These Class 8 Maths Extra Questions Chapter 15 Introduction to Graphs will help students prepare well for the exams.
Class 8 Maths Chapter 15 Extra Questions Introduction to Graphs
Extra Questions of Introduction to Graphs Class 8
Question 1.
Two friends are planning for a trip in a rented car. The line graph below shows the rent to be paid for a car they have finalized, for different number of days.
a) If they are ready to spend Rs 14000 on renting the car, for a maximum of how many FULL DAYS can the car be rented ?
b) If the same pattern is continued in the graph, how much money should be paid to rent the
same car for 7 days ?
Solution:
a) Spending money = Rs. 14,000
The car can be rented of FULL DAYS = 5 days.
b) From 1st day to pay each day = 2,000
6 Days = 15,000
∴ 7 Days = 15,000 + 2000 = Rs. 17,000
Introduction to Graphs Class 8 Extra Questions
Question 1.
(A graph on “performance’’)
The given graph (Fig) represents the total runs scored by two batsmen A and B, during each of the ten different matches in the year 2007. Study the graph and answer the following questions.
i) What information is given on the two axes ?
ii) Which line shows the runs scored by batsman A?
iii) Were the run scored by them same in any match in 2007 ? If so, in which match ?
iv) Among the two batsmen, who is steadier ? How do you judge it ?
Solution:
i) The horizontal axis (or the x-axis) indicates the matches played during the year 2007. The vertical axis (or the y-axis) shows the total runs scored in each match.
ii) The dotted line shows the runs scored by Batsman A. (This is already indicated at the top of the graph).
iii) During the 4th match, both have scored the same number of 60 runs. (This is indicated by the point at which both graphs meet).
iv) Batsman A has one great “peak” but many deep “valleys”. He does not appear to be consistent. B, on the other hand has never scored below a total of 40 runs, even though his highest score is only 100 in comparison to 115 of A. Also A has scored a zero in two matches and in a total of 5 matches he has scored less than 40 runs. Since A has a lot of ups and downs, B is a more consistent and reliable batsman.
Question 2.
The given graph (Fig) describes the distances of a car from a city P at different times when it is travelling from City P to City Q, which are 350 km apart. Study the graph and answer the following :
i) What information is given on the two axes?
ii) From where and when did the car begin its journey ?
iii) How far did the car go in the first hour?
iv) How far did the car go during (i) the 2nd hour ? (ii) the 3rd hour ?
v) Was the speed same during the first three hours ? How do you know it ?
vi) Did the car stop for some duration at any place ? Justify your answer.
vii) When did the car reach City Q ?
Solution:
i) The horizontal (x) axis shows the time. The vertical (y) axis shows the distance of the car from City P.
ii) The car started from City P at 8 a.m.
iii) The car travelled 50 km during the first hour. [This can be seen as follows.
At 8 a.m. it just started from City P. At 9 a.m. it was at the 50th km (seen from graph).
Hence during the one-hour time bet-ween 8 a.m. and 9 a.m. the car travelled 50 km].
iv) The distance covered by the car during
a) the 2nd hour (i.e., from 9 am to 10 am) is 100 km, (150 – 50).
b) the 3rd hour (i.e.. from 10 am to 11 am) is 50 km (200 – 150).
v) From the answers to questions (iii) and (iv), we find that the speed of the car was not the same all the time. (In fact the graph illustrates how the speed varied).
vi) We find that the car was 200 km away from city P when the time was 11 a.m. and also at 12 noon. This shows that the car did not travel during the interval 11 a.m. to 12 noon. The horizontal line segment representing “travel” during this period is illustrative of this fact.
vii) The car reached City Q at 2 p.m.
Question 3.
Plot the point (4, 3) on a graph sheet. Is it the same as the point (3, 4) ?
Solution:
Locate the X, Y axes, (they are actually number lines!). Start at O (0, 0). Move 4 units to the right; then move 3 units up, you reach the point (4,3). From Fig, you can see that the points (3, 4) and (4, 3) are two different points.
Question 4.
From Fig, choose the letter(s) that indicate the location of the points given below:
i) (2, 1)
ii) (0, 5)
iii) (2, 0)
Also write
iv) The coordinates of A.
v) The coordinates of F.
Solution:
i) (2, 1) is the point E (It is not D!).
ii) (0, 5) is the point B
iii) (2, 0) is the point
iv) point A is (4, 5)
v) F is (5.5, 0)
Question 5.
Plot the following points and verify if they lie on a line. If they lie on a line, name it.
i) (0, 2), (0, 5), (0, 6), (0, 3.5)
Solution:
These lie on a line. The line is y-axis.
ii) A (1, 1), B (1, 2), C (1, 3), D (1, 4)
Solution:
These lie on a line. The line is AD.
(You may also use other ways of naming it). It is parallel to the y-axis
iii) K (1, 3), L (2, 3), M (3, 3), N (4, 3)
Solution:
These lie on a line. We can name it as KL or KM or MN etc. It is parallel to x- axis
iv) W (2, 6), X (3, 5), Y (5, 3), Z (6, 2)
Solution:
These lie on a line. We can name it as XY or WY or YZ etc.
Note that in each of the above cases, graph obtained by joining the plotted points is a line. Such graphs are called linear graphs.
Question 6.
(Quantity and Cost)
The following table gives the quantity of petrol and its cost.
| No. of Litres of petrol | 10 | 15 | 20 | 25 |
| Cost of petrol in ₹ | 500 | 750 | 1000 | 1250 |
Plot a graph to show the data.
Solution:
i) Let us take a suitable scale on both the axes (Fig).
ii) Mark number of litres along the horizontal axis.
iii) Mark cost of petrol along the vertical axis.
iv) Plot the points : (10,500), (15,750), (20,1000), (25,1250).
v) Join the points.
Question 7.
(Principal and Simple Interest)
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
a) the annual interest obtainable for an investment of ₹ 250.
b) the investment one has to make to get an annual simple interest of ₹ 70.
Solution:
Steps to follow :
1. Find the quantities to be plotted as Deposit and SI.
2. Decide the quantities to be taken on x-axis and on y-axis.
3. Choose a scale.
4. Plot points.
5. Join the points.
We get a table of values.
| Deposit (in ₹) | 100 | 200 | 300 | 500 | 1000 |
| Annual S.I. (in ₹) | 10 | 20 | 30 | 50 | 100 |
i) Scale : 1 unit = ₹ 100 on horizontal axis; 1 unit = ₹ 10 on vertical axis.
ii) Mark Deposits along horizontal axis.
iii) Mark Simple Interest along vertical axis.
iv) Plot the points : (100, 10), (200, 20), (300, 30), (500, 50) etc.
v) Join the points. We get a graph that is a line (Fig).
a) Corresponding to ₹ 250 on horizontal axis, we get the interest to be ₹ 25 on vertical axis.
b) Corresponding to ₹ 70 on the vertical axis, we get the sum to be ₹ 700 on the horizontal axis.
Question 8.
(Time and Distance)
Ajit can ride a scooter constantly at a speed of 30 kms/hour. Draw a time-distance graph for this situation. Use it to find
i) the time taken by Ajit to ride 75 km.
ii) the distance covered by Ajit in 3\(\frac{1}{2}\) hours.
Solution:
| Hours of ride | Distance covered |
| 1 hour | 30 km |
| 2 hours | 2 × 30 km = 60 km |
| 3 hours | 3 × 30 km = 90 km |
| 4 hours | 4 × 30 km = 120 km and so on. |
We get a table of values.
| Time (in hours) | 1 | 2 | 3 | 4 |
| Distance covered (in km) | 30 | 60 | 90 | 120 |
i) Scale : (Fig)
Horizontal: 2 units = 1 hour Vertical: 1 unit =10 km
ii) Mark time on horizontal axis.
iii) Mark distance on vertical axis.
iv) Plot the points: (1, 30), (2, 60), (3, 90), (4, 120).
v) Join the points. We get a linear graph.
a) Corresponding to 75 km on the vertical axis, we get the time to be 2.5 hours on the horizontal axis. Thus 2.5 hours are needed to cover 75 km.
b) Corresponding to 3\(\frac{1}{2}\) hours on the horizontal axis, the distance covered is 105 km on the vertical axis.