5 Marks Questions

Question 15 Marks

Draw a graph for the following.

Side of square $($in $cm)$	$2$	$3$	$4$	$5$	$6$
Area $($in $cm^2)$	$4$	$9$	$16$	$25$	$36$

Is it a line graph?

Answer

$i.$ Horizontal : $1$ unit $= 1\ cm$
Vertical : $1$ unit $= 2\ cm$
$ii.$ Mark side of the square $($in $cm)$ on horizontal axis.
$iii.$ Mark area (in $cm^2$) on vertical axis.
$iv.$ Plot the points $(2, 4), (3, 9), (4, 16), (5, 25), (6, 36).$
$v.$ Join the points.
The graph we get is not line.

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Question 25 Marks

Draw a graph for the points given. Is it a linear graph?

Side of a square (in cm)	$2$	$3$	$3.5$	$5$	$6$
Perimeter (in cm)	$8$	$12$	$14$	$20$	$24$

Answer

The given data can be represented in the form of graph as:

It is clear that points are in a straight line. Therefore, it is a linear graph.

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Question 35 Marks

Draw the graph for the following table of values, with suitable sales and Interest on deposits for a year on the axis.

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

$i.$ Does the graph pass through the origin?
$ii.$ Use the graph to find the interest on $Rs. 2500$ for a year?
$iii.$To get an interest of $Rs. 280$ per year, how much money should be deposited?

Answer

$i.$ Yes! The graph passes through the origin.
$ii.$ Interest on $Rs. 2500$ for a year $= Rs. 200$
$iii.$ To get an interest of $Rs. 280$ per year, $Rs. 3500$ should be deposited.

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Question 45 Marks

Draw the graph for the following table of values , with suitable sales on the axis.Distance travelled by a car

Time $($in hours$)$	$6\ a.m.$	$7\ a.m.$	$8\ a.m.$	$9\ a.m.$
Distances $($in $km)$	$40$	$80$	$120$	$160$

$i.$ How much distances did the car cover during the period $7.30\ a.m.$ to $8\ a.m.$?
$ii.$ What was the time when the car had covered a distance of $100\ km$ since it's start?

Answer

$I.$ Horizontal : $2$ units $= 1$ hour
Vertical : $2$ units = $20\ km$
$II.$ Mark time $($in hours$)$ on horizontal axis.
$III.$ Mark distances $($in $km)$ on vertical axis.
$IV.$ Plot the points $(6\ a.m., 40), (7\ a.m., 80) (8\ a.m., 120), (9\ a.m., 160).$
$V.$ Join the points.
We get a linear graph.
$I.$ Distance covered during $7.30\ a.m.$ to $8\ a.m$.
$= 120\ km – 100\ km$ $= 20\ km$
$II.$ The time when the car had covered a distance of $100\ km$ since its start was $7.30\ a.m$.

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Question 55 Marks

Draw the graph for the following table of values , with suitable sales on the axis.Cost of apples.

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

Answer

$i.$ Scale:
Horizontal : $2$ units $= 1$ apple
Vertical : $1$ unit $= Rs. 5$
$ii.$ Mark number of apples on horizontal axis.
$iii.$ Mark cost $($in $Rs.)$ on vertical axis.

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Question 65 Marks

Use the table below to draw line graph. Population (in thousands) of men and women in a village in different years.

Year	$2003$	$2004$	$2005$	$2006$	$2007$
Number of Men	$12$	$12.5$	$13$	$13.2$	$13.5$
Number of Women	$11.3$	$11.9$	$13$	$13.6$	$12.8$

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Question 75 Marks

Use the table below to draw line graph. The number of days a hill side city received show in different years.

Year	$2003$	$2004$	$2005$	$2006$
Days	$8$	$10$	$5$	$12$

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Question 85 Marks

Ajit can ride a scooter constantly at a speed of $30 \text{kms/hour.}$ 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.

Answer

Hours of ride	Distance covered by scooter
$1$ hour	$1\times30\ km = 30\ km$
$2$ hours	$2\times30\ km = 60 km$
$3$ hours	$3\times30\ km = 90\ km$
$4$ hours	$4\times30\ km = 120\ km$ and so on.

We get a table of these values as follows:

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 the horizontal axis.
$iii.$ Mark distance on the 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.

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Question 95 Marks

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:
$i.$ the annual interest obtainable for an investment of $₹250$
$ii.$ the investment one has to make to get an annual simple interest of $₹70$

Answer

We know that simple interest $= {P\times R \times T \over 100}$

Sum deposited	Simple interest for a year
$₹100$	$₹\frac{100 \times 1 \times 10}{100}= ₹10$
$₹200$	$₹ \frac{200 \times 1 \times 10}{100}= ₹20$
$₹300$	$₹ \frac{300 \times 1 \times 10}{100}= ₹30$
$₹500$	$₹ \frac{500 \times 1 \times 10}{100}= ₹50$
$₹1000$	$₹100$

Steps to follow:
$i.$ Find the quantities to be plotted as Deposit and $SI$.
$ii.$ Decide the quantities to be taken on the $x-$axis and on the $y-$axis.
$iii.$ Choose a scale.
$iv.$ Plot points.
$v.$ 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 the 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 the horizontal axis, we get the interest to be $₹25$ on the vertical axis.
$b.$ Corresponding to $₹70$ on the vertical axis, we get the sum to be $₹700$ on the horizontal axis.

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Question 105 Marks

The following table gives the quantity of petrol and its cost. Plot a graph to show the data

No. of litres of petrol	$10$	$15$	$20$	$25$
Cost of petrol in ₹	$500$	$750$	$1000$	$1250$

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Question 115 Marks

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 $2^{nd}$ hour? $(ii)$ the $3$rd 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 $Q$?

Answer

After observing the given graph carefully, it can be concluded that
$i.$ 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 $50^{th}\ km ($seen from graph$)$. Hence during the one$-$hour time between $8\ a.m.$ and $9\ a.m.$ the car travelled $50\ km].$
$iv.$ The distance covered by the car during $(a)$ the $2$nd hour $($i.e., from $9\ am$ to $10\ am)$ is $100\ km$, $(150 – 50)$. $(b)$ the $3\ rd$ 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 $2\ p.m$.

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