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Mathematics (Maths) Class 9

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 Page 1


  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 5 
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. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. What is the decimal form of 
11
1000
? 
OR 
Is zero a rational number? Justify. 
 
2.   x + y = 2 and x – y = 4. Find the values of x and y.  
 
3. In the given figure, find the value of x? 
 
 
 
 
 
 
4. If for one of the solutions of the equation ax + by + c = 0, x is negative and y is positive, 
then a portion of the above line will lie in which Quadrant? 
OR 
The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two 
variables to represent this statement. 
 
5. The Class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, and 102. 
Determine the Class size? 
 
 
 
 
Page 2


  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 5 
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. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. What is the decimal form of 
11
1000
? 
OR 
Is zero a rational number? Justify. 
 
2.   x + y = 2 and x – y = 4. Find the values of x and y.  
 
3. In the given figure, find the value of x? 
 
 
 
 
 
 
4. If for one of the solutions of the equation ax + by + c = 0, x is negative and y is positive, 
then a portion of the above line will lie in which Quadrant? 
OR 
The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two 
variables to represent this statement. 
 
5. The Class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, and 102. 
Determine the Class size? 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
6. PQRS is a parallelogram in which ?PSR = 125°. Find ?RQT. 
 
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. If a = 2+ 3 , find the value of a +
1
a
. 
 
8. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 5 units. Write the coordinates of such a point if it lies in one 
of the following quadrants: 
 (i) I Quadrant  (ii) II Quadrant (iii) III Quadrant   (iv) IV Quadrant 
       
 
9. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR 
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet 
containing 12 such matchboxes? 
 
10. Check which of the following are solutions of the equation 7x – 5y = –3. 
i.   (–1, –2) 
ii.   (–4, –5) 
OR 
Explain linear equations in two variables. 
 
11. Find the area of an isosceles triangle with base 10 cm and perimeter 36 cm. 
 
12. Simplify: (–2x + 5y – 3z)
2
.
 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13. Express 0.001 as a fraction in the simplest form. 
OR 
Simplify 
2 2 2 2
2 2 2 2
a b a a b b
a b b a a b
? ? ? ?
?
? ? ? ?
 
 
Page 3


  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 5 
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. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. What is the decimal form of 
11
1000
? 
OR 
Is zero a rational number? Justify. 
 
2.   x + y = 2 and x – y = 4. Find the values of x and y.  
 
3. In the given figure, find the value of x? 
 
 
 
 
 
 
4. If for one of the solutions of the equation ax + by + c = 0, x is negative and y is positive, 
then a portion of the above line will lie in which Quadrant? 
OR 
The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two 
variables to represent this statement. 
 
5. The Class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, and 102. 
Determine the Class size? 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
6. PQRS is a parallelogram in which ?PSR = 125°. Find ?RQT. 
 
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. If a = 2+ 3 , find the value of a +
1
a
. 
 
8. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 5 units. Write the coordinates of such a point if it lies in one 
of the following quadrants: 
 (i) I Quadrant  (ii) II Quadrant (iii) III Quadrant   (iv) IV Quadrant 
       
 
9. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR 
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet 
containing 12 such matchboxes? 
 
10. Check which of the following are solutions of the equation 7x – 5y = –3. 
i.   (–1, –2) 
ii.   (–4, –5) 
OR 
Explain linear equations in two variables. 
 
11. Find the area of an isosceles triangle with base 10 cm and perimeter 36 cm. 
 
12. Simplify: (–2x + 5y – 3z)
2
.
 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13. Express 0.001 as a fraction in the simplest form. 
OR 
Simplify 
2 2 2 2
2 2 2 2
a b a a b b
a b b a a b
? ? ? ?
?
? ? ? ?
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
14. Find the value of x
3
 – 8y
3
 – 36xy – 216 when x = 2y + 6. 
OR 
Find the remainder when x
3
 + 3x
2
 + 3x + 1 is divided by x + p. 
    
 
15. In the figure, PQ is a line segment and O is the mid-point of PQ. R and S are on the 
same side of PQ such that ?PQS = ?QPR and ?POS = ?QOR. Prove that 
 
(i) ?PQR ? ?QOS 
(ii) PR = QS 
16. If the polynomials az
3 
+ 4z
2 
+ 3z – 4 and z
3 
– 4z + a leave the same remainder when 
divided by z – 3, then find the value of a. 
 
17. In the given figure, DE ? OR and AP and BP are bisectors of ?EAB and ?RBA, 
respectively. Find ?APB. 
 
 
 
 
 
 
 
 
 
 
 
Page 4


  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 5 
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. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. What is the decimal form of 
11
1000
? 
OR 
Is zero a rational number? Justify. 
 
2.   x + y = 2 and x – y = 4. Find the values of x and y.  
 
3. In the given figure, find the value of x? 
 
 
 
 
 
 
4. If for one of the solutions of the equation ax + by + c = 0, x is negative and y is positive, 
then a portion of the above line will lie in which Quadrant? 
OR 
The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two 
variables to represent this statement. 
 
5. The Class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, and 102. 
Determine the Class size? 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
6. PQRS is a parallelogram in which ?PSR = 125°. Find ?RQT. 
 
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. If a = 2+ 3 , find the value of a +
1
a
. 
 
8. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 5 units. Write the coordinates of such a point if it lies in one 
of the following quadrants: 
 (i) I Quadrant  (ii) II Quadrant (iii) III Quadrant   (iv) IV Quadrant 
       
 
9. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR 
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet 
containing 12 such matchboxes? 
 
10. Check which of the following are solutions of the equation 7x – 5y = –3. 
i.   (–1, –2) 
ii.   (–4, –5) 
OR 
Explain linear equations in two variables. 
 
11. Find the area of an isosceles triangle with base 10 cm and perimeter 36 cm. 
 
12. Simplify: (–2x + 5y – 3z)
2
.
 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13. Express 0.001 as a fraction in the simplest form. 
OR 
Simplify 
2 2 2 2
2 2 2 2
a b a a b b
a b b a a b
? ? ? ?
?
? ? ? ?
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
14. Find the value of x
3
 – 8y
3
 – 36xy – 216 when x = 2y + 6. 
OR 
Find the remainder when x
3
 + 3x
2
 + 3x + 1 is divided by x + p. 
    
 
15. In the figure, PQ is a line segment and O is the mid-point of PQ. R and S are on the 
same side of PQ such that ?PQS = ?QPR and ?POS = ?QOR. Prove that 
 
(i) ?PQR ? ?QOS 
(ii) PR = QS 
16. If the polynomials az
3 
+ 4z
2 
+ 3z – 4 and z
3 
– 4z + a leave the same remainder when 
divided by z – 3, then find the value of a. 
 
17. In the given figure, DE ? OR and AP and BP are bisectors of ?EAB and ?RBA, 
respectively. Find ?APB. 
 
 
 
 
 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
18. The following frequency distribution table gives the weights of 38 students of a class. 
Weight in kg Number of students 
30 – 35 10 
35 – 40 5 
40 – 45 15 
45 – 50 5 
50 – 55 1 
55 – 60 2 
Total 38 
 
Find the probability that the weight of students is  
i. more than or equal to 45 Kg 
ii. less than 30 kg 
iii. more than  or equal to 30 Kg but less than 60 Kg 
 
19. Find the area of the triangle formed by A (0, 4), O(0, 0) and B(3, 0). 
20. If x = 1+ 2 , find the value of 
??
?
??
??
3
1
x
x
. 
OR 
Find the value of x
3
 + y
3
 – 12xy + 64 when x + y = -4. 
 
21. A wooden article was made by scooping out a hemisphere from each end of a solid 
cylinder. If the height of the cylinder is 10 cm and its base is 7 cm, find the total 
surface area of the article.  
OR 
How much cardboard is required to make 35 penholders in the shape of cylinders, 
each of radius 3 cm and height 10.5 cm? 
 
 
 
 
 
 
 
 
Page 5


  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 5 
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. Use of calculator is not permitted. 
 
Section A 
(Questions 1 to 6 carry 1 mark each) 
 
1. What is the decimal form of 
11
1000
? 
OR 
Is zero a rational number? Justify. 
 
2.   x + y = 2 and x – y = 4. Find the values of x and y.  
 
3. In the given figure, find the value of x? 
 
 
 
 
 
 
4. If for one of the solutions of the equation ax + by + c = 0, x is negative and y is positive, 
then a portion of the above line will lie in which Quadrant? 
OR 
The cost of 5 pencils is equal to the cost of 2 ballpoints. Write a linear equation in two 
variables to represent this statement. 
 
5. The Class marks of a distribution are 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, and 102. 
Determine the Class size? 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
6. PQRS is a parallelogram in which ?PSR = 125°. Find ?RQT. 
 
 
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. If a = 2+ 3 , find the value of a +
1
a
. 
 
8. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 5 units. Write the coordinates of such a point if it lies in one 
of the following quadrants: 
 (i) I Quadrant  (ii) II Quadrant (iii) III Quadrant   (iv) IV Quadrant 
       
 
9. The total surface area of a cube is 294 cm
2
. Find its volume. 
OR 
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet 
containing 12 such matchboxes? 
 
10. Check which of the following are solutions of the equation 7x – 5y = –3. 
i.   (–1, –2) 
ii.   (–4, –5) 
OR 
Explain linear equations in two variables. 
 
11. Find the area of an isosceles triangle with base 10 cm and perimeter 36 cm. 
 
12. Simplify: (–2x + 5y – 3z)
2
.
 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13. Express 0.001 as a fraction in the simplest form. 
OR 
Simplify 
2 2 2 2
2 2 2 2
a b a a b b
a b b a a b
? ? ? ?
?
? ? ? ?
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
14. Find the value of x
3
 – 8y
3
 – 36xy – 216 when x = 2y + 6. 
OR 
Find the remainder when x
3
 + 3x
2
 + 3x + 1 is divided by x + p. 
    
 
15. In the figure, PQ is a line segment and O is the mid-point of PQ. R and S are on the 
same side of PQ such that ?PQS = ?QPR and ?POS = ?QOR. Prove that 
 
(i) ?PQR ? ?QOS 
(ii) PR = QS 
16. If the polynomials az
3 
+ 4z
2 
+ 3z – 4 and z
3 
– 4z + a leave the same remainder when 
divided by z – 3, then find the value of a. 
 
17. In the given figure, DE ? OR and AP and BP are bisectors of ?EAB and ?RBA, 
respectively. Find ?APB. 
 
 
 
 
 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
18. The following frequency distribution table gives the weights of 38 students of a class. 
Weight in kg Number of students 
30 – 35 10 
35 – 40 5 
40 – 45 15 
45 – 50 5 
50 – 55 1 
55 – 60 2 
Total 38 
 
Find the probability that the weight of students is  
i. more than or equal to 45 Kg 
ii. less than 30 kg 
iii. more than  or equal to 30 Kg but less than 60 Kg 
 
19. Find the area of the triangle formed by A (0, 4), O(0, 0) and B(3, 0). 
20. If x = 1+ 2 , find the value of 
??
?
??
??
3
1
x
x
. 
OR 
Find the value of x
3
 + y
3
 – 12xy + 64 when x + y = -4. 
 
21. A wooden article was made by scooping out a hemisphere from each end of a solid 
cylinder. If the height of the cylinder is 10 cm and its base is 7 cm, find the total 
surface area of the article.  
OR 
How much cardboard is required to make 35 penholders in the shape of cylinders, 
each of radius 3 cm and height 10.5 cm? 
 
 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 5 
 
     
22. 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 
i. Draw a histogram to represent the given data. 
ii. Is there any other suitable graphical representation for the same data? 
iii. Is it correct to conclude that maximum leaves are 153 mm long? Why?       
 
 
Section D 
(Questions 23 to 30 carry 4 marks each) 
 
23. Simplify:
?
?
??
3 2 2 3 12
3 2 2 3 3 2
  
OR 
Express 
3
325 ??
 with rational denominator. 
 
24. ABCD is a rhombus. Show that the diagonal AC bisects ?A as well as ?C and diagonal 
BD bisects ?B as well as ?D.  
 
25. If the polynomial x
4
 + mx
3
 – 25x
2
 – 16x + n is exactly divisible by x
2
 – 4, then what are 
the values of m and n? 
 
26. In the given figure, AC is the bisector of BAD ? . Find the measures of 
? ? ? ? 1, 2, 3 and 4. 
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