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Case Study Based Questions Class 09  Mathematics
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Case Study Based Questions Class IX
Mathematics
CASE STUDY1 CHAPTER 1 NUMBER SYSTEM
In a school one day the maths teacher told the students of class IX about the number systems. She drew a number line and told them that the number line represents various types of numbers on it.
Rational numbers can be represented on the number
line. A number is called a rational number if it can be written in the form of
p / q , where p and q are integers and q ≠ 0.
Based on the above information, answer the
following questions.
Q1) A rational number between 2 and 3 is
a) 1
b) 5/2
c) 0
d) ½
Q2) An irrational number between and is
a) 2
b) 1
c)
d)
Q3) A rational number between and is
a)
b)
c) 1.5
d) 1
Q4) The product of (2 + )(2) is
a) 4
b) 1
c) 1
d) 0
Q5) The form of is
a)
b)
c)
d)
Question  Answer 
1  b 
2  d 
3  c 
4  b 
5  c 
CASE STUDY1 CHAPTER 2 POLYNOMIALS
On the basis of above information, answer the following questions.
a) x^{10}
b) x^{10} + x^{9} + 3
c) x^{10} + 4
d) x + 10
Q5) The value of the polynomial x^{2}  3x + 2 at x = 1 is
Question  Answer 
1  d 
2  b 
3  a 
4  c 
5  b 
CASE STUDY1 CHAPTER 3 COORDINATE GEOMETRY
Four friends Rahul, Neetu, Ankit and Harsh are playing a game. They formed a coordinate plane and sat at various positions on the coordinate plane. The positions of four boys are shown in the graph given below.
Q1) What are the coordinate of the positions of four friendsa) (3, 3), ( 2, 3), ( 2,  2), (4,  2)
b) (4, 3), ( 2, 3), ( 2,  2), (4,  2)
c) (4, 3), ( 2,  2), ( 2,  2), (4,  2)
d) (4, 3), ( 2, 3), ( 2,  4), (4,  2)
Q2) What is the distance between Rahul and Neetua) 2 units b) 3 units c) 6 units d) 8 units
Q3) Abscissa of the point at which Harsh is sitting isa) 2 b)  4 c) 2 d) 4
Q4) The shape formed by joining the positions of four friends in order isa) Square b) Rectangle c) Parallelogram d) Rhombus
Q5) The area of the shape formed by joining the positions of four friends.a) 30 b) 36 c) 25 d) 32
Question
Answer
1
b
2
c
3
d
4
b
5
a
Question  Answer 
1  b 
2  c 
3  d 
4  b 
5  a 
CASE STUDY2 CHAPTER  03 COORDINATE GEOMETRY
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure.
Question 1 What are the coordinates of A and B respectively?
a) A(3, 5); B(7, 8)
b) A(5, 3); B(8, 7)
c) A(3, 5); B(7, 9)
d) A(5, 3); B(9, 7)
Answer c
Question 2 What are the coordinates of C and D respectively?
a) C(11, 5); D(7, 1)
b) C(5, 11); D(1, 7)
c) C(5, 11); D(7, 1)
d) C(5, 11); D(1, 7)
Answer a
Question 3What is the distance between B and D?
a) 5 units b) 14 units c) 8 units d) 10 units
Answer c
Question 4What is the distance between A and C?
a) 5 units b) 14 units c) 8 units d) 10 units
Answer c
Question 5What are the coordinates of the point of intersection of AC and BD?
a) (7, 5) b) (5, 7) c) (7, 7) d) (5, 5)
Answer a
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in the figure.
Question 1
What are the coordinates of A and B respectively?
a) A(3, 5); B(7, 8)
b) A(5, 3); B(8, 7)
c) A(3, 5); B(7, 9)
d) A(5, 3); B(9, 7)
Answer c
Question 2
What are the coordinates of C and D respectively?
a) C(11, 5); D(7, 1)
b) C(5, 11); D(1, 7)
c) C(5, 11); D(7, 1)
d) C(5, 11); D(1, 7)
Answer a
Question 3
What is the distance between B and D?
a) 5 units b) 14 units c) 8 units d) 10 units
Answer c
Question 4
What is the distance between A and C?
a) 5 units b) 14 units c) 8 units d) 10 units
Answer c
Question 5
What are the coordinates of the point of intersection of AC and BD?
a) (7, 5) b) (5, 7) c) (7, 7) d) (5, 5)
Answer a
CASE STUDY3 CHAPTER  03 COORDINATE GEOMETRY
Class 9 students of a school in Moti Nagar, Delhi have been allotted a rectangular plot of land, adjacent to the school, for gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular grassy lawn in the plot as shown in the figure. The students are to sow seeds of flowering plants on the remaining area of the plot. Considering A as the origin, AD along xaxis and AB along y axis, Read the above information and answer the following questions
Q1. What are the coordinates of A ?
Q2. What are the coordinates of P ?
Q3. What are the coordinates of R ?
Q4. What are the coordinates of D ?
Q5. What are the coordinates of P, if D is taken as origin, DA along negative direction of xaxis and DC along y axis?
Answer Key
Q1
(0, 0)
Q2
(4, 6)
Q3
(6, 5)
Q4
(16, 0)
Q5
(12, 6)

Answer Key 
Q1 
(0, 0) 
Q2 
(4, 6) 
Q3 
(6, 5) 
Q4 
(16, 0) 
Q5 
(12, 6) 
CASE STUDY1 CHAPTER  4
LINEAR EQUATIONS IN TWO VARIABLES
Prime Minister's National Relief Fund (also called PMNRF in short) is the fund raised to provide support for people affected by natural and manmade disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Manmade disasters that are included are major accidents, acid attacks, riots, etc. Two friends Sita and Gita, together contributed Rs. 200 towards Prime Minister's Relief Fund. Answer the following
Q1) Which out of the
following is not the linear equation in two variables ?
(a) 2x = 3
(b) x^{2} + x = 1
(c) 4 = 5x – 4y
(d) x – √2y = 3
Q2) How to represent the above situation in linear equations in two variables ?
(a) 2x + y = 200
(b) 200x = y
(c) x + y = 200
(d) 200 + x = y
Q3) If Sita contributed Rs. 76, then how much was contributed by Gita ?
a) Rs. 120 b) Rs. 124 c) Rs. 123 d) Rs. 125
Q4) If both contributed equally, then how much is contributed by each?
(a) Rs. 50, Rs. 150
(b) Rs. 50, Rs. 50
(c) Rs. 100, Rs. 100
(d) Rs. 120, Rs. 120
Q5) Which is the standard form of linear equations x = – 5 ?
(a) x + 5 = 0
(b) 1.x – 5 = 0
(c) 1.x + 0.y + 5 = 0
(d) 1.x + 0.y = 5
Question  Answer 
1  b 
2  c 
3  b 
4  c 
5  c 
CASE STUDY1 CHAPTER  4
LINEAR EQUATIONS IN TWO VARIABLES
Two friends Pankaj and Rohit went to a market. Pankaj bought 3 notebooks and 2 pens for Rs. 80. Rohit also bought the same types of notebooks and pens as Pankaj. He paid 110 for 4 notebooks and 3 pens.
From the above
information answer the following questions
Q1) Form the pair of
linear equations in two variables from this situation by taking
cost of one notebook as
Rs. x and cost of one pen as Rs. y.
(a) 3x + 2y = 80 and 4x +
3y = 110
(b) 2x + 3y = 80 and 3x +
4y = 110
(c) x + y = 80 and x + y
= 110
(d) 3x + 2y = 110 and 4x
+ 3y = 80
Solution
Here, the cost of one
notebook be Rs. x and that of pen be Rs. y.
According to the
statement, we have
3x + 2y = 80 and
4x + 3y = 110
Q2) Which is the solution satisfying both the equations formed in (i)?
(a) x = 10, y = 20
(b) x = 20, y = 10
(c) x = 15, y = 15
(d) none of these
Solution
3x + 2y = 3(20) + 2(10) =
60 + 20 = 80
4x + 3y = 4(20) + 3(10) =
80 + 30 = 110
Ans: (b) x = 20, y = 10
Q3) Find the cost of one pen?
(a) Rs. 20 (b) Rs. 10 (c) Rs. 5 (d) Rs. 15
Ans: (b) Rs. 10
Q4) Which is the
solution satisfying both the equations formed in (i)?
(a) x = 10, y = 20
(b) x = 20, y = 10
(c) x = 15, y = 15
(d) none of these
Solution
3x + 2y = 3(20) + 2(10) =
60 + 20 = 80
4x + 3y = 4(20) + 3(10) =
80 + 30 = 110
Ans: (b) x = 20, y = 10
Q5) Find the total cost if they will purchase the same type of 15 notebooks and 12 pens.
(a) Rs. 400 (b) Rs. 350 (c) Rs. 450 (d) Rs. 420
Solution
Total cost = Rs. 15 x 20
+ Rs. 12 x 10
= 300 + 120 = Rs. 420
CASE STUDY1 CHAPTER  12 HERON'S FORMULA
Mohan has a piece of land in the shape of a given figure. He divides the land into two parts to produce different crops.
On the basis of the
above information, answer the following questions:
Q1) The length of AC is
a) 40m b) 50m c) 30m d) 80 m
Q2) The area of △ABC is
a) 400 m^{2 }
Q3) The area of △ACD is
a) 1000
Q4) The cost of ploughing the land at the rate of ₹ 20 / m^{2} is (Take = 1.732)
a) ₹ 12000 b) ₹ 34640 c) ₹ 46640 d) None of these
Q5) The cost of fencing all around the land with barbed wire @ of ₹ 30 / m is
a) ₹ 6000 b) ₹ 5000 c) ₹ 6500 d) ₹ 6600
Question  Answer 
1  b 
2  c 
3  a 
4  c 
5  d 
CASE STUDY1 CHAPTER  13
SURFACE AREA AND VOLUME
Mathematics teacher of a school took her 9th standard students to show Red fort. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Red fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.
i) How much cloth material will be required to cover 2 big
domes each of radius 2.5 m Take Ï€ = 22/7
Ans:
78.57 m^{2}
ii) Write the formula to find the volume of a cylindrical pillar.
Ans: Ï€r^{2}h
iii) Find the lateral surface area of two pillars if height
of the pillar is 7m and radius of the base is 1.4m
Ans: 123.2 m^{2}
iv) How much is the volume of a hemisphere if the radius of
the base is 3.5m ?
Ans: 89.83 m^{3}
v) What is the ratio of sum of volumes of two hemisphere of
radius 1 cm each to the volume of a sphere of radius 2 cm ?
Ans: 1:8
CASE STUDY1 CHAPTER  14 STATISTICS
Height Intervals (in cms) 
No. of students 
131140 
1 
141150 
7 
151160 
5 
161170 
9 
171180 
9 
181190 
10 
Total 
41 
Q1) Class size of third class interval is
a) 8 b) 9 c) 9.5 d) 10
Q2) Upper limit of 5^{th} class interval is
a) 180 b)170.5 c) 180.5 d)179.5
Q3) Class mark of 6^{th} class interval is
a) 184.5 b)185 c)185.5 d)186
Q4) How many students have their height more than 160 cm
a) 19 b) 18 c) 27 d) 28
Q5) How many students have their height less than or equal to 180 cm ?
a) 31 b) 19 c)29 d) 22
Question  Answer 
1  d 
2  c 
3  c 
4  d 
5  a 
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