GSEB Class 8 Maths Solutions Chapter 15 Introduction to Graphs Exercise 15.1

Question 1. The following graph shows the temperature of a patient in a hospital, recorded every hour?
1. What was the patient's temperature at 1 p.m.?
2. When was the patient's temperature 38.5°C?
3. The patient's temperature was the same two times during the period given. What were these two times?
4. What was the temperature at 1:30 p.m.? How did you arrive at your answer?
5. During which periods did the patients' temperature showed an upward trend?
Answer:
1. The patient's temperature at 1 p.m. was 36.5°C.
2. The patient's temperature was 38.5°C at 12 noon.
3. The patient's temperature was the same at 1 p.m. and 2 p.m.
4. The patient's temperature at 1:30 p.m. was 36.5°C because the patient's temperature remained constant (i.e. 36.5°C) from 1 p.m. to 2 p.m.
5. The patient's temperature showed an upward trend during two periods: first from 9 a.m. to 10 a.m., then to 11 a.m., and second from 2 p.m. to 3 p.m.
In simple words: Look at the graph to find the patient's temperature at specific times, when it was 38.5°C, and when it stayed the same. Also, identify times when the temperature was going up.

Exam Tip: Always read the graph carefully, noting the units on both axes and any specific points of change or constancy to answer these types of questions accurately.

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?
Answer:
(a) (i) The company's sales in 2002 amounted to Rs 4 crores.
(ii) The company's sales in 2006 were Rs 8 crores.
(b) (i) The company's sales in 2003 amounted to Rs 7 crores.
(ii) The company's sales in 2005 were Rs 10 crores.
(c) The difference in sales between 2002 and 2006 is calculated as:
\( = \) [Rs 8 crores] - [Rs 4 crores]
\( = \) Rs 4 crores
(d) The largest difference between sales occurred in two consecutive years: 2004 and 2005.
In simple words: Check the graph to find sales for specific years, compare sales between years, and find when sales changed the most from the year before.

Exam Tip: When calculating differences from a graph, always ensure you read the values from the correct points on the line and use the appropriate units (e.g., crores of Rupees).

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.
Answer:
(a) (i) After 2 weeks, plant A measured 7 cm high.
(ii) After 3 weeks, plant A measured 9 cm high.
(b) (i) After 2 weeks, plant B measured 7 cm high.
(ii) After 3 weeks, plant B measured 10 cm high.
(c) During the 3rd week, plant A grew (9 cm – 7 cm), which means 2 cm.
(d) Plant B grew (10 cm – 7 cm), meaning 3 cm, from the close of the 2nd week to the close of the 3rd week.
(e) The growth of 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
Therefore, plant A grew the most during the 2nd week.
(f) The growth of 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
Therefore, plant B grew the least in the first week.
(g) Both plants showed nearly the same height at the close of the 2nd week.
In simple words: Use the graph to see how tall each plant was at different weeks and how much they grew each week. Also, find out when they were the same height.

Exam Tip: For growth analysis, calculate the height difference between consecutive weeks to determine the growth in each period, not just the final height.

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?
Answer:
(a) The forecast temperature matched the actual temperature on Tuesday, Friday, and Sunday.
(b) The highest forecast temperature during the week reached 35°C.
(c) The lowest actual temperature during the week was 15°C.
(d) Differences between the actual temperature and the forecast temperature are as follows:
Monday \( = \) \( 17.5^\circ C - 15^\circ C = 2.5^\circ C \)
Tuesday \( = \) \( 20^\circ C - 20^\circ C = 0^\circ C \)
Wednesday \( = \) \( 30.0^\circ C - 25^\circ C = 5^\circ C \)
Thursday \( = \) \( 22.5^\circ C - 15^\circ C = 7.5^\circ C \)
Friday \( = \) \( 15^\circ C - 15^\circ C = 0^\circ C \)
Saturday \( = \) \( 30^\circ C - 25^\circ C = 5^\circ C \)
Sunday \( = \) \( 35^\circ C - 35^\circ C = 0^\circ C \)
Therefore, the largest difference happened on Thursday.
In simple words: Look at the graph to compare daily forecast and actual temperatures, find the highest forecast, lowest actual, and the day with the biggest temperature difference.

Exam Tip: When finding maximum, minimum, or differences, be sure to compare the correct lines (forecast vs. actual) and read the values from the appropriate points on the temperature scale.

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?

Answer:
(a) Linear graph showing snow fall received in different years:
(Graph showing years on x-axis and days of snowfall on y-axis, with points (2003,8), (2004,10), (2005,5), (2006,12) connected by lines)
(b) Linear graph showing population of men and women in a village in different years:
(Graph showing years on x-axis and population in thousands on y-axis, with separate lines for men and women connecting the respective data points)
In simple words: Create line graphs using the given data. For snow, plot years against snowy days. For population, plot years against the number of men and women separately.

Exam Tip: When drawing linear graphs from tables, remember to label both axes clearly, choose an appropriate scale, and plot points accurately before connecting them with straight lines.

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?
Answer:
(a) The time is represented along the x-axis. The scale used for the x-axis is 4 units, which corresponds to 1 hour.
(b) The total travel time taken by the person was from 8 a.m. to 10 a.m. and then from 10:30 a.m. to 12 noon, totaling \( 3\frac{1}{2} \) hours.
(c) The merchant's location is 22 km away from the town.
(d) Yes, the person stopped on the way. The stop occurred between 10:00 a.m. and 10:30 a.m., indicated by a flat line segment on the graph, meaning no distance was covered during this interval.
(e) The fastest part of his ride was between 8:00 a.m. and 9:00 a.m., where the graph line is steepest, showing a greater distance covered in less time.
In simple words: Look at the graph to find the time scale, how long the trip took, the total distance, if there were any stops, and during which hour the person cycled quickest.

Exam Tip: A flat line segment on a distance-time graph signifies a period of no movement (a stop), while a steeper slope indicates a faster speed.

Question 7. Can there be a time-temperature graph as follows? Justify your answer?
(i) (Graph showing temperature increasing linearly with time)
(ii) (Graph showing temperature decreasing linearly with time)
(iii) (Graph showing temperature as a vertical line, implying infinite temperatures at one time)
(iv) (Graph showing temperature constant then increasing, like a step function)
Answer:
In the case of graph (iii), an infinite number of temperature values are shown at the same time, which is not physically possible. A single point in time can only have one specific temperature. Therefore, case (iii) does not represent a valid time-temperature graph.
In simple words: Only graphs where temperature changes predictably over time are real. Graph (iii) shows many temperatures at one exact time, which cannot happen.

Exam Tip: A valid time-temperature graph must be a function, meaning for every point in time, there can only be one corresponding temperature value. Vertical lines on such graphs are physically impossible.