NCERT Solutions for Class 8 Maths Chapter 15 Introduction To Graphs

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?

Answer :

(a) At 1 pm the patient’s temperature was \(36.5^o\)C

(b) At 12:00 noon the patient’s temperature was \(38.5^o\)C.

(c) At 1 pm and 2 pm the patient's temperature was \(36.5^o\)C.

(d) At 1:30 pm the temperature was \(36.5^o\)C. 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 \(36.5^o\)C.

(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?

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.

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?

Answer :

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

(c) \(17.5^o\)C 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.

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?

Answer :

(a) Scale taken for the time axis is : 4 units = 1 hour.
(b) The person took 3 hours 30 minutes i.e.,\(3\frac { 1 }{ 2 }\) 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.

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.