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About Introduction to Graphs — Class 8 CBSE

Read and draw bar graphs, line graphs, pie charts, and coordinate plots. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 12). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Introduction to Graphs

  • Introduction to Graphs: Understanding Data Visually
  • Bar Graphs & Histograms: Comparing and Grouping Data
  • Line Graphs: Showing Change Over Time
  • Pie Charts: Representing Parts of a Whole
  • Summary & Application: Choosing the Right Graph

Interactive lesson · about 15 minutes · checkpoint question after every unit

Introduction to Graphs — solved examples for Class 8 CBSE

Example 1easy

Which of the following statements best describes the primary use of graphs in mathematics and real-world applications?
  1. A)To perform complex calculations quickly without a calculator.
  2. B)To store large amounts of numerical data in a compact form.
  3. C)To visually represent data and show relationships or trends, making interpretation easier.
  4. D)To write down data in an organized table for future reference.

Step-by-step solution

  1. Graphs are powerful tools because they provide a visual summary of data.
  2. This visual representation makes it significantly easier to identify patterns, compare different values, and understand relationships or trends that might be difficult to spot when data is presented only in tables or text.

Answer: To visually represent data and show relationships or trends, making interpretation easier.

Example 2medium

A bar graph represents the number of bicycles sold by a shop over five months: January (120), February (150), March (180), April (160), May (200). If the sales target for the first quarter (Jan-Mar) was 500 bicycles, by what percentage did the shop miss or exceed its target?
  1. A)10% Missed
  2. B)10% Exceeded
  3. C)20% Missed
  4. D)20% Exceeded

Step-by-step solution

  1. Calculate total sales for the first quarter (January to March):
  2. Total Sales = Sales in Jan + Sales in Feb + Sales in Mar
    TotalSales=120+150+180=450bicyclesTotal Sales = 120 + 150 + 180 = 450 bicycles
  3. Compare total sales with the target:
  4. Target = 500 bicycles. Actual Sales = 450 bicycles. Since Actual Sales < Target, the shop missed the target.
  5. Calculate the difference:
  6. Difference = Target - Actual Sales = 500 - 450 = 50 bicycles
  7. Calculate the percentage missed with respect to the target:
  8. Percentage Missed = (Difference / Target) × 100
    PercentageMissed=(50/500)×100=(1/10)×100=10Percentage Missed = (50 / 500) × 100 = (1/10) × 100 = 10%

Answer: 20% Missed

Example 3hard

Points A(1, 1), B(5, 1), C(5, 4), and D(1, 4) are plotted on a Cartesian plane. What is the area of the figure ABCD?
  1. A)6 square units
  2. B)9 square units
  3. C)12 square units
  4. D)16 square units

Step-by-step solution

  1. Plot the given points: A(1,1), B(5,1), C(5,4), D(1,4).
  2. By observing the coordinates, we can see that the x-coordinates of A and D are 1, and B and C are 5, indicating vertical sides. The y-coordinates of A and B are 1, and C and D are 4, indicating horizontal sides. This forms a rectangle.
  3. Calculate the length and width: Length AB = |5 - 1| = 4 units. Width AD = |4 - 1| = 3 units.
  4. The area of a rectangle is Length × Width. So, Area = 4 × 3 = 12 square units.

Answer: 12 square units

Practice questions on Introduction to Graphs

  1. Q1.easy

    In a Cartesian coordinate system, the horizontal number line is called the _____, and the vertical number line is called the _____. Their intersection point is known as the _____.
    1. A)x-axis, y-axis, origin
    2. B)y-axis, x-axis, origin
    3. C)origin, x-axis, y-axis
    4. D)x-axis, origin, y-axis
    Show answer

    Answer: x-axis, y-axis, origin

    Hint: Recall the standard labels for the two perpendicular lines that form the basis of a coordinate plane and their meeting point.

  2. Q2.easy

    A point P is located 3 units to the right of the y-axis and 5 units above the x-axis. What are the coordinates of point P?
    1. A)(5, 3)
    2. B)(3, 5)
    3. C)(-3, 5)
    4. D)(5, -3)
    Show answer

    Answer: (3, 5)

    Hint: Remember that the first coordinate (x-value) indicates horizontal position relative to the y-axis, and the second coordinate (y-value) indicates vertical position relative to the x-axis.

  3. Q3.easy

    Which of the following is a key difference between a bar graph and a histogram?
    1. A)Bar graphs use vertical bars, while histograms exclusively use horizontal bars.
    2. B)Bar graphs are primarily used for continuous data, while histograms are used for discrete data.
    3. C)In a bar graph, the bars do not touch each other, while in a histogram, the bars always touch.
    4. D)Histograms always have a title, while bar graphs typically do not.
    Show answer

    Answer: In a bar graph, the bars do not touch each other, while in a histogram, the bars always touch.

    Hint: Consider the type of data each graph represents and how that affects the visual presentation of the bars.

  4. Q4.medium

    In a survey of 360 students, their favorite sports are represented by a pie chart. If 30% of students prefer Cricket, 25% prefer Football, and 15% prefer Basketball, what is the central angle for the sector representing students who prefer Hockey, if Hockey is the remaining sport?
    1. A)72°
    2. B)90°
    3. C)108°
    4. D)120°
    Show answer

    Answer: 108°

    Hint: Find the total percentage for the known sports first. The remaining percentage will be for Hockey. Then convert this percentage into a central angle.

  5. Q5.medium

    A histogram shows the heights of 200 plants in a nursery. The class intervals are: 0-10 cm (20 plants), 10-20 cm (45 plants), 20-30 cm (70 plants), 30-40 cm (40 plants), 40-50 cm (25 plants). How many plants have a height of 20 cm or more but less than 40 cm?
    1. A)70
    2. B)110
    3. C)115
    4. D)135
    Show answer

    Answer: 110

    Hint: Identify the class intervals that fall within the specified range (20 cm or more, but less than 40 cm) and sum their frequencies.

  6. Q6.medium

    A line graph depicts the maximum daily temperature of two cities, City A and City B, over a week. Both lines start at 25°C on Monday. On Tuesday, City A rises to 28°C while City B rises to 27°C. On Wednesday, City A drops to 26°C while City B rises to 29°C. On Thursday, City A rises to 30°C and City B drops to 28°C. What is the difference between the highest temperature recorded for City A and the lowest temperature recorded for City B during these four days?
    1. A)1°C
    2. B)2°C
    3. C)3°C
    4. D)4°C
    Show answer

    Answer: 1°C

    Hint: List all temperatures for City A and City B separately. Then identify the highest for City A and the lowest for City B, and find their difference.

  7. Q7.hard

    Two linear graphs are represented by the equations y = 2x - 3 and y = -x + 6. At what point do these two graphs intersect?
    1. A)(1, -1)
    2. B)(3, 3)
    3. C)(2, 1)
    4. D)(4, 2)
    Show answer

    Answer: (3, 3)

    Hint: The intersection point is where both equations share the same x and y values. Set the expressions for y equal to each other to find x.

  8. Q8.hard

    A car starts from City A at 8 AM and travels towards City B at a constant speed of 60 km/h. Another car starts from City A at 9 AM and travels towards City B at a constant speed of 90 km/h. If both cars follow the same straight path, at what time will the second car overtake the first car?
    1. A)10:00 AM
    2. B)10:30 AM
    3. C)11:00 AM
    4. D)11:30 AM
    Show answer

    Answer: 11:00 AM

    Hint: First, calculate the distance the first car has covered by the time the second car starts. Then, consider their relative speed to determine the time it takes to close the gap.

  9. Q9.hard

    A bar graph shows the number of students who chose different sports: Cricket (150), Football (X), Hockey (100), Basketball (Y). If the total number of students is 625, and the number of students who chose Football is twice the number who chose Basketball, find the number of students who chose Basketball.
    1. A)50
    2. B)75
    3. C)100
    4. D)125
    Show answer

    Answer: 125

    Hint: Set up an equation using the total number of students and the given relationship between the number of students choosing Football and Basketball.

These are 9 of the 60 questions available for Introduction to Graphs. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.