Chapter 15: Introduction to Graphs

Q1Written answer

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 patient’s temperature show an upward trend?

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Worked solution

(a) The patient’s temperature was 36.5^oC at 1 p.m.

(b) The patient’s temperature was 38.5^oC at 12 noon.

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

(d) The temperature at 1.30 p.m. is 36.5^oC.

The point between 1p.m.and 2 p.m., the x-axis is equidistant from the two points showing 1 p.m. and 2 p.m. So, it represents 1.30 p.m. Similarly, the point on the y-axis, between 36⁰C and 37⁰C, represents 36.5⁰C.

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

Q2Written answer

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 the previous year?

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Worked solution

(a) The sales in

(i) 2002 was Rs. 4 crores and (ii) 2006 was Rs. 8 crores

(b) The sales in

(i) 2003 was Rs. 7 crores and (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

Q3Written answer

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.

Ncert solution class 8 chapter 15-3

(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 3^rd week?

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

(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.

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Worked solution

(a)

(i) 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 = 2 cm during 3^rd week

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

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

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

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

Q4Multiple choice

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

Ncert solution class 8 chapter 15-4

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Correct option: A

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Worked solution

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

(b) The maximum forecast temperature was 35^oC.

(c) The minimum actual temperature was 15^oC.

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

Q5Written answer

Use the tables below to draw linear graphs

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

Ncert solution class 8 chapter 15-5

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

Ncert solution class 8 chapter 15-6

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Worked solution

(a) Consider “Years” along the x-axis and “Days” along the y-axis. Using the given information, the linear graph will look like this:

Ncert solution class 8 chapter 15-7

(b) Consider “Years” along the x-axis and “No. of Men and No. of Women” along the y-axis (2 graphs). Using the given information, the linear graph will look like this:

Ncert solution class 8 chapter 15-8

Q6Written answer

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?

Ncert solution class 8 chapter 15-9

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Worked solution

(a) 4 units = 1 hour

(b) The person took 3 ½ hours for the 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 9 a.m.

Q7Written answer

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

Ncert solution class 8 chapter 15-10

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Worked solution

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

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

(iii) The graph figure (iii) is not possible since the temperature is increasing very rapidly, which is not possible.

(iv) It is a time-temperature graph. It is showing constant temperature.

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Exercise 15.1