Final Exam Class 9 Mathematics Set 1

 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, 6) b) (6, 6)
c) (6, 4) d) (6, 0)
1. The point whose ordinate is 6 and which point lies on the y-axis? [1]
a)
24 x
2
 sq. units
b)
144 x
2
 sq. units
c)
12 x
2
 sq. units
d)
100 x
2
 sq. units
2. The length of the sides of a triangle are 5x, 5x and 8x. The area of the triangle is : [1]
a) 20° b) 70°
c) 50° d) 60°
3. In the given figure, O is the centre of a circle in which OAB = 20° and OCB = 50°. Then, AOC = ? 
[1]
? ? ? 4. In fig D is mid-point of AB and DE  BC then AE is equal to [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, 6) b) (6, 6)
c) (6, 4) d) (6, 0)
1. The point whose ordinate is 6 and which point lies on the y-axis? [1]
a)
24 x
2
 sq. units
b)
144 x
2
 sq. units
c)
12 x
2
 sq. units
d)
100 x
2
 sq. units
2. The length of the sides of a triangle are 5x, 5x and 8x. The area of the triangle is : [1]
a) 20° b) 70°
c) 50° d) 60°
3. In the given figure, O is the centre of a circle in which OAB = 20° and OCB = 50°. Then, AOC = ? 
[1]
? ? ? 4. In fig D is mid-point of AB and DE  BC then AE is equal to [1] ? a) EC b) AD
c) DB d) BC
a) b) 5
c) 6 d)
5.  = [1]
× 1 2 - - v 1 5 - - v 6 5 – v 5 6 – v a) BCD b) BAD
c) BCA d) BDA
6. In the adjoining figure, AB = BC and ABD = CBD, then another angle which measures  is [1] ? ? 3 0 ° ? ? ? ? a) (-5, -7) b) (3, 7)
c) (3, 9) d) (-1, 1)
7. Which of the following point does not lie on the line y = 2x + 3? [1]
a) 2 b) 8
c) 1 d) 0
8. 8 is a polynomial of degree [1]
a) 7 b) 1
c) 6 d) 3
9. If , then (x - 3)
2 [1]
x = 2 3 + 7 v a) Scalene b) Right angled
c) Equilateral d) Isosceles
10. The triangle formed by joining the mid-points of the sides of a right angled triangle is [1]
a) 0 b) -4.3
c) -3.4 d) 1.101100110001 ...
11. A rational number between -3 and 3 is [1]
12. Which of the following pair is a solution of the equation 3x – 2y = 7? [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, 6) b) (6, 6)
c) (6, 4) d) (6, 0)
1. The point whose ordinate is 6 and which point lies on the y-axis? [1]
a)
24 x
2
 sq. units
b)
144 x
2
 sq. units
c)
12 x
2
 sq. units
d)
100 x
2
 sq. units
2. The length of the sides of a triangle are 5x, 5x and 8x. The area of the triangle is : [1]
a) 20° b) 70°
c) 50° d) 60°
3. In the given figure, O is the centre of a circle in which OAB = 20° and OCB = 50°. Then, AOC = ? 
[1]
? ? ? 4. In fig D is mid-point of AB and DE  BC then AE is equal to [1] ? a) EC b) AD
c) DB d) BC
a) b) 5
c) 6 d)
5.  = [1]
× 1 2 - - v 1 5 - - v 6 5 – v 5 6 – v a) BCD b) BAD
c) BCA d) BDA
6. In the adjoining figure, AB = BC and ABD = CBD, then another angle which measures  is [1] ? ? 3 0 ° ? ? ? ? a) (-5, -7) b) (3, 7)
c) (3, 9) d) (-1, 1)
7. Which of the following point does not lie on the line y = 2x + 3? [1]
a) 2 b) 8
c) 1 d) 0
8. 8 is a polynomial of degree [1]
a) 7 b) 1
c) 6 d) 3
9. If , then (x - 3)
2 [1]
x = 2 3 + 7 v a) Scalene b) Right angled
c) Equilateral d) Isosceles
10. The triangle formed by joining the mid-points of the sides of a right angled triangle is [1]
a) 0 b) -4.3
c) -3.4 d) 1.101100110001 ...
11. A rational number between -3 and 3 is [1]
12. Which of the following pair is a solution of the equation 3x – 2y = 7? [1]
a) (-2, 1) b) (5, 1)
c) (1, -2) d) (1, 5)
a) 35° b) 65°
c) 45° d) 55°
13. In the given figure, sides CB and BA of ABC have been produced to D and E respectively such that ABD =
110° and CAE = 135°. Then ACB =? 
[1]
? ? ? ? a) b) 4
c) 2 d)
14. The value of , is
[1]
{ ÷ } 8 - 4 3 2 - 2 1 2 1 2 1 4 a)
100
o b)
70
o
c)
30
o d)
80
o
15. In the given figure, the measure of BCD is  
[1]
? a) lie in IV quadrant b) lie in III quadrant
c) lie in II quadrant d) Do not lie in the same quadrant
16. Points (1, -1), (2, -2), (4, -5), (-3, -4) [1]
a) (2, 3) b) (3, 2)
c) (0, 3) d c d n a a h t o B )
17. The graph of the line y = 3 passes through the point [1]
a) 3 b) 6
c) 2x d) 0
18. If p(x) = x + 3, then p(x) + p(-x) is equal to [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
19. Assertion (A): In ABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC
intersects FE at Q. Then, AQ = QP.  
Reason (R): Q is the midpoint of AP.
[1] ?
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, 6) b) (6, 6)
c) (6, 4) d) (6, 0)
1. The point whose ordinate is 6 and which point lies on the y-axis? [1]
a)
24 x
2
 sq. units
b)
144 x
2
 sq. units
c)
12 x
2
 sq. units
d)
100 x
2
 sq. units
2. The length of the sides of a triangle are 5x, 5x and 8x. The area of the triangle is : [1]
a) 20° b) 70°
c) 50° d) 60°
3. In the given figure, O is the centre of a circle in which OAB = 20° and OCB = 50°. Then, AOC = ? 
[1]
? ? ? 4. In fig D is mid-point of AB and DE  BC then AE is equal to [1] ? a) EC b) AD
c) DB d) BC
a) b) 5
c) 6 d)
5.  = [1]
× 1 2 - - v 1 5 - - v 6 5 – v 5 6 – v a) BCD b) BAD
c) BCA d) BDA
6. In the adjoining figure, AB = BC and ABD = CBD, then another angle which measures  is [1] ? ? 3 0 ° ? ? ? ? a) (-5, -7) b) (3, 7)
c) (3, 9) d) (-1, 1)
7. Which of the following point does not lie on the line y = 2x + 3? [1]
a) 2 b) 8
c) 1 d) 0
8. 8 is a polynomial of degree [1]
a) 7 b) 1
c) 6 d) 3
9. If , then (x - 3)
2 [1]
x = 2 3 + 7 v a) Scalene b) Right angled
c) Equilateral d) Isosceles
10. The triangle formed by joining the mid-points of the sides of a right angled triangle is [1]
a) 0 b) -4.3
c) -3.4 d) 1.101100110001 ...
11. A rational number between -3 and 3 is [1]
12. Which of the following pair is a solution of the equation 3x – 2y = 7? [1]
a) (-2, 1) b) (5, 1)
c) (1, -2) d) (1, 5)
a) 35° b) 65°
c) 45° d) 55°
13. In the given figure, sides CB and BA of ABC have been produced to D and E respectively such that ABD =
110° and CAE = 135°. Then ACB =? 
[1]
? ? ? ? a) b) 4
c) 2 d)
14. The value of , is
[1]
{ ÷ } 8 - 4 3 2 - 2 1 2 1 2 1 4 a)
100
o b)
70
o
c)
30
o d)
80
o
15. In the given figure, the measure of BCD is  
[1]
? a) lie in IV quadrant b) lie in III quadrant
c) lie in II quadrant d) Do not lie in the same quadrant
16. Points (1, -1), (2, -2), (4, -5), (-3, -4) [1]
a) (2, 3) b) (3, 2)
c) (0, 3) d c d n a a h t o B )
17. The graph of the line y = 3 passes through the point [1]
a) 3 b) 6
c) 2x d) 0
18. If p(x) = x + 3, then p(x) + p(-x) is equal to [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
19. Assertion (A): In ABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC
intersects FE at Q. Then, AQ = QP.  
Reason (R): Q is the midpoint of AP.
[1] ? 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.
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):  is an irrational number. 
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
[1] 2 + 6 – v 21. Look at the Fig. Show that length AH > sum of lengths of AB + BC + CD. 
[2]
22. Does Euclid's fifth postulate imply the existence of parallel lines ? Explain. [2]
23. In which quadrant will the point lie, if : 
(i) The y-coordinate is 3 and the x-coordinate is –4? 
(ii) The x-coordinate is –5 and the y-coordinate is –3? 
(iii) The y-coordinate is 4 and the x-coordinate is 5? 
(iv) The y-coordinate is 4 and the x-coordinate is –4?
[2]
24. Assuming that x is a positive real number and a, b, c are rational numbers, show that: =
1
[2]
OR
Evaluate: .
( ) x a x b 1 a b ( ) x b x c 1 b c ( ) x c x a 1 a c [ ( 1 6 ] ) 1 2 1 2 25. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that
covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming
that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to
make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?
[2]
OR
A room is 16 m long, 9 m wide and 3 m high. It has two doors, each of dimensions (2 m  1.5 m) and three
windows, each of dimensions (1.6 m  75 cm). Find the cost of distempering the walls of the room from inside at the
rate of Rs. 50 per square metre.
× × 26. Express in the form of : [3]
p q 0 . + 1 . 3 8 ¯ ¯ ¯ ¯ ¯ 2 7 ¯ ¯ ¯ ¯ ¯ 27. In given figure, it is given that AB = CF, EF = BD and AFE = CBD. Prove that AFE  CBD. 
[3]
? ? ? ? ? 28. Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a 
ABC as shown in Fig., Show that QR
[3]
? B C = 1 2
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, 6) b) (6, 6)
c) (6, 4) d) (6, 0)
1. The point whose ordinate is 6 and which point lies on the y-axis? [1]
a)
24 x
2
 sq. units
b)
144 x
2
 sq. units
c)
12 x
2
 sq. units
d)
100 x
2
 sq. units
2. The length of the sides of a triangle are 5x, 5x and 8x. The area of the triangle is : [1]
a) 20° b) 70°
c) 50° d) 60°
3. In the given figure, O is the centre of a circle in which OAB = 20° and OCB = 50°. Then, AOC = ? 
[1]
? ? ? 4. In fig D is mid-point of AB and DE  BC then AE is equal to [1] ? a) EC b) AD
c) DB d) BC
a) b) 5
c) 6 d)
5.  = [1]
× 1 2 - - v 1 5 - - v 6 5 – v 5 6 – v a) BCD b) BAD
c) BCA d) BDA
6. In the adjoining figure, AB = BC and ABD = CBD, then another angle which measures  is [1] ? ? 3 0 ° ? ? ? ? a) (-5, -7) b) (3, 7)
c) (3, 9) d) (-1, 1)
7. Which of the following point does not lie on the line y = 2x + 3? [1]
a) 2 b) 8
c) 1 d) 0
8. 8 is a polynomial of degree [1]
a) 7 b) 1
c) 6 d) 3
9. If , then (x - 3)
2 [1]
x = 2 3 + 7 v a) Scalene b) Right angled
c) Equilateral d) Isosceles
10. The triangle formed by joining the mid-points of the sides of a right angled triangle is [1]
a) 0 b) -4.3
c) -3.4 d) 1.101100110001 ...
11. A rational number between -3 and 3 is [1]
12. Which of the following pair is a solution of the equation 3x – 2y = 7? [1]
a) (-2, 1) b) (5, 1)
c) (1, -2) d) (1, 5)
a) 35° b) 65°
c) 45° d) 55°
13. In the given figure, sides CB and BA of ABC have been produced to D and E respectively such that ABD =
110° and CAE = 135°. Then ACB =? 
[1]
? ? ? ? a) b) 4
c) 2 d)
14. The value of , is
[1]
{ ÷ } 8 - 4 3 2 - 2 1 2 1 2 1 4 a)
100
o b)
70
o
c)
30
o d)
80
o
15. In the given figure, the measure of BCD is  
[1]
? a) lie in IV quadrant b) lie in III quadrant
c) lie in II quadrant d) Do not lie in the same quadrant
16. Points (1, -1), (2, -2), (4, -5), (-3, -4) [1]
a) (2, 3) b) (3, 2)
c) (0, 3) d c d n a a h t o B )
17. The graph of the line y = 3 passes through the point [1]
a) 3 b) 6
c) 2x d) 0
18. If p(x) = x + 3, then p(x) + p(-x) is equal to [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
19. Assertion (A): In ABC, E and F are the midpoints of AC and AB respectively. The altitude AP at BC
intersects FE at Q. Then, AQ = QP.  
Reason (R): Q is the midpoint of AP.
[1] ? 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.
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):  is an irrational number. 
Reason (R): Sum of a rational number and an irrational number is always an irrational number.
[1] 2 + 6 – v 21. Look at the Fig. Show that length AH > sum of lengths of AB + BC + CD. 
[2]
22. Does Euclid's fifth postulate imply the existence of parallel lines ? Explain. [2]
23. In which quadrant will the point lie, if : 
(i) The y-coordinate is 3 and the x-coordinate is –4? 
(ii) The x-coordinate is –5 and the y-coordinate is –3? 
(iii) The y-coordinate is 4 and the x-coordinate is 5? 
(iv) The y-coordinate is 4 and the x-coordinate is –4?
[2]
24. Assuming that x is a positive real number and a, b, c are rational numbers, show that: =
1
[2]
OR
Evaluate: .
( ) x a x b 1 a b ( ) x b x c 1 b c ( ) x c x a 1 a c [ ( 1 6 ] ) 1 2 1 2 25. Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that
covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming
that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to
make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?
[2]
OR
A room is 16 m long, 9 m wide and 3 m high. It has two doors, each of dimensions (2 m  1.5 m) and three
windows, each of dimensions (1.6 m  75 cm). Find the cost of distempering the walls of the room from inside at the
rate of Rs. 50 per square metre.
× × 26. Express in the form of : [3]
p q 0 . + 1 . 3 8 ¯ ¯ ¯ ¯ ¯ 2 7 ¯ ¯ ¯ ¯ ¯ 27. In given figure, it is given that AB = CF, EF = BD and AFE = CBD. Prove that AFE  CBD. 
[3]
? ? ? ? ? 28. Through A, B and C, lines RQ, PR and QP have been drawn, respectively parallel to sides BC, CA and AB of a 
ABC as shown in Fig., Show that QR
[3]
? B C = 1 2 Section D
29. Draw the graphs of the equations : 3x – 2y = 4 and x + y – 3 = 0 in the same graph and find the co-ordinates of
the point where two lines intersect.
[3]
30. ABCD is a square and DEC is an equilateral triangle. Prove that AE = BE. 
[3]
OR
AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that:
i. AD bisects BC.
ii. AD bisects A 
? 31. Factorise : x
3
 – 23x
2
 + 142x – 120
[3]
32. In figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to
reflected ray BD. 
[5]
OR
In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x. 
33. Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other
diagonal and hence find the area of the rhombus.
[5]