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 
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
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
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 
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 
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 = 
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 
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 ?
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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.
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. = 
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 
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.
NCERT Class 8 Mathematics Solutions
Chapter 02 - Linear Equations in One Variable
Chapter 03 -Understanding Quadrilaterals
Chapter 04 - Practical Geometry
Chapter 06 - Squares and Square Roots
Chapter 07 - Cubes and Cube Roots
Chapter 08 - Comparing Quantities
Chapter 09 - Algebraic Expressions and Identities
Chapter 10 - Visualising Solid Shapes
Chapter 12 - Exponents and Powers
Chapter 13 - Direct and Indirect proportions
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