Case Study Based Questions Class 09 | Mathematics

Case Study Based Questions Class IX

 Mathematics

Case study questions on Number System, Polynomials, Co-ordinate Geometry, Linear Equations in two Variables, Lines & Angles, Triangles, Quadrilaterals and Circles etc.

CASE STUDY-1 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 STUDY-1 CHAPTER -2 

POLYNOMIALS

An algebraic expression in which the exponent (Power) of the variable is a whole number (0, 1, 2, 3, ....... ) is called polynomials. Highest exponent of the variable in a polynomial is called its degree.

On the basis of above information, answer the following questions.

Q1) The degree of zero polynomial is 

a) 1

b) 0

c) -1

d) not defined

Q2) The degree of a  non-zero constant polynomial is 

a) 1

b) 0

c) -1

d) not defined

 Q3) The coefficient of x² in the polynomial  x³ – x² + 2x + 1  is

a) -1

b) 1

c) 0

d) 2

Q4) A binomial of degree 10 is 

a) x¹⁰

b) x¹⁰ + x⁹ + 3

c) x¹⁰ + 4

d) x + 10

Q5) The value of the polynomial  x² - 3x + 2 at x = -1 is

a) 0

b) 6

c) 5

d) 2

Question	Answer
1	d
2	b
3	a
4	c
5	b

CASE STUDY-1 CHAPTER -3 

CO-ORDINATE 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 friends

a) (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 Neetu

a)  2 units             

b) 3 units              

c) 6 units            

d) 8 units

Q3) Abscissa of the point at which Harsh is sitting is

a)  2                       

b) -4                       

c) -2                       

d) 4

Q4) The shape formed by joining the positions of four friends in order is

a)  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

CASE STUDY-2 CHAPTER - 03 

CO-ORDINATE 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 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 STUDY-1 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 man-made disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Man-made 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) x² + 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 STUDY-1 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

Answer

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

(iv) 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

(v) 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 STUDY-1 CHAPTER - 12 

HERON'S FORMULA

Shyam 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 m²

b) 500 m²  

c) 600 m²  

d) 800 m²

Q3) The area of △ACD  is

a) 1000  m²

b) 500  m²

c) 1500  m²

d) 1000 m²

Q4) The cost of ploughing the land at the rate of  ₹ 20 / m² 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 STUDY-1 CHAPTER - 13 

SURFACE AREA AND VOLUME

Rohit was doing an experiment to find the radius r of a sphere. For this he look a cylindrical container with radius R = 7 cm and height = 10 cm. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere  in the container he observed as shown in the right figure. the water level in the container raises from A to B equal to 3.40 cm.

Based on the given information, answer the following questions.

Q1) If the water in the cylinder is filled to a height of 5 cm. What is the volume (in cu.cm) of water in the cylinder?

a) 145π

b) 175π

c) 245π

d) 490π

Q2) Volume (in cm³) of water displayed when sphere submerged is 

a) 166.6π

b) 83.6π

c) 41.8π

d) 333.2π

Q3) Volume (in cm³) of the sphere is equal to

a) 166.6π

b) 83.6π

c) 41.8π

d) 333.2π

Q4) The radius of sphere in cm is approximately

a) 3.5

b) 4

c) 4.5

d) 5

Q5) The ratio of the curved surface areas of the sphere and the container is 

a) 5:7

b) 7:20

c) 16:35

d) 81:140

Question	Answer
1	c
2	a
3	a
4	d
5	a

CASE STUDY-2 CHAPTER - 13 

SURFACE AREA AND VOLUME

Q3) State government wants to arrange a camp in a remote area for the welfare of villagers, who are facing health issues. They make a tent as shown in the figure below

Based on the above information answer the following questions

Q1) Slant height of the conical part is

a) 6m

b) 8m

c) 10m

d) 7.5m

Q2) Curved surface area of the conical part is 

a) 40π m²

b) 80π m²

c) 120π m²

d) 100π m²

Q3) Curved surface area of the cylindrical part is 

a) 96π m²

b) 69π m²

c) 80π m²

d) 40π m²

Q4) Volume of air in the tent is 

a) 125π m³

b) 256π m³

c) 314π m³

d) 512π m³

Q5) Cost of canvas required to make the tent at the rate of ₹ 3.50 / m²

a) ₹ 1936

b) ₹ 1639

c) ₹ 1369

d) ₹ 1963

Question	Answer
1	c
2	b
3	a
4	d
5	a

CASE STUDY-1 CHAPTER - 13 

SURFACE AREA AND VOLUME

Mathematics teacher of a school took her 9th standard students to show Gol Gumbaz. It was a part of their educational trip. The teacher had interest in history as well. She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb, located in Vijayapura, Karnataka, India, was started in 1626 and completed in 1656. It reaches up to 51 meters in height while the giant dome has an external diameter of 44 meters, making it one of the largest domes ever built. At each of the four corners of the cube is a dome shaped octagonal tower seven stories high with a staircase inside.

Q1) What is the total surface area of a cuboid?

a) lb + bh + hl

b) 2(lb + bh + hl)

c) 2(lb + bh)

d) 1² + b² + h²

Q2) What is the curved surface area of hemispherical dome ?

a) 908π m²

b) 968π m²

c) 340π m²

d) 780π m²

Q3) What is the height of the cuboidal part ?

a) 14 m

b) 7 m

c) 29 m

d) 18 m

Q4) What is the circumference of the base of the dome ?

a) 34 π m   

b) 22 π m   

c) 44 π m    

d) 55 π m

Q5) The total surface area of a hemispherical dome having radius 7 cm is

a)  462 cm²      

b) 294 cm²     

c) 588 cm²     

d) 154 cm²

Question	Option	Answer
1	b	2(lb + bh + hl)
2	b	968π m2
3	c	29 m
4	c	44 π m
5	a	462 cm2

 

CASE STUDY-1 CHAPTER - 14 

STATISTICS

Given below is the data found on a group of school going students. 

Height Intervals (in cms)	No. of students
131-140	1
141-150	7
151-160	5
161-170	9
171-180	9
181-190	10
Total	41

Study the data and answer the questions that follow

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

CASE STUDY-1 CHAPTER - 15 

PROBABILITY

Dice are small, throwable objects with marked sides that can rest in multiple positions. They are used for generating random numbers, commonly as part of tabletop games, including dice games, board games, role playing games and games of chance.

A traditional die is a cube with each of its six faces marked with a different number of dots (pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely.

A die is rolled.

Q1) The probability of getting a prime number is 

a)  4/6

b)  3/6

c) 2/6

d) None of these

Q2) The probability of getting a non-prime number is

a) 4/6

b) 3/6

c) 2/6

d) 5/6

Q3) The probability of getting a composite number is 

a) 4/6

b) 3/6

c) 2/6

d) None of these

Q4) The probability of getting a divisor of 24 is 

a) 3/6

b) 4/6

c) 5/6

d) 1

Q5) The probability of getting a number less than 8 is 

a) 0

b) 1/2

c) 1/3

d) 1

Question	Answer
1	b
2	b
3	c
4	c
5	d

Download PDF file Here

THANKS FOR YOUR VISIT

PLEASE COMMENT BELOW