NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs

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Updated at 2021-02-11


NCERT solutions for class 8 Maths Chapter 15 Introduction To Graphs Exercise 15.1

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 pm?

(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 the two times?

(d) What was the temperature at 1:30 pm? How did you arrive at your answer?

(e) During which periods did the patient’s temperature show an upward trend?



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a) At 1 pm the patient’s temperature was 36.5oC

(b) At 12:00 noon the patient’s temperature was 38.5oC.

(c) At 1 pm and 2 pm the patient's temperature was 36.5oC.

(d) At 1:30 pm the temperature was 36.5oC. We took 1:30 p.m which is the mid value of 1 pm. and 2 pm and proceeded perpendicularly upwards to meet the horizontal line showing 36.5oC.

(e) The temperature showed upwards trend in the following durations from 9 am to 10 am, 10 am to 11 am and 2pm to 3 pm

2.The following line graph shows the yearly sales figures for a manufacturing company.


(a) What were the sales in

(i) 2002

(ii) 2006?

(b) What were the sales in

(i) 2003

(ii) 2005?

(c) Compute the difference between the sales in 2002 and 2006.

(d) In which year was there the greatest difference between the sales as compared to its previous year?



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a)

(i) The sales in the year 2002 was ? 4 crore.

(ii) The sales in the year 2006 was ? 8 crore.

(b)

(i) The sales in the year 2003 was ? 7 crore.

(ii) The sales in the year 2005 was ? 10 crore.

(c) Comparision between the sales in 2002 and 2006 = ? 8 crore – ?4 crore = ? 4 crore.



(d) Year 2005 had the greatest difference between the sales as compared to its previous year is the

3.For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph :


(a) How high was Plant A after (i) 2 weeks (ii) 3 weeks?

(b) How high was Plant B after (i) 2 weeks (ii) 3 weeks?

(c) How much did Plant A grow during the 3rd week?

(d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?

(e) During which week did Plant A grow most?

(f) During which week did Plant B grow least? *

(g) Were the two plants of the same height during any week shown here? Specify.



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a) The height of the plant A
(i) after 2 weeks was 7 cm.

(ii) after 3 weeks was 9 cm.

(b) The height of the plant B


(i)after 2 weeks was 7 cm

(ii)after 3 weeks was 10 cm.

(c) The plant A grew up 2 cm during the 3rd week.

(d) The plant B grew up 3 cm from the end of the 2nd week to the end of the 3rd week.

(e) During second week, plant A grows the most.

(f) During the first week, plant B grows the most.

(g) The height of the two plants were same at the end of the 2nd week.

4.The following graph shows the temperature forecast and the actual temperature for each day of a week.


(a) On which days was the forecast temperature the same as the actual temperature?

(b) What was the maximum forecast temperature during the week?

(c) What was the minimum actual temperature during the week?

(d) On which day did the actual temperature differ the most from the forecast temperature?



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a) Tuesday, Friday and Sunday were the days on which the forecast temperature was the same as the actual temperature.
(b) 35oC is the maximum forecast temperature during the week.

(c) 17.5oC is the minimum actual temperature during the week.

(d) Thursday was the day with the the most differed temperature from actual and the forecast temperature

5.Use the tables below to draw linear graphs.
(a) The number of days a hillside city recovered show in different years.



(b)Population (in thousands) of men and women in a village in different years.



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a) For plotting the graph, take years on the x-axis and the days on the y-axis. MArk the pairs (2003, 8), (2004,10), (2005, 5) and (2006, 12) as points and then join them byline segments as shown below


(b)For plotting the graph, take years on the x-axis and the population (in thousands) on the y-axis.Mark the ordered pair as points and join them as dotted lines for the population of men and the solid line for the population of women.


6.A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph :
(a) What is the scale taken for the time axis?

(b) How much time did the person take for the travel?

(c) How far is the place of the merchant from the town?

(d) Did the person stop on his way? Explain.

(e) During which period did he ride fastest?




NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a) Scale taken for the time axis is : 4 units = 1 hour.
(b) The person took 3 hours 30 minutes i.e.,312 hours for the total journey.

(c) The merchant’s place is 22 km far from the town.

(d) Yes; this is indicated by the horizontal part of the graph that the person stopped in the duration from 10 a.m. to 10.30 a.m.

(e)He rode faster between 8 a.m. and 9 a.m.

7.Can there be a time-temperature graph as follows? Justify your answer.





NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(i) It represents a time-temperature graph because as per the graph the temperature increases as the time increase.
(ii) It shows a time-temperature graph because the temperature decreases as the time increases.

(iii) It does not represent a time-temperature graph because the temperature is increasing but the time remains constant which is not possible.

(iv) It represents a time-temperature graph because the temperature remains constant when the time is increasing.

NCERT solutions for class 8 Maths Chapter 15 Introduction To Graphs Exercise 15.2

1.Plot the following points on a graph sheet. Verify if they lie on a line.
(a) A (4, 0), B(4, 2), C(4, 6), D(4, 2.5)

(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

(c) K(2, 3), L(6, 3), M(5, 5), N (2, 5)



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :


Yes, all the coordinate points lie on a line



Yes, all the coordinate points lie on a line.



No, the coordinate points do not lie on a line.

2.Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :


We can see that CD is the required line passing through the points A(2, 3), B (3, 2) which meets the x-axis at C(5, 0) and y-axis at D(0, 5).

3.Write the coordinates of the vertices of each of these adjoining figures.



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

We have the required coordinates as follows:
For rectangle OABC are:

O(0, 0), A(2, 0), B(2, 3), C(0, 3)

For parallelogram PQRS:

P(4, 3), Q(6, 1), R(6, 5), S(4, 7)

For triangle KLM :

K(10, 5), L(7, 7), M (10, 8).

4.State whether True or False. Correct that is false.
(i) A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis.

(ii) A point whose y-coordinate is zero and x-coordinate is 5 will lie on y-axis.

(iii) The coordinates of the origin are (0, 0).



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(i) True
(ii) False because the point will lie on the x-axis if the y-coordinate is zero and x-coordinate is 5.

(iii) True

NCERT solutions for class 8 Maths Chapter 15 Introduction To Graphs Exercise 15.3

1.Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples



(b) Distance travelled by car.



(i) How much distance did the car cover during the period 7:30 am to 8 am?

(ii) What was the time when the car had covered a distance of 100 km since its start?

(c) Interest on deposits for a year.



(i) Does the graph pass through the origin?

(ii) Use the graph to find the interest on ? 2500 for a year.

(iii) To get an interest of t 280 per year, how much money should be deposited?



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :

(a)For plotting the graph take ‘Number of apples, on the x-axis and ‘Cost of apples (in ?)’ on the y-axis and start marking the given data in order:


(b) (i) The distance covered by the car during the period 7:30 am to 8 am is 120 km – 100 km = 20 km.

(ii) The car had covered a distance of 100 km at 7:30 am, .


(c) (i) Yes

(ii) The interest on ? 2500 is ? 200 for 1 year.

(iii) To earn the interest of ? 280 ,? 3500 should be invested.


2.Draw the graph for the following:



NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs


Answer :



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