Mathematics Past Year Paper SA-1(Set-4)- 2014, Class 9, CBSE Class 9 Notes | EduRev

 Page 1


 
 
 
 
Summative Assessment-1 2014-2015 
Mathematics 
Class – IX 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) The question paper consists of 31 question divided into four sections A, B, C and D. 
Section – A comprises of 4 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 11 questions of 4 marks each. 
c) There is no overall choice in this question paper. 
d) Use of calculator is not permitted. 
 
 
Section – A 
Question number 1 to 4 carry one marks each 
 
1. Identify numbers 1 to 4 carry one mark each. 
2 1
(1 3),( 3 1), 2 5 5 125, ,
2 2 2
p
p
+ - + - + 
2. Find 
( )
2 f , if 
2
( ) 2 1 f x x x = + + 
3.  
  
In figure, , 135 AB CD ECD ? = ° 
 and 130 EAB ? = ° . Then find the measure of x. 
4. What is the y – ordinate of any point on the x – axis? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
1
3
4
1 1
3 3
7 27 64
? ?
? ?
? ?
+
? ? ? ?
? ? ? ?
? ?
 
6. What should be added to be polynomial 
2
5 3 x x - + , so that 3 is a zero of the polynomial? 
7. Two line segments AB and CD intersect each other at O such that AO=OB and CO=OD. Prove 
that AC=BD. 
Page 2


 
 
 
 
Summative Assessment-1 2014-2015 
Mathematics 
Class – IX 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) The question paper consists of 31 question divided into four sections A, B, C and D. 
Section – A comprises of 4 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 11 questions of 4 marks each. 
c) There is no overall choice in this question paper. 
d) Use of calculator is not permitted. 
 
 
Section – A 
Question number 1 to 4 carry one marks each 
 
1. Identify numbers 1 to 4 carry one mark each. 
2 1
(1 3),( 3 1), 2 5 5 125, ,
2 2 2
p
p
+ - + - + 
2. Find 
( )
2 f , if 
2
( ) 2 1 f x x x = + + 
3.  
  
In figure, , 135 AB CD ECD ? = ° 
 and 130 EAB ? = ° . Then find the measure of x. 
4. What is the y – ordinate of any point on the x – axis? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
1
3
4
1 1
3 3
7 27 64
? ?
? ?
? ?
+
? ? ? ?
? ? ? ?
? ?
 
6. What should be added to be polynomial 
2
5 3 x x - + , so that 3 is a zero of the polynomial? 
7. Two line segments AB and CD intersect each other at O such that AO=OB and CO=OD. Prove 
that AC=BD. 
 
 
 
 
8. In the figure, 
1 1
, ,
2 2
OX XY PX XZ = = and OX=PX. Show that XY=XZ, using Euclid’s axiom. 
 
9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 
cm. Find its area. 
10. On y – axis, plot four points such that distances between two consecutive points are equal. 
 
Section – C 
Question numbers 11 to 20 carry three marks each. 
 
11. Represent 10.5 on the number line. 
12. Which is greater: 7 3 - or 5 1 - 
13. Expand 
3
1
4
32
? ?
- ? ?
? ?
 
14. Show that -1 and 
2
3
, are the zeroes of the polynomial 
3 2
3 5 4 4 x x x - - + . Also, find the third 
zero of the polynomial. 
15. In ABC ? , the bisectors of B and C ? ? meet at O. prove that 90
2
A
BOC
?
? = ° + 
16.   
 
l and m are two parallel lines intersected by another pair of parallel lines p and q as shown in 
the figure. show that ABC CDA ? ? ? 
17.   
  
In give figure, AE=AD, BAE CAD ? = ? . Prove that AB=AC 
18.   
Page 3


 
 
 
 
Summative Assessment-1 2014-2015 
Mathematics 
Class – IX 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) The question paper consists of 31 question divided into four sections A, B, C and D. 
Section – A comprises of 4 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 11 questions of 4 marks each. 
c) There is no overall choice in this question paper. 
d) Use of calculator is not permitted. 
 
 
Section – A 
Question number 1 to 4 carry one marks each 
 
1. Identify numbers 1 to 4 carry one mark each. 
2 1
(1 3),( 3 1), 2 5 5 125, ,
2 2 2
p
p
+ - + - + 
2. Find 
( )
2 f , if 
2
( ) 2 1 f x x x = + + 
3.  
  
In figure, , 135 AB CD ECD ? = ° 
 and 130 EAB ? = ° . Then find the measure of x. 
4. What is the y – ordinate of any point on the x – axis? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
1
3
4
1 1
3 3
7 27 64
? ?
? ?
? ?
+
? ? ? ?
? ? ? ?
? ?
 
6. What should be added to be polynomial 
2
5 3 x x - + , so that 3 is a zero of the polynomial? 
7. Two line segments AB and CD intersect each other at O such that AO=OB and CO=OD. Prove 
that AC=BD. 
 
 
 
 
8. In the figure, 
1 1
, ,
2 2
OX XY PX XZ = = and OX=PX. Show that XY=XZ, using Euclid’s axiom. 
 
9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 
cm. Find its area. 
10. On y – axis, plot four points such that distances between two consecutive points are equal. 
 
Section – C 
Question numbers 11 to 20 carry three marks each. 
 
11. Represent 10.5 on the number line. 
12. Which is greater: 7 3 - or 5 1 - 
13. Expand 
3
1
4
32
? ?
- ? ?
? ?
 
14. Show that -1 and 
2
3
, are the zeroes of the polynomial 
3 2
3 5 4 4 x x x - - + . Also, find the third 
zero of the polynomial. 
15. In ABC ? , the bisectors of B and C ? ? meet at O. prove that 90
2
A
BOC
?
? = ° + 
16.   
 
l and m are two parallel lines intersected by another pair of parallel lines p and q as shown in 
the figure. show that ABC CDA ? ? ? 
17.   
  
In give figure, AE=AD, BAE CAD ? = ? . Prove that AB=AC 
18.   
 
 
 
 
  
In figure AB CD 
 find the value of x. 
19. In this figure, ABCD is a square of side 6 m. P, Q, R and S are mid-points of AB, BC, CD and DA 
respectively. Find the area of the shaded region. 
 
20. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral 
triangle of side 8 cm. Find the area of the figure so formed. 
 
Section – D 
Question number 21 to 31 carry four marks each. 
 
21. Express 0.3178 in the form of p/q where p and q are integers and 0 q ? . 
22. Rationalize the denominator of 
1
6 5 +
 and hence find its value, if 6 2.449 = and 
5 2.236 = 
23. Factorise: 
3 2
3 9 5 x x x - - + 
24. Without actual division, prove that 
4 3 2
2 2 2 3 x x x x + - + - is exactly divisible by 
2
2 3 x x + - . 
25. Factorise: 
3 2
9 3 5 1 x x x - - - 
26. Factorise: 
3 3
27 8 x y - 
27. Rehman and Prakash contributed equal amount toward Prime Minister Relief fund. Prakash 
and Rahul contributed equal amount towards Prime Minister Relief fund. If Rahul 
Contributed Rs. 500 how much Rehman contributed? What value they all are exhibiting by 
doing so? Which Euclid Axiom help in reaching the correct answer? State any one more 
Euclid Postulate. 
28. Prove that sum of the angles of a triangle is 180° . If in , 120 ABC A B ? ? + ? = ° and 
100 B C ? + ? = ° , then find B ? 
29.   
Page 4


 
 
 
 
Summative Assessment-1 2014-2015 
Mathematics 
Class – IX 
 
 Time allowed: 3:00 hours                                Maximum Marks: 90 
 
 General Instructions: 
a) All questions are compulsory. 
b) The question paper consists of 31 question divided into four sections A, B, C and D. 
Section – A comprises of 4 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 11 questions of 4 marks each. 
c) There is no overall choice in this question paper. 
d) Use of calculator is not permitted. 
 
 
Section – A 
Question number 1 to 4 carry one marks each 
 
1. Identify numbers 1 to 4 carry one mark each. 
2 1
(1 3),( 3 1), 2 5 5 125, ,
2 2 2
p
p
+ - + - + 
2. Find 
( )
2 f , if 
2
( ) 2 1 f x x x = + + 
3.  
  
In figure, , 135 AB CD ECD ? = ° 
 and 130 EAB ? = ° . Then find the measure of x. 
4. What is the y – ordinate of any point on the x – axis? 
 
Section – B 
Question numbers 5 to 10 carry two marks each. 
5. Simplify: 
1
3
4
1 1
3 3
7 27 64
? ?
? ?
? ?
+
? ? ? ?
? ? ? ?
? ?
 
6. What should be added to be polynomial 
2
5 3 x x - + , so that 3 is a zero of the polynomial? 
7. Two line segments AB and CD intersect each other at O such that AO=OB and CO=OD. Prove 
that AC=BD. 
 
 
 
 
8. In the figure, 
1 1
, ,
2 2
OX XY PX XZ = = and OX=PX. Show that XY=XZ, using Euclid’s axiom. 
 
9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54 
cm. Find its area. 
10. On y – axis, plot four points such that distances between two consecutive points are equal. 
 
Section – C 
Question numbers 11 to 20 carry three marks each. 
 
11. Represent 10.5 on the number line. 
12. Which is greater: 7 3 - or 5 1 - 
13. Expand 
3
1
4
32
? ?
- ? ?
? ?
 
14. Show that -1 and 
2
3
, are the zeroes of the polynomial 
3 2
3 5 4 4 x x x - - + . Also, find the third 
zero of the polynomial. 
15. In ABC ? , the bisectors of B and C ? ? meet at O. prove that 90
2
A
BOC
?
? = ° + 
16.   
 
l and m are two parallel lines intersected by another pair of parallel lines p and q as shown in 
the figure. show that ABC CDA ? ? ? 
17.   
  
In give figure, AE=AD, BAE CAD ? = ? . Prove that AB=AC 
18.   
 
 
 
 
  
In figure AB CD 
 find the value of x. 
19. In this figure, ABCD is a square of side 6 m. P, Q, R and S are mid-points of AB, BC, CD and DA 
respectively. Find the area of the shaded region. 
 
20. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral 
triangle of side 8 cm. Find the area of the figure so formed. 
 
Section – D 
Question number 21 to 31 carry four marks each. 
 
21. Express 0.3178 in the form of p/q where p and q are integers and 0 q ? . 
22. Rationalize the denominator of 
1
6 5 +
 and hence find its value, if 6 2.449 = and 
5 2.236 = 
23. Factorise: 
3 2
3 9 5 x x x - - + 
24. Without actual division, prove that 
4 3 2
2 2 2 3 x x x x + - + - is exactly divisible by 
2
2 3 x x + - . 
25. Factorise: 
3 2
9 3 5 1 x x x - - - 
26. Factorise: 
3 3
27 8 x y - 
27. Rehman and Prakash contributed equal amount toward Prime Minister Relief fund. Prakash 
and Rahul contributed equal amount towards Prime Minister Relief fund. If Rahul 
Contributed Rs. 500 how much Rehman contributed? What value they all are exhibiting by 
doing so? Which Euclid Axiom help in reaching the correct answer? State any one more 
Euclid Postulate. 
28. Prove that sum of the angles of a triangle is 180° . If in , 120 ABC A B ? ? + ? = ° and 
100 B C ? + ? = ° , then find B ? 
29.   
 
 
 
 
 
In figure ACB ? is a right angle and AC=CD and CDEF is a parallelogram. If 10 FEC ? = ° then 
calculate BDE ? 
30.   
  
In figure, PQRS is a quadrilateral in which PQ is the longest side and RS is its shortest side. 
Prove that R P ? > ? and S Q ? > ? . 
31.   
  
In figure, T is a point on side QR of a PQR ? . S is any point such that RS=ST. Prove that 
PQ+PR>QS.