3 Marks Question

Question 13 Marks

Draw the graphs for the following tables of values, with suitable scales on the axes.
(i) Cost of apples

Number of apples	1	2	3	4	5
Cost (in ₹)	5	10	15	20	25

(ii) Distance travelled by a car

Time (in h)	6 am	7 am	8 am	9 am
Distances (in km)	40	80	120	160

(a) How much distance did the car cover during the period 7:30 am to 8 am?
(b) What was the time when the car had covered a distance of 100 km , since it's start?
(iii) Interest on deposits for a year.

Deposit (in ₹)	1000	2000	3000	4000	5000
Simple interest (in ₹)	80	160	240	320	400

(a) Does the graph pass through the origin?
(b) Use the graph to find the interest on ₹ 2500 for a year.
(c) To get an interest of ₹ 280 per year, how much money should be deposited?

Answer

(i) To draw the graph for the following table of values, we use the following steps :
Step I Firstly, draw $X$-axis and $Y$-axis and take scale on horizontal 2 units $=$ Number of apples and on vertical 2 units $=$ ₹ $ 5$.
Step II Mark the number of apples along the $X$-axis and mark the cost (in ₹) along the $Y$-axis.
Step III Plot the points $(1,5),(2,10),(3,15),(4,20)$ and $(5,25)$ on graph paper.
Step IV Join these points. Then, we get a required linear graph which is shown below.

(ii) To draw the graph for the given table of values, we use the following steps
Step I Draw $X$-axis and $Y$-axis and take scale, on horizontal axis 3 units = 1h, on vertical axis 1 unit =20 km.
Step II Mark the time (in hours) on horizontal axis and distance (in km ) on vertical axis.
Step III Now, plot the points (6,40),(7,80),(8,120) and (9,160) on graph paper.
Step IV Join these points.
Then, we get a linear graph which is shown below

(a) In the graph, corresponding to 7:30 am on horizontal axis, we get the distance 100 km on vertical axisi.e. point $P$. Distance covered during the period 7:30 am to 8 : 00 am = (120 - 100) = 20 km
(b) In the given graph, ( from point $p$ ) at 7:30 am the car had covered a distance of 100 km , since it's start.
(iii) To draw the graph of given table of values, we use the following steps
Step I Draw $X$-axis and $Y$-axis and take scale, on
horizontal axis, 2 units $=$ ₹ $1000$
on vertical axis, 2 units $=$ ₹ $80$
Step II Mark deposit (in ₹) on horizontal axis and simple interest (in ₹) on vertical axis.
Step III Now, plot the points $(1000,80),(2000,160)$, $(3000,240),(4000,320)$ and $(5000,400)$ on the graph paper.
Step IV Join these points.
Then, we get a adjoining linear graph.

(a) Yes, the graph passes through the origin when we extending the graph towards $O$ (origin).
(b) To find the interest on ₹ 2500, locate 2500 on the horizontal axis. Follow the vertical line through 2500 till we meet the graph at P (say). From P, take a horizontal line to meet the vertical axis. This meeting point gives the simple interest ₹ 200 for ₹ 2500. Hence, the interest on ₹ 2500 for a year is ₹ 200.
(c) To get deposit money for interest of ₹ 280, locate 280 on the vertical axis. Follow the horizontal line through 280 till we meet the graph at Q (say). From Q take a vertical line to meet the horizontal axis. This meeting point gives the deposit money ₹ 3500 for interest ₹ 280.₹ 3500 should be deposited to get an interest of ₹ 280.

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Question 23 Marks

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:
(i) How high was plant A after (a) 2 weeks (b) 3 weeks?
(il) How high was plant Bafter (a) 2 weeks (b) 3 weeks?
(ill) How much did plant A grow during the 3rd week?
(iv) How much did plant B grow from the end of the 2nd week to the end of the 3rd week?
(v) During which week did plant A grow most?
(vi) During which week did plant B grow least?
(vii) Were the two plants of the same height during any week shown here? Specify.

Answer

(i) (a) From given graph, it is clear that the plant A was 7 cm high after 2 weeks.
(b) From given graph, it is clear that the plant A was 9 cm high after 3 weeks.
(ii) (a) From the given graph, it is clear that the plant B was 7 cm high after 2 weeks.
(b) From the given graph, it is clear that the plant B was 10 cm high after 3 weeks.
(iii) At the end of 2nd week height of plant A = 7 cm and at the end of 3rd week height of plant A = 9 cm.
$\therefore$ Increasing height of plant A from 2nd week to 3rd week (9-7)=2 cm
Hence, during the 3rd week plant A grow 2 cm.
(iv) At the end of 2nd week height of plant B = 7 cm. and at the end of the 3rd week height of the plant B = 10 cm. .
$\therefore$ Difference between the height from end of the 2nd week to 3rd week (10 - 7) 3 cm
Hence, the plant B grow 3 cm from the end of 2nd week to the end of 3rd week
(v) From given graph.
$\because$ Growth of plant A in 1st week
= Height at the end of 1st week
- Height at the starting of 1st week
$=2-0=2 cm$
$\therefore$ Growth of plant A in 2nd week
= Height at the end of 2nd week
- Height at the starting of 2nd week
$=7-2=5cm $
$\therefore$ Growth of plant A in 3rd week
= Height at the end of 3rd week
-Height at the starting of 3rd week
$= 9 - 7 = 2cm$
So, we can say that the plant A grow mostly in 2nd week i.e. 5 cm.
(vi) From given graph,
$\therefore$ Growth of plant B in 1st week
= Height at the end of 1st week
- Height at the starting of 1st week
$= 1 - 0 = 1cm $
$\therefore$ Growth of plant Bin 2nd week
= Height at the end of 2nd week
- Height at the starting of 2nd week
$= 7 - 1 = 6 cm$
$\therefore$ Growth of plant B in 3rd week
= Height at the end of 3rd week
- Height at the starting of 3rd week
$= 10 - 7 = 3 cm $
So, we can say that the plant B grow least in 1st week i.e. 1 cm.
(vii) From given graph, it is clearly shown that at the end of 2nd week, both the plants were of the same height i.e. 7 cm

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Question 33 Marks

Draw the line graph using suitable scale to show the annual gross profit of a company for a period of five years.

Year	1st	2nd	3rd	4th	5th
Gross Profit (in ₹)	1700000	1550000	1140000	1210000	1490000

Answer

The line graph of an annual gross profit of a company for a period of five years are given below

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Question 43 Marks

Make a line graph for the area of a square as per the given table.

Side (in cm)	1	2	3	4
Area (in cm²)	1	4	9	16

Is it a linear graph?

Answer

The line graph for the area of a square as per the given table.

No, it is not a linear graph because when we join the points, then there is not straight line formed.

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Question 53 Marks

If y-coordinate is 3 times x-coordinate, form a table for it and draw a graph.

Answer

If $y$-coordinate $=3$ times of $x$-coordinates i.e. $y=3 x$
If $x=1$, then $y=3 \times 1=3$
If $x=2$, then $y=3 \times 2=6$
If $x=3$, then $y=3 \times 3=9$

$x$	1	2	3
$y$	3	6	9

So, points are $(1,3),(2,6)(3,9)$ and graph is drawn as

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Question 63 Marks

The cost of a notebook is ₹ 10. Draw a graph after making a table showing cost of 2, 3, 4, ... notebooks. Use it to find
(i) the cost of 7 notebooks.
(ii) the number of notebooks that can be purchased with ₹ 50.

Answer

The cost of a notebook $=$ ₹ $ 10$
The cost of two notebooks will be $=2 \times 10=$ ₹ $ 20$
The cost of three notebooks will be $=3 \times 10=$ ₹ $ 30$
The cost of four notebooks will be $=4 \times 10=$ ₹ $ 40$
Hence table for the araph is ziven below

Number of notebooks	1	2	3	4	5	5	7
Cost of note books (in ₹)	10	20	30	40	50	50	70

So, the graph for given data is shown below

(i) Cost of 7 notebooks is ₹ 70.
(ii) 5 notebooks can be purchased with ₹ 50 .

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Question 73 Marks

Locate the points A(1,2), B(3, 4) and C(5.2) on a graph sheet taking suitable axes. Write the coordinates of the fourth point Dto complete the rhombus ABCD Measure the diagonals of this rhombus and find whether they are equal or not.

Answer

Given points are $A(1,2), B(3,4)$ and $C(5,2)$.
Location of given points on the graph given below.
Take $D(3,0)$

The diagonals of this rhombus are equal in length.

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Question 83 Marks

If y-coordinate is 2 times of x-coordinate, them form a table for it and draw a graph.

Answer

Given, y-coordinate = 2 times of x-coordinate.
If $x=2$, then $y=2 x=2 \times 2=4$
If $x=3$, then $y=2 x=2 \times 3=6$

$x$	2	3
$y$	4	6

So, the points are $(2,4)$ and $(3,6)$ and graph is shown below :

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Question 93 Marks

Draw a line graph of the following table which shows the relation between highest temperature in month from March to July.

Months	March	April	May	june	July
Highest Temperature (°C)	38°	40°	45°	47°	39°

Answer

A bar graph for the given temperature in month, from March to July.

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MATHS 3 Marks Question

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