Final Exam Class 9 Mathematics Set 3 | Mathematics (Maths) Class 9 PDF Download

 Page 1


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) a rational number b) an integer
c) an irrational number d) a whole number
1.  is [1] p a) no solution b) infinitely many solutions
c) a unique solution d) two solutions
2. The linear equation 3x - 5y = 15 has [1]
a) y-axis b) x-axis
c) a line parallel to y-axis d) a line parallel to x-axis
3. Two points having same abscissa but different ordinates lie on [1]
a) 6 b) 5
c) 2 d) 3
4. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
[1]
a) (0,3) b) (3,0)
5. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point [1]
Page 1 of 18
Page 2


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) a rational number b) an integer
c) an irrational number d) a whole number
1.  is [1] p a) no solution b) infinitely many solutions
c) a unique solution d) two solutions
2. The linear equation 3x - 5y = 15 has [1]
a) y-axis b) x-axis
c) a line parallel to y-axis d) a line parallel to x-axis
3. Two points having same abscissa but different ordinates lie on [1]
a) 6 b) 5
c) 2 d) 3
4. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
[1]
a) (0,3) b) (3,0)
5. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point [1]
Page 1 of 18
c) (2, 0) d) (0 ,2)
a) A postulate b) A proof
c) An axiom d) A definition
6. Euclid stated that all right angles are equal to each other in the form of [1]
a)
128
o b)
40
o
c)
140
o d)
100
o
7. In the figure AB & CD are two straight lines intersecting at O, OP is a ray. What is the measure of . [1] ? A O D a)
70
o b)
80
o
c)
90
o d)
100
o
8. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a) every real number b) 1
c) not defined d) 0
9. Zero of the zero polynomial is - [1]
a) b)
c) d)
10. Express y in terms of x in the equation 5x - 2y = 7. [1]
y = 5 x - 7 2 y = 7 - 5 x 2 y = 7 x + 5 2 y = 5 x + 7 2 a) b)
c) d)
11. ABCD is a Rhombus such that = 40 , then  is [1] ? A C B ° ? A D B 1 0 0 ° 4 0 ° 6 0 ° 5 0 ° a)
125
o b)
115
o
c)
120
o d)
135
o
12. Diagonals of a quadrilateral ABCD bisect each other. If A = 45
o
, then B =
[1]
? ? a) b)
c) d)
13. In the figure, if   then  is equal to : [1] ? D A B = , 6 0 o ? A B D = , 5 0 o ? A C B 8 0 o 6 0 o 5 0 o 7 0 o Page 2 of 18
Page 3


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) a rational number b) an integer
c) an irrational number d) a whole number
1.  is [1] p a) no solution b) infinitely many solutions
c) a unique solution d) two solutions
2. The linear equation 3x - 5y = 15 has [1]
a) y-axis b) x-axis
c) a line parallel to y-axis d) a line parallel to x-axis
3. Two points having same abscissa but different ordinates lie on [1]
a) 6 b) 5
c) 2 d) 3
4. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
[1]
a) (0,3) b) (3,0)
5. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point [1]
Page 1 of 18
c) (2, 0) d) (0 ,2)
a) A postulate b) A proof
c) An axiom d) A definition
6. Euclid stated that all right angles are equal to each other in the form of [1]
a)
128
o b)
40
o
c)
140
o d)
100
o
7. In the figure AB & CD are two straight lines intersecting at O, OP is a ray. What is the measure of . [1] ? A O D a)
70
o b)
80
o
c)
90
o d)
100
o
8. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a) every real number b) 1
c) not defined d) 0
9. Zero of the zero polynomial is - [1]
a) b)
c) d)
10. Express y in terms of x in the equation 5x - 2y = 7. [1]
y = 5 x - 7 2 y = 7 - 5 x 2 y = 7 x + 5 2 y = 5 x + 7 2 a) b)
c) d)
11. ABCD is a Rhombus such that = 40 , then  is [1] ? A C B ° ? A D B 1 0 0 ° 4 0 ° 6 0 ° 5 0 ° a)
125
o b)
115
o
c)
120
o d)
135
o
12. Diagonals of a quadrilateral ABCD bisect each other. If A = 45
o
, then B =
[1]
? ? a) b)
c) d)
13. In the figure, if   then  is equal to : [1] ? D A B = , 6 0 o ? A B D = , 5 0 o ? A C B 8 0 o 6 0 o 5 0 o 7 0 o Page 2 of 18
Section B
a) b)
c) d)
14. The simplest form of  is [1] 0 . 5 7 ¯ ¯ ¯ 2 6 4 5 5 7 9 9 5 7 1 0 0 5 7 9 0 a) (-5, -7) b) (-1, 1)
c) (3, 9) d) (3, 7)
15. Which of the following point does not lie on the line y = 2x + 3? [1]
a) ASA b) SAS
c) SSS d) RHS
16. The congruence rule, by which the two triangles in the given figure are congruent is ________. [1]
a) Width of the rectangle b) Length of the rectangle
c) Perimeter of the rectangle d) Area of the rectangle
17. In a histogram, which of the following is proportional to the frequency of the corresponding class? [1]
a) 1 : 1 b) 2 : 3
c) 1 : 2 d) 2 : 1
18. The curved surface area of a cylinder and a cone is equal. If their base radius is same, then the ratio of the slant
height of the cone to the height of the cylinder is
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 6 cm
2
. 
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area = .
[1]
( s - a ) ( s - b ) ( s - c ) - - - - - - - - - - - - - - - - v a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The point (1, 1) is the solution of x + y = 2. 
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
[1]
21. The base of an isosceles triangle measures 24 cm and its area is 192 cm
2
. Find its perimeter.
[2]
22. In given figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the
value of  ACD +  BED. 
[2]
? ? Page 3 of 18
Page 4


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) a rational number b) an integer
c) an irrational number d) a whole number
1.  is [1] p a) no solution b) infinitely many solutions
c) a unique solution d) two solutions
2. The linear equation 3x - 5y = 15 has [1]
a) y-axis b) x-axis
c) a line parallel to y-axis d) a line parallel to x-axis
3. Two points having same abscissa but different ordinates lie on [1]
a) 6 b) 5
c) 2 d) 3
4. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
[1]
a) (0,3) b) (3,0)
5. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point [1]
Page 1 of 18
c) (2, 0) d) (0 ,2)
a) A postulate b) A proof
c) An axiom d) A definition
6. Euclid stated that all right angles are equal to each other in the form of [1]
a)
128
o b)
40
o
c)
140
o d)
100
o
7. In the figure AB & CD are two straight lines intersecting at O, OP is a ray. What is the measure of . [1] ? A O D a)
70
o b)
80
o
c)
90
o d)
100
o
8. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a) every real number b) 1
c) not defined d) 0
9. Zero of the zero polynomial is - [1]
a) b)
c) d)
10. Express y in terms of x in the equation 5x - 2y = 7. [1]
y = 5 x - 7 2 y = 7 - 5 x 2 y = 7 x + 5 2 y = 5 x + 7 2 a) b)
c) d)
11. ABCD is a Rhombus such that = 40 , then  is [1] ? A C B ° ? A D B 1 0 0 ° 4 0 ° 6 0 ° 5 0 ° a)
125
o b)
115
o
c)
120
o d)
135
o
12. Diagonals of a quadrilateral ABCD bisect each other. If A = 45
o
, then B =
[1]
? ? a) b)
c) d)
13. In the figure, if   then  is equal to : [1] ? D A B = , 6 0 o ? A B D = , 5 0 o ? A C B 8 0 o 6 0 o 5 0 o 7 0 o Page 2 of 18
Section B
a) b)
c) d)
14. The simplest form of  is [1] 0 . 5 7 ¯ ¯ ¯ 2 6 4 5 5 7 9 9 5 7 1 0 0 5 7 9 0 a) (-5, -7) b) (-1, 1)
c) (3, 9) d) (3, 7)
15. Which of the following point does not lie on the line y = 2x + 3? [1]
a) ASA b) SAS
c) SSS d) RHS
16. The congruence rule, by which the two triangles in the given figure are congruent is ________. [1]
a) Width of the rectangle b) Length of the rectangle
c) Perimeter of the rectangle d) Area of the rectangle
17. In a histogram, which of the following is proportional to the frequency of the corresponding class? [1]
a) 1 : 1 b) 2 : 3
c) 1 : 2 d) 2 : 1
18. The curved surface area of a cylinder and a cone is equal. If their base radius is same, then the ratio of the slant
height of the cone to the height of the cylinder is
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 6 cm
2
. 
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area = .
[1]
( s - a ) ( s - b ) ( s - c ) - - - - - - - - - - - - - - - - v a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The point (1, 1) is the solution of x + y = 2. 
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
[1]
21. The base of an isosceles triangle measures 24 cm and its area is 192 cm
2
. Find its perimeter.
[2]
22. In given figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the
value of  ACD +  BED. 
[2]
? ? Page 3 of 18
Section C
23. The outer diameter of a spherical shell is 10 cm and the inner diameter is 9 cm. Find the volume of the metal
contained in the shell.
[2]
24. In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles.
Prove that B lies on the line segment DC. 
[2]
OR
If O is the centre of the circle, find the value of x in given figure: 
25. Find whether the given equation have x = 2, y = 1 as a solution:x + y + 4 = 0. [2]
OR
Find whether  is the solution of the equation x – 2y = 4 or not? ( , 4 ) 2 – v 2 – v 26. Give three rational numbers between  and . [3]
1 3 1 2 27. Find the value of k, if x - 1 is a factor of p(x) in case: [3] p ( x ) = 2 + k x + x 2 2 – v 28. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of
the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
[3]
OR
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and
15 m. The advertisements yield an earning of Rs2000 per m
2
 a year. A company hired one of its walls for 6 months.
How much rent did it pay?
29. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any
common such solution?
3x + 2y = 6 and 5x + 2y = 10
[3]
30. Show that the quadrilateral formed by joining the mid-points the sides of a rhombus, taken in order, form a
rectangle.
[3]
OR
In figure D is mid-points of AB. P is on AC such that PC = AP and DE  BP, then show that AE = AC. 
1 2 ? 1 3 31. In Figure, LM is a line parallel to the y-axis at a distance of 3 units. [3]
Page 4 of 18
Page 5


Time Allowed: 3 hours Maximum Marks: 80 
General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 1 mark each.
3. Section B has 5 questions carrying 02 marks each.
4. Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units of assessment carrying 04 marks each.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 5 marks, 2 Qs of 3 marks and 2 Questions of
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
a) a rational number b) an integer
c) an irrational number d) a whole number
1.  is [1] p a) no solution b) infinitely many solutions
c) a unique solution d) two solutions
2. The linear equation 3x - 5y = 15 has [1]
a) y-axis b) x-axis
c) a line parallel to y-axis d) a line parallel to x-axis
3. Two points having same abscissa but different ordinates lie on [1]
a) 6 b) 5
c) 2 d) 3
4. To draw a histogram to represent the following frequency distribution :
Class interval 5-10 10-15 15-25 25-45 45-75
Frequency 6 12 10 8 15
The adjusted frequency for the class 25-45 is
[1]
a) (0,3) b) (3,0)
5. The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point [1]
Page 1 of 18
c) (2, 0) d) (0 ,2)
a) A postulate b) A proof
c) An axiom d) A definition
6. Euclid stated that all right angles are equal to each other in the form of [1]
a)
128
o b)
40
o
c)
140
o d)
100
o
7. In the figure AB & CD are two straight lines intersecting at O, OP is a ray. What is the measure of . [1] ? A O D a)
70
o b)
80
o
c)
90
o d)
100
o
8. The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD = 50
o
, then DPC =
[1]
? ? a) every real number b) 1
c) not defined d) 0
9. Zero of the zero polynomial is - [1]
a) b)
c) d)
10. Express y in terms of x in the equation 5x - 2y = 7. [1]
y = 5 x - 7 2 y = 7 - 5 x 2 y = 7 x + 5 2 y = 5 x + 7 2 a) b)
c) d)
11. ABCD is a Rhombus such that = 40 , then  is [1] ? A C B ° ? A D B 1 0 0 ° 4 0 ° 6 0 ° 5 0 ° a)
125
o b)
115
o
c)
120
o d)
135
o
12. Diagonals of a quadrilateral ABCD bisect each other. If A = 45
o
, then B =
[1]
? ? a) b)
c) d)
13. In the figure, if   then  is equal to : [1] ? D A B = , 6 0 o ? A B D = , 5 0 o ? A C B 8 0 o 6 0 o 5 0 o 7 0 o Page 2 of 18
Section B
a) b)
c) d)
14. The simplest form of  is [1] 0 . 5 7 ¯ ¯ ¯ 2 6 4 5 5 7 9 9 5 7 1 0 0 5 7 9 0 a) (-5, -7) b) (-1, 1)
c) (3, 9) d) (3, 7)
15. Which of the following point does not lie on the line y = 2x + 3? [1]
a) ASA b) SAS
c) SSS d) RHS
16. The congruence rule, by which the two triangles in the given figure are congruent is ________. [1]
a) Width of the rectangle b) Length of the rectangle
c) Perimeter of the rectangle d) Area of the rectangle
17. In a histogram, which of the following is proportional to the frequency of the corresponding class? [1]
a) 1 : 1 b) 2 : 3
c) 1 : 2 d) 2 : 1
18. The curved surface area of a cylinder and a cone is equal. If their base radius is same, then the ratio of the slant
height of the cone to the height of the cylinder is
[1]
a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
19. Assertion (A): The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 6 cm
2
. 
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area = .
[1]
( s - a ) ( s - b ) ( s - c ) - - - - - - - - - - - - - - - - v a) Both A and R are true and R is the correct
explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
20. Assertion (A): The point (1, 1) is the solution of x + y = 2. 
Reason (R): Every point which satisfy the linear equation is a solution of the equation.
[1]
21. The base of an isosceles triangle measures 24 cm and its area is 192 cm
2
. Find its perimeter.
[2]
22. In given figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the
value of  ACD +  BED. 
[2]
? ? Page 3 of 18
Section C
23. The outer diameter of a spherical shell is 10 cm and the inner diameter is 9 cm. Find the volume of the metal
contained in the shell.
[2]
24. In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the two circles.
Prove that B lies on the line segment DC. 
[2]
OR
If O is the centre of the circle, find the value of x in given figure: 
25. Find whether the given equation have x = 2, y = 1 as a solution:x + y + 4 = 0. [2]
OR
Find whether  is the solution of the equation x – 2y = 4 or not? ( , 4 ) 2 – v 2 – v 26. Give three rational numbers between  and . [3]
1 3 1 2 27. Find the value of k, if x - 1 is a factor of p(x) in case: [3] p ( x ) = 2 + k x + x 2 2 – v 28. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of
the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
[3]
OR
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and
15 m. The advertisements yield an earning of Rs2000 per m
2
 a year. A company hired one of its walls for 6 months.
How much rent did it pay?
29. Find solutions of the form x = a, y = 0 and x = 0, y = b for the following pairs of equations. Do they have any
common such solution?
3x + 2y = 6 and 5x + 2y = 10
[3]
30. Show that the quadrilateral formed by joining the mid-points the sides of a rhombus, taken in order, form a
rectangle.
[3]
OR
In figure D is mid-points of AB. P is on AC such that PC = AP and DE  BP, then show that AE = AC. 
1 2 ? 1 3 31. In Figure, LM is a line parallel to the y-axis at a distance of 3 units. [3]
Page 4 of 18
Section D
i. What are the coordinates of the points P, R and Q?
ii. What is the difference between the abscissa of the points L and M?
32. Find the values of a and b if .
[5]
OR
If  and , find the value of p
2 
+ q
2
.
- = a + b 7 + 3 5 v 3 + 5 v 7 - 3 5 v 3 - 5 v 5 – v p = 3 - 5 v 3 + 5 v q = 3 + 5 v 3 - 5 v 33. In the adjoining figure, name:
i. Six points
ii. Five line segments
iii. Four rays
iv. Four lines
v. Four collinear points
[5]
34. In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP
and OR. Prove that  
[5]
OR
Fig., AB || CD and CD || EF. Also, EA  AB. If BEF = 55°, find the values of x, y and z. 
? R O S = ( ? Q O S - ? P O S ) . 1 2 ? ? Page 5 of 18