NCERT Solutions for Class 8 Maths Chapter 15: Introduction to Graphs - Exercise 15.1

Exercise 15.1

Refer to page 3 for Exercise 15.1 in the PDF

1. The following graph shows the temperature of a patient in a hospital, recorded every hour.

(Image Will Be Updated Soon)

(a) What was the patient’s temperature at 1 p.m.?

Ans: The temperature at 1 p.m. is denoted by the5th

dot. Now observe horizontally, the temperature assigned with the 5th dot is 36.5℃.

Therefore, the temperature at 1 p.m. is 36.5℃.

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

Ans: 38.5℃ lies in between 38℃ and 39℃. Observing the horizontal line aligned with 38.5℃,  the 4th dot lies on the very same line. Now observe the 4th dot vertically, the 4th dot is aligned with 12 noon.

Therefore at 12 noon , patient’s temperature was 38.5℃

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

Ans: Temperature for different times will be the same if dots aligned with them lie on the same horizontal line. In the given graph, 5th and 6th dots lie on the same horizontal line. Observe these dots vertically, 5th dot is aligned with 1 p.m. and 6th dot is aligned with 2 p.m.

Therefore at 1 p.m. and 2 p.m. the patient's temperature was the same.

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

Ans: 1:30 p.m. lies in between 1 p.m. and 2 p.m. Because temperature for the period 1 p.m. – 2 p.m. is a constant, 36.5℃, therefore temperature at 1:30 p.m. is 36.5℃.

(e) During which periods did the patient’s temperature show an upward trend?

Ans: The patient shows an upward trend in the temperature in the following period:

9 a.m. – 10 a.m. , 10 a.m. – 11 a.m. and 2 p.m. – 3 p.m.

2. The following line graph shows the yearly sales figure for a manufacturing company:

(Image Will Be Updated Soon)

(a) What were the sales in (i) 2002 (ii) 2006?

Ans:
(i) Year 2002 sales are denoted by 1st dot. Observing the 1st dot horizontally, sales made in 2002 were 4 crores.

(ii) Year 2006 sales are denoted by 5th dot. Observing the 5th dot horizontally, sales made in 2006 were 8 crores.

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

Ans:
(i) Year 2003 sales are denoted by 2nd  dot. Observing the 2nd  dot horizontally, sales made in 2003 were 7 crores.

(ii) Year 2005 sales are denoted by 4th dot. Observing the 4th  dot horizontally, sales made in 2005 were10 crores.

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

Ans: \[{\text{Sale in year 2002}} = 4{\text{ crores}}\]

\[{\text{Sale in year 2006}} = 8{\text{ crores}}\]

${\text{Difference in sales of 2002 and 2006}} = 8{\text{ crores}} - 4{\text{ crores}}$

${\text{Difference in sales of 2002 and 2006}} = 4{\text{ crores}}$

Thus , the difference between the sales  in 2002 and 2006 is 4 crores.

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

Ans: Years 2004 and 2006 will not be taken into consideration because sales for these years have dropped from the sales made in previous years.

${\text{Difference in sales of 2002 and 2003}} = {\text{Sales in 2003}} - {\text{Sales in 2002}}$

${\text{Difference in sales of 2002 and 2003}} = 7{\text{ crores}} - 4{\text{ crores}}$

${\text{Difference in sales of 2002 and 2003}} = 3{\text{ crores}}$

${\text{Difference in sales of 2004 and 2005}} = {\text{Sales in 2005}} - {\text{Sales in 2004}}$

${\text{Difference in sales of 2004 and 2005}} = 10{\text{ crores}} - 6{\text{ crores}}$

${\text{Difference in sales of 2004 and 2005}} = 4{\text{ crores}}$

Difference in sales  of 2004 and 2005 is more than the difference in sales of 2003 and 2002, therefore in 2005, the greatest difference between the sales compared to its previous year was there.

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:

(Image Will Be Updated Soon)

(a) How high was Plant A after (i) 2 weeks (ii) 3weeks?

Ans:
(i)3rd dot on the dashed line denotes height of plant A after 2 weeks.  Observe the 3rd dot on the dashed line horizontally, the height of plant A after 2 weeks is 7 cm.

(ii) 4th  dot on the dashed line denotes height of plant A after 3 weeks.  Observe the 4th  dot on the dashed line horizontally, the height of plant A after 3 weeks is 9 cm.

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

Ans:
(i) 3rd dot on the solid line denotes height of plant B after 2 weeks.  Observe the 3rd dot on the solid line horizontally, the height  of plant B after 2 weeks is 7 cm.

(ii) 4th  dot on the solid line denotes height of plant B after 3 weeks.  Observe the 4th  dot on the solid line horizontally, the height of plant B after 3 weeks is 10 cm.

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

Ans: \[{\text{Growth of Plant A during 3rd week}} = {\text{Growth at the end of 3rd week}} - {\text{Growth at the end of 2nd week}}\]

\[{\text{Growth of Plant A during 3rd week}} = 9{\text{ cm}} - 7{\text{ cm}}\]

\[{\text{Growth of Plant A during 3rd week}} = 2{\text{ cm}}\]

Thus, the growth of plant A during the 3rd week is 2 cm.

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

Ans: \[{\text{Growth of Plant B at the end of 2nd week}} = 7{\text{ cm}}\]

\[{\text{Growth of Plant B at the end of 3rd week}} = 10{\text{ cm}}\]

\[{\text{Growth of Plant B from the end of 2nd week to 3rd week}} = 10{\text{ cm}} - 7{\text{ cm}}\]

\[{\text{Growth of Plant B from the end of 2nd week to 3rd week}} = 3{\text{ cm}}\]

Thus, the plant grows by 3 cm from the end of the 2nd week to the end of the 3rd week.

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

Ans: \[{\text{Growth of Plant A in the 1st week}} = 2{\text{ cm}} - 0{\text{ cm}}\]

\[{\text{Growth of Plant A in the 1st week}} = 2{\text{ cm}}\]

\[{\text{Growth of Plant A in the 2nd week}} = 7{\text{ cm}} - 2{\text{ cm}}\]

\[{\text{Growth of Plant A in the 2nd week}} = 5{\text{ cm}}\]

\[{\text{Growth of Plant A in the 2nd week}} = 9{\text{ cm}} - 7{\text{cm}}\]

\[{\text{Growth of Plant A in the 2nd week}} = 2{\text{ cm}}\]

Growth of plant A is maximum in the 2nd  week ,i.e.,5 cm . Thus, Growth of plant A is most in the 2nd week.

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

Ans: \[{\text{Growth of Plant B in the 1st week}} = 1{\text{ cm}} - 0{\text{ cm}}\]

\[{\text{Growth of Plant B in the 1st week}} = 1{\text{ cm}}\]

\[{\text{Growth of Plant B in the 2nd week}} = 7{\text{ cm}} - 1{\text{ cm}}\]

\[{\text{Growth of Plant B in the 2nd week}} = 6{\text{ cm}}\]

\[{\text{Growth of Plant B in the 3rd week}} = 10{\text{ cm}} - 6{\text{ cm}}\]

\[{\text{Growth of Plant B in the 3rd week}} = 4{\text{ cm}}\]

Growth of plant B is minimum in the 1st week, i.e., 1 cm. Thus, the growth of plant B is least in the 1st week.

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

Ans: At the end of 2nd week the growth of plant A and B is the same, i.e., 7 cm.

4. The following graph shows the temperature forecast and the actual temperature for each day of a week:

(Image Will Be Updated Soon)

(a) On which days was the forecast temperature the same as the actual temperature?

Ans: On the following days the forecast temperature was the same as the actual temperature:

Tuesday, Friday and Sunday.

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

Ans: 7th dot with respect to forecast temperature line graph lies at maximum height ,i.e., it represents the maximum forecast temperature . Observing horizontally , the maximum forecast temperature was 35℃.

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

Ans:  1st and 5th dots with respect to actual temperature line graph lies at minimum height ,i.e., they represent the minimum actual temperature . Observing horizontally , the minimum actual temperature was 15℃.

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

Ans: \[{\text{Difference between actual and forecast temperature on Monday}} = {\text{Actual temperature}} - {\text{Forecast temperature}}\]

\[{\text{Difference between actual and forecast temperature on Tuesday}} = {\text{Actual temperature}} - {\text{Forecast temperature}}\]

\[{\text{Difference between actual and forecast temperature on Wednesday}} = {\text{Actual temperature}} - {\text{Forecast temperature}}\]

\[{\text{Difference between actual and forecast temperature on Thursday}} = {\text{Forecast temperature}} - {\text{Actual temperature}}\]

\[{\text{Difference between actual and forecast temperature on Friday}} = {\text{Actual temperature}} - {\text{Forecast temperature}}\]

\[{\text{Difference between actual and forecast temperature on Saturday}} = {\text{Forecast temperature}} - {\text{Actual temperature}}\]

\[{\text{Difference between actual and forecast temperature on Sunday}} = {\text{Actual temperature}} - {\text{Forecast temperature}}\]

Difference between actual and forecast temperature is maximum on Thursday, i.e., 7.5℃. Thus, on Thursday actual temperature differs the most from the forecast temperature.

5. Use the tables below to draw linear graphs:

(a) The number of days a hillside city received snow in different years.

Ans: Take years on the horizontal line(x-axis) and days on the vertical line(y-axis).

Take scale for x-axis as \[{\text{2 units }} = {\text{1 year}}\]and for y-axis as \[1{\text{ unit }} = 2{\text{ days}}\]

Now each piece of data is shown by a point on the square grid. Then join these point to get the desired linear graph

(Image Will Be Updated Soon)

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

Ans: Take years on the horizontal line(x-axis) and population on the vertical line(y-axis).

Take scale for x-axis as \[{\text{2 units }} = {\text{1 year}}\] and for y-axis as \[1{\text{ unit }} = 0.5{\text{ thousand}}\].

The solid line will represent the number of men and the dashed line will represent the number of women.

Now each piece of data is shown by a point on the square grid. Then join these point to get the desired linear graph:

(Image Will Be Updated Soon)

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:

(Image Will Be Updated Soon)

(a) What is the scale taken for the time axis?

Ans: The difference between the intervals on the time axis is 1 hour, therefore the scale taken for the time axis is \[{\text{4 units }} = {\text{1 hour}}\].

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

Ans: The person travelled from 8 a.m. to 11:30 a.m. ,i.e., \[11:30 - 8 = 3:30{\text{ hours}}\].

Thus, the person takes 3 hours 30 minutes to travel.

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

Ans: The person travelled 22 km to deliver the parcel to the merchant. Thus, the place of the merchant is 22 km far away from the town.

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

Ans: The person should have stopped  for a period if the distance left  is a constant\[{\text{Distance travelled between 8 a}}{\text{.m}}{\text{. and 9 a}}{\text{.m}}{\text{.}} = 10{\text{ km}} - 0{\text{ km}}\] throughout the interval ,i.e., line between two points is a straight line(the distance left is same).

The linear graph for the interval 10 a.m. – 10:30 a.m. is a straight line, therefore the person stopped on his way from 10 a.m. to 10 a.m.

(e) During which period did he ride fastest?

Ans: \[{\text{Distance travelled between 8 a}}{\text{.m}}{\text{. and 9 a}}{\text{.m}}{\text{.}} = 10{\text{ km}} - 0{\text{ km}}\]

\[{\text{Distance travelled between 8 a}}{\text{.m}}{\text{. and 9 a}}{\text{.m}}{\text{.}} = 10{\text{ km}}\]

\[{\text{Distance travelled between 9 a}}{\text{.m}}{\text{. and 10 a}}{\text{.m}}{\text{.}} = 16{\text{ km}} - 10{\text{ km}}\]

\[{\text{Distance travelled between 9 a}}{\text{.m}}{\text{. and 10 a}}{\text{.m}}{\text{.}} = 6{\text{ km}}\]

\[{\text{Distance travelled between 10 a}}{\text{.m}}{\text{. and 10:30 a}}{\text{.m}}{\text{.}} = {\text{ 16 km}} - 16{\text{ km}}\]

\[{\text{Distance travelled between 10 a}}{\text{.m}}{\text{. and 10:30 a}}{\text{.m}}{\text{.}} = {\text{ 0 km}}\]

\[{\text{Distance travelled between 10:30 a}}{\text{.m}}{\text{. and 11:30 a}}{\text{.m}}{\text{.}} = {\text{ 22 km}} - 16{\text{ km}}\]

\[{\text{Distance travelled between 10:30 a}}{\text{.m}}{\text{. and 11:30 a}}{\text{.m}}{\text{.}} = {\text{ 6 km}}\]

Distance travelled between 8 a.m. and 9 a.m. is the most , therefore he rides fastest during 8 a.m. to 9 a.m.

7. Can there be a time temperature graph as follows? Justify your answer:

(i)

(Image Will Be Updated Soon)

Ans: In the given time-temperature graph temperature is increasing with time, which can be the case. Thus, this can be the time-temperature graph.

(ii)

(Image Will Be Updated Soon)

Ans: In the given time-temperature graph temperature is decreasing with time, which can be the case. Thus, this can be the time-temperature graph.

(iii)

(Image Will Be Updated Soon)

Ans: In the given time-temperature graph it is shown that there were different temperatures at the same time, which is not possible. Thus, this cannot be a time-temperature graph.

(iv)

(Image Will Be Updated Soon)

Ans: In the given time-temperature graph temperature remains constant with time, which can be the case. Thus, this can be the time-temperature graph.

NCERT Solutions For Class 8 Maths Chapter 15 Introduction To Graphs Exercise 15.1

Opting for the NCERT solutions for Ex 15.1 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 15.1 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 8 students who are thorough with all the concepts from the Subject Introduction to Graphs textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 8 Maths Chapter 15 Exercise 15.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

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