Important Questions for CBSE Class 8 Maths Chapter 15 - Introduction to Graphs

Very Short Answer Type Questions: (1 Marks)

1. The point where $x - $ axis and $y - $ axis meet is called $\_\_\_\_\_\_\_\_\_\_$?

Ans: Origin

2. In which quadrant does the point $s( - 3,2)$ lie?

(a) II

(b) I

(c) III

(d) IV

Ans: (a) II

3. On which axis does the point $(0, - 6)$ lie

(a) ${\text{x}} - $ axis

(b) ${\text{y}} - $ axis

(c) origin

(d) None of these

Ans: (b) $y - $ axis

4. Perpendicular distance of the point $(2,3)$ from ${\text{x}} - $ axis is

(a) $2$

(b) $3$

(c) $0$

(d) None of these

Ans: (b) $3$

5. A pictorial representation of data in the form of rectangular bars to show comparison among categories is called $\_\_\_\_\_\_\_\_\_\_$?

Ans: Bar graph

6. The co-ordinates of origin is

(a) $({\text{x}},0)$

(b) $(0,y)$

(c) $(0,0)$

(d) None of these

Ans: (c) $(0,0)$

7. What is a pie graph?

Ans: Data can be represented by dividing a circle into sectors. This type of representation of data is called a pic graph. It shows us the relation of parts to the whole.

Short Answer Type Questions: (2 Marks)

8. Find the co-ordinates of the points $A,{\text{ }}B,{\text{ }}C,{\text{ }}D$ from the graph

Ans: The co-ordinates of the point

$A = ( - 1,3)$

$B = (3,3)$

$C = ( - 2,3)$

$D = ( - 1, - 2)$

9. If a man moves $6$ units right due (east) from point $A$, then find the co-ordinates of his new position.

Ans: The position of point $A = (3,0)$

If a man moves $6$ units right from point $A$ then new position of man will be at $B = (6,3)$.

10. In a class of $40$ students, the marks obtained in maths subject (out of $50$) are as given below

Draw histogram?

Ans:

11. Find the time taken by a body to cover $30$ meters. Hence find speed?

Ans: Time taken to cover a distance of $30\;{\text{m}} = 6$ seconds

${\text{Speed }} = \dfrac{{{\text{ Distance covered }}}}{{{\text{ Time taken }}}}$

${\text{Speed}} = \dfrac{{30m}}{{6s}} = 5m{s^{ - 1}}$

12. Plot the following points. Verify if they lie on a line? $(1,3),{\text{ }}(2,3),{\text{ }}(3,3),{\text{ }}(4,3)$

Ans: We plot the given point on a graph to check if they lie on line

Yes, they lie on a line.

Short Answer Type Questions: (3 Marks)

13. Draw a line passing through $(3,1)$ and $(1,3)$. Find the co-ordinates of the points at which this line meets the $x - $ axis and $y - $ axis.

Ans: The co-ordinates of the point on $x - $ axis and $y - $ axis is where the line meets axes.

$x - $ axis, $P = (4,0)$

$y - $ axis, $Q = (0,4)$

14. Following graph gives the movement of a car from a town $A$ to town $D$. Study the graph and answer the following questions:

(a) What is the distance between town $A$ and town $D$ ?

Ans: $A = (5.5,100) = ({X_1},{Y_1})$

$D = (11.5,500) = ({X_2},{Y_2})$

(b) At what time did car start from town $A$?

Ans: Car starts from town $A$ by $5:30$ am.

(c) Where did the car stop and for what duration?

Ans: Car stopped at town $B$ by $1$ hour duration.

15. Plot the points $A(4,0)$ and $B(0,3)$ on the graph. Also find the length of hypotenuse of triangle $AOB$

Ans: $OA = x - $ co-ordinate of point $A = 4$

${\text{OB}} = y - $ co-ordinate of point $B = 3$

Hypotenuse $AB = \sqrt {{4^2} + {3^2}} $

$AB = \sqrt {16 + 9} $

$AB = \sqrt {25} $ 

$AB = 5.$

16. Make a table of values for the function $y = 4x$, From the table find the value's of $y$ when $x = 4$ and $x = 5$

Ans: $y = 4x$

At $x = 4$, $y = 4(4) = 16$

$x = 5$, $y = 4(5) = 20$

17. State true or false

(a) A point whose $x - $co-ordinates is zero and $y - $ co-ordinates is non-zero will lie on the $y - $axis

(b) The co-ordinates of the origin are $(0,0)$

(c) A point whose $y - $co-ordinates is zero and $x - $ co-ordinates is $4$ will lie on the $y - $axis

Ans:

(a) True

(b) True

(c) False

18. From the given graph, compute the difference between the sales of $2013$ and $2015$

In which year sales are high?

Ans:

Sales in $2015 - 12$ million

Sales in $2013 - 8$ million

The difference between the sales in $2015$ and 2013

$ = 12 - 8 = 4$ million

In $2015$ the sales are high.

19. Draw the histogram to represent the following data and define linear graph.

Ans:

A line graph which is a whole unbroken line is called a linear graph.

20. Plot the points $A(2,3),{\text{ }}B(5,3),{\text{ }}C(5,5)$ and $D(2,5)$ on graph. Connect the points in that order. So as to get a closed figure ${\text{ABCD}}$. What type of figure do you get?

Ans:

The figure ${\text{ABCD}}$ obtained is a rectangle.

Long Answer Type Questions: (5 Marks)

21. Reena deposited Rs$12,000$ in a bank at the rate of $10\% $ per annum. Draw a linear graph showing the relationship between the time and simple interest. Also find the simple interest for $4$ years.

Ans: $P = 12,000$

$R = 10\% $

Simple interest for one year $ = \dfrac{{PTR}}{{100}}$

$ = 12000 \times \dfrac{{10}}{{100}} \times 1$

$ = 1200$

Simple interest after $4$ years is $4800$.

22. Hundred students from a certain locality use different modes of travelling to school as given below. Draw a bar graph which is maximum mode of travel?

Ans: Scale: on $x - $ axis $1{\text{cm}} = 1$ unit

On $y - $ axis $1\;{\text{cm}} = 8$ units

Maximum mode of travel is bus.

23. Study the following graph and answer the following questions

Ans:

(a) Which year has better rainfall?

Ans: $2007$

(b) On how many days the rainfall was same?

Ans: For ${8^{{\text{th }}}}$ July and ${9^{{\text{th }}}}$ July of $2007$ the rainfall was same.

(c) Name the only date on which $2008$ got more rainfall?

Ans: On ${6^{{\text{n }}}}$ July of $2008$ rainfall is max $(7\;{\text{cm}})$

(d) On which date the difference between the rainfall of the $2$ years was biggest?

Ans: ${8^{{\text{hy }}}}$ July

(e) What is the difference between the rainfall of $2007$ and $2008$ on July ${8^{{\text{th }}}}$ ?

Ans: $3\;{\text{cm}}$ of difference

On July ${8^{{\text{th }}}}$ in $2007 = $ Rainfall $ = 5{\text{cm}}$

On July ${8^{{\text{th }}}}$ in $2008 = $ Rainfall $ = 2\;{\text{cm}}$

Difference $ = 5 - 2 = 3\;{\text{cm}}$

24. If $y = {x^2}$, then draw a graph.

Ans:

The graph is drawn as follows:

Scale: On $x - $ axis $5$ units $ = 1{\text{cm}}$

On $y - $ axis $10$ units $ = 1{\text{cm}}$

25. A train is moving at a constant speed of $60\;{\text{km}}{{\text{h}}^{ - 1}}$. Draw a distance - time graph

(a) How far will it travel in $2$ hours $30$ minutes

(b) Find the time required to cover a distance of $260\;{\text{km}}.$

Ans:

Speed of train$ = 60\;{\text{km}}/{\text{hr}}$

Table for distance - time graph is as follows:

Scale:

On $x - $ axis $1\;{\text{cm}} = 1{\text{hr}}$

On $y - $ axis $1\;{\text{cm = }}60\;{\text{km}}$

(a) Distance covered in $2$ hours $30$ minutes$ = 150\;{\text{km}}$

(b) Time required to cover a distance of $260\;{\text{km}} = 4.33$ hrs.

What are the Benefits of Important Questions from Vedantu for Class 8 Maths Chapter 15 - Introduction to Graph

• Focus on key topics for efficient studying.

• Prepares students for exams and reduces anxiety.

• Reinforces understanding of fundamental concepts.

• Teaches effective time management.

• Enables self-assessment and progress tracking.

• Strategic approach for higher scores.

• Covers a wide range of topics for comprehensive understanding.

• Supports exam preparation and boosts confidence.

Conclusion

Reviewing all the crucial questions for Class 8 Maths Chapter 15 - “Introduction to Graph” provides students with a solid grasp of the chapter's topics. The extra and important questions for Class  8 Maths Chapter 15 - “Introduction to Graph” engage in a concept-focused discussion encompassing all chapter themes. This question-and-answer method proves time-saving during exam prep, offering an efficient way to revise the chapter and enhance understanding. Practicing these important questions streamlines preparation and boosts confidence for the upcoming exams.