Class 9 Math: Sample Practice Question Paper- 4 PDF Download

 Page 1


  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 4 
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. Write the decimal form of
56
1000
. 
OR 
Simplify 
4
3
by rationalizing the denominator. 
 
2. What is Linear Equation in two variables? 
 
3. If a triangle and a parallelogram are on the same base and between same parallels, 
then find the ratio of the area of the triangle to the area of parallelogram? 
 
4. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?  
OR 
Is g(x) = vx – 3 polynomial? Justify. 
 
5. 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, 35. Find the range of the data? 
 
6. Three angles of a quadrilateral are 60°, 110° and 86°. What is the measure of the 
fourth angle of the quadrilateral? 
 
 
 
 
 
 
Page 2


  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 4 
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. Write the decimal form of
56
1000
. 
OR 
Simplify 
4
3
by rationalizing the denominator. 
 
2. What is Linear Equation in two variables? 
 
3. If a triangle and a parallelogram are on the same base and between same parallels, 
then find the ratio of the area of the triangle to the area of parallelogram? 
 
4. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?  
OR 
Is g(x) = vx – 3 polynomial? Justify. 
 
5. 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, 35. Find the range of the data? 
 
6. Three angles of a quadrilateral are 60°, 110° and 86°. What is the measure of the 
fourth angle of the quadrilateral? 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify: 
??
??
??
??
??
5
1
2
5
1
5
12
27
 
 
8. How many integral zeroes does the polynomial 3z
3
 + 8z
2
 – 1 have?
   
 
 
9. See the given figure and answer the following: 
 
(i)   Coordinates of point A 
 (ii)  Abscissa of point D 
 (iii) The point indentified by the coordinates (5, 4) 
 (iv) Coordinates of point C 
 
10. In the given figure, ABCD is parallelogram, AE ? DC and CF ? AD. If AB = 16 cm. AE = 
8 cm and CF = 10 cm, find AD.  
 
OR 
The lengths of the diagonals of a rhombus are 12 cm and 16 cm. Find the area of the 
rhombus. 
 
Page 3


  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 4 
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. Write the decimal form of
56
1000
. 
OR 
Simplify 
4
3
by rationalizing the denominator. 
 
2. What is Linear Equation in two variables? 
 
3. If a triangle and a parallelogram are on the same base and between same parallels, 
then find the ratio of the area of the triangle to the area of parallelogram? 
 
4. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?  
OR 
Is g(x) = vx – 3 polynomial? Justify. 
 
5. 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, 35. Find the range of the data? 
 
6. Three angles of a quadrilateral are 60°, 110° and 86°. What is the measure of the 
fourth angle of the quadrilateral? 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify: 
??
??
??
??
??
5
1
2
5
1
5
12
27
 
 
8. How many integral zeroes does the polynomial 3z
3
 + 8z
2
 – 1 have?
   
 
 
9. See the given figure and answer the following: 
 
(i)   Coordinates of point A 
 (ii)  Abscissa of point D 
 (iii) The point indentified by the coordinates (5, 4) 
 (iv) Coordinates of point C 
 
10. In the given figure, ABCD is parallelogram, AE ? DC and CF ? AD. If AB = 16 cm. AE = 
8 cm and CF = 10 cm, find AD.  
 
OR 
The lengths of the diagonals of a rhombus are 12 cm and 16 cm. Find the area of the 
rhombus. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
11. How many litres of water flow out through a pipe having 5 cm
2
 area of cross section in 
one minute, if the speed of water in the pipe is 30 cm/sec?  
OR 
Find the volume, the total surface area of a cuboid which is 15 m long, 12 m wide and 
4.5 m high. 
 
12. Two angles are complementary. The larger angle is 3° less than twice the measure of 
the smaller angle. Find the measure of each angle. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Express 0.001 as a fraction in the simplest form. 
OR 
Simplify by rationalizing the denominator: 
6 4 3
6 4 3
 
 
14. Which of the following expression are polynomials in one variable? State reasons for 
your answers: 
 
? ? ? ?
? ?
? ?
22
22
x 1 x 2
(i)           (ii) t t 3
x
1
(iii) x 4x 5 (iv) 3x 6 x
2
1
(v) z
z
??
?
? ? ?
?
 
 
15. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0 
OR 
If p = 2 – a, prove that a
3
 + 6ap + p
3
 – 8 = 0 
 
16. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
  
Page 4


  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 4 
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. Write the decimal form of
56
1000
. 
OR 
Simplify 
4
3
by rationalizing the denominator. 
 
2. What is Linear Equation in two variables? 
 
3. If a triangle and a parallelogram are on the same base and between same parallels, 
then find the ratio of the area of the triangle to the area of parallelogram? 
 
4. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?  
OR 
Is g(x) = vx – 3 polynomial? Justify. 
 
5. 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, 35. Find the range of the data? 
 
6. Three angles of a quadrilateral are 60°, 110° and 86°. What is the measure of the 
fourth angle of the quadrilateral? 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify: 
??
??
??
??
??
5
1
2
5
1
5
12
27
 
 
8. How many integral zeroes does the polynomial 3z
3
 + 8z
2
 – 1 have?
   
 
 
9. See the given figure and answer the following: 
 
(i)   Coordinates of point A 
 (ii)  Abscissa of point D 
 (iii) The point indentified by the coordinates (5, 4) 
 (iv) Coordinates of point C 
 
10. In the given figure, ABCD is parallelogram, AE ? DC and CF ? AD. If AB = 16 cm. AE = 
8 cm and CF = 10 cm, find AD.  
 
OR 
The lengths of the diagonals of a rhombus are 12 cm and 16 cm. Find the area of the 
rhombus. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
11. How many litres of water flow out through a pipe having 5 cm
2
 area of cross section in 
one minute, if the speed of water in the pipe is 30 cm/sec?  
OR 
Find the volume, the total surface area of a cuboid which is 15 m long, 12 m wide and 
4.5 m high. 
 
12. Two angles are complementary. The larger angle is 3° less than twice the measure of 
the smaller angle. Find the measure of each angle. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Express 0.001 as a fraction in the simplest form. 
OR 
Simplify by rationalizing the denominator: 
6 4 3
6 4 3
 
 
14. Which of the following expression are polynomials in one variable? State reasons for 
your answers: 
 
? ? ? ?
? ?
? ?
22
22
x 1 x 2
(i)           (ii) t t 3
x
1
(iii) x 4x 5 (iv) 3x 6 x
2
1
(v) z
z
??
?
? ? ?
?
 
 
15. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0 
OR 
If p = 2 – a, prove that a
3
 + 6ap + p
3
 – 8 = 0 
 
16. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
  
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
 
17. 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 
 
 
18. The distribution of weight (in kg) of 100 people is given below. 
Weight in kg Frequency 
40-45 13 
45-50 25 
50-55 28 
55-60 15 
60-65 12 
65-70 5 
70-75 2 
Construct a histogram for the above distribution.  
OR 
The runs scored by a cricket player in the last 30 innings are: 
75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 
08, 24, 136, 117, 22, 99, 80, 112, 35. 
Arrange these scores in an ascending order and answer the following: 
(i) Find the highest score. 
(ii) Find the number of centuries scored by him. 
(iii) Find the number of times he scored over 50. 
 
 
19. Prove that the quadrilateral formed by the bisectors of internal angles of a cyclic 
quadrilateral is also cyclic. 
 
20. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at 
right angles. 
 
 
 
Page 5


  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
CBSE Board 
Class IX Mathematics 
Sample Paper 4 
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. Write the decimal form of
56
1000
. 
OR 
Simplify 
4
3
by rationalizing the denominator. 
 
2. What is Linear Equation in two variables? 
 
3. If a triangle and a parallelogram are on the same base and between same parallels, 
then find the ratio of the area of the triangle to the area of parallelogram? 
 
4. Find the value of p such that (x – 1) is a factor of the polynomial x
3 
+ 10x
2 
+ px?  
OR 
Is g(x) = vx – 3 polynomial? Justify. 
 
5. 70, 65, 75, 71, 36, 55, 61, 62, 41, 40, 39, 35. Find the range of the data? 
 
6. Three angles of a quadrilateral are 60°, 110° and 86°. What is the measure of the 
fourth angle of the quadrilateral? 
 
 
 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
Section B 
(Questions 7 to 12 carry 2 marks each) 
 
7. Simplify: 
??
??
??
??
??
5
1
2
5
1
5
12
27
 
 
8. How many integral zeroes does the polynomial 3z
3
 + 8z
2
 – 1 have?
   
 
 
9. See the given figure and answer the following: 
 
(i)   Coordinates of point A 
 (ii)  Abscissa of point D 
 (iii) The point indentified by the coordinates (5, 4) 
 (iv) Coordinates of point C 
 
10. In the given figure, ABCD is parallelogram, AE ? DC and CF ? AD. If AB = 16 cm. AE = 
8 cm and CF = 10 cm, find AD.  
 
OR 
The lengths of the diagonals of a rhombus are 12 cm and 16 cm. Find the area of the 
rhombus. 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
11. How many litres of water flow out through a pipe having 5 cm
2
 area of cross section in 
one minute, if the speed of water in the pipe is 30 cm/sec?  
OR 
Find the volume, the total surface area of a cuboid which is 15 m long, 12 m wide and 
4.5 m high. 
 
12. Two angles are complementary. The larger angle is 3° less than twice the measure of 
the smaller angle. Find the measure of each angle. 
 
Section C 
(Questions 13 to 22 carry 3 marks each) 
 
13.  Express 0.001 as a fraction in the simplest form. 
OR 
Simplify by rationalizing the denominator: 
6 4 3
6 4 3
 
 
14. Which of the following expression are polynomials in one variable? State reasons for 
your answers: 
 
? ? ? ?
? ?
? ?
22
22
x 1 x 2
(i)           (ii) t t 3
x
1
(iii) x 4x 5 (iv) 3x 6 x
2
1
(v) z
z
??
?
? ? ?
?
 
 
15. The polynomials p(x) = ax
3
 + 3x
2
 – 3 and q(x) = 2x
3
 – 5x + a when divided by (x – 4) 
leave the remainders R1 and R2. Find ‘a’ if R1 + R2 = 0 
OR 
If p = 2 – a, prove that a
3
 + 6ap + p
3
 – 8 = 0 
 
16. In figure, AB = AC, D is the point in the interior of ? ABC such that ? DBC = ? DCB. 
Prove that AD bisects ? BAC of ? ABC. 
  
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
 
17. 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 
 
 
18. The distribution of weight (in kg) of 100 people is given below. 
Weight in kg Frequency 
40-45 13 
45-50 25 
50-55 28 
55-60 15 
60-65 12 
65-70 5 
70-75 2 
Construct a histogram for the above distribution.  
OR 
The runs scored by a cricket player in the last 30 innings are: 
75, 125, 36, 89, 154, 56, 12, 28, 96, 142, 78, 54, 30, 88, 116, 104, 55, 84, 10, 29, 31, 
08, 24, 136, 117, 22, 99, 80, 112, 35. 
Arrange these scores in an ascending order and answer the following: 
(i) Find the highest score. 
(ii) Find the number of centuries scored by him. 
(iii) Find the number of times he scored over 50. 
 
 
19. Prove that the quadrilateral formed by the bisectors of internal angles of a cyclic 
quadrilateral is also cyclic. 
 
20. In a parallelogram, show that the angle bisectors of two adjacent angles intersect at 
right angles. 
 
 
 
  
 
CBSE IX | Mathematics 
Sample Paper 4 
 
     
21. If a dice is rolled once, what is the probability that it will show  
 i. A multiple of 1? ii. A multiple of 7?  
OR 
 Two coins are tossed simultaneously 400 times, and we get 
 Two heads: 180 times 
 One head : 148 times 
 No head: 72 times 
 If two coins tossed at random, what is the probability of getting 2 heads, 1 head and 
zero head? 
 
22. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete 
revolutions to move over once to level a playground. Find the area of the playground 
in m
2
? 
22
7
??
??
??
??
 
 
Section D 
(Questions 23 to 30 carry 4 marks each) 
 
23. If 
1
m
23
?
?
 
and 
1
n
23
?
?
, then what is the value of 7m
2
 + 11mn – 7n
2
? 
OR 
If both a and b are rational numbers, find a and b in the following expression:
 
35
a 5 b
3 2 5
?
??
?
 
 
 
24. In the figure, l1 || l2 and a1 || a2. Find the value of x. 
 
 
25. Without actual division, prove that 2x
4 
+ x
3
 – 14x
2 
– 19x – 6 is exactly divisible by  
x
2 
+ 3x + 2. 
OR 
Factorise 2x
3
 - 3x
2
 - 17x + 30.