CBSE Class 8 Maths Exemplar Chapter 12: Introduction to Graphs NCERT Solutions
CBSE Class 8 Maths Chapter 12, NCERT Solutions, introduces the fundamental concepts of graphs for data representation. This chapter explores various graph types, including bar graphs, pie charts, and line graphs, explaining their appropriate uses in visualizing data. Students will learn to interpret coordinates on a Cartesian plane, locate points using their coordinates, and understand the role of the origin. Key skills developed include plotting points accurately, extracting information from graphs, and recognizing the connection between data sets and their graphical forms. These solutions aim to solidify students' understanding of graphical data representation, a vital skill for analytical reasoning and mathematical problem-solving. They offer a clear and structured approach to mastering these concepts, making them an invaluable tool for exam preparation and building confidence.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 8 |
| Subject | Maths Exemplar |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 12 |
Chapter summary
Chapter 12, 'Introduction to Graphs,' focuses on the basics of data representation using different types of graphs. The NCERT Solutions cover the comparison of data using pie charts, understanding continuous data changes with line graphs, and interpreting coordinates on a graph. Students will practice identifying points on a Cartesian plane and understanding the origin. This chapter is essential for developing visual data analysis skills.
Learning outcomes
- Understand the purpose of different types of graphs (bar, pie, line).
- Identify and interpret coordinates of points on a Cartesian plane.
- Determine the correct graph type for comparing data or showing trends.
- Locate points on a graph given their coordinates.
- Understand the significance of the origin (0,0) in a coordinate system.
Topics covered
Paper topics
- Introduction to Graphs
- Bar Graphs
- Line Graphs
- Pie Charts
- Cartesian Coordinate System
- Plotting Points
- Interpreting Coordinates
- Origin
- Distance from Axes
Important topics
- Interpreting Line Graphs
- Understanding Coordinates
- Identifying Points on a Graph
- Choosing the Right Graph Type
- The Origin (0,0)
PDF preview
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Questions and Solutions
Question 1
(a) bar graph
(b) line graph
(c) pie chart
(d) histogram
The correct option is (c) pie chart.
A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. Each slice's arc length (and consequently its central angle and area) is proportional to the quantity it represents. Pie charts are best used for showing how a whole is divided into parts.
Question 2
(a) bar graph
(b) pie chart
(c) histogram
(d) line graph
The correct option is (d) line graph.
A line graph is used to represent data that changes continuously over a period of time. It connects a series of data points with straight line segments, making it easy to visualize trends, increases, or decreases in data such as temperature, speed, or distance covered over time.
Question 3
(a) (0, 2)
(b) (2, 3)
(c) (3, 2)
(d) (3, 0)
The graph shows axes with values 0, 1, 2, 3, 4, 5, 6. Point x is located above the value 3 on the x-axis and aligns with the value 2 on the y-axis.
The correct option is (c) (3, 2).
To find the coordinates of point x, we need to determine its position relative to the x-axis and the y-axis. We draw a perpendicular line from point x to the x-axis and another perpendicular line from point x to the y-axis.
From the given figure, the point x is located at the 3rd unit on the x-axis and the 2nd unit on the y-axis.
Therefore, the coordinates of point x are (3, 2).
Question 4
(a) P
(b) Q
(c) R
(d) S
The graph displays points P, Q, R, and S. Point P is at (3,0), point Q is at (2,1), point R is at (0,3), and point S is at (3,3).
The correct option is (c) R.
To identify the point (0, 3), we look for a point where the x-coordinate is 0 and the y-coordinate is 3.
A point with an x-coordinate of 0 lies on the y-axis.
From the given figure:
- The coordinates of S are (3, 3).
- The coordinates of P are (3, 0).
- The coordinates of R are (0, 3).
Therefore, the letter that indicates the point (0, 3) is R.
Question 5
(a) 3 from both the axes
(b) 4 from both the axes
(c) 4 from the x axis and 3 from y axis
(d) 3 from x axis and 4 from y axis
The correct option is (c) 4 from the x axis and 3 from y axis.
In a coordinate pair (x, y), the first number (x) represents the distance from the y-axis, and the second number (y) represents the distance from the x-axis.
For the point (3, 4):
- The x-coordinate is 3, which means the point is 3 units away from the y-axis.
- The y-coordinate is 4, which means the point is 4 units away from the x-axis.
Therefore, the point (3, 4) is at a distance of 4 units from the x-axis and 3 units from the y-axis.
Question 6
(a) (0, 0)
(b) (0, 1)
(c) (1, 0)
(d) (1, 1)
The correct option is (a) (0, 0).
The x-axis and the y-axis are two perpendicular lines that intersect at a single point. This point of intersection is called the origin.
Any point lying on the x-axis has a y-coordinate of 0 (e.g., (1, 0), (-2, 0)). Any point lying on the y-axis has an x-coordinate of 0 (e.g., (0, 1), (0, -3)).
The only point that lies on both the x-axis and the y-axis is the origin, where both coordinates are zero, i.e., (0, 0).
Common mistakes
- Confusing the x and y coordinates when identifying a point.
- Incorrectly determining the distance of a point from the axes.
- Misinterpreting the type of graph suitable for specific data sets.
- Errors in reading values from a graph.
Revision tips
- Practice plotting points on a graph paper to visualize coordinate positions.
- Review the characteristics of each graph type (bar, pie, line) and their uses.
- Work through the examples to understand how to read and interpret graph data.
- Pay close attention to the order of coordinates (x, y) when identifying points.
Practice MCQs
Q1. Which type of graph is best suited for comparing parts of a whole?
Explanation: A pie chart is specifically designed to show the proportion of different categories within a whole dataset, making it ideal for comparisons of parts.
Q2. A graph that displays data that changes continuously over periods of time is called a:
Explanation: Line graphs are used to represent data that shows a continuous trend or change over time, such as temperature fluctuations or distance covered.
Q3. In a coordinate system, the point (3, 2) means:
Explanation: The first coordinate (3) represents the horizontal distance along the x-axis (usually to the right), and the second coordinate (2) represents the vertical distance along the y-axis (usually upwards).
Q4. Which letter indicates the point (0, 3) on a standard Cartesian graph?
Explanation: A point with an x-coordinate of 0 lies on the y-axis. The y-coordinate of 3 means it is 3 units up from the origin, which corresponds to point R in the provided context.
Q5. The point (3, 4) is located at a distance of:
Explanation: In the coordinate (3, 4), the first number (3) is the distance from the y-axis (x-coordinate), and the second number (4) is the distance from the x-axis (y-coordinate).
Q6. The point that lies on both the x-axis and the y-axis is:
Explanation: The origin, denoted as (0, 0), is the unique point where the x-axis and y-axis intersect. Any point on either axis will have one coordinate as zero, but only the origin lies on both.
Frequently asked questions
What is the main purpose of Chapter 12: Introduction to Graphs in Class 8 Maths Exemplar?
This chapter introduces students to the fundamental concepts of graphical representation of data, helping them understand how to visualize and interpret information using various types of graphs like bar graphs, line graphs, and pie charts, as well as the basics of the coordinate system.
How do these NCERT Solutions help with understanding graphs?
The solutions provide clear, step-by-step explanations for each question, breaking down complex concepts like plotting points, reading coordinates, and choosing appropriate graphs for different data scenarios, making learning more accessible.
What is the difference between a bar graph and a line graph?
A bar graph uses rectangular bars to compare discrete categories, while a line graph connects data points with lines to show trends or continuous changes over time.
What does a coordinate pair like (3, 2) represent on a graph?
The coordinate pair (3, 2) represents a point on a Cartesian plane where '3' is the distance along the x-axis (horizontal) from the origin, and '2' is the distance along the y-axis (vertical) from the origin.
Where is the origin on a Cartesian graph?
The origin is the point where the x-axis and y-axis intersect. Its coordinates are always (0, 0).
Can these solutions be used for exam revision?
Yes, these solutions are ideal for exam revision as they cover key concepts and provide practice in interpreting and solving problems related to graphs and coordinates, reinforcing understanding for tests.
Content reviewed by the NCERT Help team. Editorial Team and update policy
NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.