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Mathematics (Maths) Class 9

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Class 9 : Notes | EduRev

 Page 1


  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 2 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Question numbers 1 to 6 in Section A are multiple choice questions where you are to 
select one correct option out of the given four. 
4. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify: 
? ? ? ? ? ?
? ? ? ? ? 6 27 3 3 1 2 3  
 
2. Find the value of the polynomial x
2
 – x – 1 at x = –1. 
 
3. Give the definition of Parallel Lines. 
 
4. Is (2, 0) a solution of x – 2y = 4?  
OR 
 The graph of the linear equation 2x – y = 4 cut x-axis at? 
 
5. PQRS is a parallelogram in which m ?PSR = 125°. What is the measurement of ?RQT?  
 
6. Find the Class size, if the Class marks of a frequency distribution are 6, 10, 14, 18, 22, 
26 and 30? 
OR 
The class marks of a distribution are : 47, 52, 57, 62, 67, and 72 
Determine the class size. 
 
Page 2


  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 2 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Question numbers 1 to 6 in Section A are multiple choice questions where you are to 
select one correct option out of the given four. 
4. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify: 
? ? ? ? ? ?
? ? ? ? ? 6 27 3 3 1 2 3  
 
2. Find the value of the polynomial x
2
 – x – 1 at x = –1. 
 
3. Give the definition of Parallel Lines. 
 
4. Is (2, 0) a solution of x – 2y = 4?  
OR 
 The graph of the linear equation 2x – y = 4 cut x-axis at? 
 
5. PQRS is a parallelogram in which m ?PSR = 125°. What is the measurement of ?RQT?  
 
6. Find the Class size, if the Class marks of a frequency distribution are 6, 10, 14, 18, 22, 
26 and 30? 
OR 
The class marks of a distribution are : 47, 52, 57, 62, 67, and 72 
Determine the class size. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. The volume of a cuboid is given by the algebraic expression ky
2
 – 6ky + 8k. Find the 
possible expressions of the dimensions of the cuboid. 
 
8. If a point C lies between two points A and B such that AC = BC, then prove that                    
AC = 
1
2
AB. Explain by drawing a figure. 
 
9. In the figure below, BC = AC = AD and ? DAE = 75°. Find the value of y. 
 
 
 
 
 
 
 
 
 
10. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR  
A metal cube of side 4 cm is immersed in a water tank. The length and breadth of the 
tank are 8 cm and 4 cm respectively. Find the rise in level of the water. 
11. In a particular section of Class IX, 40 students were asked about their birth month  
and the following graph was prepared for the data so obtained: 
 
Find the probability that a student of Class IX was born in August. 
 
Page 3


  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 2 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Question numbers 1 to 6 in Section A are multiple choice questions where you are to 
select one correct option out of the given four. 
4. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify: 
? ? ? ? ? ?
? ? ? ? ? 6 27 3 3 1 2 3  
 
2. Find the value of the polynomial x
2
 – x – 1 at x = –1. 
 
3. Give the definition of Parallel Lines. 
 
4. Is (2, 0) a solution of x – 2y = 4?  
OR 
 The graph of the linear equation 2x – y = 4 cut x-axis at? 
 
5. PQRS is a parallelogram in which m ?PSR = 125°. What is the measurement of ?RQT?  
 
6. Find the Class size, if the Class marks of a frequency distribution are 6, 10, 14, 18, 22, 
26 and 30? 
OR 
The class marks of a distribution are : 47, 52, 57, 62, 67, and 72 
Determine the class size. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. The volume of a cuboid is given by the algebraic expression ky
2
 – 6ky + 8k. Find the 
possible expressions of the dimensions of the cuboid. 
 
8. If a point C lies between two points A and B such that AC = BC, then prove that                    
AC = 
1
2
AB. Explain by drawing a figure. 
 
9. In the figure below, BC = AC = AD and ? DAE = 75°. Find the value of y. 
 
 
 
 
 
 
 
 
 
10. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR  
A metal cube of side 4 cm is immersed in a water tank. The length and breadth of the 
tank are 8 cm and 4 cm respectively. Find the rise in level of the water. 
11. In a particular section of Class IX, 40 students were asked about their birth month  
and the following graph was prepared for the data so obtained: 
 
Find the probability that a student of Class IX was born in August. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
12. The angles of a quadrilateral are in the ratio 2 : 5 : 8 : 9. Find all the angles in the 
quadrilateral. 
OR 
 Three angles of a quadrilateral are 50°, 110° and 40°. Find the fourth angle of a 
quadrilateral. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  If a = 3 + b, then prove that a
3
 – b
3
 – 9ab = 27. 
OR 
 If 3x + 2y = 12 and xy = 6, find the value of 9x
2
 + 4y
2
. 
 
14. In the figure, AB DC, ? BDC = 30° and ? BAD = 80°, find the values of x, y and z. 
  
 
 
  
 
 
 
 
 
OR 
 PQRS is a square. Determine ? SRP. 
 
15. Use a suitable identity to factorise 27p
3
 + 8q
3
 + 54p
2
q + 36pq
2
. 
 
16. Factorise: b
2
 + c
2
 + 2(ab + bc + ca). 
 
17. In the figure, l1 || l2 and a1 || a2. Find the value of x. 
 
 
Page 4


  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 2 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Question numbers 1 to 6 in Section A are multiple choice questions where you are to 
select one correct option out of the given four. 
4. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify: 
? ? ? ? ? ?
? ? ? ? ? 6 27 3 3 1 2 3  
 
2. Find the value of the polynomial x
2
 – x – 1 at x = –1. 
 
3. Give the definition of Parallel Lines. 
 
4. Is (2, 0) a solution of x – 2y = 4?  
OR 
 The graph of the linear equation 2x – y = 4 cut x-axis at? 
 
5. PQRS is a parallelogram in which m ?PSR = 125°. What is the measurement of ?RQT?  
 
6. Find the Class size, if the Class marks of a frequency distribution are 6, 10, 14, 18, 22, 
26 and 30? 
OR 
The class marks of a distribution are : 47, 52, 57, 62, 67, and 72 
Determine the class size. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. The volume of a cuboid is given by the algebraic expression ky
2
 – 6ky + 8k. Find the 
possible expressions of the dimensions of the cuboid. 
 
8. If a point C lies between two points A and B such that AC = BC, then prove that                    
AC = 
1
2
AB. Explain by drawing a figure. 
 
9. In the figure below, BC = AC = AD and ? DAE = 75°. Find the value of y. 
 
 
 
 
 
 
 
 
 
10. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR  
A metal cube of side 4 cm is immersed in a water tank. The length and breadth of the 
tank are 8 cm and 4 cm respectively. Find the rise in level of the water. 
11. In a particular section of Class IX, 40 students were asked about their birth month  
and the following graph was prepared for the data so obtained: 
 
Find the probability that a student of Class IX was born in August. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
12. The angles of a quadrilateral are in the ratio 2 : 5 : 8 : 9. Find all the angles in the 
quadrilateral. 
OR 
 Three angles of a quadrilateral are 50°, 110° and 40°. Find the fourth angle of a 
quadrilateral. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  If a = 3 + b, then prove that a
3
 – b
3
 – 9ab = 27. 
OR 
 If 3x + 2y = 12 and xy = 6, find the value of 9x
2
 + 4y
2
. 
 
14. In the figure, AB DC, ? BDC = 30° and ? BAD = 80°, find the values of x, y and z. 
  
 
 
  
 
 
 
 
 
OR 
 PQRS is a square. Determine ? SRP. 
 
15. Use a suitable identity to factorise 27p
3
 + 8q
3
 + 54p
2
q + 36pq
2
. 
 
16. Factorise: b
2
 + c
2
 + 2(ab + bc + ca). 
 
17. In the figure, l1 || l2 and a1 || a2. Find the value of x. 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
18. A bag contains 12 balls out of which x are white. If one ball is taken out from the bag, 
find the probability of getting a white ball. If 6 more white balls are added to the bag 
and the probability now for getting a white ball is twice the previous one, find the 
value of x. 
19. A storehouse measures 40 m × 25 m × 10 m. Find the maximum number of wooden 
crates, each measuring 1.5 m × 1.25 m × 0.5 m, which can be stored in the storehouse.  
OR 
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover 
in 5 revolutions? (p = 22/7) 
 
20. A hemispherical bowl, made of steel, is 0.25 cm thick. The inner radius of the bowl is 5 
cm. Find the outer curved surface area of the bowl. 
OR 
Find the area of the base of a right circular cone is 314 cm
2
 and its height is 15 cm. 
Find the volume of the cone. Also find the slant height of the cone if the radius is 10 
cm. 
 
21. The length of 40 leaves of a plant are measured correct to one millimeter, and the data 
obtained is represented in the following table: 
 
Length (in mm) Number of leaves 
118 – 126 
127 – 135 
136 – 144 
145 – 153 
154 – 162 
163 – 171 
172 – 180 
3 
5 
9 
12 
5 
4 
2 
Draw a histogram to represent the given data. 
i. Is there any other suitable graphical representation for the same data? 
ii. Is it correct to conclude that maximum leaves are 153 mm long? Why?       
 
22. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at 
right angles. 
 
Section D 
(Questions 23 to 30 carry 4 marks each) 
 
23. If AD is the median of ?ABC, then prove that AB + AC > 2AD. 
 
24. Simplify: 
n 1 n
n 2 n 2
16 2 4 2
16 2 2 2
?
??
? ? ?
? ? ?
  
OR 
Page 5


  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 2 
Time: 3 hrs  Total Marks: 80 
      
General Instructions:  
1. All questions are compulsory. 
2. The question paper consists of 30 questions divided into four sections A, B, C, and D. 
Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions 
of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D 
comprises of 8 questions of 4 marks each. 
3. Question numbers 1 to 6 in Section A are multiple choice questions where you are to 
select one correct option out of the given four. 
4. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. Simplify: 
? ? ? ? ? ?
? ? ? ? ? 6 27 3 3 1 2 3  
 
2. Find the value of the polynomial x
2
 – x – 1 at x = –1. 
 
3. Give the definition of Parallel Lines. 
 
4. Is (2, 0) a solution of x – 2y = 4?  
OR 
 The graph of the linear equation 2x – y = 4 cut x-axis at? 
 
5. PQRS is a parallelogram in which m ?PSR = 125°. What is the measurement of ?RQT?  
 
6. Find the Class size, if the Class marks of a frequency distribution are 6, 10, 14, 18, 22, 
26 and 30? 
OR 
The class marks of a distribution are : 47, 52, 57, 62, 67, and 72 
Determine the class size. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. The volume of a cuboid is given by the algebraic expression ky
2
 – 6ky + 8k. Find the 
possible expressions of the dimensions of the cuboid. 
 
8. If a point C lies between two points A and B such that AC = BC, then prove that                    
AC = 
1
2
AB. Explain by drawing a figure. 
 
9. In the figure below, BC = AC = AD and ? DAE = 75°. Find the value of y. 
 
 
 
 
 
 
 
 
 
10. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR  
A metal cube of side 4 cm is immersed in a water tank. The length and breadth of the 
tank are 8 cm and 4 cm respectively. Find the rise in level of the water. 
11. In a particular section of Class IX, 40 students were asked about their birth month  
and the following graph was prepared for the data so obtained: 
 
Find the probability that a student of Class IX was born in August. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
12. The angles of a quadrilateral are in the ratio 2 : 5 : 8 : 9. Find all the angles in the 
quadrilateral. 
OR 
 Three angles of a quadrilateral are 50°, 110° and 40°. Find the fourth angle of a 
quadrilateral. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  If a = 3 + b, then prove that a
3
 – b
3
 – 9ab = 27. 
OR 
 If 3x + 2y = 12 and xy = 6, find the value of 9x
2
 + 4y
2
. 
 
14. In the figure, AB DC, ? BDC = 30° and ? BAD = 80°, find the values of x, y and z. 
  
 
 
  
 
 
 
 
 
OR 
 PQRS is a square. Determine ? SRP. 
 
15. Use a suitable identity to factorise 27p
3
 + 8q
3
 + 54p
2
q + 36pq
2
. 
 
16. Factorise: b
2
 + c
2
 + 2(ab + bc + ca). 
 
17. In the figure, l1 || l2 and a1 || a2. Find the value of x. 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
18. A bag contains 12 balls out of which x are white. If one ball is taken out from the bag, 
find the probability of getting a white ball. If 6 more white balls are added to the bag 
and the probability now for getting a white ball is twice the previous one, find the 
value of x. 
19. A storehouse measures 40 m × 25 m × 10 m. Find the maximum number of wooden 
crates, each measuring 1.5 m × 1.25 m × 0.5 m, which can be stored in the storehouse.  
OR 
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover 
in 5 revolutions? (p = 22/7) 
 
20. A hemispherical bowl, made of steel, is 0.25 cm thick. The inner radius of the bowl is 5 
cm. Find the outer curved surface area of the bowl. 
OR 
Find the area of the base of a right circular cone is 314 cm
2
 and its height is 15 cm. 
Find the volume of the cone. Also find the slant height of the cone if the radius is 10 
cm. 
 
21. The length of 40 leaves of a plant are measured correct to one millimeter, and the data 
obtained is represented in the following table: 
 
Length (in mm) Number of leaves 
118 – 126 
127 – 135 
136 – 144 
145 – 153 
154 – 162 
163 – 171 
172 – 180 
3 
5 
9 
12 
5 
4 
2 
Draw a histogram to represent the given data. 
i. Is there any other suitable graphical representation for the same data? 
ii. Is it correct to conclude that maximum leaves are 153 mm long? Why?       
 
22. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at 
right angles. 
 
Section D 
(Questions 23 to 30 carry 4 marks each) 
 
23. If AD is the median of ?ABC, then prove that AB + AC > 2AD. 
 
24. Simplify: 
n 1 n
n 2 n 2
16 2 4 2
16 2 2 2
?
??
? ? ?
? ? ?
  
OR 
  
 
CBSE IX | Mathematics 
Sample Paper 2 
 
     
If 25
x – 1
 = 5
2x – 1
 – 100, find the value of x. 
 
25. In the figure, PQRS is a square and SRT is an equilateral triangle. Prove that:  
a) ? PST = ? QRT 
b) PT = QT 
c) ? TQR = 15°  
 
 
OR 
Ajay was asked to find the sum of the four angles of a quadrilateral. He found the sum 
of the four angles as 270° by giving the reasoning as follows: 
 Sum of the three angles of a triangle [made up of three sides]  
= 2 right angles = (3 – 1) right angles. 
 So, the sum of the four angles of quadrilateral [made up of four sides]  
= (4 – 1) right angles = 3 right angles = 270°. 
 His classmate Anju pointed out that the sum obtained is incorrect and found the 
correct sum. Ajay accepted his mistake and thanked Anju for the same. Write the 
correct solution. What value is depicted from this action? 
26. (a)Simplify:
? ?
??
?
??
??
1
3 4
11
33
5 8 27 
 (b) Represent 7 on the number line. 
 
27. Find the median of 41, 43, 127, 99, 61, 92, 71, 58, and 57. 
If 58 is replaced by 85, what will be the new median? 
 
28. The following table gives the distribution of students of two sections according to the 
marks obtained by them: 
 
 
 
 
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