NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs are very important for students in order to develop logical and mental ability. Exercise-wise solutions for all the questions are prepared by subject experts as per the latest CBSE Class 8 Syllabus. Class 8 Mathematics NCERT Solutions for the year 2020-21 are a valuable help to students in their assignments and preparation of their exams.

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Access Answers to NCERT Class 8 Maths Chapter 15 Introduction to Graphs

Exercise 15.1 PageNo: 236

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

(a) What was the patient’s temperature at 1 p.m.?

(b) When was the patient’s temperature 38.5° C?

Ncert solution class 8 chapter 15-1

(c) The patient’s temperature was the same two times during the period given.

What were these two times?

(d) What was the temperature at 1.30p.m.? How did you arrive at your answer?

(e) During which periods did the patients’ temperature show an upward trend?

Solution:

(a) The patient’s temperature was 36.5oC at 1 p.m.

(b) The patient’s temperature was 38.5oC at 12noon.

(c) The patient’s temperature was same at 1 p.m. and 2p.m

(d)The temperature at 1.30p.m. is 36.5oC.

The point between 1p.m.and 2 p.m., x-axis is equidistant from the two points showing 1p.m. and 2p.m. Soit represents 1.30 p .m similarly the point on y axis, between 360 C and 370 C will Represent 36.50 C.

(e) The patient’s temperature showed an upward trend from 9a.m.to 11a.m. and from 2 p.m. to 3 p.m.

2. The following line graph shows the yearly sales figures for a manufacturing company.

Ncert solution class 8 chapter 15-2

(a) What were the sales in (i) 2002 (ii) 2006?

(b) What were the sales in (i) 2003 (ii) 2005?

(c) Compute the difference between the sales in 2002and 2006.

(d) In which year was there the greatest difference between the sales as compared to its

previous year?

Solution:

(a) The sales in:

(i) 2002 was Rs.4 crores and (ii) 2006 was Rs.8 crores

(b) The sales in:

(i) 2003 was Rs.7 crores and (ii) 2005 was Rs.10 crores.

(c) The difference of sales in 2002 and 2006 = Rs.8 crores–Rs.4 crores= Rs.4 crores

(d)In the year 2005, there was the greatest difference between the sales and compared to its previous year, which is (Rs. 10crores –Rs. 6crores) = Rs. 4crores.

3. For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

Ncert solution class 8 chapter 15-3

(a) How high was Plant A after (i) 2 weeks (ii) 3weeks?

(b) How high was Plant B after (i) 2 weeks (ii) 3 weeks?

(c) How much did Plant A grow during the 3rd week?

(d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?

(e) During which week did Plant A grow most?

(f) During which week did Plant B grow least?

(g) Were the two plants of the same height during any week shown here? Specify.

Solution:

(a)

(i)The plant A was 7 cm high after 2 weeks and

(ii) After 3 weeks it was 9 cm high

(b)

(i)Plant B was also 7cm high after 2 weeks and

(ii) After 3 weeks it was 10 cm high

(c) Plant A grew=9 cm–7 cm = 2cm during 3rd week.

(d) Plant B grew during end of the 2nd week to the end of the 3rdweek= 10cm–7cm= 3cm

(e) Plant A grew the highest during second week.

(f)Plant B grew the least during first week.

(g) Yes. At the end of the second week, plant A and B were of the same height, which is 7 cm.

4. The following graph shows the temperature forecast and the actual temperature for each day of a week.

(a) On which days was the forecast temperature the same as the actual temperature?

(b) What was the maximum forecast temperature during the week?

(c) What was the minimum actual temperature during the week?

(d) On which day did the actual temperature differ the most from the forecast temperature?

Ncert solution class 8 chapter 15-4

Solution:

(a) On Tuesday, Friday and Sunday, the forecast temperature was same as the actual

temperature.

(b) The maximum forecast temperature was 35oC.

(c) The minimum actual temperature was 15oC.

(d) The actual temperature differed the most from the forecast temperature on

Thursday.

5. Use the tables below to draw linear graphs

(a) The number of days a hill side city received snow in different years.

Ncert solution class 8 chapter 15-5

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

Ncert solution class 8 chapter 15-6

Solution:

(a) Consider “Years” along x-axis and “Days” along y-axis. Using given information, linear graph will looks like:

Ncert solution class 8 chapter 15-7

(b) Consider “Years” along x-axis and “No. of Men and No. of Women” along y-axis (2 graphs). Using given information, linear graph will looks like:

Ncert solution class 8 chapter 15-8

6. A courier-person cycles from a town to a neighboring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

(a) What is the scale taken for the time axis?

(b) How much time did the person take for the travel?

(c) How far is the place of the merchant from the town?

(d) Did the person stop on his way? Explain.

(e) During which period did he ride fastest?

Ncert solution class 8 chapter 15-9

Solution:

(a) 4 units = 1hour

(b) The person took 3 ½ hours for the travel.

(c) It was 22 km far from the town.

(d) Yes, this has been indicated by the horizontal part of the graph. He stayed from 10 a.m. to 10.30 a.m.

(e) He rides the fastest between 8 a.m. and 9a.m.

7. Can there be a time-temperature graph as follows? Justify your answer.

Ncert solution class 8 chapter 15-10

Solution:

(i) It is a time-temperature graph. It is showing the increase in temperature as time increases.

(ii) It is a time-temperature graph. It is showing the decrease in temperature as time increases.

(iii) The graph figure (iii)is not possible since temperature is increasing very rapidly

which is not possible.

(iv) It is a time-temperature graph. It is showing constant temperature.


Exercise 15.2 PageNo: 243

1. Plot the following points on a graph sheet. Verify if they lie on a line

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

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

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

Solution:

Plot all the points on the graph.

Ncert solution class 8 chapter 15-11

(a) All points A,B, C and D lie on a vertical line.

(b) P,Q, R and S points also make a line .It verifies that these points lie on a line.

(c) Points K, L, M and N. These points do not lie in a straight line.

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.

Solution:

Graph for the Line passes through points (2, 3) and (3, 2) is:

Ncert solution class 8 chapter 15-12

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

Y axis at (0,5).

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

Ncert solution class 8 chapter 15-13

Solution:

We can observe three figures named as, OABC, PQRS and LMK.

Vertices of figure OABC

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

Vertices of figure PQRS

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

Vertices of figure LMK

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

4. State whether True or False. Correct that are false.

(i) A point whose x coordinate is zero and y-coordinate is non-zero will lie on the y-axis.

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

(iii) The co-ordinates of the origin are (0, 0).

Solution:

i) True

ii) False, it will lie on x axis

(iii) True


Exercise 15.3 Page No: 247

1. Draw the graphs for the following tables of values, with suitable scales on the axes.

(a) Cost of apples

Ncert solution class 8 chapter 15-14

(b) Distance travelled by a car

Ncert solution class 8 chapter 15-15

(i) How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?

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

(c) Interest on deposits for a year.

Ncert solution class 8 chapter 15-16

(i) Does the graph pass through the origin?

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

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

Solution:

Mark “number of apples” on x-axis and “cost” on y-axis. The graph is

Ncert solution class 8 chapter 15-17

(b) Represent the “time” on x-axis and “distance” on y-axis.

Ncert solution class 8 chapter 15-18

(i) The car covered 20 km distance

(ii) It was 7.30 am, when it covered 100 km distance.

(c) Represent “Deposit” on y-axis and “simple interest” on x-axis.

Ncert solution class 8 chapter 15-19

(i) Yes, the graph passes through the origin.

(ii) Interest on Rs. 2500 is Rs. 200 for a year.

(iii) Rs. 3500 should be deposited for interest of Rs. 280

2. Draw a graph for the following

Ncert solution class 8 chapter 15-20

Solution:

(i) Yes, it is linear graph

Ncert solution class 8 chapter 15-21

(ii) No, it is not a linear graph because the graph does not provide a straight line.

Ncert solution class 8 chapter 15-22


NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

Class 8 NCERT exercise wise questions and answers will help students get a step-by-step explanation to every question specified in the textbooks. Some of the important topics introduced in Class 8 NCERT Solutions of Maths are a graphical presentation of data using a bar graph, pie graph, histogram, line graph, and also students will study about Linear Graphs and some of the basic applications of graphs.

NCERT Solutions For Class 8 Maths Chapter 15 Exercises:

Get a detailed solution for all the questions listed under the below exercises:

Exercise 15.1 Solutions : 7 Questions (Long answer type)

Exercise 15.2 Solutions : 4 Questions (Short answer type)

Exercise 15.3 Solutions : 2 Questions (Short answer type)

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

NCERT Class 8 Maths Chapter 15, deals primarily with the representation of data using different graph diagrams. In this section, students will learn mainly about, Introduction to Graphs, A Bar graph, A Pie graph (or a circle-graph), A histogram, A line graph, Linear Graphs, Location of a point, Coordinates and Some Applications.

The main Topics and Subtopics of NCERT Chapter 15 Class 8 Maths are below:

Exercise Topics/Subtopics
15.1 Introduction to Graphs
15.1.1 A Bar Graphs
15.1.2 A Pie Graphs or a circle graph
15.1.3 A Histogram
15.1.4 A Line Graphs
15.2 Linear Graphs
15.2.1 Location of a Point
15.2.2 Coordinates
15.3 Some Applications

Key Features of NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

  1. The subject experts have solved each question of NCERT exercise meticulously with the help of diagrams.
  2. A simple and easy language used.
  3. Step-by-step explanation to every question specified in the textbooks.
  4. These NCERT solutions are valuable to help students in their homework and competitive exams.

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