# NCERT Solutions Class 8 Maths Chapter 15 Exercise 15.1

The books that NCERT produces provide comprehensive knowledge on a range of topics. NCERT provides a variety of instructional tools, not just books. To provide educational and instructional materials to schools, the government founded the National Council of Educational Research and Teaching. Many schools have joined with NCERT in order to give their students educational resources and train new teachers. In order to prepare for a variety of exams, including the Class 10 and Class 12 board exams and various entrance exams, such as JEE, NEET, NDA, CUET, etc. In order to get into the courses and institutions of their choosing, students usually use the NCERT study resources. The NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 contains the solutions to the issues in the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. These NCERT solutions are beneficial for students. Since it provides students with the resources they need to solve the questions in the NCERT-published book, the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 is a helpful tool. Using the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 will help students understand the chapter, the correct answers, and the most effective approaches to answering each question.

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## NCERT Class 8 Maths Solutions, Chapter 15: Introduction to Graphs (EX 15.1) Exercise 15.1

Students can obtain NCERT solutions for Class 8 for every chapter on the Extramarks website and mobile app. Students should use NCERT Solutions when studying because they will help them understand the material. They should remember that working through NCERT books can help them perform better in board examinations as well as on admission tests like JEE and CUET, among others. Students can increase their comprehension of the chapter’s core concepts and how to respond to questions with the aid of NCERT. The NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 may be of assistance.

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### Access NCERT Solutions for Class 8 Chapter 15 – Introduction To Graphs

The objectives of NCERT exercises are to evaluate students’ comprehension of the concepts covered in a specific chapter. NCERT solutions are crucial for board examinations. Use the NCERT Solutions for Class 8 Maths, Chapter 15, Exercise 15.1 on the Extramarks website and app if they’re having any difficulties learning Chapter 15 of Mathematics. Students who find this chapter difficult usually use the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1, which offers answers to the exercise questions in addition to the several benefits described.

The  NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 also include an overview or brief synopsis of Class 8 Maths Chapter 15 Exercise 15.1. The chapter contains several important questions and concepts, according to the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1, such as an introduction to graphs, a bar graph, a pie graph (or a circle graph), a histogram, a line graph, linear graphs, the location of a point, coordinates, and applications of graphs. It is natural that students would find it difficult to understand the concepts without help. Students would put in more effort than necessary to study a new chapter, which is already pretty difficult. There are numerous crucial ideas about statistics, data analytics, and data representation in the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. Since they will score higher on the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 issues throughout their board exams, students will benefit from this. The NCERT Solutions for Class 8 Maths, Chapter 15, Exercise 15.1 are intended to assist students in getting past a current difficulty so they may study and apply new concepts from multiple textbooks. Students had more time to study for exams and take practise tests since they could finish the chapter’s NCERT tasks with the aid of the study guide for  NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. They might score better on the final board exams if they adhere to these guidelines in the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1.

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### NCERT for Class 8 Maths Solutions, Chapter 15: Introduction To Graphs, Exercise 15.1

Introduction To Graphs is the title of Chapter 15 in the NCERT Mathematics textbook for Class 8. The NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 will provide an overview of the chapter. Following a brief introduction, the following list of concepts makes up this chapter: a bar graph, a pie graph (or a circle graph), a histogram, a line graph, linear graphs, the location of a point, coordinates, and applications of graphs. It serves as the foundation for NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. As a result, understanding the  NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 is critical for studentsr to perform well in tests.

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By using the precise answers and explanations offered in the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1, students can more fully comprehend the ideas in Exercise 15.2. for the purpose of selecting an appropriate response to a range of questions, students must completely comprehend the material covered in Exercise 15.1. They can make use of this while solving issues where the query merely provides sparse information. Understanding the various stages could be helpful for students. As a result, students must take in and remember this knowledge if they want to perform well on tests. If students need help, they could go to the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. Reading through the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 can help students find the answers to any questions they may have about Exercise 15.1. Exercise 15.1 concepts are essential for students’ board and entrance exams. As a result, since doing so might boost academic performance, it is vital for students to understand how specific questions should be answered. Students must use Extramarks to help them if necessary. They could refer to the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 for help with their exam. In order to increase their performance on board exams or year-end exams, students should study the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1.

As the name suggests, this chapter has students understanding graphical representation of data. It introduces to them various types of graphs like a bar graph, a pie graph, a histogram, a line graph and their applications. The teacher teaches them about the graph sheet, how to draw a graph properly and the various terms used for graphs like coordinates, variables, dependent or independent variable, x-coordinate, y-coordinate, cartesian plane, etc. They will help students solve exercises and better understand the concept as a whole. It will help them advance questions in later exercises in chapters and apply these methods to solve various types of questions and to get good grades in their exams.

### NCERT Solutions for Class 8

Extramarks offers study materials as part of its academic support services for the CBSE, ICSE, and many state boards. for instance, Extramarks provides NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1 in both Hindi and English, as well as additional study tools. It helps many children from all around the nation learn and perform better. Additionally, NCERT solutions, study guides, and other resources are available on Extramarks for a variety of classes and subject areas, including the NCERT Solutions for Class 8 Maths Chapter 15 Exercise 15.1. for the purpose of assisting students with their academic preparation and journey, Extramarks offers materials.

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Q.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?
(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?

Ans

(a) The patient’s temperature was 36.5°C at 1 p.m.
(b) At 12 noon, the patient’s temperature was 38.5°C.
(c) The two times when the patient’s temperature was same, were 1 p.m. and 2 p.m.
(d) The temperature at 1:30 p.m. is 36.5°C.
(e) The patient’s temperature showed an upward trend during the following periods: 9 a.m. to 10 a.m., 10 a.m. to 11 a.m., 2 p.m. to 3 p.m.

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

Ans

(a)
(i) The sales in 2002 were ₹ 4 crores.
(ii) The sales in 2006 were ₹ 8 crores.
(b)
(i) The sales in 2003 were ₹ 7 crores.
(ii) The sales in 2005 were ₹ 10 crores.
(c)
(i) The difference between the sales in 2002 and 2006 = ₹ (8 − 4) crores = ₹ 4 crores
(d) For finding the greatest difference between the sales as compared to its previous year, we have to find compare all the years.
Therefore, the difference between the sales of the year 2006 and 2005 = ₹ (10 − 8) crores = ₹ 2 crores
Difference between the sales of the year 2005 and 2004 = ₹ (10 − 6) crores = ₹ 4 crores
Difference between the sales of the year 2004 and 2003 = ₹ (7 − 6) crore = ₹ 1 crore
Difference between the sales of the year 2003 and 2002 = ₹ (7 − 4) crores = ₹ 3 crores
Hence, the difference was the maximum in the year 2005 as compared to its previous year 2004.

Q.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.
(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.

Ans

(a)
(i) The height of plant A was 7 cm after 2 weeks.
(ii) The height of plant A was 9 cm after 3 weeks.
(b)
(i) The height of plant B was 7 cm after 2 weeks.
(ii) The height of plant B was 10 cm after 3 weeks.
(c) The growth of plant A during 3rd week = 9 cm − 7 cm = 2 cm
(d) The growth of plant B from the end of the 2nd week to the end of the 3rd week = 10 cm − 7 cm = 3 cm
(e) The growth of plant A during 1st week = 2 cm − 0 cm = 2 cm
The growth of plant A during 2nd week = 7 cm − 2 cm = 5 cm
The growth of plant A during 3rd week = 9 cm − 7 cm = 2 cm
Therefore, plant A grew the most, i.e. 5 cm, during the 2nd week.

(f) The growth of the plant B during 1st week = 1 cm − 0 cm = 1 cm
The growth of the plant B during 2nd week = 7 cm − 1 cm = 6 cm
The growth of plant B during 3rd week = 10 cm − 7 cm = 3 cm
Therefore, plant B grew the least, during the 1st week.

(g) The two plants were of the same height during the 2nd week.

Q.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?

Ans

(a) The forecast temperature was same as the actual temperature on Tuesday, Friday, and Sunday.
(b) The maximum forecast temperature during the week was 35°C.
(c) The minimum actual temperature during the week was 15°C.
(d) The actual temperature differs the most from the forecast temperature on Thursday.

Q.5 Use the tables below to draw linear graphs.

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

 Year 2003 2004 2005 2006 Days 8 10 5 12

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

 Year 2003 2004 2005 2006 2007 Number of Men 12 12.5 13 13.2 13.5 Number of Women 11.3 11.9 13 13.6 12.8

Ans

1.  Year 2003 2004 2005 2006 Days 8 10 5 12

2.  Year 2003 2004 2005 2006 2007 Number of Men 12 12.5 13 13.2 13.5 Number of Women 11.3 11.9 13 13.6 12.8

Q.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.
(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?

Ans

(a) Scale taken for the time axis is 4 units = 1 hour
(b)

$\mathrm{The}\mathrm{person}\mathrm{took}3\frac{1}{2}\mathrm{hours}\mathrm{to}\mathrm{travel}.$

(c) The merchant is 22 km far from the town.
(d) Yes, the person stopped on his way from 10 a.m. to 10: 30 a.m. It is clearly shown by the horizontal line in the graph.
(e) From 8 a.m. to 9 a.m., the person travelled the maximum distance. So, the person’s ride was the fastest between 8 a.m. and 9 a.m.

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

Ans

(i) As the temperature can increase with the increase in time, so it can be a time−temperature graph..
(ii) As the temperature can decrease with the decrease in time, so it can be a time−temperature graph.
(iii) Since different temperatures at the same time are not possible, so it cannot be a time−temperature graph.
(iv) As same temperature at different times is possible, so it can be a time−temperature graph.