Case study (4 Marks)

Question 14 Marks

A forest ranger keeps track of bears in his area. He plotted their location on a graph. The origin
represents the ranger's control room’s location. To access and maintain equipment, Road $x$ and
Road yhave been laid and paved inside the forest. They pass through the control room.

One unit on the graph paper represents $1\ km.$
$1.$ Which bear is nearest to a paved road$?$
$A$. Bear 389
$B.$ Bear $415$
$C.$ Bear $425$
$D.$ Bear $467$
$2.$ Bear $467$ has been injured. The forest rescue team starts from the control room and decides to use the paved road as much as possible. Which road should they take$?$
$3.$ How far is Bear $425$ from Road $x?$
$4. A$ tiger is at $(11, 4)$. How far from it is the nearest bear$?$
$A. 2\ km$
$B. 4\ km$
$C. 5 \ km$
$D. 7\ km$
$5.$ In the forest, rain shelters are at an interval of $2\ km$ along paved roads. $A$ forest ranger is travelling on Road $x.$ He crosses a rain shelter located at $(3, 0).$
What is likely to be the location of the next shelter$?$
$6.$ The control room receives a message about trespassers located at $(–9, –8).$ The trespassers were seen moving towards Road $x$ on foot. The ranger immediately dispatches a team of guards in a jeep towards them. The guards encounter the trespassers before crossing Road $x.$
Which of the following is most likely to be the location of the encounter$?$
$A. (–9, –14)$
$B. (–9, –5)$
$C. (–9, 4)$
$D. (9, 5)$
$7.$ Ravi planted a red maple tree sapling. The height of the sapling is $0.25 m.$ The average growth rate of the height of a red maple tree is $0.27 m$ per year.
The average life of a red maple tree is $80–100$ years. Ravi estimated that his tree will grow up to $27 m.$
What is the likely reason behind his estimation?
$8.$ Which of the following equations represents the height $(h)$ of the red maple tree after $‘t’$ years of planting?
$A. h=0.25+0.27$
$B. h=0.25t+0.27$
$C. h=0.25+0.27t$
$D. h=0.25+0.27t$
$9.$ Which of the following is true for the line with equation: $1.x+0.y-4=0?$
$A.$ The distance of the line from the $x-$axis is $1.$
$B.$ The distance of the line from the $Y-$axis is $4$.
$C.$ The distance of the line from the $Y-$axis is $–1.$
$D.$ The distance of the line from the $x-$axis changes from $1$ to $–4.$
$10.$ The equation of a line is $ax+by+c=0.$
What conditions ensure that the distance of the line from an axis is constant?
$A. c = 0$ and $a, b ≠ 0$
$B. c < 0$ and a, b ≠ 0
$C. c, b ≠ 0$ and $a =1$
$D. c, b ≠ 0$ and $a = 0$

Answer

1. B. Bear 415
2. Writes Road y OR y
3. Writes 13 km OR 13
4. A. 2 km
5. Gives a point which is at a distance of 2 units from (3, 0)
● (5, 0)
● (1, 0)
6. B. (–9, –5)
7. Writes coordinates which are at a distance of 1 km from either of the jeeps including decimal values
● (2, –9)
● (3, –10)
8. ( – 7, – 9)
9. Writes four coordinates that are at equal distance from the control room
and paved roads including decimal values
For example:
●(5, 5), (–5, 5), (–5, –5), (5, –5)
●(2.5, 2.5), (–2.5, 2.5), (–2.5, –2.5), (2.5, –2.5)
10. y = x and x = y

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Question 24 Marks

Read the Source/ Text given below and answer these questions:

There is a square park $\text{ABCD}$ in the middle of Saket colony in Delhi.Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak, Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point $O$ in the direction of $XOY, X'OY, X'OY'$ and $XOY'.$ Their balls stopped as shown in the above image. Answer the following questions:
$i.$ What are the coordinates of the ball of Ashok$?$
$a. (4, 3)$
$b. (3, 4)$
$c. (4, 4)$
$d. (3, 3)$
$ii.$ What are the coordinates of the ball of Deepa$?$
$a. (2, -3)$
$b. (3, 2)$
$c. (2, 3)$
$d. (2, 2)$
$iii.$ What the line $\text{XOX'}$ is called$?$
$a. y-$axis.
$b.$ ordinate.
$c. x-$axis.
$d.$ origin.
$iv.$ What the point $O(0, 0)$ is called$?$
$y-$axis.
ordinate.
$x-$axis.
origin.
$v.$ What is the ordinate of the ball of Arjun$?$
$a. -3$
$b. 3$
$c. 4$
$d. 2$

Answer

$(i)$	$(b)$	$(3, 4)$
$(ii)$	$(a)$	$(2, -3)$
$(iii)$	$(c)$	$x-$axis.
$(iv)$	$(d)$	origin.
$(v)$	$(a)$	$-3$

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Question 34 Marks

Read the Source/ Text given below and answer these questions:

In the above picture, one small square is of size $1\ km \times 1\ km.$ From the starting point $O(0, 0)$ Deepak started to drive towards his home. He first drives $3\ km$ in left then he turned to his left and drove $2\ km,$ there he found a temple. He worshipped there and drove $6\ km$ in the left direction, there is a zoo and from the zoo, he drives $2\ km$ on the right side, then he reached his home. From $O$ Sanjay drove for his school, he drove $1\ km$ to his right then took a left turn and drives $2\ km$ then again took a right turn and drives $2\ km$. He found a hospital in the way. From Hospital he drove $3\ km$ and finally reached his school.
$i.$ What are the coordinates of the Hospital?
$a. (3, 2)$
$b. (2, 3)$
$c. (3, 3)$
$d. (5, 5)$
$ii.$ What is common abscissa of school, Hospital, Zoo and Deepak's home$?$
$a. 3$
$b. 5$
$c. -3$
$d. -5$
$iii.$ What is the common ordinate of temple and Zoo$?$
$a. 3$
$b. 5$
$c. -3$
$d. -2$
$iv.$ Deepak Drove in which quadrants$?$
$a. I$ and $II$
$b. II$ and $III$
$c. III$ and $IV$
$d. IV$ and $I$
$v.$ Sanjay Drove in which quadrants$?$
$a. I$ only
$b. II$ and $III$
$c. III$ and $IV$
$d. II$ and $I$

Answer

$(i)$	$(a)$	$(3, 2)$
$(ii)$	$(a)$	$3$
$(iii)$	$(d)$	$-2$
$(iv)$	$(c)$	$III $and $IV$
$(v)$	$(a)$	$I$ only

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Question 44 Marks

Read the Source/ Text given below and answer any four questions:

Rohit was putting up one of his paintings in his living room. Before this Rohit had put a grid on the wall where each unit measured equal to a foot. The upper$-$left corner of the frame is at point $C(1, 8)$ and the upper$-$right corner at $D(7, 8).$ The bottom$-$left corner is at $A(1, 2)$ and the bottom$-$right corner at $B(7, 2).$ Please answer the following questions:
$i.$ What is the width of the painting plus frame$?$
$a. 5$ feet
$b. 8$ feet
$c. 9$ feet
$d. 6$ feet
$ii.$ What is the length of the painting plus frame$?$
$a. 9$ feet
$b. 8$ feet
$c. 6$ feet
$d. 5$ feet
$iii.$ Which sides of the painting are parallel to $x-$axis$?$
$a. AB$ and $CD$
$c. AC$ and $BD$
$c.$ Diagonals $AD$ and $BC$
$d.$ No one
$iv.$ Which sides of the painting are parallel to $y-$axis$?$
$a. AB$ and $CD$
$b.AC$ and $BD$
$c.$ Diagonals $AC$ and $BD$
$d.$ No one
$v.$ Point $A, B, C$ and $D$ lie in which quadrant$?$
$a. I$
$b. II$
$c. III$
$d. IV$

Answer

$i$	$d$	$6$ feet
$ii$	$c$	$6$ feet
$iii$	$a$	$AB$ and $CD$
$iv$	$b$	$AC$ and $BD$
$v$	$a$	$I$

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Question 54 Marks

Read the Source/ Text given below and answer these questions:

Arun is participating in an $8$ miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at $A (3, 1).$ At $B (3, 4),$ there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at $C (6,4)$ a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination $D$ to complete $8$ miles.
$i.$ How far is the water station $B$ from the starting point $A?$
$a. 4$ miles
$b. 3$ miles
$c. 1$ mile
$d. 5$ miles
$ii.$ How far is the water station $B$ from garden $C?$
$a. 3$ miles
$b. 4$ miles
$c. 1$ mile
$d. 5$ miles
$iii.$ What is the abscissa of destination point $D:$
$a. 3$
$b. 5$
$c. 3$
$d. 6$
$iv$. What is the ordinate of destination point $D?$
$a. 3$
$b. 2$
$c. 6$
$d. 5$
$v.$ What are the coordinates of destination point $D?$
$a. (5, 6)$
$b. (6, 5)$
$c. (3, 9)$
$d. (6, 6)$

Answer

$(i)$	$(b)$	$3$ miles
$(ii)$	$(a)$	$3$ miles
$(iii)$	$(d)$	$6$
$(iv)$	$(c)$	$6$
$(v)$	$(d)$	$(6, 6)$

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Question 64 Marks

Read the Source/ Text given below and answer these questions:

Roshan decorated one of his bathroom wall with tiles as shown in the picture. He was having tiles of four colours orange, yellow, green and blue. He fitted the tiles in $8$ columns and $12$ rows. The size of one tile was $1$ foot $\times \ 1$ foot and the area of each tile is $1$ foot$^2$. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange $\rightarrow $ Yellow $\rightarrow $ green $\rightarrow $ Blue $\rightarrow $ Orange $\rightarrow .....$ and so on. Now answer the following questions:
$i.$ Which colour tile was fitted at the point with coordinates $(5, 3)?$
$a.$ Orange.
$b.$ Yellow.
$c.$ Green.
$d.$ Blue.
$ii.$ Which colour tile was fitted at the point with coordinates $(7, 7)$?
$a.$ Orange.
$b.$ Yellow.
$c.$ Green.
$d.$ Blue.
$iii.$ Which colour tile was fitted at the point with coordinate $(2, 5)$?
$a.$ Orange.
$b.$ Yellow.
$c.$ Green.
$d.$ Blue.
$iv.$ What is the area of the tiles fitted in the rectangular part $\text{OABX}$?
$a. 50$ foot$^2$
$b. 24$ foot$^2$
$c. 12$ foot$^2$
$d. 48$ foot$^2$
$v.$ What is the ordinate of top row tiles?
$a. 8$
$b. 12$
$c. 16$
$d. 6$

Answer

$(i)$	$(c)$	Green.
$(ii)$	$(a)$	Orange.
$(iii)$	$(b)$	Yellow.
$(iv)$	$(d)$	$48$ foot$^2$
$(v)$	$(b)$	$12$

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Question 74 Marks

A forest ranger keeps track of bears in his area. He plotted their location on a graph. The origin
represents the ranger's control room’s location. To access and maintain equipment, Road x and
Road yhave been laid and paved inside the forest. They pass through the control room.

One unit on the graph paper represents 1 km.
Q.1. In the forest, rain shelters are at an interval of 2 km along paved roads. A forest ranger is travelling on Road x. He crosses a rain shelter located at (3, 0). What is likely to be the location of the next shelter?
Q.2. The control room receives a message about trespassers located at (–9, –8). The trespassers were seen moving towards Road x on foot. The ranger immediately dispatches a team of guards in a jeep towards them. The guards encounter the trespassers before crossing Road x. Which of the following is most likely to be the location of the encounter?
A. (–9, –14)
B. (–9, –5)
C. (–9, 4)
D. (9, 5)
Q.3. Ravi planted a red maple tree sapling. The height of the sapling is 0.25 m. The average growth rate of the height of a red maple tree is 0.27 m per year. The average life of a red maple tree is 80–100 years. Ravi estimated that his tree will grow up to 27 m. What is the likely reason behind his estimation?
Q.4. Which of the following equations represents the height (h) of the red maple tree after ‘t’ years of planting?
A. h=0.25+0.27
B. h=0.25t+0.27
C. h=0.25+0.27t
D. h=0.25+0.27t

Answer

1. Gives a point which is at a distance of 2 units from (3, 0)
● (5, 0)
● (1, 0)
2. B. (–9, –5)
3. Writes coordinates which are at a distance of 1 km from either of the jeeps including decimal values
● (2, –9)
● (3, –10)
4. ( – 7, – 9)

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Maths Case study (4 Marks)

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