CBSE Class 8 Maths Chapter 15: Introduction to Graphs NCERT Solutions
This chapter, "Introduction to Graphs," for CBSE Class 8 Mathematics, provides a foundational understanding of graphical representations. The NCERT Solutions cover exercises that involve interpreting various types of graphs, including line graphs, to represent data. Students will learn to read information directly from graphs, identify trends, and make comparisons. The solutions explain how to plot points, understand axes, and derive conclusions from visual data. These detailed solutions are designed to help students grasp the concepts of data visualization and analysis, crucial for their upcoming examinations. By working through these problems, students can build confidence in interpreting and using graphs effectively for problem-solving and revision.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 15 |
Chapter summary
Chapter 15, "Introduction to Graphs," focuses on teaching students how to interpret and use line graphs to represent data. The NCERT Solutions provide step-by-step explanations for reading information from graphs, identifying specific data points, understanding trends over time, and calculating differences. This chapter is essential for developing data analysis skills through visual representation, preparing students for more complex graphical interpretations in higher classes.
Learning outcomes
- Understand the concept of a line graph and its components.
- Interpret data presented in line graphs.
- Identify specific values and trends from a given graph.
- Calculate differences and compare data points using graphs.
- Determine periods of increase or decrease in data trends.
Topics covered
Paper topics
- Introduction to Graphs
- Line Graphs
- Interpreting Line Graphs
- Reading Data from Graphs
- Identifying Trends
- Data Visualization
- Time-Temperature Graphs
- Yearly Sales Graphs
- Comparing Data Points
- Calculating Differences
Important topics
- Interpreting Line Graphs
- Identifying Trends from Graphs
- Reading Specific Data Points
- Comparing Data Using Graphs
- Understanding Axes and Scales
PDF preview
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Questions and Solutions
Exercise 15.1, Question 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?
The provided graph illustrates the patient's temperature fluctuations over a period. We can interpret the graph to answer the following:
(a) Patient's temperature at 1 p.m.:
Looking at the graph, find 1 p.m. on the time axis (x-axis). Move vertically up to the line graph and then horizontally to the temperature axis (y-axis). The temperature at 1 p.m. was 36.5° C.
(b) Time when temperature was 38.5° C:
Locate 38.5° C on the temperature axis. Move horizontally to the line graph and then vertically down to the time axis. The patient's temperature was 38.5° C at 12 noon.
(c) Times when temperature was the same:
Observe the graph for any horizontal segments or points at the same height on the temperature axis. The temperature was 36.5° C at 1 p.m. and also at 2 p.m. Thus, these were the two times when the temperature was the same.
(d) Temperature at 1.30 p.m.:
To find the temperature at 1.30 p.m., we need to estimate the value on the graph. 1.30 p.m. is exactly halfway between 1 p.m. and 2 p.m. on the time axis. The graph shows that the temperature at 1 p.m. was 36.5° C and at 2 p.m. was also 36.5° C. Since the temperature remained constant between 1 p.m. and 2 p.m., the temperature at 1.30 p.m. was 36.5° C.
(e) Periods of upward trend:
An upward trend indicates that the temperature is increasing over time. Observing the graph, the temperature line goes up from 9 a.m. to 11 a.m. Therefore, the patient's temperature showed an upward trend during the period from 9 a.m. to 11 a.m.
Exercise 15.1, Question 2
The following line graph shows the yearly sales figures for a manufacturing company.
1. What were the sales in (i) 2002 (ii) 2006?
2. What were the sales in (i) 2003 (ii) 2005?
3. Compute the difference between the sales in 2002 and 2006.
4. In which year was there the greatest difference between the sales as compared to its previous year?
The line graph displays the company's sales figures in crores of rupees for the years 2002 to 2006. We can read the sales for each year directly from the graph.
1. Sales in 2002 and 2006:
(i) To find the sales in 2002, locate the year 2002 on the horizontal axis (Years) and move vertically up to the line graph. Then, move horizontally to the vertical axis (Sales in Rs crores). The sales in 2002 were ₹ 4 crores.
(ii) Similarly, for the year 2006, the sales were ₹ 8 crores.
2. Sales in 2003 and 2005:
(i) For the year 2003, the sales figure on the graph is ₹ 7 crores.
(ii) For the year 2005, the sales figure on the graph is ₹ 10 crores.
3. Difference between sales in 2002 and 2006:
The sales in 2006 were ₹ 8 crores and the sales in 2002 were ₹ 4 crores. The difference is calculated as:
Difference = Sales in 2006 – Sales in 2002 = ₹ 8 crores – ₹ 4 crores = ₹ 4 crores.
4. Year with the greatest difference in sales compared to the previous year:
We need to calculate the difference in sales between each year and its preceding year:
* 2003 vs 2002: ₹ 7 crores – ₹ 4 crores = ₹ 3 crores
* 2004 vs 2003: ₹ 6 crores – ₹ 7 crores = -₹ 1 crore (a decrease)
* 2005 vs 2004: ₹ 10 crores – ₹ 6 crores = ₹ 4 crores
* 2006 vs 2005: ₹ 8 crores – ₹ 10 crores = -₹ 2 crores (a decrease)
Comparing these differences, the greatest positive difference (increase) occurred in 2005, with sales increasing by ₹ 4 crores compared to 2004. Therefore, the year with the greatest difference between sales compared to its previous year was 2005.
Common mistakes
- Misinterpreting the scale on the axes.
- Incorrectly reading values between marked points.
- Confusing the x-axis and y-axis.
- Errors in calculating differences between data points.
Revision tips
- Practice reading all types of line graphs presented in the chapter.
- Pay close attention to the units and scales on both axes.
- Redraw graphs yourself to better understand data plotting.
- Explain the trends shown in the graphs in your own words.
Practice MCQs
Q1. What does the x-axis typically represent in a line graph?
Explanation: The x-axis, or the horizontal axis, usually represents the independent variable, such as time or categories, against which the dependent variable is plotted.
Q2. In a patient's temperature graph, what does a horizontal line segment indicate?
Explanation: A horizontal line segment on a graph signifies that the value of the variable on the y-axis (in this case, temperature) remains unchanged over the period represented on the x-axis.
Q3. What is the primary purpose of a line graph?
Explanation: Line graphs are best suited for displaying trends or changes in data over a continuous period, such as time, making them ideal for tracking progress or fluctuations.
Q4. If a line graph shows sales figures over several years, what does a steep upward slope indicate?
Explanation: A steep upward slope on a line graph representing sales indicates a substantial and rapid increase in sales figures from one period to the next.
Frequently asked questions
What is the main focus of Chapter 15, Introduction to Graphs, for Class 8 Maths?
Chapter 15 focuses on teaching students how to interpret and use line graphs to represent and understand data, including identifying trends and specific values.
How do these NCERT Solutions help students?
These solutions provide clear, step-by-step explanations for each question in Chapter 15, helping students understand how to read and analyze line graphs effectively for their exams.
What kind of graphs are covered in this chapter?
The chapter primarily covers line graphs, using examples like patient temperature over time and company sales over years.
Why is understanding graphs important for Class 8 students?
Understanding graphs is a fundamental skill in mathematics and data analysis, crucial for interpreting information presented visually and for future studies.
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