NCERT Solutions Class 8 Mathematics
Chapter – 15 (Introduction to Graphs)
The NCERT Solutions in English Language for Class 8 Mathematics Chapter – 15 Introduction to Graphs Exercise 15.1 has been provided here to help the students in solving the questions from this exercise.
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 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 pm, the patient’s temperature was 36.5°C.
(b) The patient’s temperature was 38.5°C at 12 noon.
(c) The patient’s temperature was same at 1 p.m. and 2p.m
(d) The graph between the times 1 pm and 2 pm is parallel to the x-axis. The temperature at 1 pm and 2 pm is 36.5°C. So, the temperature at 1:30 pm is 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.
(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) In the year 2005, there was the greatest difference between the sales and compared to its previous year, which is (Rs. 10 crores – Rs. 6 crores) = Rs. 4 crores.
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) 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) The plant A was 7 cm high after 2 weeks
(ii) After 3 weeks it was 9 cm high
(b)
(i) Plant B was also 7 cm high after 2 weeks
(ii) After 3 weeks it was 10 cm high
(c) Plant A grew = 9 cm – 7 cm = 2cm during 3rd week.
(d) Plant B grew during end of the 2nd week to the end of the 3rdweek = 10 cm – 7 cm = 3 cm
(e) Growth of plant A during 1st week = 2 cm – 0 cm = 2 cm
Growth of plant A during 2nd week = 7 cm – 2 cm = 5 cm
Growth of plant A during 3rd week = 9 cm – 7 cm = 2 cm
Therefore, plant A grew the most, i.e. 5 cm, during the 2nd week.
(f) Growth of plant B during 1st week = 1 cm – 0 cm = 1 cm
Growth of plant B during 2nd week = 7 cm – 1 cm = 6 cm
Growth of plant B during 3rd week = 10 cm – 7 cm = 3 cm
Therefore, plant B grew the least, i.e. 1cm, during the 1st week.
(g) Yes. At the end of the 2nd week, the heights of both plants were the same i.e. 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?
Solution –
(a) On Tuesday, Friday and Sunday, the forecast temperature was same as the actual temperature.
(b) The maximum forecast temperature was 35oC.
(c) The minimum actual temperature was 15oC.
(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.
(b) Population (in thousands) of men and women in a village in different years.
Solution –
(a) Consider “Years” along x-axis and “Days” along y-axis. Using given information, linear graph will look like:
(b) Consider “Years” along x-axis and “No. of Men and No. of Women” along y-axis (2 graphs). Using given information, linear graph will look like:
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?
Solution –
(a) Scale taken for the time axis i.e. x-axis is 4 units = 1 hour
(b) The person travelled during the time 8 a.m. – 11:30 a.m. Therefore, the person took hours to travel.
(c) It was 22 km far from the town.
(d) Yes, 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.
Solution –
(i) This can be a time-temperature graph, as the temperature can increase with the increase in time.
(ii) This can be a time-temperature graph, as the temperature can decrease with the decrease in time.
(iii) This cannot be a time-temperature graph since different temperatures at the same time are not possible
(iv) It is a time-temperature graph. It is showing constant temperature.
