Mathematics – Class 8 – Chapter 15 – Introduction to Graphs – Exercise 15.1 – NCERT Exercise Solution

1. The following graph shows the temperature of a patient in a hospital, recorded every hour.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

(a) What was the patient’s temperature at 1 p.m.?

(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 these two times?

(d) What was the temperature at 1.30p.m.? How did you arrive at your answer?

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

Solution:

(a) At 1 p.m. the patient’s temperature was 36.5oC.

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

(c) At 1 p.m. and 2p.m the patient’s temperature was same.

(d) At 1.30p.m. the temperature is 36.5oC.

I arrived at my answer by following the path i.e. i have taken the mid value of 1 pm. and 2 pm, i.e., 1:30 p.m and proceed perpendicularly upwards to meet the horizontal line showing 36.5°C.

(e) The patient’s temperature showed an upward trend from 9a.m.to 11a.m. and from 2 p.m. to 3 p.m.

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

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

(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 2002and 2006.

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

Solution:

(a) The sales in:

(i)2002 was Rs.4 crores

(ii)2006 was Rs.8 crores

(b) The sales in:

(i)2003 was Rs.7 crores

(ii)2005 was Rs.10 crores.

(c) The difference of sales in 2002 and 2006 = Rs.8 crores–Rs.4 crores

                                                                       = Rs.4 crores

(d) As compared to previous year the greatest difference between the sales was in the year 2005.

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.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

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

(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.

Solution:

(a)

(i) After 2 weeks the plant A was 7 cm high.

(ii) After 3 weeks it’s high was  9 cm.

(b)

(i)Plant B was also 7cm high after 2 weeks

(ii) After 3 weeks it was 10 cm high

(c) During 3rd week Plant A grew =9 cm–7 cm

                                                     = 2cm.

(d) During end of the 2nd week to the end of the 3rdweek Plant B grew                        = 10cm–7cm

= 3cm

(e) During second week Plant A grew the highest.

(f) During first week Plant B grew the least.

(g) Yes. At the end of the second week, plant A and B were of the same height, which is 7 cm.

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?

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

Solution:

(a) On Tuesday, Friday and Sunday, the forecast temperature was same as the actual temperature.

(b) 35oC was the maximum forecast temperature.

(c) 15oC was the minimum actual temperature.

(d) The actual temperature differed the most from the forecast temperature on Thursday.

5. Use the tables below to draw linear graphs

(a) The number of days a hill side city received snow in different years.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

Solution:

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

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

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

Solution:

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution
blue line for no. of Men

red line for no. of women

6. A courier-person cycles from a town to a neighboring 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?

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

Solution:

(a) 4 units = 1hour

(b) The person took 3 ½ hours for the travel.

(c) It was 22 km far from the town.

(d) Yes, person stopped on his way this has been indicated by the horizontal part of the graph. He stayed from 10 a.m. to 10:30 a.m.

(e) He rides the fastest between 8 a.m. and 9a.m.

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

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

It is a time-temperature graph. It is showing the increase in temperature as time increases.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

It is a time-temperature graph. It is showing the decrease in temperature as time increases.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

The given figure is not possible since temperature is increasing very rapidly

which is not possible.

Mathematics - Class 8 - Chapter 15 - Introduction to Graphs - Exercise 15.1 - NCERT Exercise Solution

It is a time-temperature graph. It is showing constant temperature.

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