Mathematics Past Year Paper SA-1(Set-7)- 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 contains of 31 questions 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 compromises of 10 questions of 3 marks 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 numbers 1 to 4 carry one mark each. 
1. Express 0.3 in the form 
p
q
, where p and q are integers and 0. q ? 
2. If 
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 
3. If fig, AB XY 
 , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 
 
4. Write the distance of point A(3,5) from x-axis. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the value of x if 
5
5 2 2 x + = 
6. Factorise: ( )
3
3
8 2 x x y - - 
7. State any two Euclid’s axioms. 
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that 
ABD ACD ? = ? . 
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 contains of 31 questions 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 compromises of 10 questions of 3 marks 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 numbers 1 to 4 carry one mark each. 
1. Express 0.3 in the form 
p
q
, where p and q are integers and 0. q ? 
2. If 
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 
3. If fig, AB XY 
 , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 
 
4. Write the distance of point A(3,5) from x-axis. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the value of x if 
5
5 2 2 x + = 
6. Factorise: ( )
3
3
8 2 x x y - - 
7. State any two Euclid’s axioms. 
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that 
ABD ACD ? = ? . 
 
 
 
 
 
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. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is 
formed on joining the points in order? Also, identify the shape of figure. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Simplify: 
72
5 72 3 288 2 648 + - 
12. If 5 2 6, p = - find 
2
2
1
p
p
- 
13. Factorise: 
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 
14. Prove that 
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by 
2
3 2 x x - + 
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° + 
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 
 
17. In figure; if l m 
 and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 
 
18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 
1 2 ? = ? . 
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 contains of 31 questions 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 compromises of 10 questions of 3 marks 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 numbers 1 to 4 carry one mark each. 
1. Express 0.3 in the form 
p
q
, where p and q are integers and 0. q ? 
2. If 
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 
3. If fig, AB XY 
 , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 
 
4. Write the distance of point A(3,5) from x-axis. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the value of x if 
5
5 2 2 x + = 
6. Factorise: ( )
3
3
8 2 x x y - - 
7. State any two Euclid’s axioms. 
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that 
ABD ACD ? = ? . 
 
 
 
 
 
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. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is 
formed on joining the points in order? Also, identify the shape of figure. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Simplify: 
72
5 72 3 288 2 648 + - 
12. If 5 2 6, p = - find 
2
2
1
p
p
- 
13. Factorise: 
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 
14. Prove that 
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by 
2
3 2 x x - + 
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° + 
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 
 
17. In figure; if l m 
 and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 
 
18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 
1 2 ? = ? . 
 
 
 
 
 
19. 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. 
20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area 
( )
2
108 FBE cm ? = , find the length of AB. 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Find the values of a and b if 
7 1 7 1
7
7 1 7 1
a b
- +
- = +
+ - 
22. Simplify: 
1 1 1 1
2 5 5 6 6 7 7 8
+ + +
+ + + +
 
23. If x-5 and 
1
5
x - are the factors of the polynomial
2
3 px x r + + , show that p=r. 
24. Show that 2x-1 is a factor of the polynomial
3 2 2
2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise 
the polynomial. 
25. Divide polynomial 
4 3 2
( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in 
p(x) so that it is divisible by q(x). 
26. Factorise: 
6 3
5 8 x x + + 
27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting 
by doing so 
In the figure below, AB CD 
 . 
  
What is the value of x? 
Also find angle A and B. 
28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE 
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 contains of 31 questions 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 compromises of 10 questions of 3 marks 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 numbers 1 to 4 carry one mark each. 
1. Express 0.3 in the form 
p
q
, where p and q are integers and 0. q ? 
2. If 
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient. 
3. If fig, AB XY 
 , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? = 
 
4. Write the distance of point A(3,5) from x-axis. 
 
Section B 
Question numbers 5 to 10 carry two marks each. 
5. Find the value of x if 
5
5 2 2 x + = 
6. Factorise: ( )
3
3
8 2 x x y - - 
7. State any two Euclid’s axioms. 
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that 
ABD ACD ? = ? . 
 
 
 
 
 
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. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is 
formed on joining the points in order? Also, identify the shape of figure. 
 
Section C 
Question numbers 11 to 20 carry three marks each. 
11. Simplify: 
72
5 72 3 288 2 648 + - 
12. If 5 2 6, p = - find 
2
2
1
p
p
- 
13. Factorise: 
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - - 
14. Prove that 
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by 
2
3 2 x x - + 
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° + 
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD 
 
17. In figure; if l m 
 and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles. 
 
18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that 
1 2 ? = ? . 
 
 
 
 
 
19. 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. 
20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area 
( )
2
108 FBE cm ? = , find the length of AB. 
 
Section D 
Question numbers 21 to 31 carry four marks each. 
21. Find the values of a and b if 
7 1 7 1
7
7 1 7 1
a b
- +
- = +
+ - 
22. Simplify: 
1 1 1 1
2 5 5 6 6 7 7 8
+ + +
+ + + +
 
23. If x-5 and 
1
5
x - are the factors of the polynomial
2
3 px x r + + , show that p=r. 
24. Show that 2x-1 is a factor of the polynomial
3 2 2
2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise 
the polynomial. 
25. Divide polynomial 
4 3 2
( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in 
p(x) so that it is divisible by q(x). 
26. Factorise: 
6 3
5 8 x x + + 
27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting 
by doing so 
In the figure below, AB CD 
 . 
  
What is the value of x? 
Also find angle A and B. 
28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE 
 
 
 
 
 
29. Sides BC, CA and BA of a triangle ABC are produced to D, Q, P, respectively as shown in the 
figure. If 100 , 35 ACD QAP ? = ° ? = ° , find all the angles of the triangle. 
 
30. In figure, AB=BC and AD=EC, then show that ABE CBD ? ? ? 
 
31. Prove that the angles opposite to equal sides of a triangle are equal.