, so we can easily find that the number with a greater whole number is greater.
Hence 682.26 > 532.48
2. If the whole number is the same
If the whole numbers of the decimals are same then we will compare the tenth and then the hundredth part if required.
The number with the greater tenth number is greater than the other.
Example
Compare 42.36 and 42.68.
Solution
As the whole number is the same in both the numbers so we have to compare the tenth part.
Hence 42.68 > 42.36
Using Decimals
Generally, decimals are used in money, length and weight.
1. Money
Example: 1
Write 25 paise in decimals.
Solution:
100 paise = 1 Rs.
1 paise = 1/100 Rs. = 0.01 Rs.
25 paise = 25/100 Rs. = 0.25 Rs.
Example: 2
Write 7 rupees and 35 paise in decimals.
Solution:
7 rupees is the whole number, so
7 + 35/100 = 7 + 0.35 = 7.35 Rs.
2. Length
Example
If the height of Rani is 175 cm then what will be her height in meters?
Solution
100 cm = 1 m
1 cm = 1/100 m = 0.01 m
175 cm = 175/100 m
Hence, the height of Rani is 1.75 m.
3. Weight
Example
If the weight of a rice box is 4725 gram then what will be its weight in a kilogram?
Solution
1000 gm = 1 kg
1 gm = 1/1000 kg = 0.001 kg
Addition of Decimal numbers
To add the decimal numbers we can add them as whole numbers but the decimal will remain at the same place as it was in the given numbers. It means that we have to line up the decimal point in each number while writing them, and then add them as a whole number.
Example: 1
Add 22.3 and 34.1
Solution:
Write the numbers as given below, and then add them.
Example: 2
Add 1.234 and 4.1.
Solution:
There are three numbers after decimal in one number and one number after decimal in another number. So we should not get confused and write the numbers by lining up the decimal points of both the numbers, then add them.
Another way is to write the numbers in the place value chart, so that it will be easy to identify, how to write numbers.
Ones (1)
Tenths (1/10)
Hundredths (1/100)
Thousandths (1/1000)
+
4
1
0
0
=
5
3
3
4
Subtraction of Decimal Numbers
Subtraction is also done as normal whole numbers after lining up the decimals of the given number.
Example
Subtract 243.86 from 402.10.
Solution
Write the numbers in a line so that the decimal points of both the numbers lined up.
Then subtract and borrow as we do in whole numbers.
A Fraction is a part of whole. The ‘whole’ here could be an object or the group of objects. But all the parts of the whole must be equal.
The first one is the whole i.e. a complete circle.
In the second circle, if we divide the circle into two equal parts then the shaded portion is the half i.e. ½ of the circle.
In the third circle, if we divide the circle into four equal parts and shade only one part then the shaded part is the one fourth i.e. ¼ of the whole circle.
In the fourth circle, if we divide the circle into four equal parts and shade three parts then the shaded part is the three fourth i.e. ¾ of the whole circle.
Numerator and Denominator
The upper part of the fraction is called Numerator. It tells the number of parts we have.
The lower part of the fraction is called Denominator. It tells the total parts in a whole.
It reads as “three-fifths”.
Representation of fraction on Number line
Example
Solution
Draw a number line.
We know that ½ is less than 1 and greater than 0, so we have to divide the gap between two equal parts and then mark the middle point as ½.
As the denominator is the whole and the numerator is the part, so we have to divide the gap between 0 and 1 in the number of parts as the denominator is given.
For 1/3, divide into 3 equal parts.
For ¼, divide into 4 equal parts and so on.
Proper Fractions
If the numerator is less than the denominator then it is called proper fraction. If we represent a proper fraction on the number line than it will always lie between 0 and 1.
Examples
Improper fractions and Mixed fractions
When the numerator is greater than the denominator then it is called Improper fraction.
The above fraction is made by adding one whole part and one-fourth part.
The fraction made by the combination of whole and a part is called Mixed fraction.
Convert Mixed fraction into Improper fraction
A mixed fraction is in the form of
We can convert it in the form of an improper fraction by
Example
Solution
Equivalent Fractions
Equivalent fractions are those fractions which represent the same part of a whole.
All the above images are different but equivalent fractions as they represent the same i.e. half part of a whole circle.
Finding equivalent fractions
Multiplying the same number
If we multiply the numerator and denominator of any fraction with the same number then we will get the equivalent fraction. There could be more than one equivalent fractions of one fraction.
Example
Find three equivalent fraction of ½.
Solution
Dividing the same number
If we divide the numerator and denominator of any fraction with the same number then we will get the equivalent fraction.
Example
Find the equivalent fraction of 18/27 with denominator 9.
Solution
To get the denominator 9 we need to divide it by 3.
So to find the equivalent fraction we need to divide the fraction by 3.
Hence the equivalent fraction with denominator 9 is 6/9.
The simplest form of a Fraction
If the numerator and denominator do not have any other common factor than 1 then it is said to be the simplest or lowest form of that fraction.
Example–
To find the equivalent fraction which is the simplest form we have to find the HCF of numerator and denominator and then divide them both by that HCF.
Example
Reduce the fraction 18/27 in the simplest form.
Solution
HCF of 18 and 27 is 9.
Hence,
2/3 is the lowest form of 18/27.
Like Fractions and Unlike Fractions
Fractions which have same denominators are known as Like fractions.
Example
Fractions which have different denominators are known as unlike fractions.
Example
Comparing fractions
If we have to compare the above two fractions then it is easy as the first one is less than 3 and the second one is greater than 3. So we can clearly say that
But sometimes it is not easy to compare it so easily. So we need some accurate procedure.
Comparing like fractions
Like fractions are the fractions with the same denominator so we have to compare them with the numerator only. The fraction with greater numerator is greater.
In the above example, both are divided into 8 equal parts, so the fraction with seven shaded part is greater than the 5 shaded parts.
Comparing unlike fractions
The fractions with different denominators are unlike fractions.
Unlike fraction with the same numerator
If we have to compare the fractions with different denominator but same numerator, we have to compare with the denominator only.
In that case, the fraction with the small denominator is greater than the other.
Example
Here the numerator is same i.e.3 so we will compare with the denominator.
The fraction with small denominator i.e. ¾ is greater than the fraction with the large denominator i.e. 3/8.
Unlike fraction with different numerators
If the numerator and denominator both are different then we have to make the denominator same by finding the equivalent fraction of both the fractions then compare the fractions as like fractions.
To find the equivalent fraction of both the fractions with the same denominator, we have to take the LCM of the denominator.
Example
Compare 6/7 and 3/5.
Solution
The product of 7 and 5 is 35.
So we will find the equivalent fraction of both the fractions with the denominator 35.
Now we can compare them as like fractions.
Addition and Subtraction of Fractions
Adding like fractions
In case of like fractions, the denominator is same so we can add them easily.
Steps to add like fractions-
Add the numerators.
Leave the common denominator same. (Don’t add the denominator).
Write the answer as
Example
Solution
Subtracting like fractions
Steps to subtract the like fractions-
Subtract the small numerator from the bigger one.
Leave the common denominator same.
Write the answer as
Example
Solution
Adding unlike fraction
If we have to add the unlike fractions, first we have to find the equivalent fraction of the given fractions with the same denominator then add them.
Steps to add unlike fractions-
Take the LCM of the denominator of the given fractions.
Find the equivalent fractions of both fractions with LCM as the denominator.
Add them as the like fractions.
Example
Solution
Take the LCM of 5 and 8, which is 40.
Subtracting unlike fractions
Steps to subtract unlike fractions-
Take the LCM of the denominator of the given fractions.
Find the equivalent fractions of both fractions with LCM as the denominator.
Subtract them as the like fractions.
Example
Solution
LCM of 4 and 5 is 20.
Remark: To add or subtract the mixed fractions, simply convert them in the improper fraction then add and subtract them directly
Th ere are so many situations where we have to use negative numbers. Negative Numbers are the numbers with the negative sign. These numbers are less than zero.
Example
We use negative numbers to represent temperature.
Where +10 shows 10° hotter than 0 and -10 shows 10° colder than 0.
Successor and Predecessor
If we move 1 to the right then it gives the successor of that number and if we move 1 to the left then it gives the predecessor of that number.
Number
Predecessor
Successor
2
1
3
-8
-9
-7
-3
-4
-2
4
3
5
Tag me with a sign
In the case of accounting we use negative sign to represent the loss and positive to represent the profit.
In the case of sea level, we use a negative sign to represent the height of the place below the sea level and positive sign to represent the place above the sea level.
Integers
The collection of whole numbers and negative numbers together is called the Integers.
All the positive numbers are positive integers and all the negative numbers are negative integers. Zero is neither a positive nor a negative integer.
Representation of Integers on Number Line
To represent the integers on a number line, first, we have to draw a line and mark a point zero on it.
Then mark all the positive integers on the right side with the same distance as 1, 2, 3… and the entire negative numbers on the left side as -1,-2,-3…
Example
To mark (-7) we have to move 7 points to the left of zero.
Ordering of Integers
From the above number line, we can see that as we go to the right side the numbers are getting larger and as we move to the left the numbers are getting smaller.
Hence, any number on the right side on the number line is greater than the number on its left.
Example
5 is to the right of 2 so 5>2.
4 is to the right of -2, so 4>-2.
-4 is to the left of -1, so -4 < -1.
Some facts about Integers
Any positive integer is always greater than any negative integer.
Zero is less than every positive integer.
Zero is greater than every negative integer.
Zero doesn’t come in any of the negative and positive integers.
Addition of Integers
1. Addition of Two Positive Integers
If you have to add two positive integers then simply add them as natural numbers.
(+6) + (+7) = 6 + 7 = 13
2. Addition of Two Negative Integers
If we have to add two negative integers then simply add them as natural numbers and then put a negative sign on the answer.
(-6) + (-7) = – (6+7) = -13
3. Addition of One Negative and One Positive Integer
If we have to add one negative and one positive integer then simply subtract the numbers and put the sign of the bigger integer. We will decide the bigger integer ignoring the sign of the integers.
The re are so many shapes around us made up of lines and curves like line segments, angles, triangles, polygons and circles etc. These shapes are of different sizes and measures.
Measuring Line Segments
A line segment is a fixed part of the line, so it must have some length. We can compare any line segment on the basis of their length.
1. Comparison by Observation
We can tell which line segment is greater than other just by observing the two line segments but it is not sure.
Here we can clearly say that AB > CD but sometimes it is difficult to tell which one is greater.
2. Comparison by Tracing
In this method we have to trace one line on paper then put the traced line segment on the other line to check which one is greater.
But this is a difficult method because every time to measure the different size of line segments we have to make a separate line segment.
3. Comparison using Ruler and a Divider
We can use a ruler to measure the length of a line segment.
Put the zero mark at point A and then move toward l to measure the length of the line segment, but it may have some errors on the basis of the thickness of the ruler.
This could be made accurate by using a Divider.
Put the one end of the divider on point A and open it to put another end on point B.
Now pick up the divider without disturbing the opening and place it on the ruler so that one end lies on “0”.
Read the marking on the other end and we can compare the two line.
Angles – “Right” and “Straight”
We can understand the concept of right and straight angles by directions.
There are four directions-North, South, East and West.
When we move from North to East then it forms an angle of 90° which is called Right Angle.
When we move from North to South then it forms an angle of 180° which is called Straight Angle.
When we move four right angles in the same direction then we reach to the same position again i.e. if we make a clockwise turn from North to reach to North again then it forms an angle of 360° which is called a Complete Angle.This is called one revolution.
In a clock, there are two hands i.e. minute hand and hour hand, which moves clockwise in every minute. When the clock hand moves from one position to another then turns through an angle.
When a hand starts from 12 and reaches to 12 again then it is said to be completed a revolution.
Acute, Obtuse and Reflex Angles
There are so many other types of angles which are not right or straight angles.
Angles
Meaning
Image
Acute Angle
An angle less than the right angle is called Acute angle.
Obtuse Angle
An angle greater than a right angle and less than straight angle is called Obtuse angle.
Reflex Angle
Angle greater than the straight angle is called Reflex angle.
Measuring Angles
By observing an angle we can only get the type of angle but to compare it properly we need to measure it.
An angle is measured in the “degree”. One complete revolution is divided into 360 equal parts so each part is one degree. We write it as 360° and read as “three hundred sixty degrees”.
We can measure the angle using a ready to use device called Protractor.
It has a curved edge which is divided into 180 equal parts. It starts from 0° to 180° from right to left and vice versa.
To measure an angle using protractor-
Place the protractor on the angle in such a way that the midpoint of protractor comes on the vertex B of the angle.
Adjust it so that line BC comes on the straight line of the protractor.
Read the scale which starts from 0° coinciding with the line BC.
The point where the line AB comes on the protractor is the degree measure of the angle.
Hence, ∠ABC = 72°
Perpendicular Lines
If two lines intersect with each other and form an angle of 90° then they must be perpendicular to each other.
Here AB and MN are intersecting at point N and form a right angle. We will write it as
AB ⊥ MN or MN ⊥ AB
Reads as AB is perpendicular to MN or MN is perpendicular to AB.
Perpendicular Bisector
If a perpendicular divides another line into two equal parts then it is said to be a perpendicular bisector of that line.
Here, CD is the perpendicular bisector of AB as it divides AB into two equal parts i.e. AD = DB.
Classification of Triangles
Triangle is a polygon with three sides. It is the polygon with the least number of sides. Every triangle is of different size and shape. We classify them on the basis of their sides and angles.
1. Classification on the basis of sides
Triangle
Meaning
Image
Scalene
If all the sides are different then it is called scalene triangle.
Isosceles
If two sides are equal then it is called isosceles triangle.
Equilateral
If all the sides are equal then it is called equilateral triangle.
2. Classification on the basis of Angles
Triangle
Meaning
Image
Acute Angled Triangle
If all the angles are less than 90° then this is called the acute-angled triangle.
Right Angled Triangle
If one of the angles is 90°then it is called the right-angled triangle.
Obtuse-angled Ariangle
If one of the angles of the triangle is obtuse angle then it is called Obtuse angled triangle.
Quadrilaterals
A polygon with four sides is called Quadrilateral.
S.No.
Name
Properties
Image
1.
Rectangle
It has two pairs of equal opposite sides.Opposite sides are parallel.All the angles are the right angle.
2.
Square
All the four sides are equal.Opposite sides are parallel.All the angles are the right angle.
3.
Parallelogram
It has two pairs of parallel opposite sides.Square and rectangle are also parallelograms.
4.
Rhombus
All the four sides are equal.Opposite sides are parallel.Opposite angles are equal.Diagonals intersect each other at the centre and at 90°.
5.
Trapezium
One pair of opposite sides is parallel.
Polygons
Any closed figure made up of three or more line segments is called Polygon.
We can classify the polygons on the basis of their sides and vertices –
Number of sides
Name of Polygon
Figure
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
n
n-gon
Three-dimensional Shapes
The solid shapes having three dimensions are called 3D shapes.
Some of the 3D shapes around us
Cone
ice-cream cone
Cube
Block
Cuboid
Match-box
Cylinder
Glass
Sphere
Ball
Pyramid
Rubrics in a pyramid shape
Faces, Edges and Vertices
All the flat surfaces of the solid shape are called the Faces of that figure.
The line segment where the two faces meet with each other is called Edge.
The point where the two edges meet with each other is called Vertex.
No. of Faces, Edges and Vertices in some common 3- D shapes
The term ‘Geometry’ is derived from the Greek word ‘Geometron’. This has 2 equivalents. ‘Geo’ means Earth and ‘metron’ means Measurement.
Points
It is a position or location on a plane surface, which are denoted by a single capital letter.
Line Segment
It is a part of a line with the finite length and 2 endpoints.
The points A and B are called the endpoints of the segment.
It is named as:
Line
It is made up of infinitely many points with infinite length and no endpoint.
It extends indefinitely in both directions.
Named as:
Or sometimes
Intersecting Lines
The two lines that share one common point are called Intersecting Lines.
This shared point is called the point of intersection.
Here, line l and m are intersecting at point C.
Real life example of intersecting lines:
Parallel Lines
Two or more lines that never intersect (Never cross each other) are called Parallel Lines.
Real life examples of parallel lines:
Ray
It is a part of a line with one starting point whereas extends endlessly in one direction.
Real life examples of the ray are:
Curves
Anything which is not straight is called a curve.
1. Simple Curve – A curve that does not cross itself.
2. Open Curve – Curve in which its endpoints do not meet.
3. Closed Curve – Curve that does not have an endpoint and is an enclosed figure.
A closed curve has 3 parts which are as follows
1. Interior of the curve
It refers to the inside/inner area of the curve.
The blue coloured area is the interior of the figure.
2. The exterior of the curve.
It refers to the outside / outer area of the curve.
The point marked A depicts the exterior of the curve.
3. The boundary of the curve
It refers to the dividing line thus it divides the interior and exterior of the curve.
The black line which is dividing the interior and exterior of the curve is the boundary.
The interior and boundary of the curve together are called the curves “region”.
Polygons
It is a 2d closed shape made of line segments / straight lines only.
Sides –It refers to the line segments which form the polygon, as in the above figure AB, BC, CD, DA are its sides.
Vertex – Point where 2 line segments meet, as in the above figure A, B, C and D are its vertices.
Adjacent Sides – If any 2 sides share a common endpoint they are said to be adjacent to each other thus called adjacent sides, as in the above figure AB and BC, BC and CD, CD and DA, DA and AB are adjacent sides.
Adjacent Vertices – It refers to the endpoints of the same side of the polygon. As in the above figure A and B, B and C, C and D, D and A are adjacent vertices.
Diagonals – It refers to the joins of the vertices which are not adjacent to each other. As in the above figure, AC and BD are diagonals of the polygon.
Angles
A figure formed from 2 rays which share a common endpoint is called Angle.
The rays forming the angle are known as its arms or sides.
The common endpoint is known as its vertex.
An angle is also associated with 3 parts
1. Interior – It refers to the inside/inner area.
The green coloured area is the interior of the angle.
2. Angle/boundary – It refers to the arms of the angle.
The red point is on the arm of the angle.
3. Exterior – It refers to the outside / outer area.
The blue point depicts the exterior of the figure.
Naming an Angle
While naming an angle the letter depicting the vertex appears in the middle.
Example
The above angle can also be named as ∠CBA.
An angle can also be named just by its vertex.
Example
Triangle
It is a 3 sided polygon. It is also the polygon with the least number of the sides.
Vertices: A, B and C
Sides: AB, BC and CA
Angles: ∠A, ∠B and ∠C
Here, the light blue coloured area is the interior of the angle.
The black line is the boundary.
Whereas, the dark blue area is the exterior of the angle.
Quadrilaterals
It is a 4 sided polygon
Vertices: A, B, C, D
Sides: AB, BC, CD, DA
Angle: ∠A, ∠B, ∠C, ∠D
Opposite Sides: AB and DC, BC and AD
Opposite Angles: ∠B and ∠D, ∠A and ∠C
Adjacent Angles: ∠A and ∠B, ∠B and ∠C, ∠C and ∠D, ∠D and ∠A.
Circles
It is a simple closed curve and is not considered as a polygon.
Parts of Circles
1. Radius – It is a straight line connecting the centre of the circle to the boundary of the same. Radii is the plural of ‘radius’.
2. Diameter –It is a straight line from one side of the circle to the other side passing through the centre.
3. Circumference – It refers to the boundary of the circle.
4. Chord – Any line that connects two points on the boundary of the circle is called Chord. Diameter is the longest chord.
5. Arc – It is the portion of the boundary of the circle.
6. Interior of the Circle – Area inside the boundary of the circle is called the Interior of the Circle.
7. The Exterior of the Circle – Area outside the boundary of the circle is called the Exterior of the Circle.
8. Sector– It is the region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides.
9. Segment – It is the region in the interior of the circle enclosed by an arc and a chord.
Semi-circle
A diameter divides the circle into two semi-circles. Hence the semicircle is the half of the circle, which has the diameter as the part of the boundary of the semicircle.
The numbers which exactly divides the given number are called the Factors of that number.
As we can see that we get the number 12 by
1 × 12, 2 × 6, 3 × 4, 4 × 3, 6 × 2 and 12 ×1
Hence,
1, 2, 3, 4, 6 and 12 are the factors of 12.
The factors are always less than or equal to the given number.
Multiples
If we say that 4 and 5 are the factors of 20 then 20 is the multiple of 4 and 5 both.
List the multiples of 3
Multiples are always more than or equal to the given number.
Some facts about Factors and Multiples
1 is the only number which is the factor of every number.
Every number is the factor of itself.
All the factors of any number are the exact divisor of that number.
All the factors are less than or equal to the given number.
There are limited numbers of factors of any given number.
All the multiples of any number are greater than or equal to the given number.
There are unlimited multiples of any given numbers.
Every number is a multiple of itself.
Perfect Number
If the sum of all the factors of any number is equal to the double of that number then that number is called a Perfect Number.
Perfect Number
Factors
Sum of all the factors
6
1, 2, 3, 6
12
28
1, 2, 4, 7, 14, 28
56
496
1, 2, 4, 8, 16, 31, 62, 124, 248, 496
992
Prime Numbers
The numbers whose only factors are 1 and the number itself are called the Prime Numbers.
Like 2, 3, 5, 7, 11 etc.
Composite Numbers
All the numbers with more than 2 factors are called composite numbers or you can say that the numbers which are not prime numbers are called Composite Numbers.
Like 4, 6, 8, 10, 12 etc.
Remark: 1 is neither a prime nor a composite number.
Sieve of Eratosthenes Method
This is the method to find all the prime numbers from 1 to 100.
Step 1: First of all cross 1, as it is neither prime nor composite.
Step 2: Now mark 2 and cross all the multiples of 2 except 2.
Step 3: Mark 3 and cross all the multiples of 3 except 3.
Step 4: 4 is already crossed so mark 5 and cross all the multiples of 5 except 5.
Step 5: Continue this process until all the numbers are marked square or crossed.
This shows that all the covered numbers are prime numbers and all the crossed numbers are composite numbers except 1.
Even and Odd Numbers
All the multiples of 2 are even numbers. To check whether the number is even or not, we can check the number at one’s place. If the number at ones place is 0,2,4,6 and 8 then the number is even number.
The numbers which are not even are called Odd Numbers.
Remark: 2 is the smallest even prime number. All the prime numbers except 2 are odd numbers.
Tests for Divisibility of Numbers
1. Divisibility by 2:
If there are any of the even numbers i.e. 0, 2, 4, 6 and 8 at the end of the digit then it is divisible by 2.
Example
Check whether the numbers 63 and 240 are divisible by 2 or not.
Solution:
1. The last digit of 63 is 3 i.e. odd number so 63 is not divisible by 2.
2. The last digit of 240 is 0 i.e. even number so 240 is divisible by 2.
2. Divisibility by 3:
A given number will only be divisible by 3 if the total of all the digits of that number is multiple of 3.
Example
Check whether the numbers 623 and 2400 are divisible by 3 or not.
Solution:
1. The sum of the digits of 623 i.e. 6 + 2 + 3 = 11, which is not the multiple of 3 so 623 is not divisible by 3.
2. The sum of the digits of 2400 i.e. 2 + 4 + 0 + 0 = 6, which is the multiple of 3 so 2400 is divisible by 3.
3. Divisibility by 4:
We have to check whether the last two digits of the given number are divisible by 4 or not. If it is divisible by 4 then the whole number will be divisible by 4.
Example
Check the number 23436 and 2582 are divisible by 4 or not.
Solution:
1. The last two digits of 23436 are 36 which are divisible by 4, so 23436 are divisible by 4.
2. The last two digits of 2582 are 82 which are not divisible by 4 so 2582 is not divisible by 4.
4. Divisibility by 5:
Any given number will be divisible by 5 if the last digit of that number is ‘0′ or ‘5′.
Example
Check whether the numbers 2348 and 6300 are divisible by 5 or not.
Solution:
1. The last digit of 2348 is 8 so it is not divisible by 5.
2. The last digit of 6300 is 0 so it is divisible by 5.
5. Divisibility by 6:
Any given number will be divisible by 6 if it is divisible by 2 and 3 both. So we should do the divisibility test of 2 and 3 with the number and if it is divisible by both then it is divisible by 6 also.
Example
Check the number 342341 and 63000 are divisible by 6 or not.
Solution:
1. 342341 is not divisible by 2 as the digit at ones place is odd and is also not divisible by 3 as the sum of its digits i.e. 3 + 4 + 2 + 3 + 4 + 1 = 17 is also not divisible by 3.Hence 342341 is not divisible by 6.
2. 63000 is divisible by 2 as the digit at ones place is even and is also divisible by 3 as the sum of its digits i.e. 6 + 3 + 0 + 0 + 0 = 9 is divisible by 3.Hence 63000 is divisible by 6.
6. Divisibility by 7:
Any given number will be divisible by 7 if we double the last digit of the number and then subtract the result from the rest of the digits and check whether the remainder is divisible by 7 or not. If there is a large number of digits then we have to repeat the process until we get the number which could be checked for the divisibility of 7.
Example
Check the number 2030 is divisible by 7 or not.
Solution:
Given number is 2030
1. Double the last digit, 0 × 2 = 0
2. Subtract 0 from the remaining number 203 i.e. 203 – 0 = 203
3. Double the last digit, 3 × 2 = 6
4. Subtract 6 from the remaining number 20 i.e. 20 – 6 = 14
5. The remainder 14 is divisible by 7 hence the number 203 is divisible by 7.
7. Divisibility by 8:
We have to check whether the last three digits of the given number are divisible by 8 or not. If it is divisible by 8 then the whole number will be divisible by 8.
Example
Check whether the number 74640 is divisible by 8 or not.
Solution:
The last three digit of the number 74640 is 640.
As the number 640 is divisible by 8 hence the number 74640 is also divisible by 8.
8. Divisibility by 9:
Any given number will be divisible by 9 if the total of all the digits of that number is divisible by 9.
Example
Check whether the number 2320 and 6390 are divisible by 9 or not.
Solution:
1. The sum of the digits of 2320 is 2 + 3 + 2 + 0 = 7 which is not divisible by 9 so 2320 is not divisible by 9.
2. The sum of the digits of 6390 is 6 + 3 + 9 + 0 = 18 which is divisible by 9 so 6390 is divisible by 9.
9. Divisibility by 10:
Any given number will be divisible by 10 if the last digit of that number is zero.
Example
Check the number 123 and 2630 are divisible by 10 or not.
Solution:
1. The ones place digit is 3 in 123 so it is not divisible by 10.
2. The ones place digit is 0 in 2630 so it is divisible by 10.
Common Factors and Common Multiples
Example: 1
What are the common factors of 25 and 55?
Solution:
Factors of 25 are 1, 5.
Factors of 55 are 1, 5, 11.
Common factors of 25 and 55 are 1 and 5.
Example: 2
Find the common multiples of 3 and 4.
Solution:
Common multiples of 3 and 4 are 0, 12, 24 and so on.
Co-prime Numbers
If 1 is the only common factor between two numbers then they are said to be Co-prime Numbers.
Example
Check whether 7 and 15 are co-prime numbers or not.
Solution:
Factors of 7 are 1 and 7.
Factors of 15 are 1, 3, 5 and 15.
The common factor of 7 and 15 is 1 only. Hence they are the co-prime numbers.
Some more Divisibility Rules
1. Let a and b are two given numbers. If a is divisible by b then it will be divisible by all the factors of b also.
If 24 is divisible by 12 then 24 will be divisible by all the factors of 12(i.e.2, 3, 4, 6) also.
2. Let a and b are two co-prime numbers. If c is divisible by a and b then c will be divisible by the product of a and b (ab) also.
If 24 is divisible by 2 and 3 which are the co-prime numbers then 24 will also be divisible by the product of 2 and 3 (2×3=6).
3. If a and b are divisible by c then a + b will also be divisible by c.
If 24 and 12 are divisible by 4 then 24 + 12 = 36 will also be divisible by 4.
4. If a and b are divisible by c then a-b will also be divisible by c.
If 24 and 12 are divisible by 4 then 24 -12 = 12 will also be divisible by 4.
Prime Factorisation
Prime Factorisation is the process of finding all the prime factors of a number.
There are two methods to find the prime factors of a number-
1. Prime factorisation using a factor tree
We can find the prime factors of 70 in two ways.
The prime factors of 70 are 2, 5 and 7 in both the cases.
2. Repeated Division Method
Find the prime factorisation of 64 and 80.
The prime factorisation of 64 is 2 × 2 × 2 × 2 × 2 × 2.
The prime factorisation of 80 is 2 × 2 × 2 × 2 × 5.
Highest Common Factor (HCF)
The highest common factor (HCF) of two or more given numbers is the greatest of their common factors.
Its other name is (GCD) Greatest Common Divisor.
Method to find HCF
To find the HCF of given numbers, we have to find the prime factorisation of each number and then find the HCF.
Example
Find the HCF of 60 and 72.
Solution:
First, we have to find the prime factorisation of 60 and 72.
Then encircle the common factors.
HCF of 60 and 72 is 2 × 2 × 3 = 12.
Lowest Common Multiple (LCM)
The lowest common multiple of two or more given number is the smallest of their common multiples.
Methods to find LCM
1. Prime Factorisation Method
To find the LCM we have to find the prime factorisation of all the given numbers and then multiply all the prime factors which have occurred a maximum number of times.
Example
Find the LCM of 60 and 72.
Solution:
First, we have to find the prime factorisation of 60 and 72.
Then encircle the common factors.
To find the LCM, we will count the common factors one time and multiply them with the other remaining factors.
LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 = 360
2. Repeated Division Method
If we have to find the LCM of so many numbers then we use this method.
Example
Find the LCM of 105, 216 and 314.
Solution:
Use the repeated division method on all the numbers together and divide until we get 1 in the last row.
LCM of 105,216 and 314 is 2 × 2 × 2 × 3 × 3 × 3 × 5 × 7 × 157 = 1186920
Real life problems related to HCF and LCM
Example: 1
There are two containers having 240 litres and 1024 litres of petrol respectively. Calculate the maximum capacity of a container which can measure the petrol of both the containers when used an exact number of times.
Solution:
As we have to find the capacity of the container which is the exact divisor of the capacities of both the containers, i. e. maximum capacity, so we need to calculate the HCF.
The common factors of 240 and 1024 are 2 × 2 × 2 × 2. Thus, the HCF of 240 and 1024 is 16. Therefore, the maximum capacity of the required container is 16 litres.
Example: 2
What could be the least number which when we divide by 20, 25 and 30 leaves a remainder of 6 in every case?
Solution:
As we have to find the least number so we will calculate the LCM first.
LCM of 20, 25 and 30 is 2 × 2 × 3 × 5 × 5 = 300.
Here 300 is the least number which when divided by 20, 25 and 30 then they will leave remainder 0 in each case. But we have to find the least number which leaves remainder 6 in all cases. Hence, the required number is 6 more than 300.
• Symbols used for counting and measuring the objects are called numbers.
• A group of digits, denoting a number, is called a numeral.
• Writing a number in words is called numeration.
• 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits or figures.
• Counting Numbers are called natural numbers.
• Counting Numbers alongwith zero is called whole numbers.
• Successor: The number that comes just after a given number. Example: Successor of 7 = 7+1=8
• Predecessor: The number that comes just before a given number. Example: Predecessor of 7 = 7 -1 = 6
Comparing Numbers
• The number with more digits > number with less digits. For example, 215 > 81.
• If two numbers have the same number of digits, then compare the digits on the extreme left and decide. If the extreme left digits are the same, compare the next digits to the right, and so on… For example: 57405926> 57405921.
• Ascending order means arrangement from the smallest to the greatest.
• Descending order means arrangement from the greatest to the smallest.
• The smallest four digit number is 1000 (one thousand). It follows the largest three digit number 999.
• The smallest five digit number is 10,000. It is ten thousand and follows the largest four digit number 9999.
• The smallest six digit number is 100,000. It is one lakh and follows the largest five digit number 99,999. This carries on for higher digit numbers in a similar manner.
Indian System of Numeration
• We use ones, tens, hundreds, thousands, lakhs and crores.
• Commas are used to mark thousands, lakhs, and crores. For example: 3, 32, 40, 781 – Three crore thirty two lakh forty thousand seven hundred eighty one.
• Face value of a digit : The face value of a digit remains as it is, whatever place it may be occupying in the place value chart.
• Place value of a digit : The place value of digit in a numeral depends upon the place it occupies in the place value chart.
• Place value of a digit in a number = Face value × Position value.
International System of Numeration
• We use ones, tens, hundreds, thousands and millions. To express numbers larger than a million, a billion is used. 1 billion = 1,000 million.
• Commas are used to mark thousands and millions. For example: 3, 32, 40, 781 – Thirty three million two hundred forty thousand seven hundred eighty-one.
• If the digit in the units place is less than 5, then the units digit is replaced by 0.
• If the digit in units place is greater or equal to 5, then the unit place is replaced by zero and tens place is increased by 1.
Nearest 100
• If the digit in the tens place < 5, then the tens and units place are replaced by zero.
• If the digit in the tens place is equal to or > 5 then the tens and units place is replaced by zero and the hundreds place is increased by 1.
Nearest 1000
• If the digit in the hundreds place is < 5, then the hundreds, tens and units place is replaced by 0.
• If the digit in the hundreds place is equal to or > 5, then the hundreds, tens and units place is replaced by 0 and the thousands place is increased by 1.
Roman Numerals
• Roman numerals are one of the early systems of writing numerals.
I = 1
II = 2
III = 3
IV= 4
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
Rules of Roman Numeral System
• If a symbol is repeated, its value is added as many times as it occurs.
• A symbol is not repeated more than three times. But the symbols V, L and D are never repeated.
• If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.
• If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
• The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted. The symbol I can be subtracted from V and X only. The symbol X can be subtracted from L, M and C only.
Question 1. Choose the correct answer. Sound can travel through (a) gases only (b) solids only (c) liquids only (d) solids, liquids, and gases Answer: (d) solids, liquids, and gases.
Question 2. Voice of which of the following is likely to have a minimum frequency? (a) Baby girl (b) Baby boy (c) A man (d) A woman Answer: (c) A man
Question 3. In the following statements, tick ‘T’ against those which are true and ‘F’ against those which are false.
Sound cannot travel in a vacuum.
The number of oscillations per second of a vibrating object is called its time period.
If the amplitude of vibration is large, the sound is feeble.
For human ears, the audible range is 20 Hz to 20,000 Hz.
The lower the frequency of vibration, the higher is the pitch.
Unwanted or unpleasant sound is termed as music.
Noise pollution may cause partial hearing impairment.
Answer:
True
False
False
True
False
False
True
Question 4. Fill in the blanks with suitable words.
Time taken by an object to complete one oscillation is called _______
Loudness is determined by the ________ of vibration.
The unit of frequency is ________
Unwanted sound is called _______
The shrillness of a sound is determined by the ______ of vibration.
Answer:
Time period
Amplitude
Hertz (Hz)
Noise
Frequency
Question 5. A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency. Answer: No. of oscillation = 40 Total time is taken = 4 seconds
Question 6. The sound from a mosquito is produced when it vibrates its wings at an average rate of 500 vibrations per second. What is the time period of the vibration? Answer: Number of vibrations per second = 500
Question 7. Identify the part which vibrates to produce sound in the following instruments.
Dholak
Sitar
Flute
Answer:
Stretched membrane
String of sitar
Air column
Question 8. What is the difference between noise and music? Can music become noise sometimes? Answer: The type of sound which are unpleasant to listen is known as noise whereas music is a pleasant sound, which produces a sensation. Yes, music can become noise when it’s too loud.
Question 9. List the sources of noise pollution in your surroundings. Answer: Following are the major sources of noise pollution:
Sound of vehicles
Sound of kitchen appliances
Sound of bursting crackers
Sound of loudspeakers, TV, transistors
Question 10. Explain in what way noise pollution is harmful to humans. Answer: Noise pollution causes: (a) Lack of sleep (b) Anxiety (c) Hypertension and these are harmful to health.
Question 11. Your parents are going to buy a house. They have been offered one on the roadside and another three lanes away from the roadside. Which house would you suggest your parents should buy? Explain your answer. Answer: I would suggest my parents buy a house three lanes away from the roadside because house on the roadside would be much noisy in both days and night due to running vehicles. Whereas, a house three lanes away would be comparatively quieter as the intensity of noise decreases with the distance between the source and the listener.
Sound Class 8 Science NCERT Intext Activities Solved
Activity 1 Take a metal plate (or a shallow pan). Hang it at a convenient place in such a way that it does not touch any wall. Now strike it with a stick (Fig. 13.1). Touch the plate or pan gently with your finger. Do you feel the vibrations? Again strike the plate with the stick and hold it tightly with your hands immediately after striking. Do you still hear the sound? Touch the plate after it stops producing sound. Can you feel vibrations now? Solution: When we touch the pan gently with our finger after striking we feel the vibration. When we hold the pan tightly after striking it, we do not hear the sound. When the pan stops producing sound it also stops vibrating. Thus, we can conclude that vibrating body produces sound.
Activity 2 Jake a rubber band. Put it around the, longer side of a pencil box (Fig. 13.2). Insert two pencils between the box and the stretched rubber. Now, pluck the rubber band somewhere in the middle. Do you hear any sound? Does the band vibrate? Solution: Yes, we hear the sound on plucking the rubber band. Also, we find that the band is vibrating. Thus, all vibrating bodies produce sound.
Activity 3 Take a metal dish. Pour water in it. Strike it at its edge with a spoon (Fig. 13.3). Do you hear a sound? Again strike the dish and then touch it. Can you feel the dish vibrating? Strike the dish again. Look at the surface of water. Do you see any waves there? Now hold the dish. What change do you observe on the surface of water? Can you explain the change? Is there a hint to connect sound with the vibrations of a body? Solution: On striking the metal dish we hear sound and on touching it we feel the dish vibrating. Striking the dish with water we see circular wave are produced. Thus vibrating object produces sound.
Activity 4 Take a hollow coconut shell and make a musical instrument ektara. You can also make it with the help of an earthen pot (Fig. 13.4). Play this instrument and identify its vibrating part. Solution: We observed that the vibrating part of the musical instrument ektara is stretched string.
Activity 5 Take 6-8 bowls or tumblers. Fill them with water upto different levels, increasing gradually from one end to the other. Now take a pencil and strike the bowls gently. Strike all of them in succession. You will hear pleasant sounds. This is your Jaltarang (Fig. 13.5). Solution: We can hear a pleasant sound. This is due to different levels of water in the bowls. Thus, we find that shorter the length of the vibrating air column, higher is the pitch of the sound produced.
Activity 6 Take two rubber strips of the same size. Place these two pieces one above the other and stretch them tight. Now blow air through the gap between them [Fig. 13.6(a)]. As the air blows through the stretched rubber strips, a sound is produced. You can also take a piece of paper with a narrow slit and hold it between your fingers as shown in [Fig. 13.6(b)]. Now blow through the slit and listen to the sound. Solution: This activity shows that vocal cords also produce sound in a similar manner when they vibrate.
Activity 7 Take a metal or glass tumbler. Make sure that it is dry. Place a cell phone in it. Ask your friend to give a ring on this cell phone from another cell phone. Listen to the ring carefully. Now, surround the rim of the tumbler with your hands (Fig. 13.7). Put your mouth on the opening between your hands. Indicate to your friend to give a ring again. Listen to the ring while sucking air from the tumbler. Does the sound become fainter as you suck air? Remove the tumbler from your mouth. Does the sound become loud again? Solution: We observed that sound becomes fainter than earlier when we try to suck air. But when we remove tumbler from our mouth the sound again becomes loud. Thus, sound needs a medium to travel.
Activity 8 Take a bucket or a bathtub. Fill it with clean water. Take a small bell in one hand. Shake this bell inside the water to produce sound. Make sure that the bell does not touch the body of the bucket or the tub. Place your ear gently on the water surface (Fig. 13.8). Can you hear the sound of the bell? Does it indicate that sound can travel through liquids? Solution: We can hear the sound of the bell which indicates that sound can travel through liquids.
Activity 9 Take a metre scale ora long metal rod and hold its one end to your ear. Ask your friend to gently scratch or tap at the other end of the scale (Fig. 13.9). Can you hear the sound of the scratching? Ask your friends around you if they were able to hear the same sound? Solution: Yes, we find that we can hear the sound of the scratch. But, the people standing around us cannot hear the same sound or we can say that it is limping not audible to them.
Activity 10
Take a plastic or tin can. Cut its ends. Stretch a piece of rubber balloon across one end of the can and fasten it with a rubber band. Put four or five grains of dry cereal on the stretched rubber. Now ask your friend to speak”Hurrey, Hurrey”from the open end (Fig. 13.10). Observe what happens to the grain. Why do the grain jump up and down? Solution: The grain jump up and down because of the vibration caused underneath the stretched rubber. Thus when sound waves fall on the eardrum, it starts vibrating back and forth rapidly.
NCERT Solutions for Class 8 Science Chapter 13 – 1 Mark Questions and Answers
Question 1. Choose the correct answer. Sound can travel through
Gases only
Solids only
Liquids only
Solids, liquids and gases.
Answer: Solids, liquids and gases.
Question 2. Voice of which of the following is likely to have minimum frequency ? [NCERT]
Baby girl
Baby boy
A man
A woman
Answer: Aman
Question 3. Identify the part which vibrates to produce sound in the following instruments. [NCERT]
Dholak
Sitar
Flute
Answer:
Dholak – stretched membrane
Sitar – stretched string
Flute – air column
Question 4. In the following statements, tick ‘T’ against those which are true and ‘F’ against those which are false. [NCERT]
Sound cannot travel in vacuum. (T/F)
The number of oscillations per second of a vibrating object is called its time period. (T/F)
If the amplitude of vibration is large, sound is feeble. (T/F)
For human ears, the audible range is 20 Hz to 20,000 Hz. (T/F)
The lower the frequency of vibration, the higher is the pitch. (T/F)
Unwanted or unpleasant sound is termed as music. (T/F)
Noise pollution may cause partial hearing impairment. (T/F)
Answer:
T
F
F
T
F
F
T
Question 5. Fill in the blanks with suitable words. [NCERT]
Time taken by an object to complete one oscillation is called …………
Loudness is determined by the ………….. of vibration.
The unit of frequency is ……………
Unwanted sound is called …………….
Shrillness of a sound is determined by the …………….. of vibration.
Answer:
time period
amplitude
Hertz
noise
frequency
Question 6. Define vibration. Answer: Vibration is the to and fro or back and forth motion of an object.
Question 7. Which part of the human body is responsible for producing sound ? [NCT 2011] Answer: In humans, the sound is produced by the voice box or larynx
Question 8. What is the length of vocal cords in men ? Answer: The vocal cords in men are about 20 mm long.
Question 9. Can sound travel in vacuum ? Answer: No, sound cannot travel in vacuum.
Question 10. What is meant by oscillatory motion ? Answer: The to and fro motion of an object is known as oscillatory motion.
NCERT Solutions for Class 8 Science Chapter 13 – 2 Mark Questions and Answers
Question 1. The sound from a mosquito is produced when it vibrates its wings at an average rate of 500 vibrations per second. What is the time period of the vibration ? [NCERT] Answer: Time taken for 500 vibrations = 1 second Time taken for 1 vibration = 1/500 second. ∴ Time period = 1/500 second.
Question 2. How do plants help in reducing noise pollution ? Answer: Plants absorb sound and so help us in minimizing noise pollution.
Question 3. How can we control the sources of noise pollution ? Answer: We can control noise pollution by designing and installing silencing devices in machines.
Question 4. How can a hearing impaired child communicate ? Answer: A hearing impaired child can communicate effectively by using sign language.
Question 5. If the amplitude increases 3 times, by how much will the loudness increase ? Answer: If the amplitude increases three times, the loudness will increase by a factor of 9.
Question 6. The frequency of a given sound is 1.5 kHz. How many vibrations is it completing in one second ? Answer: Frequency = No.of vibrations/time ∴ No. of vibrations = Frequency x time = 1.5 x 1000 x 1 = 1500 vibrations
Question 7. Which characteristic of a vibrating body determines
loudness
pitch of the sound produced by it ?
Answer:
Amplitude.
Frequency.
Question 8. Why do we not hear echoes in our ordinary surroundings ? Answer: We do not hear echoes in our ordinary surroundings because the distance to hear echo should be more than 17 m.
Question 9. We cannot hear the sound of the exploding meteors in the sky, though we can see them. Why ? Answer: Sound cannot travel through vacuum. In space there is vacuum. Light can travel through vacuum, so we can see the exploding meteor but cannot hear the explosion.
Question 10. We can hear the supersonic jet planes flying. How ? Answer: The supersonic jet planes fly in the air. Since sound can travel through air, we can hear then flying.
Question 11. What are vocal cords ? What is their function ? [NCT 2011] Answer: The larynx has a pair of membranes known as vocal cords stretched across their length. The vocal cords vibrate and produce sound.
Question 12. When does a thud become music ? Answer: When thuds are repeated at’regular intervals, it becomes music, e.g., beating of drums or wood.
Question 13. How do birds and insects produce sound ? Answer: Birds chirp with the help syrinx in their wind pipe. Insects produce sound by flapping their wings.
Question 14. What is the function of eusfachian tube in human ear ? Answer: The vibrations of the spoken words reach our ears through eustachian tubes.
Question 15.
In our body which part of the ear receives sound waves ?
What may happen if the eardrum is absent from our ear ?
Answer:
Pinna helps in receiving sound waves.
If the eardrum is absent we would not be able to hear.
NCERT Solutions for Class 8 Science Chapter 13 – 3 Mark Questions and Answers
Question 1. List sources of noise pollution in your surroundings. [NCERT] Answer: The major sources of noise pollution are sounds of vehicles, explosions, machines, loudspeakers.
Question 2. What are the effects of noise pollution ? Answer: Due to noise pollution a person may suffer from lack of sleep, hypertension and anxiety. If a person is exposed to noise continuously he may get temporary or permanent deafness.
Question 3. How can the noise pollution be controlled in residential area ? Answer:
The noisy operations must be conducted away from residential areas.
Noise producing industries should be set away from such areas.
Use of automobile horns be minimized.
TV and music systems should be run at lower volumes.
Question 4. A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency. [NCT 2011, NCERT] Answer: 40 vibrations in 4 seconds. 10 vibrations in 1 second Frequency =10 vibrations/sec. or 10 Hz. ∴ Time period = 1/10 sec.
Question 5. Your parents are going to buy a house. They have been offered one on the roadside and another three lanes away from the roadside. Which house would you suggest your parents should buy ? Explain your answer. [NCERT] Answer: I would advise my parents to buy the house three lanes away from the roadside because there the noise from automobiles would be much less.
Question 6. What happens when we pluck the strings of a sitar ? Answer: When we pluck the strings of a sitar, the whole instrument vibrates and the sound is heard.
Question 7. Why is the voice of men, women and children different ? Answer: The voice of men, women and children are different because the length of vocal cords are different. The length of vocal cords is longest in men and shortest in children.
Question 8. How are we able to hear sound ? Answer: The eardrum is like a stretched rubber sheet. Sound vibrations make the eardrum vibrate. The eardrum sends vibrations to the inner ear. From there, the signal goes to the brain and we are able to hear.
Question 9. What sources in the home may lead to noise ? Answer: Television and transistor at high volumes, some kitchen appliances, desert coolers, air conditioners all contribute to noise pollution.
Question 10. What is the-difference between noise and music ? Can music become noise sometimes,? Answer: Unpleasant sounds are called noise. Music is a sound which produces a pleasing sensation. If the music is too loud, it becomes noise.
Question 11. Draw a labelled diagram showing the structure of the human ear. Answer:
Question 12. What is the function of:
External ear.
Internal ear.
Answer:
The external ear helps us in receiving the sound waves and directing them to the eardrum.
The internal ear has cochlea which is filled with a fluid and having tiny hair cells inside. The hairy cells change the sound vibrations into nerve impulse which travels to the brain. The internal ear also helps us in balancing the body.
Question 13. Give some suggestions by which we can keep our ears healthy. Answer:
Never insert any pointed object into the ear. Tt can damage the eardrum and make a person deaf.
Never shout loudly in someone’s ear.
Never hit anyone hard on their ear.
Question 14. Can you hear the sound on the moon ? Explain. Answer: We cannot hear the sound on the moon because sound requires a material medium to travel. On the moon there is no atmosphere and sound cannot travel in vacuum.
Question 15. What are ultrasounds ? How are they useful to us? Answer: Sound having frequency higher than 20kHz is known as ultrasound, is used for
detecting finer faults in metal sheets.
scanning and imaging the body for stones, tumour and foetus.
NCERT Solutions for Class 8 Science Chapter 13 – 5 Mark Questions and Answers
Question 1. Sketch larynx and explain its function in your own words. [NCERT] Answer: We produce sound in the larynx of our throats. The larynx has two vocal cords, which are folds of tissue with a slit like opening between them. When we speak, air passes through the opening and the vocal cords vibrate to produce sound.
Question 2. Lightning and thunder take place in the sky at the same time and at the same distance from us. Lightning is seen earlier and thunder is heard later. Can you explain why ? [NCERT] Answer: The speed of light is more than the speed of sound. Therefore, even though thunder and lightning take place simultaneously, we see the lightning earlier.
Question 3.
What is SONAR?
What is the basic principle of its working ?
Explain its use.
Answer:
SONAR refers to Sound Navigation and Ranging.
The principle of reflection of sound is used in SONAR.
SONAR is used to measure the depth of the ocean. Ultrasonic waves are sent from the ship down into the sea. They are received back after reflection from the sea bed. The depth is calculated by noting the time period.
Question 4. What is the use of ultrasound in medicine and industry ? Answer: Use of ultrasound in medicine :
For scanning and imaging the body for stones, tumour and foetus.
For relieving pain in muscles and joints.
Use of ultrasound in industry :
For detecting finer faults in metal sheets.
In dish washing machines where water and detergent are vibrate with ultrasonic vibrators.
For homogenising milk in milk plants.
Question 5. What is a sonogram ? Why is it preferred to X-rays ? Answer: Sonogram is image of the internal organs. Ultrasound can pass through the human body and are reflected back. The reflections are recorded by computer and images are generated on the screen. Sonogram is not harmful and is therefore used for studying the foetus or stone or tumor in the organs. On the other hand, X-rays can be harmful if humans are exposed for longer time.
Question 6.
Name a property of sound which is (i) similar to the property of light. (ii) different from that of light.
Why do some people have hearing impairment ? How do they communicate with others ?
Answer:
(i) The property of sound similar to light is that in both reflection takes place. (ii) Sound can travel around comers but light cannot.
Some people suffer from hearing impairment because their ear drum is damaged or absent. This can be from birth or may occur later on. Such people communicate with “sign language”. They can also use “hearing aids”.
NCERT Solutions for Class 8 Science Chapter 13 MCQs
Question 1. The maximum displacement of a vibrating body on either side of its mean position, is known as its (a) Frequency (b) Loudness (c) Amplitude (d) Pitch Answer: (c)
Question 2. The frequency of a given sound is 1.5 kHz. The vibrating body is (a) completing 1,500 vibrations in one second. (b) taking 1,500 seconds to complete one vibration. (c) taking 1.5 seconds to complete one vibration. (d) completing 1.5 vibrations in one second Answer: (a)
Question 3. A given sound is inaudible to the human ear, if (a) its amplitude is too small. (b) its frequency is below 20 Hz. (c) its frequency is above 20 kHz. (d) it has any of the three characteristics listed above. Answer: (d)
Question 4. Sound can propagate (a) through vacuum as well as gases (b) only through gases and liquids (c) only through gases and solids (d) any of the three states of the matter. Answer: (d)
Question 5. When lightning and thunder take place, they (a) occur together and are also observed together. (b) occur one after the other but are observed together. (c) occur together but the thunder is observed a little after the lightning. (d) occur together but the thunder is observed a little before the lightning Answer: (c)
Question 6. Soundshaving frequency more than 20 Hz are called (a) Infrasonic (b) Supersonic (c) Ultrasonic (d) None of these Answer: (c)
Question 7. Hertz is the unit of (a) Amplitude (b) Frequency (c) Pitch (d) Wavelength Answer: (b)
Question 8. Loudness of sound is expressed in (a) Hertz (b) Decibel (c) Seconds (d) None of these Answer: (b)
