The National Council of Educational Research and Training (NCERT) is an autonomous body of the Indian government that formulates the curricula for schools in India that are governed by the Central Board of Secondary Education (CBSE) and certain state boards. Therefore, students who will be taking the Class 10 tests administered by various boards should consult this NCERT Syllabus in order to prepare for those examinations, which in turn will assist those students get a passing score.

You can also download the NCERT SOLUTION FOR CLASS 8 MATHS CHAPTER 15 INTRODUCTION TO GRAPHS to assist you in comprehensively reviewing the course material and achieving a higher score on your upcoming assessments.

Students are able to create a strong conceptual basis with the help of the NCERT Solutions PDFs available at SWC. This base plays a key part in the students’ preparation for the later phases of the competitive examinations. We give comprehensive answers to challenges posed by NCERT in accordance with the methodology provided by CBSE. The students are able to effortlessly prepare all of the ideas that are presented in their respective courses better and more successfully, and they are even able to succeed in passing the most difficult competitive examinations, such as JEE Main, JEE Advanced, NEET, AIMS, and so on.

Your academic journey begins a new stage as you reach the eighth grade, and a new facet of learning awaits you. This is the year where pupils begin to acquire an interest in the topic at hand, and it is also the year in which you choose whether you will study business, humanity, or science in the following year (class 12). As a consequence of this, having a solid foundation of knowledge in fields such as mathematics and physics comes highly recommended. The NCERT textbook for class 8 is the greatest book now available on the market for enhancing one’s education in the areas of mathematics and science. Read up on the theory that is presented in the book for grade 8 and answer all of the questions that are posed in the practice section of the NCERT textbook.

When working through the exercises in the NCERT textbook, if you run into any type of difficulty or uncertainty, you may use the SWC NCERT Solutions for class 8 as a point of reference. While you are reading the theory from the textbook, it is imperative that you always have notes prepared. You should make an effort to understand things from the very beginning so that you may create a solid foundation in the topic. Use the NCERT as your parent book to ensure that you have a strong foundation. After you have finished reading the theoretical section of the textbook, you should go to additional reference books.


NCERT Solutions for Class 8 Maths Exercise 15.1

Question 1.

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

Introduction to Graphs/image001.jpg

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

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

(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 1.30 p.m.? How did you arrive at your answer?

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

solution :

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

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

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

(d) The temperature at 1.30 p.m. is 36.5o C. The point between 1 p.m. and 2 p.m., Introduction to Graphs/image002.pngaxis is equidistant from the two points showing 1 p.m. and 2 p.m. So it represents 1.30 p.m. Similarly the point on Introduction to Graphs/image003.pngaxis, between 36o C and 37o C will represent 36.5o C.

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

Question 2.

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

Introduction to Graphs/image004.jpg

(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 2002 and 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.8crores.

(b) The sales in:

(i) 2003 was Rs.7crores

(ii) 2005 was Rs.10crores.

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

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

Question 3.

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

Introduction to Graphs/image005.jpg

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

(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 7 cm high after 2 weeks and

(ii) after 3 weeks it was 10 cm high.

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

(d) Plant B grew during end of the 2nd week to the end of the 3rd week

= 10 cm – 7 cm = 3 cm.

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

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

(g) At the end of the second week, plant A and B were of the same height.

Question 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


Introduction to Graphs/image006.jpg

solution :

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

(b) The maximum forecast temperature was 35o C.

(c) The minimum actual temperature was 15o C.

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

Question 5.

Use the tables below to draw linear graphs.

Introduction to Graphs/image007.png

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

Introduction to Graphs/image008.jpg

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

solution :


Introduction to Graphs/image009.png


Introduction to Graphs/image010.jpg

Question 6.

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.

Introduction to Graphs/image011.jpg

(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?

solution :

(a) 4 units = 1 hour.

(b) The person took Introduction to Graphs/image012.pnghours 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 am to 10.30 am.

(e) He rode the fastest between 8 am and 9 am.

Question 7.

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

Introduction to Graphs/image013.jpg

solution :

(i) It is showing the increase in temperature.

(ii) It is showing the decrease in temperature.

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

(iv) It is showing constant temperature.

NCERT Solutions for Class 8 Maths Exercise 15.2

Question 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 :

Introduction to Graphs/image001.jpg

(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) These points do not lie in a straight line.

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.

solution :

Introduction to Graphs/image002.jpg

The coordinates of the points at which this line meets the Introduction to Graphs/image003.pngaxis at (5, 0) and Introduction to Graphs/image004.pngaxis at (0, 5).

Question 3.

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

Introduction to Graphs/image005.jpg

solution :

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)

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

Ans. (i) True (ii) False, it will lie on Introduction to Graphs/image003.pngaxis. (iii) True

NCERT Solutions for Class 8 Maths Exercise 15.3

Question 1.

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

(a) Cost of apples

Introduction to Graphs/image002.jpg

(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 :


Introduction to Graphs/image001.png

(b) (i) The car covered 20 km distance.

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

Introduction to Graphs/image002.jpg

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

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

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

Introduction to Graphs/image003.png

Question 2.

Draw a graph for the following.


solution :

(i) Yes, it is a linear graph.

Introduction to Graphs/image004.png

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

Introduction to Graphs/image005.png

Conclusions for NCERT Solutions For Class 8 Maths Chapter 15

SWC academic staff has developed NCERT answers for the 15th chapter of the eighth-grade mathematics curriculum. We have solutions prepared for all of the exercises in the 15th chapter. The answers, broken down into steps, to all of the questions included in the NCERT textbook’s first chapter are provided here. Read the 15th chapter on theory. Be certain that you have read the theory section of chapter15 of the NCERT textbook and that you have learned the formulas for the chapter that you are studying. 

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