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Maths Case study (4 Marks)

Coordinate Geometry · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 6 questions.

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Case study (4 Marks)

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6 questions · timed · auto-graded

Question 14 Marks
Read the Source/ Text given below and answer these questions:

In the above picture, one small square is of size 1km × 1km. From the starting point O(0, 0) Deepak started to drive towards his home. He first drives 3km in left then he turned to his left and drove 2km, there he found a temple. He worshipped there and drove 6km in the left direction, there is a zoo and from the zoo, he drives 2km on the right side, then he reached his home. From O Sanjay drove for his school, he drove 1km to his right then took a left turn and drives 2km then again took a right turn and drives 2km. He found a hospital in the way. From Hospital he drove 3km and finally reached his school.
  1. What are the coordinates of the Hospital?
  1. (3, 2)
  2. (2, 3)
  3. (3, 3)
  4. (5, 5)
  1. What is common abscissa of school, Hospital, Zoo and Deepak's home?
  1. 3
  2. 5
  3. -3
  4. -5
  1. What is the common ordinate of temple and Zoo?
  1. 3
  2. 5
  3. -3
  4. -2
  1. Deepak Drove in which quadrants?
  1. I & II
  2. II and III
  3. III and IV
  4. IV and I
  1. Sanjay Drove in which quadrants?
  1. I only
  2. II and III
  3. III and IV
  4. 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 24 Marks
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 34 Marks
Answer
(i)(b)(3, 4)
(ii)(a)(2, -3)
(iii)(c)x-axis.
(iv)(d)origin.
(v)(a)-3
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Question 44 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. 

Image
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 54 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 × 1 foot and the area of each tile is 1 foot2. He arranged the tile in such a way that colour of tiles in each row and column were in the pattern: Orange → Yellow → green → Blue → Orange → ..... and so on. Now answer the following questions:
  1. Which colour tile was fitted at the point with coordinates (5, 3)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. Which colour tile was fitted at the point with coordinates (7, 7)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. Which colour tile was fitted at the point with coordinate (2, 5)?
  1. Orange.
  2. Yellow.
  3. Green.
  4. Blue.
  1. What is the area of the tiles fitted in the rectangular part OABX?
  1. 50 foot2
  2. 24 foot2
  3. 12 foot2
  4. 48 foot2
  1. What is the ordinate of top row tiles?
  1. 8
  2. 12
  3. 16
  4. 6
Answer
(i)(c)Green.
(ii)(a)Orange.
(iii)(b)Yellow.
(iv)(d)48 foot2
(v)(b)12
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Question 64 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.
  1. How far is the water station B from the starting point A?
  1. 4 miles
  2. 3 miles
  3. 1 mile
  4. 5 miles
  1. How far is the water station B from garden C?
  1. 3 miles
  2. 4 miles
  3. 1 mile
  4. 5 miles
  1. What is the abscissa of destination point D:
  1. 3
  2. 5
  3. 3
  4. 6
  1. What is the ordinate of destination point D?
  1. 3
  2. 2
  3. 6
  4. 5
  1. What are the coordinates of destination point D?
  1. (5, 6)
  2. (6, 5)
  3. (3, 9)
  4. (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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Case study (4 Marks) - Maths STD 9 Questions - Vidyadip