Mathematics Past Year Paper SA-1(Set-6)- 2014, Class 9, CBSE | Extra Documents & Tests for Class 9 PDF Download

 Page 1


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 34 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 8 are very short type questions, carrying 1 mark each. Question No. 9 to 
14 questions are of short answer type questions, carrying 2 marks each. Question No. 15 
to 24 carry 3 marks each. Question No. 25 to 34 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 8 carry 1 mark each. For each question, four alternative choices have 
been provided of which only one is correct. You have to select the correct choice. 
1. The value of ( )
1
5
243 is equal to  
a) 5 
b) 3 
c) 6 
d) 1 
2. The degree of polynomial 
3 4 9
5 2 3 x x x - - + 
a) -9 
b) 9 
c) 3 
d) 0 
3. The degree of a zero polynomial is: 
a) 1 
b) 0 
c) Any natural number 
d) Not defined 
4. One of the factors of 
2
42 y y + - is 
a) (7+y) 
b) (6-y) 
c) (7-y) 
d) (-6+y) 
5. The angle which is one fifth of its complement is: 
a) 15° 
Page 2


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 34 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 8 are very short type questions, carrying 1 mark each. Question No. 9 to 
14 questions are of short answer type questions, carrying 2 marks each. Question No. 15 
to 24 carry 3 marks each. Question No. 25 to 34 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 8 carry 1 mark each. For each question, four alternative choices have 
been provided of which only one is correct. You have to select the correct choice. 
1. The value of ( )
1
5
243 is equal to  
a) 5 
b) 3 
c) 6 
d) 1 
2. The degree of polynomial 
3 4 9
5 2 3 x x x - - + 
a) -9 
b) 9 
c) 3 
d) 0 
3. The degree of a zero polynomial is: 
a) 1 
b) 0 
c) Any natural number 
d) Not defined 
4. One of the factors of 
2
42 y y + - is 
a) (7+y) 
b) (6-y) 
c) (7-y) 
d) (-6+y) 
5. The angle which is one fifth of its complement is: 
a) 15° 
 
 
 
 
b) 30° 
c) 45° 
d) 60° 
6. If D is a point on the side BC of ABC ? such that AD bisect BAC ? , then: 
a) BD=DC 
b) AB>BD 
c) BD>AB 
d) DC>AC 
7. The perimeter of an equilateral triangle is 60 cm. its area (in 
2
cm ) is: 
a) 10 3 
b) 100 3 
c) 15 3 
d) 20 3 
8. Area of an isosceles right triangle is 
2
8cm . Its hypotenuse is: 
a) 32cm 
b) 4cm 
c) 4 3cm 
d) 2 6cm 
 
Section B 
Question numbers 9 to 14 carry two marks each. 
9. Express 
1
5 2 +
 
10. If a + b + c = 9, ab + bc + ca = 26, find the value of 
2 2 2
a b c + + 
11. What will be the value of quotient if 
3
(8 2 2 ) x y z + + is divided by 
3
(4 ) x y z + + ? 
12. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. 
13. In the given figure, the diagonal AC of a quadrilateral ABCD bisects the angles A and C, prove 
that AB=AD and CB=CD. 
 
Or 
In the given figure, if OA, OB, OC and OD are the rays such that 150 AOB COD ? = ? = ° , 
30 BOC ? = ° and 30 AOD ? = ° . Is it true AOC and BOD are straight lines? Justify your answer. 
Page 3


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 34 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 8 are very short type questions, carrying 1 mark each. Question No. 9 to 
14 questions are of short answer type questions, carrying 2 marks each. Question No. 15 
to 24 carry 3 marks each. Question No. 25 to 34 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 8 carry 1 mark each. For each question, four alternative choices have 
been provided of which only one is correct. You have to select the correct choice. 
1. The value of ( )
1
5
243 is equal to  
a) 5 
b) 3 
c) 6 
d) 1 
2. The degree of polynomial 
3 4 9
5 2 3 x x x - - + 
a) -9 
b) 9 
c) 3 
d) 0 
3. The degree of a zero polynomial is: 
a) 1 
b) 0 
c) Any natural number 
d) Not defined 
4. One of the factors of 
2
42 y y + - is 
a) (7+y) 
b) (6-y) 
c) (7-y) 
d) (-6+y) 
5. The angle which is one fifth of its complement is: 
a) 15° 
 
 
 
 
b) 30° 
c) 45° 
d) 60° 
6. If D is a point on the side BC of ABC ? such that AD bisect BAC ? , then: 
a) BD=DC 
b) AB>BD 
c) BD>AB 
d) DC>AC 
7. The perimeter of an equilateral triangle is 60 cm. its area (in 
2
cm ) is: 
a) 10 3 
b) 100 3 
c) 15 3 
d) 20 3 
8. Area of an isosceles right triangle is 
2
8cm . Its hypotenuse is: 
a) 32cm 
b) 4cm 
c) 4 3cm 
d) 2 6cm 
 
Section B 
Question numbers 9 to 14 carry two marks each. 
9. Express 
1
5 2 +
 
10. If a + b + c = 9, ab + bc + ca = 26, find the value of 
2 2 2
a b c + + 
11. What will be the value of quotient if 
3
(8 2 2 ) x y z + + is divided by 
3
(4 ) x y z + + ? 
12. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. 
13. In the given figure, the diagonal AC of a quadrilateral ABCD bisects the angles A and C, prove 
that AB=AD and CB=CD. 
 
Or 
In the given figure, if OA, OB, OC and OD are the rays such that 150 AOB COD ? = ? = ° , 
30 BOC ? = ° and 30 AOD ? = ° . Is it true AOC and BOD are straight lines? Justify your answer. 
 
 
 
 
  
14. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 3 units. write the co-ordinates of the point if it lies in the: 
a) I Quadrant 
b) II Quadrant 
c) III Quadrant 
d) IV Quadrant 
 
Section C 
Question numbers 15 to 25 carry 3 marks each. 
15. If 2 3 a = + , then find the value of 
1
a
a
+ 
Or 
If a=2, b=3 then find the values of the following: 
a) 
( )
1
b a
a b
- + 
b) 
( )
1
a b
a b + - 
16. Represent 3.2 on the number line. 
17. Factorize:
3
3
1 2
2 a a
a a
- - + 
Or 
If (x-3) and 
1
3
x
? ?
- ? ?
? ?
are the factors of 
2
5 ax x b + + , then show that a=b. 
18. Find the value of 
3 3
12 64 x y xy + - + when x + y = -4 
19. In the given figure QP ML 
 . Find the value of x. 
 
Or 
If two parallel lines are intersected by a transversal prove that the bisectors of the two pairs 
of interior angles enclose a rectangle. 
Page 4


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 34 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 8 are very short type questions, carrying 1 mark each. Question No. 9 to 
14 questions are of short answer type questions, carrying 2 marks each. Question No. 15 
to 24 carry 3 marks each. Question No. 25 to 34 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 8 carry 1 mark each. For each question, four alternative choices have 
been provided of which only one is correct. You have to select the correct choice. 
1. The value of ( )
1
5
243 is equal to  
a) 5 
b) 3 
c) 6 
d) 1 
2. The degree of polynomial 
3 4 9
5 2 3 x x x - - + 
a) -9 
b) 9 
c) 3 
d) 0 
3. The degree of a zero polynomial is: 
a) 1 
b) 0 
c) Any natural number 
d) Not defined 
4. One of the factors of 
2
42 y y + - is 
a) (7+y) 
b) (6-y) 
c) (7-y) 
d) (-6+y) 
5. The angle which is one fifth of its complement is: 
a) 15° 
 
 
 
 
b) 30° 
c) 45° 
d) 60° 
6. If D is a point on the side BC of ABC ? such that AD bisect BAC ? , then: 
a) BD=DC 
b) AB>BD 
c) BD>AB 
d) DC>AC 
7. The perimeter of an equilateral triangle is 60 cm. its area (in 
2
cm ) is: 
a) 10 3 
b) 100 3 
c) 15 3 
d) 20 3 
8. Area of an isosceles right triangle is 
2
8cm . Its hypotenuse is: 
a) 32cm 
b) 4cm 
c) 4 3cm 
d) 2 6cm 
 
Section B 
Question numbers 9 to 14 carry two marks each. 
9. Express 
1
5 2 +
 
10. If a + b + c = 9, ab + bc + ca = 26, find the value of 
2 2 2
a b c + + 
11. What will be the value of quotient if 
3
(8 2 2 ) x y z + + is divided by 
3
(4 ) x y z + + ? 
12. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. 
13. In the given figure, the diagonal AC of a quadrilateral ABCD bisects the angles A and C, prove 
that AB=AD and CB=CD. 
 
Or 
In the given figure, if OA, OB, OC and OD are the rays such that 150 AOB COD ? = ? = ° , 
30 BOC ? = ° and 30 AOD ? = ° . Is it true AOC and BOD are straight lines? Justify your answer. 
 
 
 
 
  
14. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 3 units. write the co-ordinates of the point if it lies in the: 
a) I Quadrant 
b) II Quadrant 
c) III Quadrant 
d) IV Quadrant 
 
Section C 
Question numbers 15 to 25 carry 3 marks each. 
15. If 2 3 a = + , then find the value of 
1
a
a
+ 
Or 
If a=2, b=3 then find the values of the following: 
a) 
( )
1
b a
a b
- + 
b) 
( )
1
a b
a b + - 
16. Represent 3.2 on the number line. 
17. Factorize:
3
3
1 2
2 a a
a a
- - + 
Or 
If (x-3) and 
1
3
x
? ?
- ? ?
? ?
are the factors of 
2
5 ax x b + + , then show that a=b. 
18. Find the value of 
3 3
12 64 x y xy + - + when x + y = -4 
19. In the given figure QP ML 
 . Find the value of x. 
 
Or 
If two parallel lines are intersected by a transversal prove that the bisectors of the two pairs 
of interior angles enclose a rectangle. 
 
 
 
 
20. In the following figure, in , 62 XYZ YXZ ? ? = ° and 54 XYZ ? = ° , if YO and ZO are bisectors of 
XYZ ? and XZY ? respectively of XYZ ? , find OZY ? and YOZ ? . 
 
21. Show that angle of an equilateral triangle are 60° each. 
22. Diagonals PR and SQ of a quadrilateral PQRS meet in O. Prove that PQ + QR + RS + SP<2(PR + 
QS) 
23. In XYZ ? , YO and ZO are the bisector of XYZ ? and XZY ? respectively. 
If 62 , 54 X XYZ ? = ° ? = ° , then find OZY ? . 
24. Find the area of a triangle whose perimeter is 42 cm and two of its sides are 18cm and 10 cm. 
 
Section D 
Question numbers 25 to 34 carry four marks each. 
25. Find the rational number a and b in the following:
5 2 3
3
7 4 3
a b
+
= +
+
 
Or 
Find the values of a and b if: 
7 3 5 7 3 5
5
3 5 3 5
a b
+ - - = +
+ - . 
26. Express 1.32 0.35 + as a fractional in simplest form. 
27. Verify that: ( )
2
3 3 3 2 2
1
3 ( ) ( ) ( )
2
x y z xyz x y z x y y z z x
? ?
+ + - = + + - + - + - ? ?
 
28. Using factor theorem, find the value of a if 
4 3 2
(2 4 2) x ax x x - + - + 
29. Simplify: 
2 2 3 2 2 3 2 2 3
3 3 3
( ) ( ) ( )
( ) ( ) ( )
x y y z z x
x y y z z x
- + - + - - + - + - 
Or 
Find the values of a and b so that (x+1) and (x-2) are factors of 
3 2
( 2 ) ax ax x b + + + 
30. (i) Plot the points A(-5,-2), B(1,-2), C(6,4) and D(0,4) 
(ii) Join the points to get AB, BC, CD and DA. Name the figure so obtained. 
31. In the figure below, the sides AB and AC of triangle ABC are produced to P and Q respectively. 
The bisector of PBC ? and QCB ? meet at O. Prove that 
1
90
2
BOC A ? = ° - ? . 
Page 5


 
 
 
 
Summative Assessment-1 (2014-15) 
 Mathematics 
Class – IX 
 
Time allowed: 3:00 hours                                Maximum Marks: 90 
 
General Instructions: 
a) All questions are compulsory. 
b) Question paper contains 34 questions divide into 4 sections A, B, C and D. 
c) Question No. 1 to 8 are very short type questions, carrying 1 mark each. Question No. 9 to 
14 questions are of short answer type questions, carrying 2 marks each. Question No. 15 
to 24 carry 3 marks each. Question No. 25 to 34 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 8 carry 1 mark each. For each question, four alternative choices have 
been provided of which only one is correct. You have to select the correct choice. 
1. The value of ( )
1
5
243 is equal to  
a) 5 
b) 3 
c) 6 
d) 1 
2. The degree of polynomial 
3 4 9
5 2 3 x x x - - + 
a) -9 
b) 9 
c) 3 
d) 0 
3. The degree of a zero polynomial is: 
a) 1 
b) 0 
c) Any natural number 
d) Not defined 
4. One of the factors of 
2
42 y y + - is 
a) (7+y) 
b) (6-y) 
c) (7-y) 
d) (-6+y) 
5. The angle which is one fifth of its complement is: 
a) 15° 
 
 
 
 
b) 30° 
c) 45° 
d) 60° 
6. If D is a point on the side BC of ABC ? such that AD bisect BAC ? , then: 
a) BD=DC 
b) AB>BD 
c) BD>AB 
d) DC>AC 
7. The perimeter of an equilateral triangle is 60 cm. its area (in 
2
cm ) is: 
a) 10 3 
b) 100 3 
c) 15 3 
d) 20 3 
8. Area of an isosceles right triangle is 
2
8cm . Its hypotenuse is: 
a) 32cm 
b) 4cm 
c) 4 3cm 
d) 2 6cm 
 
Section B 
Question numbers 9 to 14 carry two marks each. 
9. Express 
1
5 2 +
 
10. If a + b + c = 9, ab + bc + ca = 26, find the value of 
2 2 2
a b c + + 
11. What will be the value of quotient if 
3
(8 2 2 ) x y z + + is divided by 
3
(4 ) x y z + + ? 
12. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. 
13. In the given figure, the diagonal AC of a quadrilateral ABCD bisects the angles A and C, prove 
that AB=AD and CB=CD. 
 
Or 
In the given figure, if OA, OB, OC and OD are the rays such that 150 AOB COD ? = ? = ° , 
30 BOC ? = ° and 30 AOD ? = ° . Is it true AOC and BOD are straight lines? Justify your answer. 
 
 
 
 
  
14. The perpendicular distance of a point from the x-axis is 2 units and the perpendicular 
distance from the y-axis is 3 units. write the co-ordinates of the point if it lies in the: 
a) I Quadrant 
b) II Quadrant 
c) III Quadrant 
d) IV Quadrant 
 
Section C 
Question numbers 15 to 25 carry 3 marks each. 
15. If 2 3 a = + , then find the value of 
1
a
a
+ 
Or 
If a=2, b=3 then find the values of the following: 
a) 
( )
1
b a
a b
- + 
b) 
( )
1
a b
a b + - 
16. Represent 3.2 on the number line. 
17. Factorize:
3
3
1 2
2 a a
a a
- - + 
Or 
If (x-3) and 
1
3
x
? ?
- ? ?
? ?
are the factors of 
2
5 ax x b + + , then show that a=b. 
18. Find the value of 
3 3
12 64 x y xy + - + when x + y = -4 
19. In the given figure QP ML 
 . Find the value of x. 
 
Or 
If two parallel lines are intersected by a transversal prove that the bisectors of the two pairs 
of interior angles enclose a rectangle. 
 
 
 
 
20. In the following figure, in , 62 XYZ YXZ ? ? = ° and 54 XYZ ? = ° , if YO and ZO are bisectors of 
XYZ ? and XZY ? respectively of XYZ ? , find OZY ? and YOZ ? . 
 
21. Show that angle of an equilateral triangle are 60° each. 
22. Diagonals PR and SQ of a quadrilateral PQRS meet in O. Prove that PQ + QR + RS + SP<2(PR + 
QS) 
23. In XYZ ? , YO and ZO are the bisector of XYZ ? and XZY ? respectively. 
If 62 , 54 X XYZ ? = ° ? = ° , then find OZY ? . 
24. Find the area of a triangle whose perimeter is 42 cm and two of its sides are 18cm and 10 cm. 
 
Section D 
Question numbers 25 to 34 carry four marks each. 
25. Find the rational number a and b in the following:
5 2 3
3
7 4 3
a b
+
= +
+
 
Or 
Find the values of a and b if: 
7 3 5 7 3 5
5
3 5 3 5
a b
+ - - = +
+ - . 
26. Express 1.32 0.35 + as a fractional in simplest form. 
27. Verify that: ( )
2
3 3 3 2 2
1
3 ( ) ( ) ( )
2
x y z xyz x y z x y y z z x
? ?
+ + - = + + - + - + - ? ?
 
28. Using factor theorem, find the value of a if 
4 3 2
(2 4 2) x ax x x - + - + 
29. Simplify: 
2 2 3 2 2 3 2 2 3
3 3 3
( ) ( ) ( )
( ) ( ) ( )
x y y z z x
x y y z z x
- + - + - - + - + - 
Or 
Find the values of a and b so that (x+1) and (x-2) are factors of 
3 2
( 2 ) ax ax x b + + + 
30. (i) Plot the points A(-5,-2), B(1,-2), C(6,4) and D(0,4) 
(ii) Join the points to get AB, BC, CD and DA. Name the figure so obtained. 
31. In the figure below, the sides AB and AC of triangle ABC are produced to P and Q respectively. 
The bisector of PBC ? and QCB ? meet at O. Prove that 
1
90
2
BOC A ? = ° - ? . 
 
 
 
 
 
32. Q is a point on side SR of triangle PSR as shown in the figure below such that PQ=PR. Show 
that PS>PQ 
 
33. In the figure below, PQ=QR and x y ? = ? . Prove that AR=PB. 
 
34. If BE and CF are equal altitudes of a triangle ABC, then prove that triangle ABC is isosceles.