Class 9 Maths: CBSE Past Year Paper (SA-1) - 17 PDF Download

 Page 1


 
 
 
 
Summative Assessment-1 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Solve
( )( )
3 11 3 11 - + 
2. An angle of equal to twice of its supplement, find the angle. 
3. Find the value of 
2 2
(525) (475) - 
4. In , 120 ABC A ? ? = ° and AB=AC then find B ? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Simplify the following: ( )
2
5
0.00032
- 
6. Evaluate using identities ( )
3
998 
Or 
Factorise: 
2 2
1 9 1
27
216 2 4
p p p - - + 
7. Two angles forming linear pair in ration 11:7, find the triangles. 
8. State Euclid’s fifth postulate. 
9. Find the value of polynomial 
2 2
( ) 4 2 p x x x x = + - + at x=1 
10. Factorise: 
2 2
2 1 x x y + + - 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Express the following in the form of 
p
q
: 0.407 
Page 2


 
 
 
 
Summative Assessment-1 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Solve
( )( )
3 11 3 11 - + 
2. An angle of equal to twice of its supplement, find the angle. 
3. Find the value of 
2 2
(525) (475) - 
4. In , 120 ABC A ? ? = ° and AB=AC then find B ? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Simplify the following: ( )
2
5
0.00032
- 
6. Evaluate using identities ( )
3
998 
Or 
Factorise: 
2 2
1 9 1
27
216 2 4
p p p - - + 
7. Two angles forming linear pair in ration 11:7, find the triangles. 
8. State Euclid’s fifth postulate. 
9. Find the value of polynomial 
2 2
( ) 4 2 p x x x x = + - + at x=1 
10. Factorise: 
2 2
2 1 x x y + + - 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Express the following in the form of 
p
q
: 0.407 
 
 
 
 
12. Find the value of k if the division of 
2 2
9 4 10 3 kx x x byx + + - + leaves a remainder -22. 
Or 
If x=-2 is a factor of 
5 4 3 3 2
3 3 3 2 4 x x ax ax ax ax - - + + + + then find value of a. 
13. In a isosceles ABC ? ,AB=AC. D is a point on BC such that AD BC ? . Prove that
BAD CAD ? = ? 
14. C is mid-point AB. P, Q are mid points of AC and BC, prove that
1
AP BQ
4
AB = = 
15. If x + y + z = 0, show that
3 3 3
3 x y z xyz + + = 
16. If , 65 , 140 ABC A B B C ? ? + ? = ° ? + ? = ° . Find the measure of each angle of triangle.. 
Or 
In figure, o is the midpoint of AB and CD, prove that AC=BD and AC BD 
 
  
17. In figure, AB CD 
 and DE CF 
 . Find , x y ? ? 
 
18. Prove that in a triangle exterior angle is equal to sum of interior opposite angles. 
19. A park in the shape of a quadrilateral ABCD has 90 , C ? = ° AB=9m, BC=12m, CA=7m and 
AD=8m. How much area does it occupy? 
20. Rationalize the denominator of 
1 2
2 2
+
- 
 
Section D 
Question number 21 to 31 carry 4 marks each: 
21. Find the value of a and b so that the polynomial 
3 2
13 a ax x b - - + has x-1 and x+3 as factors 
22. If 
5 21
2
x
- = find the value of
1
x
x
+ 
23. AD and BC are equal perpendicular to a line segment AB. Show that CD bisect AB. 
Page 3


 
 
 
 
Summative Assessment-1 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 31 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 4 are very short type questions, carrying 1 mark each. Question No. 5 to 
10 questions are of short answer type questions, carrying 2 marks each. Question No. 11 
to 20 carry 3 marks each. Question No. 21 to 31 carry 4 marks each. 
d) There are no overall choices in the question paper.  
e) Use of calculator is not permitted. 
 
 
Section A 
Question numbers 1 to 4 carry 1 mark each. 
1. Solve
( )( )
3 11 3 11 - + 
2. An angle of equal to twice of its supplement, find the angle. 
3. Find the value of 
2 2
(525) (475) - 
4. In , 120 ABC A ? ? = ° and AB=AC then find B ? 
 
Section B 
Question numbers 5 to 10 carry 2 marks each. 
5. Simplify the following: ( )
2
5
0.00032
- 
6. Evaluate using identities ( )
3
998 
Or 
Factorise: 
2 2
1 9 1
27
216 2 4
p p p - - + 
7. Two angles forming linear pair in ration 11:7, find the triangles. 
8. State Euclid’s fifth postulate. 
9. Find the value of polynomial 
2 2
( ) 4 2 p x x x x = + - + at x=1 
10. Factorise: 
2 2
2 1 x x y + + - 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Express the following in the form of 
p
q
: 0.407 
 
 
 
 
12. Find the value of k if the division of 
2 2
9 4 10 3 kx x x byx + + - + leaves a remainder -22. 
Or 
If x=-2 is a factor of 
5 4 3 3 2
3 3 3 2 4 x x ax ax ax ax - - + + + + then find value of a. 
13. In a isosceles ABC ? ,AB=AC. D is a point on BC such that AD BC ? . Prove that
BAD CAD ? = ? 
14. C is mid-point AB. P, Q are mid points of AC and BC, prove that
1
AP BQ
4
AB = = 
15. If x + y + z = 0, show that
3 3 3
3 x y z xyz + + = 
16. If , 65 , 140 ABC A B B C ? ? + ? = ° ? + ? = ° . Find the measure of each angle of triangle.. 
Or 
In figure, o is the midpoint of AB and CD, prove that AC=BD and AC BD 
 
  
17. In figure, AB CD 
 and DE CF 
 . Find , x y ? ? 
 
18. Prove that in a triangle exterior angle is equal to sum of interior opposite angles. 
19. A park in the shape of a quadrilateral ABCD has 90 , C ? = ° AB=9m, BC=12m, CA=7m and 
AD=8m. How much area does it occupy? 
20. Rationalize the denominator of 
1 2
2 2
+
- 
 
Section D 
Question number 21 to 31 carry 4 marks each: 
21. Find the value of a and b so that the polynomial 
3 2
13 a ax x b - - + has x-1 and x+3 as factors 
22. If 
5 21
2
x
- = find the value of
1
x
x
+ 
23. AD and BC are equal perpendicular to a line segment AB. Show that CD bisect AB. 
 
 
 
 
 
24. Factorise: 
3 2
( ) 6 11 6 p x x x x = + + + 
Or 
8 8
( ) p x x y = - 
25. Locate points A (-4,8), B(-4,2), C(6,-5) and D(6, -1). Join the points and name the figure 
formed. Also find its area. 
26. Mr. George wants to divide his triangular field into his two sons equally having perimeter 
540m and its sides are in ratio of 25:17:12. Find how much area each son gets. Comment on 
behaviour of Mr. George as a father. 
27. In figure POQ is a line. Ray OR is perpendicular to PQ. OS is another ray lying between rays 
CP and OR. Prove that ( )
1
2
ROS QOS POS ? = ? - ? 
 
28. Find four rational numbers between 
2
5
and
3
4
 
Or 
Represented 5 on number line. 
29. In give figure PR, PQ and PS bisects angle QPR. Prove that PSR PSQ ? = ? 
 
30. Prove that 
( ) ( ) ( )
( ) ( ) ( )
3 3 3
2 2 2 2 2 2
3 3 3
a b b c c a
a b b c c a
- + - + - =
- + - + - 
31. Two lines AB and CD are intersecting at O, prove that each pair of vertically opposite angles 
are equal.