MP Board Class 8th Maths Solutions Chapter 15 Introduction to Graphs Ex 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 patient’s temperature showed an upward trend?
Solution:
(a) At 1 p.m. patient’s temperature was 36.5°C.
(b) At 12 noon the patient’s temperature was 38.5°C.
(c) The patient’s temperature was 36.5°C at 1 p.m. and 2 p.m.
(d) The patient’s temperature was 36.5°C at 1.30 p.m. (because the temperature of the patient was constant from 1 p.m. to 2 p.m.). The point between 1 p.m. and 2 p.m. on the x-axis and equidistant from them will represent 1 : 30 p.m. Similarly, the point on the y-axis, between 36°C and 37°C and equidistant from them will represent 36.5° C.
(e) 9 a.m. to 10 a.m., 10 a.m. to 11 a.m. and 2 p.m. to 3 p.m.
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?
Solution:
(a) (i) In 2002 company’s sales were ₹ 4 crores.
(ii) In 2006 company’s sales were ₹ 8 crores.
(b) (i) The sales of a manufacturing company in 2003 were ₹ 7 crores.
(ii) The sales of a manufacturing company in 2005 were ₹ 10 crores.
(c) The difference between the sales in 2002 and 2006.
= Sales in 2006 – Sales in 2002
= ₹ 8 crores – ₹ 4 crores = ₹ 4 crores.
(d) In year 2005, the difference between the sales was greatest as compared to its previous year.
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.
Solution:
(a) (i) After 2 weeks the height of plant A was 7 cm.
(ii) After 3 weeks the height of plant A was 9 cm.
(b) (i) After 2 weeks the height of plant B was 7 cm.
(ii) After 3 weeks the height of plant B was 10 cm.
(c) During the 3rd week plant A grew (9 – 7) cm = 2 cm.
(d) The plant B grew from the end of 2nd week to the end of 3rd week
= 10 cm – 7 cm = 3 cm
(e) The plant A grew most during second week.
(f) The plant B grew least during first week.
(g) Yes, at the end of second week.
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?
Solution:
(a) The forecast temperature is the same as actual temperature on : Tuesday, Friday and Sunday.
(b) The maximum forecast temperature during the week was 35°C.
(c) The minimum actual temperature during the week was 15°C.
(d) On Thursday, the actual temperature differed 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.
Solution:
(a) By using a given information we draw a line graph, where the horizontal line i.e. x-axis shows the year and the vertical line i.e. y-axis shows the number of days.
(b) The horizontal line i.e. x-axis shows the year and the vertical line i.e. y-axis shows the number of men and number of women.
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?
Solution:
(a) 4 units = 1 hour is the scale taken for the time axis.
(b) Time taken by a person for the travel = (1 +1 + 1+ \(\frac{1}{2}\)) hours = 3\(\frac{1}{2}\) hours.
(c) The place of the merchant from the town is at a distance of 22 km.
(d) Yes, this is indicated by the horizontal part of the graph from 10 a.m. -10.30 a.m. where the stability of a distance has been shown.
(e) Between 8.00 a.m. – 9.00 a.m. he rode the fastest.
Question 7.
Can there be a time-temperature graph as follows? Justify your answer.
Solution:
Figure (i) shows temperature is increasing over time.
Figure (ii) shows temperature is decreasing over time.
Figure (iii) is not a possible time – temperature graph. because, at the same time, temperature can’t be different.
Figure (iv) shows temperature is constant over time