## Chapter 15 Introduction to Graphs Exercise 15.1

Question 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 1.30 p.m.? How did you arrive at your answer?

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

Answer:

a) The patient’s temperature was 36.5°C at 1 p.m.

b) The patient’s temperature was 38.5°C at 12 noon.

c) The patient’s temperature was same at 1 p.m. and 2 p.m.

d) 36.5°C; Since 1.30 p.m. lies in between 1 - 2 p.m. therefore the temperature is same as that on 1 pm and 2 pm i.e. 36.5°C. Hence the temperature at 1.30 p.m. is 36.5°C.

e) During 9 a.m. to 10 a.m. and 10 a.m. to 11 a.m., the temperature showed upwards trend.

Question 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 2002 was ₹4 crore.

ii) The sales in 2006 was ₹8 crore.

b)

i) The sales in 2003 was ₹7 crore.

ii) The sales in 2005 was ₹10 crore.

c)

Sales in 2002 = ₹ 4 crore

Sales in 2006 = ₹ 8 crore

Difference = 8 - 4 = ₹ 4 crore

d) In the year 2005, there was the greatest difference between the sales and compared to its previous year, which is (₹10 crore - ₹6 crore) = ₹4 crore.

Question 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)

i) Plant A was 7 cm long after 2 weeks.

ii) Plant A was 9 cm long after 3 weeks.

b)

i) Plant B was 7 cm long after 2 weeks.

ii) Plant B was 10 cm long after 3 weeks.

c)

Plant A height during 2nd week = 7 cm

Plant A height during 3rd week = 9 cm

= 9 - 7 = 2 cm

Therefore, the Plant A grew 2 cm long during the 3rd week.

d)

Plant B height during 2nd week = 7 cm

Plant B height during 3rd week = 10 cm

= 10 - 7 = 3 cm

Therefore, the Plant B grew 3 cm long during the 3rd week.

e) Plant A grew the highest during 2nd week.

f) Plant B grew the least during 1st week.

g) Yes, at the end of the 2nd week, Plant A and B were of the same height i.e. 7 cm.

Question 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) On 3 days i.e. Tuesday, Friday and Sunday, the forecast temperature was same as the actual temperature.

b) The maximum forecast temperature was 35°C.

c) The minimum actual temperature was 15°C.

d) On Thursday, the actual temperature differ the most from the forecast temperature.

Question 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.

Answer:

a)

b)

Question 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) 4 units = 1 hour is the scale taken for the time axis.

b) 3 1/2 hours

c) The distance between merchant’s house and town is 22 km.

d) Yes, the person stopped on his way. This has been indicated by the horizontal part of the graph (10 a.m. - 10.30 a.m.).

e) He rode the fastest during 8 a.m. to 9 a.m.

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

Answer:

i) can be a time-temperature graph as it is showing the increase in temperature as time increases.

ii) can be a time-temperature graph as it is showing the decrease in temperature as time increases.

iii) can’t be a time-temperature graph as it is showing the sudden increase in temperature which is not possible.

iv) can be a time-temperature graph as it is showing constant temperature as the time increases.

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