NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

 

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs: In daily life, you must have seen different types of graphs like in newspapers- business analysis, on television -cricket match comparison of the score of two teams, or score of a player over a period of time or in books, etc. What is a graph? What is the purpose of graphs? What are the types of graphs? In NCERT solutions for class 8 maths chapter 15 introduction to graphs, you will get answers to all these questions. The graph is a visual representation of data. The purpose of the graph is to show collected data or numerical facts in visual form so that anyone can understand it easily, quickly and clearly. Graphs have the ability to compare and reveal a trend, so it is better to represent data in a graph rather than in a table. In solutions of NCERT for class 8 introduction to graphs, you will find different types of graphs like- Bar graph, Histogram, Pie graph ( or pie chart or a circle graph), Line graph, and Linear graph in the 3 exercises. These different type of graphs that you will use depends on your data and need. If data changes continuously with the time you will be using a line graph. You can use histogram(bar graph) to show data in any intervals. There are 3 exercises with 65 questions in NCERT the textbook. All these questions are explained in CBSE NCERT solutions for class 8 maths chapter 15 introduction to graphs which will build basic knowledge about the graphs. You can get NCERT solutions from class 6 to 12 to by clicking on the above link.

Topics of NCERT class 8 maths chapter 15- Introduction to Graphs

  • 15.1      Introduction
  • 15.1.1    A Bar graph
  • 15.1.2    A Pie graph (or a circle-graph)
  • 15.1.3    A histogram
  • 15.1.4    A line graph
  • 15.2       Linear Graphs
  • 15.2.1    Location of a point
  • 15.2.2    Coordinates
  • 15.3      Some Applications

NCERT solutions for class 8 maths chapter 15 Introduction to Graphs for all the exercises

NCERT solutions for class 8 chapter 15 introduction to graphs-Exercise: 15.1

Question:1(a) The following graph shows the temperature of a patient in a hospital , recorded every hour .

What was the patient's temperature at 1 p.m 

Answer:

(a) The patient's temperature at 1 p.m is 36.5 \degree celsius.

Question:1(c) The following graph shows the temperature of a patient in a hospital  recorded every hour.

 

Answer:

 (c)  The patients temperature was the same two times during the period given these two times are 1 p.m. and 2 p.m.

Question:1(d) The following graph shows the temperature of a patient in a hospital  recorded every hour.

What was the temperature at 1:30 p.m? How did you arrive at your answer? 

 

Answer:

 (d) The temperature  at 1:30 p.m is  36.5\degreecelsius. The temperature at 1 p.m. to 2 p.m. is same  i.e. 36.5\degreecelsius so it is also same as at 1:30 p.m is  36.5\degreecelsius.

Question:1(e) The following graph shows the temperature of a patient in a hospital  recorded every hour.

During which periods did the patients temperature showed an upward trend ?

Answer:

(e) The patients temperature showed an upward trend-  9 am to 10 am., 10 am. to 11 am. and 2pm to 3pm

Question:2(a) The following line graph shows the yearly sales figure for a manufacturing company.

 What are the sales in (1) 2002  (2) 2006 ?

Answer:

(a) The sales in

 (1) 2002  = 4 crore

 (2) 2006 = 8 crore

Question:2(b) The following line graph shows the yearly sales figure for a manufacturing company.

 What are the sales in (1) 2003  (2) 2005 ?

Answer:

(b) The sales in

(1) 2003  = 7 crore

(2) 2005  = 10 crore

Question:2(d) The following line graph shows the yearly sales figure for a manufacturing company

In which year was there the greatest difference between the sales as compared to its previous year  ?

Answer:

(d) The greatest difference between the sales as compared to its previous year is 10-6=4 crores between 2004 and 2005.

Question:4(a) The following graph shows the temperature forecast and the actual temperature for each day of a week.
On which days was the forecast temperature the same as the actual temperature?

Answer:

(a)  The forecast temperature is the same as the actual temperature on Tuesday, Friday and Sunday.

Question:5(a) Use the tables below to draw linear graphs.
The number of days a hill side city received snow in different years.

Answer:

(a) The linear graph of data given above is as shown : 

Question:5(b) Use the tables below to draw linear graphs.

Population (in thousands) of men and women in a village in different years.

Answer:

(b) The graph of data given above is as shown :

Taking years as x-axis and population as y- axis.

Question:6(e) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant  .His distance from the town at different times is shown by the following graph .

During which period did he ride fastest ?

Answer:

(e) From graph we can observe person travels maximum distance from 8 a.m. to 9 a.m.

  Hence,person travels fastest from 8 a.m. to 9 a.m.

Question:7(i) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(i)  Yes, there can be a time-temperature graph as shown with the increase in time, temperature also increases.

Question:7(ii) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(ii) Yes, it is possible that with increase in time temperature decreases.

Question:7(iii) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(iii) No,this type of graph is not possible because different temperature at same time are not posiible.

Question:7(iv) Can there be a time-temperature graph as follows? Justify your answer

Answer:

(iv) Yes, it is possible i.e. same temperature at different time  is possible.

NCERT solutions for class 8 maths chapter 15 introduction to graphs-Exercise: 15.2

Question:1(i) Plot the following points on a graph sheet. Verify if they lie on a line

  A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

Answer:

(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

Question:1(b) Plot the following points on a graph sheet. Verify if they lie on a line

P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

Answer:

(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

The graph is as shown :

 

Question:1(c) Plot the following points on a graph sheet. Verify if they lie on a line

 K(2, 3), L(5, 3), M(5, 5), N(2, 5)

Answer:

(iii) K(2, 3), L(5, 3), M(5, 5), N(2, 5)

The graph is as shown :

 

Question:2 Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at
which this line meets the x-axis and y-axis.

Answer:

As shown below is graph :

 

 

 

 

 

 

 

 

 

 

The coordinates of the points at which this line meets the x-axis and y-axis are (5,0) and (0,5)

Question:3 Write the coordinates of the vertices of each of these adjoining figures.

Answer:

The coordinates of vertices are:

O(0,0), A(2,0)B(2,3),C(0,3),

P(4,3),Q(6,1),R(6,5),S(4,7)

L(7,7),M(10,8),K(10,5)

Question:4(i) State whether True or False. Correct that are false.
 A point whose x coordinate is zero and y-coordinate is non-zero will
lie on the y-axis
.

Answer:

(i) True .A point whose x coordinate is zero and y-coordinate is non-zero will
lie on the y-axis. = (0,y) here, y is variable.

Question:4(ii) State whether True or False. Correct that are false.

A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

Answer:

(ii) False.Point (5,0) does not lie on y-axis.A point whose y coordinate is zero and x-coordinate is 5 will not lie on
y-axis.

Question:4(iii) State whether True or False. Correct that are false. 

The coordinates of the origin are (0, 0).

Answer:

(iii)True. The coordinates of the origin are (0, 0).

NCERT solutions for class 8 maths chapter 15 introduction to graphs topic 15.3 some applications

Question:1 In the above example, use the graph to find how much petrol can be purchased for Rs 800.

Answer:

From the graph given below we can say that for  Rs 800 we can buy 16 litres.

Question:2 A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph Try a case of direct variation?

Answer:

Taking a case of direct variation the graph is as shown below.

Taking sum deposite as 100,200,300,500 ,1000. 

and  10% Simple Interest (S.I.).

 

NCERT solutions for class 8 maths chapter 15 Introduction to Graphs-Exercise: 15.3 

Question:1(a) Draw the graphs for the following tables of values, with suitable scales on the axes.
Cost of apples

Answer:

(a) Cost of apples

Question:1(b) Draw the graphs for the following tables of values, with suitable scales on the axe. 

Distance travelled by a car.

(ii) What was the time when the car had covered a distance of 100 km since it’s star

Answer:

(b) 

(ii)From above graph we conclude that at 7:30 a.m.,  the car had covered a distance of 100 km since it’s start.

Question:1(c) Interest on deposits for a year .

(i) Does the graph pass through the origin?

Answer:

(c) 

 

Taking x axis as 1000 units = 1 box and y axis as 100 units = 1 box.

(i)Yes, the graph pass through the origion.

Question:1(c) Interest on deposits for a year 

(ii) Use the graph to find the interest on Rs 2500 for a year.

Answer:

(c) 

(ii) Using the graph, the interest on Rs 2500 for a year is Rs 200.

Question:1(c) Interest on deposits for a year .

(iii)To get an interest of Rs 280 per year  how much money should be deposited ? 

Answer:

(iii) From the graph,to get an interest of Rs 280 per year  Rs 3500 money should be deposited.

Question:2(i) Draw a graph for the following Is it a linear graph 

Answer:

From the above graph ,we conclude that graph is linear.

Question:2(ii) Draw a graph for the following

Is it a linear  graph? 

Answer:

From above graph,we conclude that graph is not linear.

NCERT solutions for class 8 maths: Chapter-wise

Chapter -1

NCERT solutions for class 8 maths chapter 1 Rational Numbers             

Chapter -2 

Solutions of NCERT for class 8 maths chapter 2 Linear Equations in One Variable

Chapter-3

CBSE NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals

Chapter-4

NCERT solutions for class 8 maths chapter 4 Practical Geometry

Chapter-5

Solutions of NCERT for class 8 maths chapter 5 Data Handling

Chapter-6

CBSE NCERT solutions for class 8 maths chapter 6 Squares and Square Roots

Chapter-7

NCERT solutions for class 8 maths chapter 7 Cubes and Cube Roots

Chapter-8

Solutions of NCERT for class 8 maths chapter 8 Comparing Quantities

Chapter-9

NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities

Chapter-10

CBSE NCERT solutions for class 8 maths chapter 10 Visualizing Solid Shapes

Chapter-11

NCERT solutions for class 8 maths chapter 11 Mensuration

Chapter-12

Solutions of NCERT for class 8 maths chapter 12 Exponents and Powers

Chapter-13

CBSE NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions

Chapter-14

NCERT solutions for class 8 maths chapter 14 Factorization

Chapter-15

NCERT solutions for class 8 maths chapter 15 Introduction to Graphs

Chapter-16

CBSE NCERT solutions for class 8 maths chapter 16 Playing with Numbers

NCERT solutions for class 8: Subject-wise

Benefits of NCERT solutions for class 8 maths chapter 15 introduction to graphs-

  • You will get to know the different applications of the graph based on the need and given data.
  • It will help you in your homework as all the practice questions including questions given below every topic are covered in this article.
  • You can predict future events with the help of graphs using data of past events.
  • You will also get solutions to the practice questions given below every topic which will give you conceptual clarity.
  • You should draw the graphs given in the NCERT textbook. You can take help from the NCERT solutions for class 8 maths chapter 15 introduction to graphs.

Happy learning!!!

 

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