Key Concepts and Sample Questions on Graphs for Class 8
MCQ on Graph Theory with Answers
When it comes to education, we have numerous subjects to learn and appear to examine. Out of all the subjects, mathematics is one that most of the students find difficult. But the pattern in which it is designed for students makes this subject much easier. From class 1 to class 7, students understand the basic concepts and skills of mathematics, which can be used in further higher classes. They learn everything from scratch.
Finally, the class 8 mathematics syllabus is designed in a manner to recapitulate all the learned ideas and concepts in the past classes. Class 8 consists of 16 chapters of different topics and concepts.
Introduction to Graphs
Out of all these chapters, “Introduction to Graphs” is completely a new and fun way of learning higher mathematics for the students. This concept includes the representation of bulky data and information into manageable graphs like line graphs, bar graphs, etc. This chapter is very important to gain mental and logical ability to handle difficult cases in the arrangement of data.
Although many students neglect this chapter, the examination weightage of this chapter is quite significant and remarkable. To score full marks in Introduction to graphs, first of all, you must understand the type and pattern of questions that drop into the examination.
Questions are generally MCQs on graph theory with answers, answers in a sense, you have to choose the correct one out of four. And out of all the multiple-choice questions, most students made mistakes in Introduction to Graphs class 8 MCQs because they always miss this chapter considering it only meant for five marks questions of plotting graphs and hence forgot about MCQs.
There are several important concepts that you have to prepare for scoring full marks in this lesson.
What are the Graphs?
Graphs are the visual or 2D or 3D representation of a given data or information prepared with different bars or lines or points on a sheet of paper. These graphs generally are used for comparing different business situations or fall and rise in goods in markets, etc.
What are the Different Types of Graphs?
There are different types of graphs in the syllabus of class 8 like:
Bar graphs
Pie charts
Histograms
Double bar graphs
Line graphs, etc
You may be asked questions in the form of graph representation as MCQs also. So, always have a clear understanding of graphs.
About Linear Graphs
Questions from this area are generally asked in the five marks section. Graph questions for grade 8 are maximum from this part of the chapter.
Graph Theory
MCQs on graph theory with answers are given and asked from this concept and are easy to attempt if understood well. You have to have a complete idea about dependent and independent variables and the role of the x-axis and y-axis. The dependent variable is placed on the y-axis(vertical), and the independent variable is on the x-axis(horizontal).
Important Example Question In CLASS 8 MATHEMATICS Introduction to Graphs - MCQs
Q1. Which Form of Graph is Used to Compare Parts of a Whole?
A. Pie graph
B. Bar graph
C. Histogram
Answer: Option B – Pie Graph
Q2. Which Type of Graph Represents Data that Changes Continuously Over a Course of Time?
A. Bar graph
B. Line graph
C. Pie graph
Answer: Option B – Line Graph
Q3. What Does a Graph Represent by Connecting Point (–1, –1), (0, 0) and (3, 3)
A. A triangle
B. A straight line not crossing across origin.
C. a straight line crossing across origin
Answer: Option C - a straight line crossing across origin
Q4. What is the Point that Lies in the 3rd Quadrant Called?
A. (5, 5)
B. (5, -5)
C. (-5, -5)
Answer: Option C (-5, -5)
Q5. What is the Point that Represents the X-axis Called?
A. x = 0
B. y= 0
C. x = y
Answer: Option B; Y = 0
FAQs on Introduction to Graphs: Class 8 Maths MCQs
1. What are the basic components of a Cartesian graph as per the Class 8 syllabus?
A Cartesian graph, also known as a coordinate graph, is built on a two-dimensional plane. Its basic components are:
The x-axis: The horizontal line on the graph.
The y-axis: The vertical line on the graph.
The Origin: The point where the x-axis and y-axis intersect, denoted by the coordinates (0, 0).
Quadrants: The four regions that the two axes divide the plane into.
These components work together to define the exact location of any point on the plane.
2. What are the main types of graphs explained in the NCERT Class 8 Maths chapter, Introduction to Graphs?
The chapter 'Introduction to Graphs' primarily focuses on visually representing data. The main types of graphs covered are:
Bar Graph: Used to show comparison among discrete categories.
Pie Chart (or Circle Graph): Used to compare parts of a whole, where the whole circle represents 100%.
Histogram: A special type of bar graph used to show frequencies of data arranged in continuous class intervals. There are no gaps between the bars.
Line Graph: Used to display data that changes continuously over a period of time.
3. How do you decide whether to use a line graph or a bar graph to display a given set of data?
The choice depends on the type of data you are representing. You should choose a line graph when you want to show a trend or how data changes continuously over time, such as tracking a patient's temperature every hour. In contrast, you should use a bar graph to compare quantities across different, separate categories, such as the number of students who prefer different fruits. A bar graph is ideal for discrete data, while a line graph is best for continuous data.
4. What is the fundamental difference between a bar graph and a histogram?
The fundamental difference lies in the type of data they represent. A bar graph is used to plot discrete, separate categories (e.g., colours, cities), and the bars have gaps between them to show this separation. A histogram, on the other hand, is used to plot the frequency of numerical data that is grouped into continuous ranges or intervals (e.g., age groups 0-10, 10-20, 20-30). In a histogram, the bars have no gaps between them, signifying the continuous nature of the data.
5. How are coordinates, like (4, 5), used to pinpoint the exact location of a point on a graph?
Coordinates, written as an ordered pair (x, y), provide a precise address for a point on a Cartesian plane. The first number, the x-coordinate, tells you how far to move horizontally from the origin (0,0) along the x-axis. The second number, the y-coordinate, tells you how far to move vertically along the y-axis. For the point (4, 5), you start at the origin, move 4 units to the right along the x-axis, and then move 5 units up, parallel to the y-axis.
6. In a real-world scenario, what does a straight, horizontal line on a distance-time graph signify?
A straight, horizontal line on a distance-time graph signifies a state of no change in position. This means that while time is progressing (moving forward on the horizontal axis), the distance from the starting point is remaining constant. For example, this could represent a car that has stopped at a traffic light or a person standing still for a period. Essentially, it indicates that the object's speed is zero.
7. Can any set of data be represented by a single straight line on a graph? Explain the condition required.
No, not just any set of data can be represented by a single straight line. For data points to form a straight line, they must have a linear relationship. This means that the rate of change between the two variables being plotted (e.g., cost and quantity) must be constant. If you plot the points and can draw a single straight line that passes through all of them, the graph is called a linear graph.
