Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.1 Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths 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?

- What was the patient’s temperature at 1 p.m.?
- When was the patient’s temperature 38.5°C?
- The patient’s temperature was the same two times during the period given. What were these two times?
- What was the temperature at 1:30 p.m.? How did you arrive at your answer?
- During which periods did the patients’ temperature showed an upward trend?

Solution:

- The patient’s temperature at 1 p.m. was 36.5°C.
- The patient’s temperature was 38.5°C at 12 noon.
- The patient’s temperature was same at 1 p.m. and 2 p.m.
- The patient’s temperature at 1:30 p.m. was 36.5°C [because the temperature of the patient was constant (i.e. 36.5°C) from 1 p.m. to 2 p.m.]
- The temperature of patient showed an upward trend during 9 a.m. to 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 and (ii)2006?

(b) What were the sales in (i) 2003 and (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) Company’s sale in 2002 was ₹ 4 crores.

(ii) Company’s sale in 2006 was ₹ 8 crores.

(b) (i) Company’s sale in 2003 was ₹ 7 crores.

(ii) Company’s sale in 2005 was ₹ 10 crores.

(c) Difference in sales between 2002 and 2006

= [₹ 8 crores] – [₹ 4 crores]

= ₹ 4 crores

(d) The greatest difference between the sales was in two consecutive years 2004 and 2005.

Question 3.

For an experiment in Botany, two different plants, plant A and B were grown under similar laboratory conditions. Their height 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 and (ii) 3 weeks?

(b) How high was plant B after

(i) 2 weeks and (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:

The plant A was 9 cm high.

(b) (i) After 2 weeks:

The plant B was 7 cm high.

(ii) After 3 weeks:

The plant B was 10 cm high.

(c) During the 3rd week, the plant A grew (9 cm – 7 cm), i.e., 2 cm.

(d) The plant B grew 10 cm – 7 cm = 3 cm from the end of 2nd week to the end of the 3rd week.

(e) The growth of the plant A:

During the 1st week = 2 cm – 0 cm = 2 cm, During the 2nd week = 7 cm – 2 cm = 5 cm

During the 3rd week = 9 cm – 7 cm = 2 cm

Thus, during the 2nd week, the plant A grew the most.

(f) The growth of the plant B during:

the 1st week = 1 cm – 0 cm = 1 cm, the 2nd week = 7 cm – 1 cm = 6 cm

the 3rd week = 10 cm – 7 cm = 3 cm

Thus, the plant-B grew the least in the first week.

(g) Both the plants have shown almost the same height at the end of the 2nd 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 was the same as the 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) Difference between the actual temperature and the forecast temperature on

Monday = 17.5°C – 15°C = 2.5°C

Tuesday = 20°C – 20°C = 0°C

Wednesday = 30.0°C – 25°C = 5°C

Thursday = 22.5°C – 15°C = 7.5°C

Friday = 15°C – 15°C = 0°C

Saturday = 30°C – 25°C = 5°C

Sunday = 35°C – 35°C = 0°C

Thus, the maximum difference was on Thursday.

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) Linear graph to show snow fall received in different years:

(b) Linear graph showing population of men and women in a village in different years:

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) The time is taken along the x – axis. The scale along x – axis is 4 units = 1 hour.

(b) Total travel time = 8 a.m. to 10 a.m. and further 10:30 a.m. to 12 noon = 3\(\frac{1}{2}\) hours

(c) Distance of the merchant from the town = 22 km

(d) Yes, the stopage time = 10:00 a.m. to 10.30 a.m.

(e) His fastest ride is between 8:00 a.m. and 9:00 a.m.

Question 7.

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

Solution:

In case of (iii), there are an infinite number of temperature at the same time which is not possible.

∴ Case (iii) does not represent a time – temperature graph.