Maths Past Year Paper SA-1(Set -8) - 2016, Class 9, CBSE Class 9 Notes | EduRev

 Page 1


LFHG3JR 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, (2016 – 17) 
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
Page 2


LFHG3JR 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, (2016 – 17) 
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
Page 3


LFHG3JR 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, (2016 – 17) 
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
Page 4


LFHG3JR 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, (2016 – 17) 
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
13. ???
2
2
1
34 z
z
+ = ??, ??
1
z
z
+ ?? ???? ???J? ??? ?? ??? ???? ??,
3
3
1
z
z
+ ??
??? A?? ????? |
If 
2
2
1
34, z
z
+ = find the value of 
3
3
1
, z
z
+ using only the positive value of 
1
. z
z
+ 
14. ???
2
2 ax x b + + ?? (x + 2) ?? (2x + 1) ????? ??????? ?, ?? ??E ????? ?? a –
b=0 ?? |
If both (x + 2) and (2x + 1) are factors of 
2
2 , ax x b + + prove that a – b = 0.
15. ????? ?, ?? ??? ?????? PQ ?? PS ??K? ????? O?? ??.?? ???? ? | ???
75 POT ? = °??, ?? a, b ?? c ?? ??? A?? ????? |
In the figure, two straight lines PQ and PS intersect each other at O. If 
0
75 , POT ? = find the
value of a, b and c. 
16. ??? l||m ??, n ?? ???$? ???? ?? (??6?? ?????) ??? 1: 2 7:5 ? ? = ??, ?? ???
??? A?? ????? |
If l||m, n is a transversal (see figure) and 1: 2 7:5, ? ? = then find all the angles.
Page 5


LFHG3JR 
?????? ???
? – I, 2016-17 
SUMMATIVE ASSESSMENT – I, (2016 – 17) 
???? / MATHEMATICS
?
? - IX / CLASS: IX
?????? ???: 3 ?? ?????? ??? : 90
Time Allowed : 3 hours  Maximum Marks : 90 
???? ????:
1.???  ?????? ? |
2.??  ?
 ? 31  ?, ?? ??? ??? ?, ?, ? ??? ? ? ????? ??? ?? | ?-
? ? 4  ? ???? ?? 1 ??? ?? ??; ?-? ? 6  ?? ???? ?? ?? 2 ???
?; ?-? ? 10  ? ???? ?? ?? 3 ??? ?; ??? ?-? ? 11  ? ???? ??? ?? 4 ??? ? |
3.??  ?
 ? ??? ???  ???? ?? |
4.????????? ?? ??? ???$? ?? |
General Instructions: 
1. All questions are compulsory.
2. The question paper consists of 31 questions divided into four sections A, B, C and D. Section-
A comprises of 4 questions of 1 mark each; Section-B comprises of 6 questions of 2 marks
each; Section-C comprises of 10 questions of 3 marks each and Section-D comprises of 11
questions of 4 marks each.
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
?-? / SECTION-A
 ??%? 1 ?? 4 ? ?? ?? 1 ??? ?? |
Question numbers 1 to 4 carry one mark each. 
1. ??? ?????: 
2/3 1/5
3 .3
Simplify: 
2/3 1/5
3 .3
2. 
3 3
8 125 y x - ?? ???????? ????? |
Factorise:
3 3
8 125 . y x - 3. ?? ???$? ???? l ?? ?????? m ?? n ?? ?? ??? ??.?? ???? ?? ?? ???/?
???? ????? ?? ?? ??1 ????? ?? | ??, ?? ?????? m ?? n ?? ???? ? 3? ??
???? ??
A transversal l intersects two line m and n such that a pair of alternate interior angles is 
equal. Then, what can you say about the lines m and n? 
4. ????? P(a, b), IV ??????? ? 67?? ?? | a ?? b ? ?? ???? ??? ?????
The point P(a, b) lies in the IV Quadrant. Find which of a or b greater?
? – ? / SECTION – B
 ??%? 5 ?? 10 ?? ?? 2 ??? ? |
Question numbers 5 to 10 carry two marks each. 
5. 18.48 ?? p/q ?? 9? ? :; ?????, ???? p ?? q ????>? ? ???, 0 q ?
Express 18.48 in the form of p/q, where p and q are integers, 0 q ?
6. ??? y = 2 ?? y = 0, ????
3 2
( ) 2 5 f y y y ay b = - + + ?? ??@? ?? ?? a ?? b ??
??? A?? ????? |
If y = 2 and y = 0 are the zeroes of the polynomial
3 2
( ) 2 5 , f y y y ay b = - + + find the values
of a and b.
7. ??
 ?, ???
1 1
,
2 2
OX XY PX XZ = = ?? OX = PX ??, ?? ??6B? ?? ?? ???????? D??
??E ????? ?? XY = XZ ?? |
In the figure, if 
1 1
,
2 2
OX XY PX XZ = = and OX = PX, then using an Euclid’s axiom show that
XY = XZ. 
8. ??
 ?, AB||CD ?? | x ?? ?? A?? ????? |
In the figure, AB||CD. Find x. 
9. ?? ????? x-?F ?? y-?F ?? 5 ???? ?? ???? ?? ?? | ???? ???G???? A?? ????? |
????? ?? ???G???? 3? ?????, ??? ?? y-?F ?? ?? ??? x-?F ?? 5 ???? ?? ???? ??
??
A point lies on x-axis at a distance of 5 units from y-axis. What are its co-ordinates? What
will be its co-ordinates, if it lies on y-axis at a distance of 5 units from x-axis?
10. ???? ?
??? ?? ?????? 15 cm, 25cm ?? 20cm ? | ???? F?
?? A?? ????? |
The sides of a triangle are 15 cm, 25 cm and 20 cm. Find its area.
? – ? / SECTION – C
 ??%? 11 ?? 20 ? ?? ?? 3 ??? ? |
Question numbers 11 to 20 carry three marks each. 
11. ??? ?????: 
5 1
3 45 4 3
2 3
- +
Simplify: 
5 1
3 45 4 3
2 3
- +
12. a ?? b, ?? ??? A?? ?????, ???
3 2
2
3 2
a b
+
= +
- ?? |
Find the value of a and b, if 
3 2
2.
3 2
a b
+
= +
- 
13. ???
2
2
1
34 z
z
+ = ??, ??
1
z
z
+ ?? ???? ???J? ??? ?? ??? ???? ??,
3
3
1
z
z
+ ??
??? A?? ????? |
If 
2
2
1
34, z
z
+ = find the value of 
3
3
1
, z
z
+ using only the positive value of 
1
. z
z
+ 
14. ???
2
2 ax x b + + ?? (x + 2) ?? (2x + 1) ????? ??????? ?, ?? ??E ????? ?? a –
b=0 ?? |
If both (x + 2) and (2x + 1) are factors of 
2
2 , ax x b + + prove that a – b = 0.
15. ????? ?, ?? ??? ?????? PQ ?? PS ??K? ????? O?? ??.?? ???? ? | ???
75 POT ? = °??, ?? a, b ?? c ?? ??? A?? ????? |
In the figure, two straight lines PQ and PS intersect each other at O. If 
0
75 , POT ? = find the
value of a, b and c. 
16. ??? l||m ??, n ?? ???$? ???? ?? (??6?? ?????) ??? 1: 2 7:5 ? ? = ??, ?? ???
??? A?? ????? |
If l||m, n is a transversal (see figure) and 1: 2 7:5, ? ? = then find all the angles.
17. ??? ???? ????? ?
??? ? ?? @????? ????? @????? ?? ?????? ??, ?? ??E ?????
?? ??$ ???? ???? ???? ?? ?????? ???? |
In a right angled triangle, if one acute of angle is double the other, then prove that the
hypotenuse is double the smallest side.
18. ??? ?? ??
 ? ABC ? ?? ??6M?? AD ?? | B ?? C ?? ?N BM ?? CN O???
AD ?? ???? ?? AD ?? ????? ?? ? | ???$?? ?? BM = CN ?? |
In given figure AD is the median of . ABC ? BM and CN are perpendiculars drawn from B
and C to AD and AD produced respectively. Show that BM = CN.  
19. P(3, 2) ?? Q(7, 7) ?? ????? ? | P ?? Q ?? x-?F ?? ??? ????? ?? ? ?? ?? ??? O??? L ?? M ?? ????? ? |
(a) L ?? M ?? ???G???? A?? ????? |
(b) LM ?? ?N?? A?? ????? |
P(3, 2) and Q(7, 7) are two points. Perpendiculars are drawn to x-axis from P and Q meeting
the x-axis at L and M respectively.
(a) Find the co-ordinates of L and M.
(b) Find the length of LM.