Class 9 Maths: CBSE Past Year Paper (SA-1) - 13 | Past Year Papers For Class 9

 Page 1


SUMMATIVE ASSESSMENT- I 
MATHEMATICS 
Class – IX 
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question are compulsory.
2. The question paper consists of 31questions 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 
Question numbers 1 to 4 carry one mark each. 
1. Simplify 2 3 3 + 
2. Factorise : 
3 3
8 y . - 125x
3. In the given figure, O is the mid-Point of AB and B Q O A PO , ? ? ? then O A P ? is equal to which
angle? 
4. If (a, b) = (0, -2), find value of a and b
Section-B 
Question numbers 5 to 10 carry two marks each. 
5. Rationalize 
3 2
7
3 2 - 
6. If 3x + 2y= 12 and xy = 6, then find 
3 3
27 x 8 y . ?
7. In the figure, PR is the angle bisector of A PQ ? . Prove that AB||CD.
Page 2


SUMMATIVE ASSESSMENT- I 
MATHEMATICS 
Class – IX 
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question are compulsory.
2. The question paper consists of 31questions 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 
Question numbers 1 to 4 carry one mark each. 
1. Simplify 2 3 3 + 
2. Factorise : 
3 3
8 y . - 125x
3. In the given figure, O is the mid-Point of AB and B Q O A PO , ? ? ? then O A P ? is equal to which
angle? 
4. If (a, b) = (0, -2), find value of a and b
Section-B 
Question numbers 5 to 10 carry two marks each. 
5. Rationalize 
3 2
7
3 2 - 
6. If 3x + 2y= 12 and xy = 6, then find 
3 3
27 x 8 y . ?
7. In the figure, PR is the angle bisector of A PQ ? . Prove that AB||CD.
8. If a point P lies between two points A and B such that AP = BP, then prove that AP=
1
2
 AB.   
9. Plot three points A(4, 0), B(0,-4) and C(-4, 0) on the coordinate place. Now plot point D so that
ABCD is a rhombus. Give coordinates of the point D.  
10. Find the area of the right angled triangle in which sides other than hypotenuse are 18 cm and 80
cm. Also, find the perimeter of the triangle. 
Section-C 
Question numbers 11 to 20 carry three marks each. 
11. Show that 
? ? ? ? ? ?
x y y z z x
x y y z z x
a a a 1
? ? ?
? ? ?
?
12. Simplify : 
? ?
1 / 4
3
1 / 3 1 / 3
5 8 27
? ?
?
? ?
? ?
13.find the product of 
4
2 4
1 1 1 1
a a a a
a a a a
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
 using a suitable identify : 
14. Evaluate 
3
9 2 , using a suitable identify.
15. Prove that the two lines which parallel to the same line, are parallel to each other.
16. In the figure, sides AB and BC of A B C ? are produced to point E and D  respectively. If
O
EB C 110 ? ? and 
O
A C D 135 ? ? , Find B A C ? . 
Page 3


SUMMATIVE ASSESSMENT- I 
MATHEMATICS 
Class – IX 
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question are compulsory.
2. The question paper consists of 31questions 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 
Question numbers 1 to 4 carry one mark each. 
1. Simplify 2 3 3 + 
2. Factorise : 
3 3
8 y . - 125x
3. In the given figure, O is the mid-Point of AB and B Q O A PO , ? ? ? then O A P ? is equal to which
angle? 
4. If (a, b) = (0, -2), find value of a and b
Section-B 
Question numbers 5 to 10 carry two marks each. 
5. Rationalize 
3 2
7
3 2 - 
6. If 3x + 2y= 12 and xy = 6, then find 
3 3
27 x 8 y . ?
7. In the figure, PR is the angle bisector of A PQ ? . Prove that AB||CD.
8. If a point P lies between two points A and B such that AP = BP, then prove that AP=
1
2
 AB.   
9. Plot three points A(4, 0), B(0,-4) and C(-4, 0) on the coordinate place. Now plot point D so that
ABCD is a rhombus. Give coordinates of the point D.  
10. Find the area of the right angled triangle in which sides other than hypotenuse are 18 cm and 80
cm. Also, find the perimeter of the triangle. 
Section-C 
Question numbers 11 to 20 carry three marks each. 
11. Show that 
? ? ? ? ? ?
x y y z z x
x y y z z x
a a a 1
? ? ?
? ? ?
?
12. Simplify : 
? ?
1 / 4
3
1 / 3 1 / 3
5 8 27
? ?
?
? ?
? ?
13.find the product of 
4
2 4
1 1 1 1
a a a a
a a a a
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
 using a suitable identify : 
14. Evaluate 
3
9 2 , using a suitable identify.
15. Prove that the two lines which parallel to the same line, are parallel to each other.
16. In the figure, sides AB and BC of A B C ? are produced to point E and D  respectively. If
O
EB C 110 ? ? and 
O
A C D 135 ? ? , Find B A C ? . 
17. If a transversal intersects two parallel lines, the prove that bisectors of alternate interior angles
are parallel. 
18. In the given figure, OP||RS. If 
O
O P Q 11 0 ? ? and
O
S R Q 1 30 ? ? , find PQ R ? .
19. Plot the points (2, 3), (-2, 3), (-2, -3) and (2, -3) on a graph sheet. Join these points in order.
Identify the figure obtained. Also, find the area of the figure. 
20. In a four-sided field, the length of the longer diagonal is 120 m. The lengths of the
perpendiculars from the opposite vertices upon this diagonal are 127 m and 7.3 m. Find the area of 
the field. 
Section-D 
Question numbers 21 to 31 carry four marks each. 
21. Rationalise the denominator of the following :
22. Express 0 . 3 178
? ? ? ? ? ?
 in the form of p/q where p and q are integers and q 0 ? . 
23. Prove that ? ? ? ? ? ? ? ? ? ? ? ?
3 3 3
X Y y z z x 3 x y y z z x ? ? ? ? ? ? ? ? ?
? ?
3 3 3
2 x y z 3x y z ? ? ? ?
24. Divide polynomial 
4 3 2
p ( x ) x 4 x 4 x 3x 4 ? ? ? ? ? by q ( x ) x 1 ? ? and find what should be added in
p(x) so that it is divisible by q(x).  
25. Using factor theorem, show that (m- n), (n- P) and (p- m) are factors of
? ? ? ? ? ?
2 2 2 2 2 2
m n p n p m p m n ? ? ? ? ? .
26. Show that 2 x 1 ? is a factor of the polynomial 
3 2 2 3
2 x x 6 2 x 2 x 8 x 4 ? ? ? ? ? Hence factories’
the polynomial. 
27. For spreading the message “Save Girl Child Save Future” a rally was organized by some students
of a school. They were given triangular cardboard piece PQR which they divided in to two parts by 
drawing the angle bisectors QO and RO of base angles Q and R and wrote a slogan. Prove that 
o
1
Q O R 9 0 P
2
? ? ? ? What is the benefit of these types of rallies?
28. “A square is a polygon made up of four line segments, cut of which, length of three line segments
are equal to the length of fourth one and all its angles are right angles”.        
Define the terms used in this definition which have been highlighted/underlined. 
Page 4


SUMMATIVE ASSESSMENT- I 
MATHEMATICS 
Class – IX 
 Time allowed: 3 hours     Maximum Marks: 90 
General Instructions: 
1. All question are compulsory.
2. The question paper consists of 31questions 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 
Question numbers 1 to 4 carry one mark each. 
1. Simplify 2 3 3 + 
2. Factorise : 
3 3
8 y . - 125x
3. In the given figure, O is the mid-Point of AB and B Q O A PO , ? ? ? then O A P ? is equal to which
angle? 
4. If (a, b) = (0, -2), find value of a and b
Section-B 
Question numbers 5 to 10 carry two marks each. 
5. Rationalize 
3 2
7
3 2 - 
6. If 3x + 2y= 12 and xy = 6, then find 
3 3
27 x 8 y . ?
7. In the figure, PR is the angle bisector of A PQ ? . Prove that AB||CD.
8. If a point P lies between two points A and B such that AP = BP, then prove that AP=
1
2
 AB.   
9. Plot three points A(4, 0), B(0,-4) and C(-4, 0) on the coordinate place. Now plot point D so that
ABCD is a rhombus. Give coordinates of the point D.  
10. Find the area of the right angled triangle in which sides other than hypotenuse are 18 cm and 80
cm. Also, find the perimeter of the triangle. 
Section-C 
Question numbers 11 to 20 carry three marks each. 
11. Show that 
? ? ? ? ? ?
x y y z z x
x y y z z x
a a a 1
? ? ?
? ? ?
?
12. Simplify : 
? ?
1 / 4
3
1 / 3 1 / 3
5 8 27
? ?
?
? ?
? ?
13.find the product of 
4
2 4
1 1 1 1
a a a a
a a a a
? ? ? ? ? ? ? ?
? ? ? ?
? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ?
 using a suitable identify : 
14. Evaluate 
3
9 2 , using a suitable identify.
15. Prove that the two lines which parallel to the same line, are parallel to each other.
16. In the figure, sides AB and BC of A B C ? are produced to point E and D  respectively. If
O
EB C 110 ? ? and 
O
A C D 135 ? ? , Find B A C ? . 
17. If a transversal intersects two parallel lines, the prove that bisectors of alternate interior angles
are parallel. 
18. In the given figure, OP||RS. If 
O
O P Q 11 0 ? ? and
O
S R Q 1 30 ? ? , find PQ R ? .
19. Plot the points (2, 3), (-2, 3), (-2, -3) and (2, -3) on a graph sheet. Join these points in order.
Identify the figure obtained. Also, find the area of the figure. 
20. In a four-sided field, the length of the longer diagonal is 120 m. The lengths of the
perpendiculars from the opposite vertices upon this diagonal are 127 m and 7.3 m. Find the area of 
the field. 
Section-D 
Question numbers 21 to 31 carry four marks each. 
21. Rationalise the denominator of the following :
22. Express 0 . 3 178
? ? ? ? ? ?
 in the form of p/q where p and q are integers and q 0 ? . 
23. Prove that ? ? ? ? ? ? ? ? ? ? ? ?
3 3 3
X Y y z z x 3 x y y z z x ? ? ? ? ? ? ? ? ?
? ?
3 3 3
2 x y z 3x y z ? ? ? ?
24. Divide polynomial 
4 3 2
p ( x ) x 4 x 4 x 3x 4 ? ? ? ? ? by q ( x ) x 1 ? ? and find what should be added in
p(x) so that it is divisible by q(x).  
25. Using factor theorem, show that (m- n), (n- P) and (p- m) are factors of
? ? ? ? ? ?
2 2 2 2 2 2
m n p n p m p m n ? ? ? ? ? .
26. Show that 2 x 1 ? is a factor of the polynomial 
3 2 2 3
2 x x 6 2 x 2 x 8 x 4 ? ? ? ? ? Hence factories’
the polynomial. 
27. For spreading the message “Save Girl Child Save Future” a rally was organized by some students
of a school. They were given triangular cardboard piece PQR which they divided in to two parts by 
drawing the angle bisectors QO and RO of base angles Q and R and wrote a slogan. Prove that 
o
1
Q O R 9 0 P
2
? ? ? ? What is the benefit of these types of rallies?
28. “A square is a polygon made up of four line segments, cut of which, length of three line segments
are equal to the length of fourth one and all its angles are right angles”.        
Define the terms used in this definition which have been highlighted/underlined. 
29. In the figure, two straight line PQ and RS intersect each other at O. If 
O
P O T 75 ? ? find the values
of a, b and c. 
?
???? ? ? ?is a line-segment and P and Q are points on opposite sides of AB such that each of them is 
equidistant from the points A and B. Show that PQ is perpendicular bisector of AB. 
31. The angles of a triangle are ? ? ? ?
o o
x 40 , x 2 0 ? ? and 
o
x
10
2
? ?
?
? ?
? ?
. Find the value of x and then the 
angles of the triangle.