Class 9 Maths: CBSE Past Year Paper (SA-1) - 11 PDF Download

 Page 1


SUMMATIVE ASSESSMENT –I 
Class – IX 
MATHEMATICS  
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question 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 question of 4 
marks each. 
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
Section-A 
Question number 1 to 4 carry one mark each. 
Q.1 Which is the greatest among 
3 4
2 , 4 3 and ? 
Q.2 If 2x+1 is one factor of the polynomial 
2
2 x x 1 ? ? , then find the other factor. 
Q.3 In the given figure, 
o
A B D 66 ? ? and 
o
A CD 60 ? ? . If bisector of A ? meets BC at D, then find 
A D B . ? 
Q. 4 What do you mean by ordinate of point? 
Section-B 
Question number 5 to 10 carry two marks each. 
Q.5 Is zero (0) a rational number? Justify your answer. 
Q.6 Factories’ : 
3 2
3 y y 3 y 1 ? ? ? 
Q.7 In the figure, if 
o
A O B 60 ? ? and B O C 2 x ? ? , then find the value of x so that AOC is a straight 
line. 
Page 2


SUMMATIVE ASSESSMENT –I 
Class – IX 
MATHEMATICS  
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question 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 question of 4 
marks each. 
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
Section-A 
Question number 1 to 4 carry one mark each. 
Q.1 Which is the greatest among 
3 4
2 , 4 3 and ? 
Q.2 If 2x+1 is one factor of the polynomial 
2
2 x x 1 ? ? , then find the other factor. 
Q.3 In the given figure, 
o
A B D 66 ? ? and 
o
A CD 60 ? ? . If bisector of A ? meets BC at D, then find 
A D B . ? 
Q. 4 What do you mean by ordinate of point? 
Section-B 
Question number 5 to 10 carry two marks each. 
Q.5 Is zero (0) a rational number? Justify your answer. 
Q.6 Factories’ : 
3 2
3 y y 3 y 1 ? ? ? 
Q.7 In the figure, if 
o
A O B 60 ? ? and B O C 2 x ? ? , then find the value of x so that AOC is a straight 
line. 
Q.8 In the give figure ; if 1 3 , 2 4 ? ? ? ? ? ? and 3 4 , ? ? ? write a relation between 1 and 2 ? ? by 
using an Euclid’s axiom. Write the axiom also. 
Q.9 A point is a distance of 4 units from z-axis and 5 units from the y-axis. Represent the position of 
the point in the Cartesian plane and also write its co-ordinates. 
Q.10 Compute the area of the trapezium shown in the figure : 
Section C 
Question number 11 to 20 carry three marks each. 
Q.11 Simplify : 
8 4 16 4
81 x y z 
Q.12 If x 2 3 ? ? ; find the value of 
3
3
1
x
x
?
Q.13 Using a suitable identity, evaluate 
3 3 3
( 43 ) ( 18 ) ( 24) . ? ? 
Q.14 Let 
1
R and 
2
R are the remainders when the polynomials 
3 2
f ( x ) 4 x 3x 12a x 5 ? ? ? ? and
3 2
g ( x ) 2 x ax 6 x 2 ? ? ? ? are divided by (x-1) and (x-2) respectively. 
1 2
I f 3 x R 2 8 0 ? ? ? , find the
value of ‘a’. 
Q.15 Write any three Euclid’s Postulate. 
Q.16  In the give figure, if the line segment AB is parallel to another line segment RS and O is the 
mid-point of As, then Show that : 
(a) A O B SO R ? ? ? ? 
(ii) O is also mid-point of BR 
Page 3


SUMMATIVE ASSESSMENT –I 
Class – IX 
MATHEMATICS  
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question 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 question of 4 
marks each. 
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
Section-A 
Question number 1 to 4 carry one mark each. 
Q.1 Which is the greatest among 
3 4
2 , 4 3 and ? 
Q.2 If 2x+1 is one factor of the polynomial 
2
2 x x 1 ? ? , then find the other factor. 
Q.3 In the given figure, 
o
A B D 66 ? ? and 
o
A CD 60 ? ? . If bisector of A ? meets BC at D, then find 
A D B . ? 
Q. 4 What do you mean by ordinate of point? 
Section-B 
Question number 5 to 10 carry two marks each. 
Q.5 Is zero (0) a rational number? Justify your answer. 
Q.6 Factories’ : 
3 2
3 y y 3 y 1 ? ? ? 
Q.7 In the figure, if 
o
A O B 60 ? ? and B O C 2 x ? ? , then find the value of x so that AOC is a straight 
line. 
Q.8 In the give figure ; if 1 3 , 2 4 ? ? ? ? ? ? and 3 4 , ? ? ? write a relation between 1 and 2 ? ? by 
using an Euclid’s axiom. Write the axiom also. 
Q.9 A point is a distance of 4 units from z-axis and 5 units from the y-axis. Represent the position of 
the point in the Cartesian plane and also write its co-ordinates. 
Q.10 Compute the area of the trapezium shown in the figure : 
Section C 
Question number 11 to 20 carry three marks each. 
Q.11 Simplify : 
8 4 16 4
81 x y z 
Q.12 If x 2 3 ? ? ; find the value of 
3
3
1
x
x
?
Q.13 Using a suitable identity, evaluate 
3 3 3
( 43 ) ( 18 ) ( 24) . ? ? 
Q.14 Let 
1
R and 
2
R are the remainders when the polynomials 
3 2
f ( x ) 4 x 3x 12a x 5 ? ? ? ? and
3 2
g ( x ) 2 x ax 6 x 2 ? ? ? ? are divided by (x-1) and (x-2) respectively. 
1 2
I f 3 x R 2 8 0 ? ? ? , find the
value of ‘a’. 
Q.15 Write any three Euclid’s Postulate. 
Q.16  In the give figure, if the line segment AB is parallel to another line segment RS and O is the 
mid-point of As, then Show that : 
(a) A O B SO R ? ? ? ? 
(ii) O is also mid-point of BR 
Q.17 In the figure, 
o
P Q P R , P Q || RL, R Q T 38 ? ? ? and 
o
QT L 75 ? ? . Find x and y. 
Q.18 Prove that if two lines intersect, vertically opposite angles are equal. 
Q.19 On the graph paper, plot a point A(-2,-2). Reflect point A in x-axis and y-axis. Let these points 
be B and C respectively. Guess the measure of B A C ? . 
Q.20 The Perimeter of a triangular garden is 900 cm and its sides are in the ratio 3 : 5 : 4. Using 
Heron’s formula, find the area of the garden. 
Section D 
Question number 21 to 31 carry four marks each. 
Q.21 Express in the form of 
p
q
: 0 . 3 8 1 . 2 7 ?
Q.22 Rationalise the denominator of the following: 
3
3 5 2 ? ?
Q.23 If ab + bc + ca = 0 find value of 
2 2 2
1 1 1
a bc b c a c a b
? ?
? ? ?
Q.24 Verify if -3 and 4 are zeroes of the polynomial 
3 2
2 x 3 x 23x 12. ? ? ? If yes, then factorise the 
polynomial. 
Q.25 Using long division method, show that the polynomial p(x)= 
3
x 1 ? is divisible by q(x) = x+1. 
Verify your result using factor theorem. 
Q.26 Show that ? ? ? ? ? ? ? ?
2 2 2
3 3 3
1
a b c 3 ab c a b c a b b c c a
2
?
? ?
? ? ? ? ? ? ? ? ? ?
? ?
Q. 27 For spreading the message “Save environment Save future” a rally was organized by some 
students of a school. They were given triangular cardboard piece ABC which they divided in to two 
Page 4


SUMMATIVE ASSESSMENT –I 
Class – IX 
MATHEMATICS  
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question 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 question of 4 
marks each. 
3. There is no overall choice in this question paper.
4. Use of calculator is not permitted.
Section-A 
Question number 1 to 4 carry one mark each. 
Q.1 Which is the greatest among 
3 4
2 , 4 3 and ? 
Q.2 If 2x+1 is one factor of the polynomial 
2
2 x x 1 ? ? , then find the other factor. 
Q.3 In the given figure, 
o
A B D 66 ? ? and 
o
A CD 60 ? ? . If bisector of A ? meets BC at D, then find 
A D B . ? 
Q. 4 What do you mean by ordinate of point? 
Section-B 
Question number 5 to 10 carry two marks each. 
Q.5 Is zero (0) a rational number? Justify your answer. 
Q.6 Factories’ : 
3 2
3 y y 3 y 1 ? ? ? 
Q.7 In the figure, if 
o
A O B 60 ? ? and B O C 2 x ? ? , then find the value of x so that AOC is a straight 
line. 
Q.8 In the give figure ; if 1 3 , 2 4 ? ? ? ? ? ? and 3 4 , ? ? ? write a relation between 1 and 2 ? ? by 
using an Euclid’s axiom. Write the axiom also. 
Q.9 A point is a distance of 4 units from z-axis and 5 units from the y-axis. Represent the position of 
the point in the Cartesian plane and also write its co-ordinates. 
Q.10 Compute the area of the trapezium shown in the figure : 
Section C 
Question number 11 to 20 carry three marks each. 
Q.11 Simplify : 
8 4 16 4
81 x y z 
Q.12 If x 2 3 ? ? ; find the value of 
3
3
1
x
x
?
Q.13 Using a suitable identity, evaluate 
3 3 3
( 43 ) ( 18 ) ( 24) . ? ? 
Q.14 Let 
1
R and 
2
R are the remainders when the polynomials 
3 2
f ( x ) 4 x 3x 12a x 5 ? ? ? ? and
3 2
g ( x ) 2 x ax 6 x 2 ? ? ? ? are divided by (x-1) and (x-2) respectively. 
1 2
I f 3 x R 2 8 0 ? ? ? , find the
value of ‘a’. 
Q.15 Write any three Euclid’s Postulate. 
Q.16  In the give figure, if the line segment AB is parallel to another line segment RS and O is the 
mid-point of As, then Show that : 
(a) A O B SO R ? ? ? ? 
(ii) O is also mid-point of BR 
Q.17 In the figure, 
o
P Q P R , P Q || RL, R Q T 38 ? ? ? and 
o
QT L 75 ? ? . Find x and y. 
Q.18 Prove that if two lines intersect, vertically opposite angles are equal. 
Q.19 On the graph paper, plot a point A(-2,-2). Reflect point A in x-axis and y-axis. Let these points 
be B and C respectively. Guess the measure of B A C ? . 
Q.20 The Perimeter of a triangular garden is 900 cm and its sides are in the ratio 3 : 5 : 4. Using 
Heron’s formula, find the area of the garden. 
Section D 
Question number 21 to 31 carry four marks each. 
Q.21 Express in the form of 
p
q
: 0 . 3 8 1 . 2 7 ?
Q.22 Rationalise the denominator of the following: 
3
3 5 2 ? ?
Q.23 If ab + bc + ca = 0 find value of 
2 2 2
1 1 1
a bc b c a c a b
? ?
? ? ?
Q.24 Verify if -3 and 4 are zeroes of the polynomial 
3 2
2 x 3 x 23x 12. ? ? ? If yes, then factorise the 
polynomial. 
Q.25 Using long division method, show that the polynomial p(x)= 
3
x 1 ? is divisible by q(x) = x+1. 
Verify your result using factor theorem. 
Q.26 Show that ? ? ? ? ? ? ? ?
2 2 2
3 3 3
1
a b c 3 ab c a b c a b b c c a
2
?
? ?
? ? ? ? ? ? ? ? ? ?
? ?
Q. 27 For spreading the message “Save environment Save future” a rally was organized by some 
students of a school. They were given triangular cardboard piece ABC which they divided in to two 
parts by drawing the angle bisectors BO and CO of base angles B and C. Prove that 
1
B OC 90 A .
2
? ? ? ? what is the benefit of these types of rallies?
Q.28 Solve the equation a-35=75 and state which axiom you use here. Also give two more axioms 
other than the axiom used in the above situation. 
Q.29 In the figure, two straight lines PQ and RS intersect each other at O. If 
o
PO T 75 ? ? , find the 
values of a, b and c. 
Q.30 In the given figure, prove that  
o
A B C D E F 360 ? ? ? ? ? ? ? ? ? ? ? ? . 
Q.31 The angles of a triangle are ? ? ? ?
o
o o x
x 40 , x 20 a nd 10
2
? ?
? ? ?
? ?
? ?
. Find the value of x and then the 
angles of the triangle.