Class 9 Maths: CBSE Past Year Paper (SA-1) - 12 | Past Year Papers For Class 9

 Page 1


SUMMATIVE ASSESSMENT-I 
CLASS: IX, MATHEMATICS 
 Time allowed: 3 hours     Maximum Marks: 90 
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 question 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’ 
Question numbers 1 to 4 carry one mark each. 
Q.1  Find the value of ? ? ? ?
0. 16 0.09
81 81 ? .
Q.2 Using suitable identity, find (2+3x)(2-3x). 
Q.3 In the figure, If 
o
A 40 ? ? and 
o
A 70 ? ? , then fine BC E . ? 
Q.4 In which quadrants the points P(2,-3) and Q(-3,2) lie? 
Section ‘B’ 
Question numbers 5 to 10 carry two mark each. 
Q.5 Find the value of 
2 3
, 3 1. 73
2 3
 if 
?
?
?
Q.6 Using remainder theorem, find the remainder when 
4 3 2
x 3x 2 x 4 ? ? ? is divided by x+2. 
Q.7 In given figure PR = QS, then show that PQ = RS. Name the mathematician whose postulate/axiom is used 
for the same. 
Q.8 In the give figure, B A and C< D ? ? ? ? ? , show that AD<BC. 
Page 2


SUMMATIVE ASSESSMENT-I 
CLASS: IX, MATHEMATICS 
 Time allowed: 3 hours     Maximum Marks: 90 
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 question 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’ 
Question numbers 1 to 4 carry one mark each. 
Q.1  Find the value of ? ? ? ?
0. 16 0.09
81 81 ? .
Q.2 Using suitable identity, find (2+3x)(2-3x). 
Q.3 In the figure, If 
o
A 40 ? ? and 
o
A 70 ? ? , then fine BC E . ? 
Q.4 In which quadrants the points P(2,-3) and Q(-3,2) lie? 
Section ‘B’ 
Question numbers 5 to 10 carry two mark each. 
Q.5 Find the value of 
2 3
, 3 1. 73
2 3
 if 
?
?
?
Q.6 Using remainder theorem, find the remainder when 
4 3 2
x 3x 2 x 4 ? ? ? is divided by x+2. 
Q.7 In given figure PR = QS, then show that PQ = RS. Name the mathematician whose postulate/axiom is used 
for the same. 
Q.8 In the give figure, B A and C< D ? ? ? ? ? , show that AD<BC. 
Q.9 Find the perimeter of an isosceles right angled triangle having an area of 5000
2
m .
? ?
U se 2 1. 41 ?
Q.10 On which axes the following points lie? 
? ? ? ? ? ? ? ? 0 , 4 , 5 , 0 , 5 , 0 and 0 , 3 ? ?
Section ‘C’ 
Question numbers 11 to 20 carry three mark each. 
Q.11 Find the values of a and b. if 
3 2
a b 2
3 2
?
? ?
?
Q.12 Represent 
? ?
1 9.5 ? on the number line.
Q.13  Expand 
2
1 1
x y z
2 3
? ?
? ?
? ?
? ?
Q.14 Factorise 
2 2 2
4 x y 25 z 4 xy 10 y z 20 zx ? ? ? ? ? and hence find its value when x = -1, y = 2 and z = -3. 
Q.15 In the figure, 
o o o
P DQ 45 , P QD 35 and B O P 80 ? ? ? ? ? ? . Prove that p||m. 
Q.16 In the given figure, show that XY||EF. 
Page 3


SUMMATIVE ASSESSMENT-I 
CLASS: IX, MATHEMATICS 
 Time allowed: 3 hours     Maximum Marks: 90 
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 question 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’ 
Question numbers 1 to 4 carry one mark each. 
Q.1  Find the value of ? ? ? ?
0. 16 0.09
81 81 ? .
Q.2 Using suitable identity, find (2+3x)(2-3x). 
Q.3 In the figure, If 
o
A 40 ? ? and 
o
A 70 ? ? , then fine BC E . ? 
Q.4 In which quadrants the points P(2,-3) and Q(-3,2) lie? 
Section ‘B’ 
Question numbers 5 to 10 carry two mark each. 
Q.5 Find the value of 
2 3
, 3 1. 73
2 3
 if 
?
?
?
Q.6 Using remainder theorem, find the remainder when 
4 3 2
x 3x 2 x 4 ? ? ? is divided by x+2. 
Q.7 In given figure PR = QS, then show that PQ = RS. Name the mathematician whose postulate/axiom is used 
for the same. 
Q.8 In the give figure, B A and C< D ? ? ? ? ? , show that AD<BC. 
Q.9 Find the perimeter of an isosceles right angled triangle having an area of 5000
2
m .
? ?
U se 2 1. 41 ?
Q.10 On which axes the following points lie? 
? ? ? ? ? ? ? ? 0 , 4 , 5 , 0 , 5 , 0 and 0 , 3 ? ?
Section ‘C’ 
Question numbers 11 to 20 carry three mark each. 
Q.11 Find the values of a and b. if 
3 2
a b 2
3 2
?
? ?
?
Q.12 Represent 
? ?
1 9.5 ? on the number line.
Q.13  Expand 
2
1 1
x y z
2 3
? ?
? ?
? ?
? ?
Q.14 Factorise 
2 2 2
4 x y 25 z 4 xy 10 y z 20 zx ? ? ? ? ? and hence find its value when x = -1, y = 2 and z = -3. 
Q.15 In the figure, 
o o o
P DQ 45 , P QD 35 and B O P 80 ? ? ? ? ? ? . Prove that p||m. 
Q.16 In the given figure, show that XY||EF. 
Q.17 In the given figure, AB=AC. D is a point on AC and E on AB such that AD=ED=EC=BC. Prove 
that A : B 1 : 3 ? ? ? . 
Q.18 In figure, if  l||m, 
o
3 ( x 30 ) ? ? ? and 
o
6 ( 2 x 15) ? ? ? , find 1 and 8 .  ? ? 
Q.19 Find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18 
cm. Calculate the altitude of triangle corresponding to its shortest side. 
Q.20 Plot two points P(0,-4) and Q(0,4) on the graph paper. Now, plot R and S such that 
PQ R a n d P Q S  ? ? are isosceles triangles. 
Section ‘D’ 
Question numbers 21 to 31 carry four mark each. 
Q.21 If 
2 1 2 1
x
2 1 2 1
 and y=
? ?
?
? ?
, find the value of 
2 2
x y xy . ? ? 
Q.22 Prove that : 
1 1 1 1 1
5.
3 8 8 7 7 6 6 5 5 2
? ? ? ? ?
? ? ? ? ?
 
Q.23 Find the value of ‘a’, if x + a is a factor of the polynomial 
3 2
p ( x ) x ax 2 x a 4. ? ? ? ? ? 
Q.24 If (x+1) and (x+2) are the factors of 
3 2
x ax 2 x a 4 . ? ? ? ? 
Q.25 Divide the polynomial 
3 2
x 3x 3 a x ? ? ? ? , then find a and ? . 
Q.26 If x + y + z = 1, xy + yz + zx = -1 and xyz = -1, find the value of 
3 3 3
x y z . ? ? 
Q.27 A farmer has two adjacent farms PQS and PSR as shown in the figure. He decides to give on e farm for 
hospital. What value is he exhibiting by doing so? If PQ>PR and PS is bisector of P, ? show that PS Q PS R . ? ? ? 
Page 4


SUMMATIVE ASSESSMENT-I 
CLASS: IX, MATHEMATICS 
 Time allowed: 3 hours     Maximum Marks: 90 
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 question 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’ 
Question numbers 1 to 4 carry one mark each. 
Q.1  Find the value of ? ? ? ?
0. 16 0.09
81 81 ? .
Q.2 Using suitable identity, find (2+3x)(2-3x). 
Q.3 In the figure, If 
o
A 40 ? ? and 
o
A 70 ? ? , then fine BC E . ? 
Q.4 In which quadrants the points P(2,-3) and Q(-3,2) lie? 
Section ‘B’ 
Question numbers 5 to 10 carry two mark each. 
Q.5 Find the value of 
2 3
, 3 1. 73
2 3
 if 
?
?
?
Q.6 Using remainder theorem, find the remainder when 
4 3 2
x 3x 2 x 4 ? ? ? is divided by x+2. 
Q.7 In given figure PR = QS, then show that PQ = RS. Name the mathematician whose postulate/axiom is used 
for the same. 
Q.8 In the give figure, B A and C< D ? ? ? ? ? , show that AD<BC. 
Q.9 Find the perimeter of an isosceles right angled triangle having an area of 5000
2
m .
? ?
U se 2 1. 41 ?
Q.10 On which axes the following points lie? 
? ? ? ? ? ? ? ? 0 , 4 , 5 , 0 , 5 , 0 and 0 , 3 ? ?
Section ‘C’ 
Question numbers 11 to 20 carry three mark each. 
Q.11 Find the values of a and b. if 
3 2
a b 2
3 2
?
? ?
?
Q.12 Represent 
? ?
1 9.5 ? on the number line.
Q.13  Expand 
2
1 1
x y z
2 3
? ?
? ?
? ?
? ?
Q.14 Factorise 
2 2 2
4 x y 25 z 4 xy 10 y z 20 zx ? ? ? ? ? and hence find its value when x = -1, y = 2 and z = -3. 
Q.15 In the figure, 
o o o
P DQ 45 , P QD 35 and B O P 80 ? ? ? ? ? ? . Prove that p||m. 
Q.16 In the given figure, show that XY||EF. 
Q.17 In the given figure, AB=AC. D is a point on AC and E on AB such that AD=ED=EC=BC. Prove 
that A : B 1 : 3 ? ? ? . 
Q.18 In figure, if  l||m, 
o
3 ( x 30 ) ? ? ? and 
o
6 ( 2 x 15) ? ? ? , find 1 and 8 .  ? ? 
Q.19 Find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18 
cm. Calculate the altitude of triangle corresponding to its shortest side. 
Q.20 Plot two points P(0,-4) and Q(0,4) on the graph paper. Now, plot R and S such that 
PQ R a n d P Q S  ? ? are isosceles triangles. 
Section ‘D’ 
Question numbers 21 to 31 carry four mark each. 
Q.21 If 
2 1 2 1
x
2 1 2 1
 and y=
? ?
?
? ?
, find the value of 
2 2
x y xy . ? ? 
Q.22 Prove that : 
1 1 1 1 1
5.
3 8 8 7 7 6 6 5 5 2
? ? ? ? ?
? ? ? ? ?
 
Q.23 Find the value of ‘a’, if x + a is a factor of the polynomial 
3 2
p ( x ) x ax 2 x a 4. ? ? ? ? ? 
Q.24 If (x+1) and (x+2) are the factors of 
3 2
x ax 2 x a 4 . ? ? ? ? 
Q.25 Divide the polynomial 
3 2
x 3x 3 a x ? ? ? ? , then find a and ? . 
Q.26 If x + y + z = 1, xy + yz + zx = -1 and xyz = -1, find the value of 
3 3 3
x y z . ? ? 
Q.27 A farmer has two adjacent farms PQS and PSR as shown in the figure. He decides to give on e farm for 
hospital. What value is he exhibiting by doing so? If PQ>PR and PS is bisector of P, ? show that PS Q PS R . ? ? ? 
Q.28 In an isosceles triangle ABC with AB=AC, D and E are two points on BC such that BE =CD. 
Show that AD = AE. 
Q.29 In figure, OA = OD and 1 2 . ? ? ? Prove that OC B ? is and isosceles triangle. 
Q.30 Prove that the angles opposite to equal sides of a triangle are equal. 
Q.31 In the figure, X and Y are the points on equal sides AB and AC of a A BC ? such that AX = AY. 
Prove that XC = YB.