Exercise 15.1 Exercise 15.2 Exercise 15.3

# 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 patient’s temperature show an upward trend?

Sol :

(a) At 1 p.m., 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 2 p.m.

(d) The graph between the times 1 p.m. and 2 p.m. is parallel to the *x*-axis. The temperature at 1 p.m. and 2 p.m. is 36.5°C. So, the temperature at 1:30 p.m. is 36.5°C.

(e) During the following periods, the patient’s temperature showed an upward trend.

9 a.m. to 10 a.m., 10 a.m. to 11 a.m., 2 p.m. to 3 p.m.

Question 2

The following line graph shows the yearly sales figure 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?

Sol :

(a)

(i) In 2002, the sales were Rs 4 crores.

(ii) In 2006, the sales were Rs 8 crores.

(b)

(i) In 2003, the sales were Rs 7 crores.

(ii) In 2005, the sales were Rs 10 crores.

(c)

(i) In 2002, the sales were Rs 4 crores and in 2006, the sales were Rs 8 crores.

Difference between the sales in 2002 and 2006

= Rs (8 − 4) crores = Rs 4 crores

(d) Difference between the sales of the year 2006 and 2005

= Rs (10 − 8) crores = Rs 2 crores

Difference between the sales of the year 2005 and 2004

= Rs (10 − 6) crores = Rs 4 crores

Difference between the sales of the year 2004 and 2003

= Rs (7 − 6) crore = Rs 1 crore

Difference between the sales of the year 2003 and 2002

= Rs (7 − 4) crores = Rs 3 crores

Hence, the difference was the maximum in the year 2005 as compared to its previous year 2004.

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) 3weeks?

(b) How high was Plant B after (i) 2 weeks (ii) 3weeks?

(c) How much did Plant A grow during the 3^{rd} week?

(d) How much did Plant B grow from the end of the 2^{nd} week to the end of the 3^{rd} 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.

Sol :

(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) Growth of plant A during 3^{rd} week = 9 cm − 7 cm = 2 cm

(d) Growth of plant B from the end of the 2^{nd} week to the end of the 3^{rd} week

= 10 cm − 7 cm = 3 cm

(e) Growth of plant A during 1^{st} week = 2 cm − 0 cm = 2 cm

Growth of plant A during 2^{nd} week = 7 cm − 2 cm = 5 cm

Growth of plant A during 3^{rd} week = 9 cm − 7 cm = 2 cm

Therefore, plant A grew the most, i.e. 5 cm, during the 2^{nd} week.

(f) Growth of plant B during 1^{st} week = 1 cm − 0 cm = 1 cm

Growth of plant B during 2^{nd} week = 7 cm − 1 cm = 6 cm

Growth of plant B during 3^{rd} week = 10 cm − 7 cm = 3 cm

Therefore, plant B grew the least, i.e. 1 cm, during the 1^{st} week.

(g) At the end of the 2^{nd} week, the heights of both plants were same.

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?

Sol :

(a) The forecast temperature was 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) The actual temperature differs the most from the forecast temperature 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.

**Year**2003

2004

2005

2006

**Days**8

10

5

12

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

**Year**2003

2004

2005

2006

2007

**Number of men**12

12.5

13

13.2

13.5

**Number of women**11.3

11.9

13

13.6

12.8

Sol :

(a) By taking the years on *x*-axis and the number of days on *y*-axis and taking scale as 1 unit = 2 days on *y*-axis and 2 unit = 1 year on *x*-axis, the linear graph of the given information can be drawn as follows.

(b) By taking the years on *x*-axis and population on *y*-axis and scale as 1 unit = 0.5 thousand on *y*-axis and 2 unit = 1 year on *x*-axis, the linear graph of the given information can be drawn as follows.

Question 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?

Sol :

(a) Scale taken for the time 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) The merchant is 22 km far from the town.

(d) Yes, the person stopped on his way from 10 a.m. to 10: 30 a.m. This is indicated by the horizontal part of the graph.

(e) From the graph, it can be observed that during 8 a.m. to 9 a.m., the person travelled the maximum distance. Thus, the person’s ride was the fastest between 8 a.m. and 9 a.m.

Question 7

Can there be a time temperature graph as follows? Justify you’re answer:

(i) | (ii) |

(iii) | (iv) |

Sol :

(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) This can be a time−temperature graph, as same temperature at different times is possible.