# 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.?

**Answer:** 36.5˚C

(b) When was the patient’s temperature 38.5° C?

**Answer:** 12:00 Noon

(c) The patient’s temperature was the same two times during the period given. What were these two times?

**Answer:** at 1:00 PM and 2:00 PM

(d) What was the temperature at 1.30 p.m.? How did you arrive at your answer?

**Answer:** Data Insufficient

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

**Answer:** from 10:00 to 11:00 AM and from 2:00 to 3:00 PM

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?

**Answer:** (i) Rs. 4 crores (ii) Rs. 8 crores

(b) What were the sales in (i) 2003 (ii) 2005?

**Answer:** (i) Rs. 7 Crores (ii) Rs. 10 crores

(c) Compute the difference between the sales in 2002 and 2006.

**Answer:** 8-4=4; Sales of 2006 is Rs. 4 crores more than that of 2002

(d) In which year was there the greatest difference between the sales as compared to its previous year?

**Answer:** 2005 sees the greatest jump in sales which clear from the steepest angle between these years.

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?

**Answer:** (i) 7 cm (ii) 9 cm

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

**Answer:** (i) 7 cm (ii) 10 cm

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

**Answer:** 2 cm

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

**Answer:** 3 cm

(e) During which week did Plant A grow most?

**Answer:** from week 1 to week 2 by 5 cm

(f) During which week did Plant B grow least?

**Answer:** In the first week by 1 cm

(g) Were the two plants of the same height during any week shown here? Specify.

**Answer:** Second week both have a height of 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?

**Answer:** Tuesday 20˚ c, Friday 15˚ c and Sunday 35˚ c

(b) What was the maximum forecast temperature during the week?

**Answer:** 35˚ c

(c) What was the minimum actual temperature during the week?

**Answer:** 35˚ c

(d) On which day did the actual temperature differ the most from the forecast temperature?

**Answer:** Thursday, by 7.5˚ c ( Notice the largest gap between two lines)

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 |

**Answer:**

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

Year | 2003 | 2004 | 2005 | 2006 | 2007 |
---|---|---|---|---|---|

No. of men | 12 | 12.5 | 13 | 13.2 | 13.5 |

No. of women | 11.3 | 11.9 | 13 | 13.6 | 12.8 |

**Answer:**

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?

**Answer:** Hours

(b) How much time did the person take for the travel?

**Answer:** 4 hours

(c) How far is the place of the merchant from the town?

**Answer:** 22 kms

(d) Did the person stop on his way? Explain.

**Answer:** Between 10:00 AM to 11:00 AM the line is horizontal, which explains that the person took rest between these timings

(e) During which period did he ride fastest?

**Answer:** Between 8:00 AM and 9:00 AM he traveled 10 kms, (look for the steepest angle made by the line)