Courses

# Mathematics Past Year Paper SA-1(Set-7)- 2014, Class 9, CBSE Class 9 Notes | EduRev

## Mathematics (Maths) Class 9

Created by: Indu Gupta

## Class 9 : Mathematics Past Year Paper SA-1(Set-7)- 2014, Class 9, CBSE Class 9 Notes | EduRev

``` Page 1

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper contains 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 compromises of 10 questions of 3 marks and Section-D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry one mark each.
1. Express 0.3 in the form
p
q
, where p and q are integers and 0. q ?
2. If
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient.
3. If fig, AB XY  , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? =

4. Write the distance of point A(3,5) from x-axis.

Section B
Question numbers 5 to 10 carry two marks each.
5. Find the value of x if
5
5 2 2 x + =
6. Factorise: ( )
3
3
8 2 x x y - -
7. State any two Euclid’s axioms.
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that
ABD ACD ? = ? .
Page 2

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper contains 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 compromises of 10 questions of 3 marks and Section-D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry one mark each.
1. Express 0.3 in the form
p
q
, where p and q are integers and 0. q ?
2. If
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient.
3. If fig, AB XY  , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? =

4. Write the distance of point A(3,5) from x-axis.

Section B
Question numbers 5 to 10 carry two marks each.
5. Find the value of x if
5
5 2 2 x + =
6. Factorise: ( )
3
3
8 2 x x y - -
7. State any two Euclid’s axioms.
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that
ABD ACD ? = ? .

9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54
cm. find its area.
10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is
formed on joining the points in order? Also, identify the shape of figure.

Section C
Question numbers 11 to 20 carry three marks each.
11. Simplify:
72
5 72 3 288 2 648 + -
12. If 5 2 6, p = - find
2
2
1
p
p
-
13. Factorise:
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - -
14. Prove that
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by
2
3 2 x x - +
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° +
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD

17. In figure; if l m  and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles.

18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that
1 2 ? = ? .
Page 3

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper contains 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 compromises of 10 questions of 3 marks and Section-D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry one mark each.
1. Express 0.3 in the form
p
q
, where p and q are integers and 0. q ?
2. If
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient.
3. If fig, AB XY  , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? =

4. Write the distance of point A(3,5) from x-axis.

Section B
Question numbers 5 to 10 carry two marks each.
5. Find the value of x if
5
5 2 2 x + =
6. Factorise: ( )
3
3
8 2 x x y - -
7. State any two Euclid’s axioms.
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that
ABD ACD ? = ? .

9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54
cm. find its area.
10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is
formed on joining the points in order? Also, identify the shape of figure.

Section C
Question numbers 11 to 20 carry three marks each.
11. Simplify:
72
5 72 3 288 2 648 + -
12. If 5 2 6, p = - find
2
2
1
p
p
-
13. Factorise:
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - -
14. Prove that
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by
2
3 2 x x - +
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° +
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD

17. In figure; if l m  and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles.

18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that
1 2 ? = ? .

19. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral
triangle of side 8 cm. find the area of the figure so formed.
20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area
( )
2
108 FBE cm ? = , find the length of AB.

Section D
Question numbers 21 to 31 carry four marks each.
21. Find the values of a and b if
7 1 7 1
7
7 1 7 1
a b
- +
- = +
+ -
22. Simplify:
1 1 1 1
2 5 5 6 6 7 7 8
+ + +
+ + + +

23. If x-5 and
1
5
x - are the factors of the polynomial
2
3 px x r + + , show that p=r.
24. Show that 2x-1 is a factor of the polynomial
3 2 2
2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise
the polynomial.
25. Divide polynomial
4 3 2
( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in
p(x) so that it is divisible by q(x).
26. Factorise:
6 3
5 8 x x + +
27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting
by doing so
In the figure below, AB CD  .

What is the value of x?
Also find angle A and B.
28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE
Page 4

Summative Assessment-1 2014-2015
Mathematics
Class – IX

Time allowed: 3:00 hours                                Maximum Marks: 90

General Instructions:
a) All questions are compulsory.
b) The question paper contains 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 compromises of 10 questions of 3 marks and Section-D
comprises of 11 questions of 4 marks each.
c) There is no overall choice in this question paper.
d) Use of calculator is not permitted.

Section A
Question numbers 1 to 4 carry one mark each.
1. Express 0.3 in the form
p
q
, where p and q are integers and 0. q ?
2. If
3 2
4 7 3 6 x x x + - - is divided by x+1, then find the quotient.
3. If fig, AB XY  , 35 YXC ? = ° , 53 BAC ? = ° then ? ACB ? =

4. Write the distance of point A(3,5) from x-axis.

Section B
Question numbers 5 to 10 carry two marks each.
5. Find the value of x if
5
5 2 2 x + =
6. Factorise: ( )
3
3
8 2 x x y - -
7. State any two Euclid’s axioms.
8. In figure, ABC ? and DBC ? are two isosceles triangles on the same base BC. Prove that
ABD ACD ? = ? .

9. The longest side of a right angled triangle is 90 cm and one of the remaining two sides is 54
cm. find its area.
10. If we plot the points A(-1,0), B(-1,1) C(0,1) and D(0,0) on Cartesian plane, which figure is
formed on joining the points in order? Also, identify the shape of figure.

Section C
Question numbers 11 to 20 carry three marks each.
11. Simplify:
72
5 72 3 288 2 648 + -
12. If 5 2 6, p = - find
2
2
1
p
p
-
13. Factorise:
3 3 3
( ) ( ) ( ) 3( )( )( ) x a x b x c x a x b x c - + - + - - - - -
14. Prove that
4 3 2
2 3 38 32 x x x x + + - + is exactly divisible by
2
3 2 x x - +
15. In ABC ? , the bisectors of B ? and C ? meet at O. Prove that 90
2
A
BOC
?
? = ° +
16. D is a point on side BC of ABC ? (see figure), such that AD=AC. Show that AB>AD

17. In figure; if l m  and n is a transversal such that 8: 5 13:5 ? ? = , find all the angles.

18. In figure ABC is a right angled triangle at B. BD is drawn perpendicular to AC. Show that
1 2 ? = ? .

19. An isosceles triangle of sides 10 cm, 10 cm and 8 cm is joined on side 8 cm by an equilateral
triangle of side 8 cm. find the area of the figure so formed.
20. In figure, ABCD is a square. F is the mid-point of AB and BE is one-third of BC. If area
( )
2
108 FBE cm ? = , find the length of AB.

Section D
Question numbers 21 to 31 carry four marks each.
21. Find the values of a and b if
7 1 7 1
7
7 1 7 1
a b
- +
- = +
+ -
22. Simplify:
1 1 1 1
2 5 5 6 6 7 7 8
+ + +
+ + + +

23. If x-5 and
1
5
x - are the factors of the polynomial
2
3 px x r + + , show that p=r.
24. Show that 2x-1 is a factor of the polynomial
3 2 2
2 6 2 3 2 8 4 x x x x x - + - + - . Hence factorise
the polynomial.
25. Divide polynomial
4 3 2
( ) 4 4 3 4 p x x x x x = - + - + by q(x)=x-1 and find what should be added in
p(x) so that it is divisible by q(x).
26. Factorise:
6 3
5 8 x x + +
27. An NGO is planning to make a school for girls in the rural area. What value are they exhibiting
by doing so
In the figure below, AB CD  .

What is the value of x?
Also find angle A and B.
28. In figure AC=AE, AB=AD and BAD EAC ? = ? . Prove that BC=DE

29. Sides BC, CA and BA of a triangle ABC are produced to D, Q, P, respectively as shown in the
figure. If 100 , 35 ACD QAP ? = ° ? = ° , find all the angles of the triangle.

30. In figure, AB=BC and AD=EC, then show that ABE CBD ? ? ?

31. Prove that the angles opposite to equal sides of a triangle are equal.
```

## Mathematics (Maths) Class 9

192 videos|230 docs|82 tests

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;