Final Exam Class 9 Mathematics Set 3

 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) (0, 4) b) (-4, 0)
c) (0, -4) d) (4, 0)
1. The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are [1]
a)
48 cm
2 b)
24 cm
2
c)
56 cm
2 d)
96 cm
2
2. The base of a triangle is 12cm and height is 8cm then area of triangle is [1]
a) 90° b) 30°
c) 45° d) 60°
3. In the given figure, AOB = 90° and ABC = 30°. Then, CAO = ? 
[1]
? ? ? 4. In the figure, ABCD is a Rectangle. Find the values of x and y? [1]
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) (0, 4) b) (-4, 0)
c) (0, -4) d) (4, 0)
1. The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are [1]
a)
48 cm
2 b)
24 cm
2
c)
56 cm
2 d)
96 cm
2
2. The base of a triangle is 12cm and height is 8cm then area of triangle is [1]
a) 90° b) 30°
c) 45° d) 60°
3. In the given figure, AOB = 90° and ABC = 30°. Then, CAO = ? 
[1]
? ? ? 4. In the figure, ABCD is a Rectangle. Find the values of x and y? [1]
a) x = 50° and y = 100° b) x = 55° and y = 110°
c) x = 100° and y = 100° d) x = 60° and y = 120°
a) a rational number b) a natural number
c) an irrational number d) an integer
5. If a is rational and  is irrational, then  is: [1]
b v a + b v a) 60 b) 45
c) 35 d) 50
6. In figure, what is the value of x? 
[1]
a) x - 9y = 7 b) 9x - y + 7 = 0
c) y = 9x - 7 d) x = 9y - 7
7. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) 4 b)
c) d)
8. If , then  = [1]
x - = 1 x 1 5 4 x + 1 x 1 7 4 1 4 1 3 4 a) a whole number b) a real number
c) a natural number d) an integer
9. Every rational number is [1]
a) Parallelogram b) Rhombus
c) Trapezium d) Rectangle
10. In which of the following figures are the diagonals equal? [1]
a) 0 b) 10
c) 1 d) 11
11. The value of  is
[1]
( 3 2 + ( - 7 + ( 6 4 ) 1 5 ) 0 ) 1 2 a) (2, 3) b) (-4, -6)
12. The point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1½ times its abscissa is [1]
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) (0, 4) b) (-4, 0)
c) (0, -4) d) (4, 0)
1. The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are [1]
a)
48 cm
2 b)
24 cm
2
c)
56 cm
2 d)
96 cm
2
2. The base of a triangle is 12cm and height is 8cm then area of triangle is [1]
a) 90° b) 30°
c) 45° d) 60°
3. In the given figure, AOB = 90° and ABC = 30°. Then, CAO = ? 
[1]
? ? ? 4. In the figure, ABCD is a Rectangle. Find the values of x and y? [1]
a) x = 50° and y = 100° b) x = 55° and y = 110°
c) x = 100° and y = 100° d) x = 60° and y = 120°
a) a rational number b) a natural number
c) an irrational number d) an integer
5. If a is rational and  is irrational, then  is: [1]
b v a + b v a) 60 b) 45
c) 35 d) 50
6. In figure, what is the value of x? 
[1]
a) x - 9y = 7 b) 9x - y + 7 = 0
c) y = 9x - 7 d) x = 9y - 7
7. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) 4 b)
c) d)
8. If , then  = [1]
x - = 1 x 1 5 4 x + 1 x 1 7 4 1 4 1 3 4 a) a whole number b) a real number
c) a natural number d) an integer
9. Every rational number is [1]
a) Parallelogram b) Rhombus
c) Trapezium d) Rectangle
10. In which of the following figures are the diagonals equal? [1]
a) 0 b) 10
c) 1 d) 11
11. The value of  is
[1]
( 3 2 + ( - 7 + ( 6 4 ) 1 5 ) 0 ) 1 2 a) (2, 3) b) (-4, -6)
12. The point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1½ times its abscissa is [1]
c) (4, 6) d) (-2, -3)
a) 55° b) 70°
c) 50 d) 60°
13. In the given figure, AB  CD. If EAB = 50° and ECD = 60°, then AEB =? [1] ? ? ? ? 0 a) b)
c) d)
14. The simplest rationalising factor of ,is [1] + 3 – v 5 – v + 3 – v 5 – v 3 - 5 – v - 5 3 – v - 3 – v 5 – v a) b)
c) d)
15. In the given figure, O s the centre of circle,  AC is diameter of circle, then measure of  is
: 
[1]
? B A O = , 6 8 o ? B C O 3 3 o 4 4 o 2 2 o 6 8 o a) II and IV quadrant b) II and III quadrants
c) I and III quadrants d) I and II quadrants
16. The point whose abscissa and ordinate have different signs will lie in [1]
a) b)
c) d)
17. Express y in terms of x in the equation 5y - 3x - 10 = 0. [1]
y = 3 x + 1 0 5 y = 3 - 1 0 x 5 y = 3 x - 1 0 5 y = 3 + 1 0 x 5 a) 27 b) 10
c) 23 d) 25
18. If , then [1] x + = 5 1 x + = x 2 1 x 2 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): Two opposite angles of a parallelogram are (3x - 2)
o
 and (50 - x)
o
. The measure of one of the
angle is 37
o
. 
Reason (R): Opposite angles of a parallelogram are equal.
[1]
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
20. Assertion (A): Three rational numbers between are  
Reason (B): A rational number between two rational numbers p and q is 
[1] and 
2 5 3 5 , and 
9 2 0 1 0 2 0 1 1 2 0 ( p + q ) 1 2
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) (0, 4) b) (-4, 0)
c) (0, -4) d) (4, 0)
1. The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are [1]
a)
48 cm
2 b)
24 cm
2
c)
56 cm
2 d)
96 cm
2
2. The base of a triangle is 12cm and height is 8cm then area of triangle is [1]
a) 90° b) 30°
c) 45° d) 60°
3. In the given figure, AOB = 90° and ABC = 30°. Then, CAO = ? 
[1]
? ? ? 4. In the figure, ABCD is a Rectangle. Find the values of x and y? [1]
a) x = 50° and y = 100° b) x = 55° and y = 110°
c) x = 100° and y = 100° d) x = 60° and y = 120°
a) a rational number b) a natural number
c) an irrational number d) an integer
5. If a is rational and  is irrational, then  is: [1]
b v a + b v a) 60 b) 45
c) 35 d) 50
6. In figure, what is the value of x? 
[1]
a) x - 9y = 7 b) 9x - y + 7 = 0
c) y = 9x - 7 d) x = 9y - 7
7. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) 4 b)
c) d)
8. If , then  = [1]
x - = 1 x 1 5 4 x + 1 x 1 7 4 1 4 1 3 4 a) a whole number b) a real number
c) a natural number d) an integer
9. Every rational number is [1]
a) Parallelogram b) Rhombus
c) Trapezium d) Rectangle
10. In which of the following figures are the diagonals equal? [1]
a) 0 b) 10
c) 1 d) 11
11. The value of  is
[1]
( 3 2 + ( - 7 + ( 6 4 ) 1 5 ) 0 ) 1 2 a) (2, 3) b) (-4, -6)
12. The point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1½ times its abscissa is [1]
c) (4, 6) d) (-2, -3)
a) 55° b) 70°
c) 50 d) 60°
13. In the given figure, AB  CD. If EAB = 50° and ECD = 60°, then AEB =? [1] ? ? ? ? 0 a) b)
c) d)
14. The simplest rationalising factor of ,is [1] + 3 – v 5 – v + 3 – v 5 – v 3 - 5 – v - 5 3 – v - 3 – v 5 – v a) b)
c) d)
15. In the given figure, O s the centre of circle,  AC is diameter of circle, then measure of  is
: 
[1]
? B A O = , 6 8 o ? B C O 3 3 o 4 4 o 2 2 o 6 8 o a) II and IV quadrant b) II and III quadrants
c) I and III quadrants d) I and II quadrants
16. The point whose abscissa and ordinate have different signs will lie in [1]
a) b)
c) d)
17. Express y in terms of x in the equation 5y - 3x - 10 = 0. [1]
y = 3 x + 1 0 5 y = 3 - 1 0 x 5 y = 3 x - 1 0 5 y = 3 + 1 0 x 5 a) 27 b) 10
c) 23 d) 25
18. If , then [1] x + = 5 1 x + = x 2 1 x 2 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): Two opposite angles of a parallelogram are (3x - 2)
o
 and (50 - x)
o
. The measure of one of the
angle is 37
o
. 
Reason (R): Opposite angles of a parallelogram are equal.
[1]
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
20. Assertion (A): Three rational numbers between are  
Reason (B): A rational number between two rational numbers p and q is 
[1] and 
2 5 3 5 , and 
9 2 0 1 0 2 0 1 1 2 0 ( p + q ) 1 2 Section B
Section C
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
21. In fig., if AC = BD, then prove that AB = CD 
[2]
22. In the given figure, we have  and . Show that . 
[2]
? 1 = ? 3 ? 2 = ? 4 ? A = ? C
23. See Fig. and complete the statement: The abscissa and the ordinate of the point B are ________ and ________,
respectively. Hence, the coordinates of B are (________, ________). 
[2]
24. If  find the value of x
3 
- 2x
2 
- 7x + 5.
[2]
OR
Express the decimal  in the form , where p, q are integers and q  0.
x = 1 3 - 8 v 0 . 2 3 5 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ p q ? 25. The surface area of a cuboid is 758 cm
2
. Its length and breadth are 14 cm and 11 cm respectively. Find its height.
[2]
OR
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the
solid so obtained.
26. Rationalise the denominator: [3]
1 + - 7 v 6 v 1 3 v 27. If ABC is an isosceles triangle such that AB = AC and AD is an altitude from A on BC. Prove that
i. B = C
ii. AD bisects BC
iii. AD bisects A.
[3] ? ? ? ? 28. P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such
that AC  BD. Prove that PQRS is a rectangle.
[3]
? 29. Draw the graph of the following equation and check whether : [3]
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) (0, 4) b) (-4, 0)
c) (0, -4) d) (4, 0)
1. The coordinates of a point A on y-axis, at a distance of 4 units from x-axis and below it, are [1]
a)
48 cm
2 b)
24 cm
2
c)
56 cm
2 d)
96 cm
2
2. The base of a triangle is 12cm and height is 8cm then area of triangle is [1]
a) 90° b) 30°
c) 45° d) 60°
3. In the given figure, AOB = 90° and ABC = 30°. Then, CAO = ? 
[1]
? ? ? 4. In the figure, ABCD is a Rectangle. Find the values of x and y? [1]
a) x = 50° and y = 100° b) x = 55° and y = 110°
c) x = 100° and y = 100° d) x = 60° and y = 120°
a) a rational number b) a natural number
c) an irrational number d) an integer
5. If a is rational and  is irrational, then  is: [1]
b v a + b v a) 60 b) 45
c) 35 d) 50
6. In figure, what is the value of x? 
[1]
a) x - 9y = 7 b) 9x - y + 7 = 0
c) y = 9x - 7 d) x = 9y - 7
7. If a linear equation has solutions (1, 2), (-1, -16) and (0, -7), then it is of the form [1]
a) 4 b)
c) d)
8. If , then  = [1]
x - = 1 x 1 5 4 x + 1 x 1 7 4 1 4 1 3 4 a) a whole number b) a real number
c) a natural number d) an integer
9. Every rational number is [1]
a) Parallelogram b) Rhombus
c) Trapezium d) Rectangle
10. In which of the following figures are the diagonals equal? [1]
a) 0 b) 10
c) 1 d) 11
11. The value of  is
[1]
( 3 2 + ( - 7 + ( 6 4 ) 1 5 ) 0 ) 1 2 a) (2, 3) b) (-4, -6)
12. The point on the graph of the linear equation 2x + 5y = 19, whose ordinate is 1½ times its abscissa is [1]
c) (4, 6) d) (-2, -3)
a) 55° b) 70°
c) 50 d) 60°
13. In the given figure, AB  CD. If EAB = 50° and ECD = 60°, then AEB =? [1] ? ? ? ? 0 a) b)
c) d)
14. The simplest rationalising factor of ,is [1] + 3 – v 5 – v + 3 – v 5 – v 3 - 5 – v - 5 3 – v - 3 – v 5 – v a) b)
c) d)
15. In the given figure, O s the centre of circle,  AC is diameter of circle, then measure of  is
: 
[1]
? B A O = , 6 8 o ? B C O 3 3 o 4 4 o 2 2 o 6 8 o a) II and IV quadrant b) II and III quadrants
c) I and III quadrants d) I and II quadrants
16. The point whose abscissa and ordinate have different signs will lie in [1]
a) b)
c) d)
17. Express y in terms of x in the equation 5y - 3x - 10 = 0. [1]
y = 3 x + 1 0 5 y = 3 - 1 0 x 5 y = 3 x - 1 0 5 y = 3 + 1 0 x 5 a) 27 b) 10
c) 23 d) 25
18. If , then [1] x + = 5 1 x + = x 2 1 x 2 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): Two opposite angles of a parallelogram are (3x - 2)
o
 and (50 - x)
o
. The measure of one of the
angle is 37
o
. 
Reason (R): Opposite angles of a parallelogram are equal.
[1]
a) Both A and R are true and R is the correct b) Both A and R are true but R is not the
20. Assertion (A): Three rational numbers between are  
Reason (B): A rational number between two rational numbers p and q is 
[1] and 
2 5 3 5 , and 
9 2 0 1 0 2 0 1 1 2 0 ( p + q ) 1 2 Section B
Section C
explanation of A. correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
21. In fig., if AC = BD, then prove that AB = CD 
[2]
22. In the given figure, we have  and . Show that . 
[2]
? 1 = ? 3 ? 2 = ? 4 ? A = ? C
23. See Fig. and complete the statement: The abscissa and the ordinate of the point B are ________ and ________,
respectively. Hence, the coordinates of B are (________, ________). 
[2]
24. If  find the value of x
3 
- 2x
2 
- 7x + 5.
[2]
OR
Express the decimal  in the form , where p, q are integers and q  0.
x = 1 3 - 8 v 0 . 2 3 5 ¯ ¯ ¯ ¯ ¯ ¯ ¯ ¯ p q ? 25. The surface area of a cuboid is 758 cm
2
. Its length and breadth are 14 cm and 11 cm respectively. Find its height.
[2]
OR
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the
solid so obtained.
26. Rationalise the denominator: [3]
1 + - 7 v 6 v 1 3 v 27. If ABC is an isosceles triangle such that AB = AC and AD is an altitude from A on BC. Prove that
i. B = C
ii. AD bisects BC
iii. AD bisects A.
[3] ? ? ? ? 28. P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such
that AC  BD. Prove that PQRS is a rectangle.
[3]
? 29. Draw the graph of the following equation and check whether : [3]
Section D
Section E
i. x = 2, y = 5
ii. x = –1, y = 3 are the solutions : 5x + 3y = 4
30. ABC is an isosceles triangle in which AC = BC. AD and BE are respectively two altitudes to sides BC and AC.
Prove that AE = BD.
[3]
OR
ABCD is a square. X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX
and BAY = ABX. ? ? 31. Factorise: x
3
 + x
2
 - 4x - 4
[3]
32. In the given figure, AB || CD. Prove that p + q - r = 180. 
[5]
OR
If two parallel lines are intersected by a transversal, then prove that the bisectors of the interior angles form a
rectangle.
33. In Fig., ABCD is a trapezium in which side AB is parallel to side DC and E is the mid-point of side AD. If F is a
point on the side BC such that the segment EF is parallel to side DC. Prove that F is the mid-point of BC and EF
=  (AB + DC). 
[5]
1 2 34. Find the area of the given trapezium PQRS in which RQ || SP and PQ  SP such that RQ = 7 m, RS = 13 m and
SP = 12 m.
[5]
OR
Find the area of the quadrilateral ABCD in which AB = 9 m, BC = 40 m, , CD = 15 m and AD = 28
m.
? ? A B C = 9 0 ° 35. Verify that  [5] + + - 3 x y z x 3 y 3 z 3 = ( x + y + z ) [ + + ] 1 2 ( x - y ) 2 ( y - z ) 2 ( z - x ) 2 36. Basant Kumar is a farmer. He has an agricultural field in the form of a rectangle of length 20 m and width 14 m.
He planned to prepare compost manure in his field. For this purpose, a pit 6 m long, 3 m wide and 2.5 m deep is
dug in a corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the
field.
[4]