NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

NCERT solutions for class 8 chapter 15 introduction to graphs-Exercise: 15.1

Question:1(a) 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

Answer:

(a) The patient's temperature at 1 p.m is celsius.

Question:1(b) The following graph shows the temperature of a patient in a hospital  recorded every hour.

When was the patients temperature ?

Answer:

(b) The patients temperature is at 12 noon.

Question:1(c) The following graph shows the temperature of a patient in a hospital  recorded every hour.

Answer:

(c)  The patients temperature was the same two times during the period given these two times are 1 p.m. and 2 p.m.

Question:1(d) The following graph shows the temperature of a patient in a hospital  recorded every hour.

What was the temperature at 1:30 p.m? How did you arrive at your answer?

Answer:

(d) The temperature  at 1:30 p.m is celsius. The temperature at 1 p.m. to 2 p.m. is same  i.e. celsius so it is also same as at 1:30 p.m is celsius.

Question:1(e) The following graph shows the temperature of a patient in a hospital  recorded every hour.

During which periods did the patients temperature showed an upward trend ?

Answer:

(e) The patients temperature showed an upward trend-  9 am to 10 am., 10 am. to 11 am. and 2pm to 3pm

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

What are the sales in (1) 2002  (2) 2006 ?

Answer:

(a) The sales in

(1) 2002  = 4 crore

(2) 2006 = 8 crore

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

What are the sales in (1) 2003  (2) 2005 ?

Answer:

(b) The sales in

(1) 2003  = 7 crore

(2) 2005  = 10 crore

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

Compute the difference between sales in 2002 and 2006

Answer:

(c) The difference between sales in 2002 and 2006 .

Question:2(d) The following line graph shows the yearly sales figure for a manufacturing company

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

Answer:

(d) The greatest difference between the sales as compared to its previous year is between 2004 and 2005.

Question:3(a) 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 result are shown by the following graph

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

Answer:

(a) The Plant A after

(i) 2 weeks  = 7 cm height.

(ii) 3 weeks = 9 cm height.

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

Answer:

(b) The Plant B after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 10cm height.

Question:3(c) 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.

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

Answer:

(c)The Plant A grow during the 3rd week =

Question:3(d) 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.

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

Answer:

(d)The Plant B grow from the end of the 2nd week to the end of the 3rd week height.

Question:3(e) 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.

During which week did Plant A grow most?

Answer:

(e)The week in which Plant A grow most during 2nd week = cm height.

Question:3(f) 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.

During which week did Plant B grow least?

Answer:

(f) The week in which Plant B grow least is during first week =

Question:3(g) 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.

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

Answer:

(g) At the end of second week, heights of both plants are same.

Question:4(a) The following graph shows the temperature forecast and the actual temperature for each day of a week.
On which days was the forecast temperature the same as the actual temperature?

Answer:

(a)  The forecast temperature is the same as the actual temperature on Tuesday, Friday and Sunday.

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

What was the maximum forecast temperature during the week?

Answer:

(b) The maximum forecast temperature during the week was on sunday.

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

What was the minimum actual temperature during the week ?

Answer:

(c) The minimum actual temperature during the week  is .

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

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

Answer:

(d) The actual temperature differs the most from the forecast temperature on Thursday.

Question:5(a) Use the tables below to draw linear graphs.
The number of days a hill side city received snow in different years.

Answer:

(a) The linear graph of data given above is as shown :

Question:5(b) Use the tables below to draw linear graphs.

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

Answer:

(b) The graph of data given above is as shown :

Taking years as x-axis and population as y- axis.

Question:6(a) 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.
What is the scale taken for the time axis?

Answer:

(a) The scale taken for the time axis (x-axis) is 4 units = 1 hour.

Question:6(b) 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.

How much time did the person take for the travel ?

Answer:

(b) The person travels from 8 a.m. to 11:30 a.m.

the person travels hours.

Question:6(c) 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 .

How far is the place of the merchant from the town  ?

Answer:

(c) The place of the merchant from the town is 22 km away.

Question:6(d) 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.

Did the person stop on his way? Explain.

Answer:

(d) From 10 a.m. to 10:30 a.m. ,there is a horizontal line which states that person stops from 10 a.m. to 10:30 a.m.

Question:6(e) 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 .

During which period did he ride fastest ?

Answer:

(e) From graph we can observe person travels maximum distance from 8 a.m. to 9 a.m.

Hence,person travels fastest from 8 a.m. to 9 a.m.

Question:7(i) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(i)  Yes, there can be a time-temperature graph as shown with the increase in time, temperature also increases.

Question:7(ii) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(ii) Yes, it is possible that with increase in time temperature decreases.

Question:7(iii) Can there be a time-temperature graph as follows? Justify your answer.

Answer:

(iii) No,this type of graph is not possible because different temperature at same time are not posiible.

Question:7(iv) Can there be a time-temperature graph as follows? Justify your answer

Answer:

(iv) Yes, it is possible i.e. same temperature at different time  is possible.

NCERT solutions for class 8 maths chapter 15 introduction to graphs-Exercise: 15.2

Question:1(i) Plot the following points on a graph sheet. Verify if they lie on a line

A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

Answer:

(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

Question:1(b) Plot the following points on a graph sheet. Verify if they lie on a line

P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

Answer:

(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

The graph is as shown :

Question:1(c) Plot the following points on a graph sheet. Verify if they lie on a line

K(2, 3), L(5, 3), M(5, 5), N(2, 5)

Answer:

(iii) K(2, 3), L(5, 3), M(5, 5), N(2, 5)

The graph is as shown :

Question:2 Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at
which this line meets the x-axis and y-axis.

Answer:

As shown below is graph :

The coordinates of the points at which this line meets the x-axis and y-axis are

Question:3 Write the coordinates of the vertices of each of these adjoining figures.

Answer:

The coordinates of vertices are:

, , ,

, , ,

, ,

Question:4(i) State whether True or False. Correct that are false.
A point whose x coordinate is zero and y-coordinate is non-zero will
lie on the y-axis .

Answer:

(i) True .A point whose x coordinate is zero and y-coordinate is non-zero will
lie on the y-axis. = here, y is variable.

Question:4(ii) State whether True or False. Correct that are false.

A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

Answer:

(ii) False.Point does not lie on y-axis.A point whose y coordinate is zero and x-coordinate is 5 will not lie on
y-axis.

Question:4(iii) State whether True or False. Correct that are false.

The coordinates of the origin are (0, 0).

Answer:

(iii)True. The coordinates of the origin are (0, 0).

NCERT solutions for class 8 maths chapter 15 introduction to graphs topic 15.3 some applications

Question:1 In the above example, use the graph to find how much petrol can be purchased for Rs 800.

Answer:

From the graph given below we can say that for  Rs 800 we can buy 16 litres.

Question:2 A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph Try a case of direct variation?

Answer:

Taking a case of direct variation the graph is as shown below.

Taking sum deposite as 100,200,300,500 ,1000.

and  10% Simple Interest (S.I.).

NCERT solutions for class 8 maths chapter 15 Introduction to Graphs-Exercise: 15.3

Question:1(a) Draw the graphs for the following tables of values, with suitable scales on the axes.
Cost of apples

Answer:

(a) Cost of apples

Question:1(b) Draw the graphs for the following tables of values, with suitable scales on the axes . Distance travelled by a car.

(i)How much distance did the car cover during the period 7.30 a.m. to 8 a.m?

Answer:

(b)

(i)From the above graph,the distance the car cover during the period 7.30 a.m. to 8 a.m is

Question:1(b) Draw the graphs for the following tables of values, with suitable scales on the axe.

Distance travelled by a car.

(ii) What was the time when the car had covered a distance of 100 km since it’s star

Answer:

(b)

(ii)From above graph we conclude that at 7:30 a.m.,  the car had covered a distance of 100 km since it’s start.

Question:1(c) Interest on deposits for a year .

(i) Does the graph pass through the origin?

Answer:

(c)

Taking x axis as 1000 units = 1 box and y axis as 100 units = 1 box.

(i)Yes, the graph pass through the origion.

Question:1(c) Interest on deposits for a year

(ii) Use the graph to find the interest on Rs 2500 for a year.

Answer:

(c)

(ii) Using the graph, the interest on Rs 2500 for a year is Rs 200.

Question:1(c) Interest on deposits for a year .

(iii) To get an interest of Rs 280 per year  how much money should be deposited ?

Answer:

(iii) From the graph,to get an interest of Rs 280 per year  Rs 3500 money should be deposited.

Question:2(i) Draw a graph for the following Is it a linear graph

Answer:

From the above graph ,we conclude that graph is linear.

Question:2(ii) Draw a graph for the following

Is it a linear  graph?

Answer:

From above graph,we conclude that graph is not linear.