NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs Exercise 13.1

NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs Exercise 13.1 introduces students to the basics of graphs and how to represent information visually. In this exercise, students learn about different types of graphs such as bar graphs, line graphs, and pie charts. The aim is to help students understand how to read and draw graphs accurately using simple data.

These NCERT Solutions follow the latest NCERT guidelines and explain each concept in a step-by-step, easy-to-understand manner. With the help of clear examples and diagrams, students can quickly learn how to represent data on graph paper. Practicing NCERT Solutions from Exercise 13.1 helps build strong data interpretation skills and prepares students for real-life data handling.

1.0Download NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs Exercise 13.1: Free PDF

Download the free NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs Exercise 13.1 PDF with clear, step-by-step answers to help you learn graph concepts easily.

2.0Key Concepts in Exercise 13.1 of Class 8 Maths Chapter 13

Exercise 13.1 of Chapter 13 – Introduction to Graphs introduces students to the fundamentals of graphical representation in mathematics. It lays the foundation for interpreting and plotting different types of data visually on a graph.

• Basics of Graphs:
  Students learn what a graph is and how it visually represents numerical data. This includes understanding terms like axes, origin, and coordinates.
• Types of Graphs:
  Introduction to different types of graphs, such as:
• • Bar Graphs – to compare quantities
  • Pictographs – for visual representation using pictures
  • Line Graphs – to show changes over time
  • Linear Graphs – to represent equations visually on the coordinate plane
• Reading Graphs:
  Students are trained to read values from bar graphs, line graphs, and other graphical formats to extract meaningful data.
• Drawing Graphs:
  The exercise includes basic plotting of points on the Cartesian plane and drawing simple bar and line graphs based on provided data.
• Real-Life Data Interpretation:
  Practical questions based on temperature changes, population data, sales charts, etc., help students relate graphs to real-world scenarios.

3.0NCERT Class 8 Maths Chapter 13: Other Exercises

4.0NCERT Class 8 Maths Chapter 13 Exercise 13.1: Detailed Solutions

1. The following graph shows the temperature of a patient in a hospital, recorded every hour.
   
   (i) What was the patient's temperature at 1 p.m.? (ii) When was the patient's temperature $38.5^{\circ }\mathrm{C}$ ? (iii) The patient's temperature was the same two times during the period given. What were these two times? (iv) What was the temperature at 1.30 p.m.? How did you arrive at your answer? (v) During which periods did the patient's temperature showed an upward trend? Sol. In the graph, we find that the time (in hours) are represented on the $x$-axis and the temperature (in ${}^{\circ }\mathrm{C}$ ) are represented on the y-axis. The temperature and time can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that : (i) The temperature of the patient at 1 pm was $36.5^{\circ }\mathrm{C}$. (ii) The temperature of the patient was $38.5^{\circ }\mathrm{C}$ at 12 noon. (iii) The temperature of the patient was same at 1 pm and 2 pm . (iv) The temperature of the patient at 1.30 pm was $36.5^{\circ }\mathrm{C}$. The point between 1 pm and 2 pm on the x -axis is equidistant from the two points showing 1 pm and 2 pm , so it will represent 1.30 pm . Similarly, the point on the $y$-axis, between $36^{\circ }\mathrm{C}$ and $37^{\circ }\mathrm{C}$ will represent $36.5^{\circ }\mathrm{C}$. (v) During the periods 9 am to $10\mathrm{am},10\mathrm{am}$ to 11 am and 2 pm to 3 pm the patient's temperature showed an upwards trend.
2. The following lines graph shows the yearly sales figures for a manufacturing company. (i) What were the sales in (a) 2002 (b) 2006? (ii) What were the sales in (a) 2003 (b) 2005? (iii) Compute the difference between the sales in 2002 and 2006.
   
   Sol. In the graph, we find that the years are presented on the $x$-axis and the sales (in Rs. crores) on the $y$-axis. The sales at any time (year) can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (i) (a) The sales in the year 2002 is Rs. 4 crore. (b) The sales in the year 2006 is Rs. 7 crore. (ii) (a) The sales in the year 2003 is Rs. 8 crore. (b) The sales in the year 2005 is Rs. 10 crore. (iii) The difference between the sales in 2002 and $2006=$ Rs. 7 crore - Rs. 4 crore $=$ Rs. 3 crore.
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 weeks? (d) How much did plant B grow from the end of the 2 nd week to the end of the 3rd week? (e) During which week did Plant A grow maximum? (f) During which week did Plant B grow least? (g) Were the two plants of the same height during any week shown here? Specify. coordinates of a point. From the graph, we observe that: (a) The height of the plant A after (i) 2 weeks was 7 cm (ii) 3 weeks was 9 cm (b) The height of the plant $B$ after (i) 2 weeks was 7 cm (ii) 3 weeks was 10 cm (c) The plant A grows 2 cm during the 3rd week. (d) The plant B grows 3 cm from the end of the 2 nd week to the end of the 3 rd week. (e) The plant A grows most during second week. (f) The plant B grows most during first week. (g) At the end of the 2nd week the heights of the two plants were the same.
4. The following graph shows the temperature forecase 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
   
   Sol. In the graph, we find that the days are represented on the $x$-axis and the temperature forecast/ actual $\left({}^{\circ }\mathrm{C}\right)$ on the y -axis. The temperature on any day can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (a) The days on which the forecast temperature was the same as the actual temperature are Tuesday, Friday and Sunday. (b) The maximum forecast temperature during the week was $35^{\circ }\mathrm{C}$. (c) The minimum actual temperature during the week was $15^{\circ }\mathrm{C}$. (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.

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

Sol. (a) In order to draw the required graph, we represent years on the x-axis and the days on the y -axis. We first plot the ordered pairs (2003, 8), (2004, 10), $(2005,5)$ and $(2006,12)$ as points and then join them by line segments as shown below :

6. A courier-person cycles from a town to a neighbouring sub-urban 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?
   
   Sol. In the graph, we find that the time (in hours) is represented on the x -axis and the distance (in km) is represented on the y -axis. The distance at any time can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (a) The scale taken for the time axis is : 4 units = 1 hour . (b) The person took 3.5 hours for the travel. (c) The merchant's place from the town is 22 km. (d) Yes; this is indicated by the horizontal part of the graph (10 a.m. - 10.30 a.m.) (e) Between 8 a.m. and 9 a.m. he ride faster.
7. Can there be a time temperature graph as follows? Justify your answer. (i)
   
   (ii)
   
   (iii)
   
   (iv)
   
   Sol. (i) This represents a time-temperature graph because it represents a smooth rise in temperature and is represented by a line graph. (ii) This represents a time-temperature graph because it represent a smooth fall in temperature and is represented by a line graph. (iii) This does not represent a timetemperature because it shows different temperatures at the same time. (iv) This represents a time-temperature graph because it shows a constant temperature at different times and is a line graph.

5.0Key Features and Benefits of Class 8 Maths Chapter 13 Exercise 13.1

• Introduction to Basic Graphs: Exercise 13.1 helps students understand different types of graphs like bar graphs, pie charts, line graphs, and more.
• Simple and Clear Examples: The questions use easy-to-understand examples, making it fun to read and understand data through graphs.
• Improves Data Interpretation: Students learn how to collect, organize, and present data clearly, which improves their ability to read and understand information visually.
• Builds a Strong Foundation: These concepts are helpful in subjects like Science and Geography too, where data is often shown using graphs.
• Follow NCERT Syllabus: All problems are from the NCERT textbook, which helps in school exam preparation and regular revision.